WWW.JAMRIS.ORG pISSN 1897-8649 (PRINT)/eISSN 2080-2145 (ONLINE) VOLUME 19, N° 3, 2025
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Journal of Automation, Mobile Robotics and Intelligent Systems
A peer-reviewed quarterly focusing on new achievements in the following fields: • automation • systems and control • autonomous systems • multiagent systems • decision-making and decision support • • robotics • mechatronics • data sciences • new computing paradigms •
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Journal of Automation, Mobile Robotics and Intelligent Systems
1
A Custom Robotic Vehicle Prototype For Disinfecting Workplaces
Georgios Karamitsos, Vasileios Sidiropoulos, Evangelos Syrmos, Athanasios Sidiropoulos, Xenofon Karamanos, Dimitrios Vlachos, Dimitrios Bechtsisz
DOI: 10.14313/jamris‐2025‐020
13
The design of 3D-printed Open Bearings for Human Assisting Robots
Piotr Falkowski, Bazyli Leczkowski
DOI: 10.14313/jamris‐2025‐021
25
Self-Tuning Controller for Scalar Systems: A Preselected-Time Control Approach
Ali Soltani Sharif Abadi
DOI: 10.14313/jamris‐2025‐022
38
Design and Analysis of Linear-Phase FiniteImpulse Response Filter using Henry Gas
Solubility Optimization Algorithm
Thangaraj Meena, Jampani Chandra Sekhar, Perumal Anandan, Ganesan Vinoth Chakkaravarthy, Muthaiyan Elumalai, Bellarmine Anni Princy, Thirumala Reddy
Vijaya Lakshmi
DOI: 10.14313/jamris‐2025‐023
45
Segmentation of E-Commerce Users on Cart Abandonment And Product Recommendation
Using Double Transformer Residual SuperResolution Network
Praveen Kumar P, Suguna R
DOI: 10.14313/jamris‐2025‐024
Monocular 3D Object Localization using 2D Estimates for Industrial Robot Vision System
Thanh Nguyen Canh, Du Trinh Ngoc, Xiem HoangVan
DOI: 10.14313/jamris‐2025‐025
Feedback Linearization Controller with Thau Observer Applied to an Autonom
Abderrahmane Kacimi, Abderrahmane Senoussaoui
DOI: 10.14313/jamris‐2025‐026 66
Optimization of the Nominal Capacity of on Energy Storage System for Ensuring Security of the Electrical Energy supply
Ihor Buratynskyi, Artur Zaporozhets
DOI: 10.14313/jamris‐2025‐027 53
A Kinematic Prototype of a Compliant Artificial Prosthetic Knee Joint
Michał Kowalik, Erwin Rogoża, Aleksy Figurski, Mateusz Papis
DOI: 10.14313/jamris‐2025‐028
A Health Recommender System for Sleep Apnea Using Computational Intelligence
Mubashir Khan, Yashpal Singh, Harshit Bhardwaj
DOI: 10.14313/jamris‐2025‐029 89
Submitted:12th March2025;accepted:23rd April2025
GeorgiosKaramitsos,VasileiosSidiropoulos,EvangelosSyrmos,AthanasiosSidiropoulos,XenofonKaramanos,Dimitrios Vlachos,DimitriosBechtsis
DOI:10.14313/jamris‐2025‐020
Abstract:
TheSARS‐CoV‐2pandemichasheightenedtheneedfor advancedandautomateddisinfectionmethodstoensure workplacesafetyandhygiene.Thisstudypresentsthe designandimplementationofaroboticvehiclecapable ofautonomouslydisinfectinghigh‐riskareasindiverse workenvironmentsbasedonhumanactivitylevels.The systemintegratesamachinevisionmoduleusingYOLOv5 forreal‐timehumandetection,aDecisionSupportSystem toassesscontaminationrisks,anautonomousnavigation moduleforpathplanning,andauser‐friendlyinterface foroperatorcontrol.Byleveragingreal‐timedata,the robotpreciselyappliesdisinfectanttoidentifiedhigh‐risk zones,dynamicallyadjustingthesprayvolumebasedon thelevelofcontamination.Thesystemwasvalidatedin areal‐worldworkplacesetting,demonstratingitsability toautonomouslyperformtargeteddisinfection,offering ascalablesolutiontosupportworkplacehygiene.
Keywords: roboticdisinfection,mobilerobots,robot operatingsystem,deeplearning,infectionprevention
1.Introduction
Thesupplyofworkplacehygieneserviceshas becomeasigni icantchallenge,especiallysincethe outbreakandsubsequentspreadofSevereAcuteRes‐piratorySyndromeCoronavirus(SARS‐CoV‐2).The pandemicprofoundlyaffecteddailylife,withasub‐stantialportionoftheglobalpopulationreport‐ingdisruptionstopersonal,professional,andeco‐nomicactivitiesduetolockdownrestrictions[1].Pub‐licplacesandworkplacesarerecognizedaspoten‐tialhotspotsformicrobialtransmission,emphasiz‐ingtheimportanceofproactivehygienemeasures[2, 3].AlthoughtheimmediatethreatofSARS‐CoV‐2 hasdiminished,thepandemichasheightenedaware‐nessofworkplacehygiene,promptingemployersto adoptlong‐termprotectivemeasurestomaintain cleanlinessandreducethespreadofinfectiousdis‐eases[4].Recentstudieshighlightthateveninthe post‐pandemicperiod,postCOVID‐19conditionscon‐tinuetoposeserioushealthrisks,particularlyamong vulnerablepopulationssuchasolderadultsandthose withpreexistingconditions,emphasizingtheneedfor sustainedhygieneandinfectioncontrolmeasures[5]. Itisthereforeessentialthatautomatedsolutionsare implementedtomaintainhygienestandards,reduce manuallaborandensurepublicsafety.
However,thepandemichasledtoaparadigm shiftinhowworkplacehygieneisapproached.Con‐sequently,autonomousvehicleshavebecomepromi‐nentincontrollingcontaminationinpublicplaces, healthcarefacilitiesandworkplaces.Theircapacity tocarryoutunmannedcontactlessoperationshas provencrucialtoenvironmentaldisinfection,partic‐ularlyacrosstheNationalHealthService(NHS)sup‐plychains.Recentstudieshavedemonstratedthe feasibilityofcost‐effectiveautonomousvehiclesfor real‐worldapplications,showingtheirpotentialto optimizenavigationandobstacleavoidancewhile maintaininglowimplementationcosts[6].Thesevehi‐cleshavealsosigni icantlyreducedlaborcosts,while safeguardingworkersfromexposuretopathogens andhazardousdisinfectantchemicals[7].
Historically,roboticsystemshavebeenintegrated intorehabilitationandpatientcare,reducingthebur‐denonhealthcareworkers.Forexample,assistive robotsarewidelyusedinrehabilitationsettings,such asnursinghomes,toincreasesocialinteractionamong residents[8].Duringthepandemic,robotswerecru‐cialinhelpinghealthcareworkersintheirdailyactiv‐itiesandprotectingthemfrominfection[9].Recently, apreliminarystudyhashighlightedthepotentialof mobilerobotstosupportnursingtasksinhospital settings,demonstratingtheabilitytoreducecon‐taminationrisksandimproveef iciencyinsupply deliveryandmedicationadministrationforpatients inisolationrooms[10].Inaddition,mobilerobots haveshownpotentialinhome‐carefortheelderly orbedriddenindividualsbysupportingtaskssuch asmobility,toileting,andbathinginthebed,signi i‐cantlyreducingcaregiverworkload[11].Asaresult, thedemandfordecontaminationrobotsinhealthcare facilitieshasincreaseddramatically,reachingamar‐ketsizeestimatedat714.78millionUSDin2022and projectedtoreach7,697.57millionUSDby2030at acompoundannualgrowthrate(CAGR)of32.84% from2023to2030[12].
Inresponsetoemergingtrendsforworkplace disinfection,theproposedresearch,fundedbythe EITHealthResearchGrant,introducesacustomized roboticvehicledesignedtoperformworkplacedis‐infectionprotocols.Theproposedsystemaimsto minimizetheconsumptionofdisinfectant luidsand reducetheriskofcontaminationinareasproneto virustransmission.
Theroboticsystemintegratesseveralkeycompo‐nents,includingacustomdisinfectionmechanism,a machinevisionmodule,andaDecisionSupportSys‐tem(DSS)toautomatethedisinfectionprocessbased ontheprobabilityofinfection.Inaddition,agraphical userinterface(GUI)hasbeendevelopedtoassistthe operatorinnavigationanddisinfection.Thistargeted approachreducestheamountofdisinfectantsused, improvesoverallhygiene,andensuresef icientand effectivedisinfectionofhigh‐riskareas.
Thisstudyfocusesnotonevaluatingtheeffec‐tivenessofthedisinfectantsolventusedbutonthe roboticsystem’stechnologicaldevelopment,assem‐bly,andprogramming.Bydemonstratingthesuccess‐fulintegrationofthetechnologicalcomponents,the systempresentsascalablesolutionforcontinuousand preventivemeasuresinindoorworkspaces,aimingto enhanceanticontaminationmeasuresandworkplace safety.
2.LiteratureReview
Severalsolutionshavebeenproposedtomitigate theimpactoftheSARS‐CoV‐2pandemic,involving autonomousrobotsequippedwithdisinfectionmech‐anisms.Theserobotscandisinfectpremises,thereby ensuringpersonalhygieneandreducingthereliance onmanuallabor.
Chemicaldisinfectionrobotstypicallyusedisin‐fectantsthatdiffuseintotheatmospheretodisinfect theair,surfacesofobjects,andhard‐to‐reachareas. Forexample,Zhaoetal.[13]developedarobotic systemthatef icientlydisinfectsareascontaminated withpathogenicmicroorganismsbyusingacombi‐nationofInternetofThings(IoT)technologiesand chlorinedioxidedisinfectionthroughaerosolspray‐ing.Thesystemwasaimedatimprovingworkplace safetyandreducetheneedformanuallabor.Simi‐larly,Chioetal.[14]introducedamobilerobotfor autonomousairandsurfacedisinfectionusingthe aerosolizedhydrogenperoxidedisinfectionmethod, demonstratinghighef iciencyinanindoorof iceenvi‐ronment.Furthermore,Leetal.[15]developedan autonomousrobotthatusestheaerosolizedhydrogen peroxidedisinfectionmethodwithatargetdetection algorithmtodisinfectthepremises.Theeffectiveness ofthisdesignwasveri iedthroughairandsurface qualitymonitoring.
Analternativeapproachtoroboticdisinfection involvesshort‐waveultravioletC(UVC)lamps.UVC lightcaneffectivelydestroytheDNA/RNAofmicroor‐ganismsbyimpedingcellularactivityandreplication. RobotsequippedwithUVClampshavebeenshown topreventinfectiousdiseasessuchasSARS‐CoV‐2, in luenza,andtuberculosis[16].Huetal.[17]intro‐ducedarobotwithUVClampstodisinfecthigh‐traf ic environmentssuchashospitals,schools,airports,and transitsystems.
ThisrobotemployedtheSimultaneousLocaliza‐tionandMapping(SLAM)algorithmtocreateanoccu‐pancygridmapoftheenvironmentandimagerecog‐nitiontoidentifyareasatriskofcontamination.In addition,DogruandMarques[18]developedatrajec‐torygenerationframeworkthatformulatesthedisin‐fectionpathasaEulerCircuit,ensuringcompletesur‐facecoveragewhileminimizingtraveldistance.Their workdemonstratestheeffectivenessofoptimizing robotmovementtobalancedisinfectiontime,energy consumption,andexposureconsistency,whichiscru‐cialforimprovingUV‐C‐basedroboticdisinfectionsys‐tems.Similarly,Camachoetal.[19]proposedarobotic platformforUVCdisinfectionofindoorenvironments. Therobotwascapableofautonomousoperation, ensuringthemaximumpossiblesurfaceareawithout directsupervision.Buildingontheseapproaches,Liu etal.[20]introducedanadvanceddisinfectionrobot schedulingandroutingframeworkthatintegratesa mixed‐integerprogramming(MIP)modeltooptimize taskschedulingandminimizepathogentransmission risks.Theirapproachdynamicallyadjustsdisinfection timingbasedonreal‐timeenvironmentalconditions andhumanactivitypatterns,reducingunnecessary energyconsumptionwhilemaximizingdecontamina‐tionef iciency.
However,despitetheadvantagesofUVCdisinfec‐tion,theserobotsfacechallengeswhendisinfecting morecomplexenvironmentswithvaryinganglesand shadowedareas.SeveralUVCrobotshaveincorpo‐ratedoptionalsprayattachmentstoaddressthisissue andenhancecoverageinhard‐to‐reachareas[21].Cao etal.[22]developedadual‐functionautonomousdis‐infectionrobotthatintegratesUVClightwithhydro‐genperoxideaerosolspraying,signi icantlyimproving decontaminationcoverage.Theirstudydemonstrated thatcombiningthesemethodsincreaseddisinfection ef iciencyby53.4percent,effectivelymitigatingshad‐owingissuesassociatedwithUVCalone.Anothersig‐ni icantconsiderationisbatteryconsumption,asUVC robotsmustbalancetheenergyusagerequiredfor disinfectionandsystemoperation.Mantellietal.[23] presentedanautonomousUVCrobotthatcreatesa dynamicradiationmapoftheenvironment.Themap illustratestheenergyappliedtoeacharea,allowing therobottooptimizenavigation.Therobotmoves fasterinareaswithlowerenergyrequirements,while slowingdowninareasrequiringhigherenergyto ensureadequatedisinfectioncoverage.
Inadditiontogeneraldisinfectionsystems,robots havealsobeendevelopedtotargetspeci icobjects thatmayharborpathogens.Ramalingametal.[24] proposedanautomateddoorhandlecleaningtech‐niqueusingtheToyotaHSRmobilerobotplatform. Therobotusesadeeplearningmodeltrainedtodetect doorhandles,enablingittogenerateasetofcoor‐dinatesfortargeteddisinfection.Theeffectiveness oftheproposedframeworkwasvalidatedinindoor publicspaces,demonstratingitspotentialtoimprove hygieneinareasofhighcontact.
Whilenumerousresearchteamshaveproposed functionalandadvancedfeaturesofroboticdisin‐fectionsystems,anintegratedsolutionthatfocuses onthereal‐timeprioritizationofhigh‐riskareasand minimisesdisinfectionliquidconsumptionislack‐ing.Zhaoetal.(2021)proposedasemi‐automatic ClO₂sprayingrobotthatreliesonremotecontrol and ixedwaypoints,withoutadequatelyaddress‐ingautonomousnavigationandrisk‐basedanalysis. Chioetal.(2022)integratedaerosolizedhydrogen‐peroxidesprayingwithSLAMforfull‐coveragepath planning,buttheirsystemcannotsuf icientlyadaptto real‐timehumanpresence.Huetal.(2020)employed deeplearningtosegmentUVC‐criticalzones.The publicationdoesnotadequatelyaddressreal‐time humandetectionanddecisionsupportforzonepri‐oritization.DogruandMarques(2023)optimized UV‐Ctrajectoriesunderkinodynamicconstraintsbut didnotsuf icientlyaddresscoverageef iciencyin dynamic,human‐occupiedsettings.Camachoetal. (2021)developedtheROS‐based“COVIBOT,”which autonomouslymapsanddisinfectsusingUVC,but theprioritizationofhigh‐riskareasisnotsuf iciently articulated.Finally,Liuetal.introducedamixed‐integerprogrammingschedulertominimizeinfection risk,buttheirrobotdoesnotsuf icientlyshowcase onboardvisionandreal‐timeadaptability.
Previousdisinfectionrobotshavedemonstrated exceptionalperformanceinindividualcomponents however,thereispotentialforimprovementintheir overallfunctionality.Withtheproposedroboticvehi‐cle,weenhanceef iciencyandeffectivenessbyinte‐gratingreal‐timehumandetection,density‐basedrisk scoring,adaptiveelectrostaticspraying,andaGraph‐icalUserInterfacefortheoperatorsintoanef icient roboticsystem.Theproposedsystemfocusesonthe real‐timeprioritizationofhigh‐riskareasandmin‐imisesdisinfectionliquidconsumption.Theprimary contributionoftheproposedresearchistheintegra‐tionofmultipletechnologicalcomponentstodevelop auni iedroboticsystemcapableofreal‐timepri‐oritizationofhigh‐riskareaswhilesimultaneously minimizingthedisinfectionliquidconsumption.The proposedsystemleveragestheROS2frameworkfor robotoperationandtheYOLOv5objectdetection modelforreal‐timedetectionofindividualswithinthe workspace.ADecisionSupportSystem(DSS)isinte‐gratedtoassesstheprobabilityofinfectionbasedon humanpresence,enablingprecisedisinfectionofthe identi iedhigh‐riskareas.Furthermore,thesystem featuresagraphicaluserinterface(GUI)tofacilitate robotcontrol,enhanceuser‐robotinteraction,anda customdisinfectionmechanismforresource‐ef icient disinfectantuse.Thisend‐to‐endsolutionisaplug‐and‐playautonomousroboticsystemthatrequires onlyenvironmentmappingandeliminatestheneed forextensiveparameterization.
3.SystemArchitectureandDesign
Thedisinfectionrobotisdesignedtoidentifyand autonomouslydisinfecthigh‐riskworkplaceareasby integratingnavigation,humandetectionanddisin‐fectionmechanisms.Thissectionprovidesadetailed overviewoftherobot’sarchitecture,subsystems,and modi icationstooptimizeitsperformancefortar‐geteddisinfectiontasks.AsshowninFig. 1,thedis‐infectionrobotisbasedontheTurtlebot4,awidely usedopen‐sourceroboticsplatformforresearchand educationalapplications.Severalmodi icationswere madetoadapttheTurtlebot4fordisinfectiontasks. Initially,acustomwoodenframewasinstalledto securethespraycanistercontainingthedisinfectant liquid,preventingitfromfallingduringmovement. Additionally,therobotwasequippedwithacamera andLIDARsensorstofacilitateautonomousnaviga‐tionandreal‐timeimagerecognitiontoidentifyand disinfecthigh‐riskareas.
Therobot’sarchitecturecomprises ivesubsys‐tems:thedisinfectionsubsystem,themobileappli‐cationsubsystem,themachinevisionsubsystem,the decisionsupportsystem(DSS),andthenavigation subsystem.Thedisinfectionsubsystemmanagesthe electrostaticsprayingmechanism,whichdisperses disinfectantoveridenti iedhigh‐riskareas.Thespray actuatoriscontrolledbyanArduinoMegaMicro‐controllerUnit(MCU),ensuringthattheappropriate amountofdisinfectantisappliedbasedonthecontam‐inationriskineacharea.Themobileapplicationfea‐turesagraphicaluserinterface(GUI)thatallowsthe operatortomonitortherobot’sstatusandoperations inreal‐time.TheGUIdisplayskeyinformationsuch astheenvironmentmap,batterystatus,andareas withdetectedhumanactivity,whileallowingusersto controltherobot’snavigationanddisinfectionprocess asnecessary.
ThemachinevisionsubsystemusestheRealSense D435stereodepthcameraandtheYOLOv5object detectionmodeltodetectandlocateindividuals withintheworkspace.Byproviding3Dcoordinatesof thedetectedindividuals,therobotcanidentifyareas withahighhumanpresence.TheDecisionSupport System(DSS)iscriticalinanalyzingreal‐timehuman positioningdatatoassesscontaminationrisks.Based onthisanalysis,theDSSsendscommandstothe robot’snavigationanddisinfectionsystems,prioritiz‐inghigh‐riskareasfordisinfectionandoptimizingthe overallprocess.TheNavigationSubsystemutilizesthe RPLIDARsensorandtheRobotOperatingSystem2 (ROS2)toenabletherobottomoveautonomously throughtheenvironment.Thissubsystemusesthe SLAMalgorithmtocreateareal‐timeoccupancygrid mapoftheworkspaceandensuresthattherobot followsoptimalpathstoreachthehigh‐riskareas identi iedbytheDSS.Thecoordinationofallthese subsystemsismanagedbytheCentralControlUnit (CCI),whichispoweredbytheJetsonNanoXavier NX,anembeddedSystem‐on‐Module(SoM)equipped withanintegratedGraphicsProcessingUnit(GPU).
Figure1. Therobotchassisconsistsoftherobotic vehiclebasestationandahigh‐topframeformounting thedepthcameraandthedisinfectionelectrostatic sprayer.Adepthcameraismountedontopofthe frame,andadisinfectionsubsystemismountedinside theframe,culminatinginthespraynozzle
Together,thesesubsystemsworkinunison, enablingtherobottonavigateautonomously,detect thepresenceofhumans,assesscontamination risks,andperformtargeteddisinfection,thereby maintainingeffectivehygiene.
4.Methodology
Thedisinfectionprocessinvolvesseveralstepsto ensurethoroughandef icientcoverage.Theprocess beginswithcreatingadetailedmapofthetargetarea usingtheSLAMalgorithm.Initially,anoperatorman‐uallynavigatestherobotthroughtheenvironment tocapturespatialdataandidentifyrelevantareas, obstacles,andpathways,whichformthebasisforall subsequentnavigationanddisinfectionactivities.The mapiscontinuouslyupdatedtore lectthepositionof staticobjects,suchasfurnitureorwalls,anddynamic objects,includinghumans,animals,andothermoving obstacles.
Oncethemapiscreated,therobotnavigatesthe environmentbasedoncommandsissuedbytheoper‐ator.Uponreceivinganavigationcommand,therobot movesthroughtheworkspace,continuouslyscanning forhumanpresenceusingmachinevision.
Duringtheprocess,thesystemprocesseshuman positioningdatatoevaluatethecontaminationrisk levelsinvariousareas.Therisklevelsaredetermined basedonthefrequencyofhumanpresencedetected ineacharea,allowingforamorepreciseidenti ica‐tionofhigh‐riskzones.Thesehigh‐riskareasarevisu‐allyhighlightedonareal‐timemapdisplayedthrough thewebinterface.Thehighlightedzones’colorand sizecorrespondtotherisklevel:greenindicateslow presence,orangeindicatesmediumpresence,andred indicateshighpresence.Thisreal‐timevisualization providestheoperatorwithanoverviewofpotential contaminationhotspots,aidinginevaluatingthedisin‐fectionprocess.ThismethodissimilartoRamalingam etal.[24],whoutilizeddeeplearningtoguideamobile robotfortargeteddisinfection,ensuringef icientsan‐itation.
Followingidentifyinghigh‐riskareas,therobot autonomouslynavigatestothesezonesandperforms targeteddisinfection.Usinganelectrostaticsprayer, therobotappliesdisinfectantproportionallytothe assessedrisklevel.Inhigh‐riskareas,therobot reducesitsspeedtoapplymoredisinfectant,whereas inlow‐riskareas,itmovesatnormalspeedtoconserve resources.Thedisinfectionprocessisconsideredsuf‐icienttoensureadequatedisinfectantapplication whentherobotremainsineachlocationforapre‐de inedduration,withlongerdurationsinhigh‐risk regionsandshorterdurationsinlow‐riskareas.This adaptiveapproachalignswithMantellietal.[23],who optimizedUVCdisinfectionbydynamicallyadjusting robotspeedbasedonradiationenergymapping.The robotreturnstoitschargingstationandremainsidle, waitingfortheoperatortoexecutetheforthcoming mission.
5.SystemOverview
AsshowninFig. 2,thedisinfectionrobotcom‐prises ivesubsystems,eachplayingaspeci icrole inthedisinfectionprocessandoverallsystemarchi‐tecture.Thefollowingsubsectionsprovideadetailed analysisofthekeytechnologiesandmechanismsthat enabletherobottooperateeffectively.
5.1.DisinfectionSubsystem
Thedisinfectionsubsystemisresponsibleforthe disinfectionprocess.Itsprimarycomponentsarethe sprayer,acustomizeddeviceforsolubletablets,anda microcontroller.Areviewoftheliterature[25]ondis‐infectionsprayersidenti iedthreemarket‐readysolu‐tions:liquidsprayers,mistsprayers,andelectrostatic sprayers.Thekeyfactordistinguishingthesesprayer categoriesistheproportionofdisinfectantappliedto acontaminatedarea.
Afterconductingacomparativeanalysisofthevar‐ioussprayersandtheirrespectivefeatures,electro‐staticsprayersweredeterminedtobethemostsuit‐ableoptionduetotheiref iciencyinapplyingdisin‐fectantsacrossawiderangeofsurfaces,makingthe disinfectionprocessmoreeffective.
Followingextensiveresearchintotheelectrostatic sprayermarket,theVP300ESelectrostaticsprayer fromVictoryInnovations.Inparallelwithsprayer selection,amarketsurveywasconductedtoidentify asuitabledisinfectantsolventtablet.Thefactorsthat playedadecisiveroleintheselectionofthedisinfec‐tanttabletwerethefollowing:
‐ Effectivenessofthedisinfectantagainstawiderange ofpathogens,includingsuchasSARS‐CoV‐2,andthe timerequiredtocombatthepathogens.
‐ Versatilityofuse,consideringpotentialapplications inhealthcaresettings,educationalfacilities,rooms, entrances,andotherhigh‐touchareas.
‐ CompliancewithEuropeandisinfectionprotocols andregulations.
‐ Safetyandprotectionofstaffandroomoccupants.
‐ Costeffectiveness.
Basedontheseconsiderations,theresearchteam choseDustbaneProductsLtd’sUnitabdissolving tabletsduetotheireffectivenessagainstvarious pathogens,includingSARS‐CoV‐2.Tointegratethese componentsontotherobot,acustommechanism wasdevelopedtocombinetheelectrostaticsprayer withthedualtabletdropmechanism.Thismecha‐nismisconnectedtoacircuitthatincludestheESP32 MCU,theelectrostaticsprayer,andthetabletdrop‐pingmechanism,whichareconnectedtotheCentral ControlInterface(CCI)viaaserialconnection.Upon receivingacommandfromtheCCI,themechanismis activatedtospraydisinfectantordropatabletintothe liquidcontainer.
5.2.MobileApplicationSubsystem
Toprovideaninterfacewiththeenduser,agraphi‐caluserinterface(GUI)wasdevelopedtovisualizethe disinfectionprocessandreal‐timedataoftherobot’s operations.
Figure2. Thediagramillustratesthesystemarchitecture oftheautonomousdisinfectionrobot.Thesystem comprisesthemachinevisionsubsystemforhuman detection,thenavigationsubsystemforrobot navigationandobstacleavoidance,thedisinfection subsystemfordisinfectiontasks,thedecisionsupport systemfordataanalysisandoptimization,andthe mobileapplicationsubsystemforuserinteractionand operation.Thearrowsindicatethedataflow(blue)and controlflow(yellow)betweenthecomponents
Figure3. Thedisinfectionrobotsystemdisplaysthe environment,theAGV’sposition,andoptionsfor disinfectionandnavigation
TheGUIdisplayscriticalinformation,including theworkplacemap,therobot’sbatterystatus,posi‐tion,andorientation,thedisinfectionstatusandthe mostfrequentlyvisitedhumanlocations.Thisdata iscollectedthroughsensorsmountedontherobot, suchasLiDAR,inertialmeasurementunit(IMU),and encoders.
TheGUIfeaturesseveralfunctionalbuttonsde‐signedtomanagetherobot’soperations,asshown inFig. 3.The“InitializeAGVPosition”buttonallows userstoassigntherobot’spositiononthemap. Incontrast,the“InitializeAGVOrientation”button adjuststherobot’sorientation.The“MoveAGV”but‐tonenablestheselectionofapointonthemap,direct‐ingtherobottonavigatetowardsadesiredlocation. Fordisinfectiontasks,the“EnableDisinfection”but‐toninitiatesthedisinfectionprocedureofidenti ied high‐riskareas.
The“DropTablet”alsoreleasesadissolvingtablet intotheliquidcontainer.Finally,the“GotoDocking Station”buttondirectstherobotbacktoitsdesig‐natedhomelocationforcharging,ensuringitisready forfuturetasks.Thesystemisdesignedtooperate withahighdegreeofautonomy,withtheoperator assumingasupervisoryroleprimarilyforinitialsetup andmonitoring.Theoperatorissuesnavigationcom‐mandsandtherobotnavigatesautonomouslyfroma startingpointtoaspeci iedlocation.WhentheDSS identi ieshigh‐riskareas,theoperatorissuesthedis‐infectioncommand,andtherobotnavigatestothe speci iedlocationtoperformthedisinfectiontask.
5.3.MachineVisionSubsystem
Objectdetectionisacrucialtaskincomputer vision,focusingonidentifyinginstancesofvisual objectssuchaspeople,animals,orcarswithindig‐italimages.Therecentsurgeinthedevelopment ofdeeplearningalgorithmshassigni icantlypro‐pelledtheadvancementofobjectdetection,result‐inginremarkablebreakthroughsandwidespread adoptioninapplicationssuchasautonomousdriv‐ing,machinevision,andvideosurveillance[26].For instance,AI‐drivensurveillancesystemshavesuc‐cessfullyimplementeddeeplearning‐basedtracking methodstoenhancereal‐timemonitoringandsecu‐rity,allowingforaccuratedetectionandreidenti ica‐tionofindividualsacrossdifferentcameraviews[27].
Deeplearning‐basedcomputervisionhasalso beenwidelyusedinCOVID‐19prevention,suchas real‐timefacemaskdetectionsystemsthatmoni‐torcompliancewithpublichealthguidelines[28]. Thesesystemsleverageconvolutionalneuralnet‐works(CNNs)toclassifymaskedandunmaskedindi‐vidualsinpublicspacesaccurately.Similarly,this studyemploysamachinevisionsubsystemfordetect‐ingindividualsanddeterminingtheirlocationsinan indoorenvironment.ThesystemintegratesanIntel RealSenseD435stereodepthcameraandtheYOLOv5 (YouOnlyLookOnce)objectdetectionmodel[29], providingpreciseandef icientdetectionandlocaliza‐tion.
YOLOv5isalightweight,real‐timeobjectdetection modeldevelopedbyUltralyticsin2020.Itisknown foritsaccuracy,speed,andlowcomputationalcost. YOLOv5usesconvolutionalneuralnetworks(CNNs) topredictclassprobabilitiesofobjectsdetectedwithin images.Themodelrequiresonlyasingleforward propagationforobjectdetection,simultaneouslypre‐dictingdifferentclassprobabilitiesandthebounding boxesthatencompassobjects.Recentstudieshave demonstratedtheeffectivenessofYOLO‐basedmodels inreal‐timeobjectdetectionforassistivetechnolo‐gies,includingtheirapplicationinvisualassistantsfor thevisuallyimpaired[30],highlightingtheversatility ofYOLOv5foref icientobjectdetectioninreal‐time environments.ThearchitectureofYOLOv5consists ofthreecomponents:thebackbone,neck,andhead, asillustratedinFig. 4.Thebackboneisresponsi‐bleforextractingessentialfeaturesfromtheinput images.YOLOv5usestheCSPDarknet53backboneto enhancecomputationalef iciencythroughabottle‐neckCross‐StagePartialNetworks(CSP)technique. Theneckservesasanintermediarythatcombinesfea‐turesfromdifferentlayerstoimproveobjectdetection atvariousscales.Finally,theheadgeneratesoutput predictionsusingananchor‐baseddetectionstrategy andtheSiLUactivationfunctiontoenhancelearn‐ingef iciency.YOLOv5hasdifferentversions(Nano, Small,Medium,Large,Extra‐Large)toaccommodate differentcomputationalneeds,makingitidealfor real‐timeapplications.Inthisstudy,theYOLOv5Nano variantwasutilized.
TheYOLOv5nmodelwastrainedthroughout100 epochsonadatasetcomprising4,407images,encom‐passing11,000instancesofthe“person”category. Thetrainingwasconductedwiththeprimaryobjec‐tivesofprecision,recall,andmeanaveragepreci‐sion(mAP@0.5)atthe1071‐imagevalidationsplit. Byepoch100,themodelhadconvergedtoprecision =0.837,recall=0.707,mAP@0.5=0.795,F1score =0.77,whichoccursatacon idencethresholdof approximately0.31,whilerequiringonly4.1GFLOPs perinferenceandmaintainingreal‐timeframerates ontheJetsonNano.
Itscon idence‐thresholdbehaviorischaracterized usingprecision‐recallandF1‐con idencecurves:the PRcurvecon irmsthemAP@0.5of0.795,withapeak precisionof1.00atathresholdof0.94andapeak recallof0.91atanear‐zerothreshold,andtheF1curve peaksat0.77usingathresholdof0.31.Together,these resultsdemonstraterobusthumandetectioninreal time.
TheplotsillustratedinFig.5showcasehowhuman detectionperformancevarieswiththecon idence threshold,themodel’sinternalprobability(0–1)that aboundingboxcontainsaperson.Whenthethresh‐oldisverylow(e.g.,near0.0),almosteverybox underconsiderationisaccepted,resultinginhigh recall(≈0.91)butthisleadstomanyfalsepositives; inhigherthresholdsthedetectorbecomesmoreselec‐tive,reducingtherecallscoreandimprovingprecision untilitreaches100%aroundacutoffvalueof0.94. Theprecision‐recallcurve(mAP@0.5=0.795)sum‐marizesthistradeoffacrossallthresholds,andtheF1 con idencecurvefurthershowsthatanintermediate cutoffvalueof0.31maximizesthebalancebetween precisionandrecall(F1=0.77).Inpractice,these resultsindicatethatusinga31%con idencethreshold yieldsthemostreliablereal‐timedetectionresults, capturingmostoftruepositiveswhilelimitingfalse alarms.
IntandemwithYOLOv5,theIntelRealSenseD435 stereodepthcameraextractsdetectedindividuals’3D coordinates.RGB‐Dsensorshavebeenwidelyapplied forhumanmotiontrackingandpostureclassi ication, providingrobustspatialawarenessforintelligentsys‐tems[31].TheRealSenseD435usestwosynchro‐nizedinfraredcamerastocapturestereoscopicimages andastructuredlightinfraredprojectortocreatea depthmapofascene.Thestereoscopicdepthcam‐erausesprojectiontoconvert3Dpointsto2Dpixel positionsanddeprojectionconverts2Dpixellocations withspeci ieddepthinto3Dcoordinates.Therefore, whenYOLOv5detectsindividualsandplacesthem inaboundingbox,itcalculatesthecenterpointof theboundingbox,andthedistancebetweendetected individualsandthecamera,asillustratedinFig. 6. Thispointisthendeprojectedtoobtainthe3Dcoor‐dinatesoftheindividualsdetectedwithintheimage. The3Dcoordinatesaretransformedfromthecam‐era’scoordinatesystemtotherobot’smapcoordi‐natesystem.Thistransformationensuresthatthe robot’soccupancygridmapaccuratelyre lectsthe positionsofdetectedhumans,allowingtherobotto navigatetohigh‐riskareasbasedonhumanpres‐enceautonomously.Bycontinuouslymonitoringand updatingtheoccupancymapbasedonhumanpres‐ence,thesystemensuresthatdisinfectioneffortsare focusedonthebusiestareas,optimizingdisinfectant useandimprovingoverallhygiene.
Figure4. YOLOv5architectureoverview:(a)Backbone withCSPbottleneck(BCSP)andSPPmodulesforfeature extraction,(b)NeckwithPANetstructureforfeature fusion,and(c)HeadwithConv1x1layersforfinalobject detection
Figure5. Evaluationofthefine‐tunedYOLOv5Nano humandetectoralgorithm/methodologyacrossvarious confidencethresholds:(a)Recall–Confidencecurve, showingmaximumrecallof0.91atthresholdsnear 0.00.(b)Precision–Confidencecurve,withpeak precisionof1.00ata0.94threshold.(c) Precision–Recallcurve,yieldingmAP@0.50.795.(d) F1–Confidencecurve,withthehighestF1valueof0.77 ata0.31threshold
5.4.DecisionSupportSystem
Tomonitorandoptimizethedisinfectionprocess, aDecisionSupportSystem(DSS)wasdevelopedto prioritizethesanitationoftheworkarea.TheDSS isdesignedtocommunicateandexchangeinforma‐tionwiththemachinevisionandnavigationsubsys‐tems.Speci ically,theDSSreceivesinputdatafrom thevisionsubsystemtodeterminethepresenceof individualsintheareaandsendsinformationabout high‐riskzonestothenavigationsubsystem.
Theprimarygoalofanalyzingtheinputdataisto identifyhigh‐riskareasintheworkplaceanddirect therobottothoseareas.Theinputdataconsistsofx‐y coordinatesdescribingthepositionofindividualsin eachregionduringthesystem’soperationalperiod.
Figure6. Thisfigureillustratesthedetectionof individualsinanindoorenvironmentusingYOLOv5and theRealSensestereodepthcamera.Thebounding boxeshighlighteachdetectedperson,andthedistance fromthecameraisalsoannotated.Thevisualoutput demonstratesthesystem’scapacitytoestimate individuals’distancesinrealtime
After inetuningandintegratingthehumandetec‐tionalgorithm/methodology,theDSSemploysDen‐sity‐BasedSpatialClusteringofApplicationswith Noise(DBSCAN),usinganeighborhoodradiousofε =0.5metersandaminimumclustersizeofminPts =20togroupnearbydetectionsintospatialclusters. Thefuzzyapproximationalgorithm[32]clustersthe identi iedlocationpointsbasedondensity,andhigh‐lightsareaswithahighconcentrationofindividuals.
Oncetheinputdataisclustered,individuals observedpositionsarevisualizedasspheresinthe mobileapplicationsubsystem.Thesizeandthresh‐oldofthespheresre lectthefrequencyofindividuals observedineacharea.Thresholdsaresetbasedonthe frequencyofindividualsobserved;ifthenumberof pointscountedexceedsthesetthreshold,theareais classi iedashighrisk.High‐riskareasareeasilyiden‐ti iabletotheuserthroughmoreprominentspheresin thegraphicalinterface.Theclustersaredividedinto groupsofdifferentcolorswithadjustablethreshold distancesandradiusforeachproposeddisinfection area.
5.5.NavigationSubsystem
Thenavigationsubsystemgeneratesamapofthe surroundingenvironment,localizestherobotwithin thatmap,planspaths,andnavigatestotargetloca‐tionsfordisinfection.Theinitialstageinvolvescre‐atingadetailedenvironmentmapusingtheSLAM algorithm[33].Thisalgorithmallowstherobottocon‐structamapbyutilizingdatafromLIDARorcamera sensorswhilemaintainingawarenessofitscurrent position.TheSLAMalgorithmisusedwith0.05mres‐olution,a5‐secondmapupdateinterval,andenabled loopclosureovera3‐metersearchradious.
ThisapplicationutilizesaLIDARsensortocollect environmentaldataduringexplorationbyemittinga lightbeamina360‐degreesweep.
Thedistancetoanobstacleiscalculatedbasedon thetimethelightbeamtakestoreachtheobstacleand returntothesensor.Thecollecteddataisthenpro‐cessedtocreateanoccupancygridmaprepresenting theenvironment,includingwalls,obstacles,andopen spaces.Aftergeneratingtheenvironmentmap,the AdaptiveMonteCarloLocalization(AMCL)algorithm isemployedtolocalizetherobotwithinthemap[34]. AMCLusesaparticle iltertoestimatetherobot’sposi‐tionandorientation,whichiscontinuouslyupdated basedonsensordatafromtheLIDARandencoders. TheAMCLlocalizationisusingwith500–2000par‐ticlesandisresamplingoneveryscantomaximize pose idelity.AMCLoperatesatafrequencyof20Hz, withamaximumlinearvelocityof0.26metersper second,amaximumangularvelocityof1.0radiansper second,andgoaltolerancesof0.25meterslocallyand 0.5metersglobally.
Oncethemapiscreatedandtherobotislocalized, pathplanningandnavigationarethenextsteps.The robotmustnavigatefromitscurrentpositiontoiden‐tifyhigh‐riskareasfordisinfection,whichinvolves atwo‐stepapproach:globalpathplanningandlocal pathplanning.Forglobalpathplanning,theA*algo‐rithmisused.A*isawidelyrecognizedalgorithm thatdeterminestheshortestroutefromthecurrent robot’spositiontoatargetarea,consideringdis‐tanceandobstacleavoidancetogenerateanoptimal path[35].TheTimedElasticBand(TEB)algorithmis usedforlocalpathplanning.TEBdynamicallyadjusts therobot’strajectorytoaccountformovingobstacles andenvironmentalchanges[36],continuouslyre in‐ingtherobot’strajectorytoensureeffectiveobstacle avoidanceduringnavigation[37].
Intheabsenceofanexternalground‐truthsys‐tem,thevalidationofthemappingandlocalization qualitywasachievedthroughadirectcomparisonof theSLAM‐generatedoccupancygridwiththeknown loorplanandsensor‐derivedscans.Speci ically,the ROS‐orientedmapwasoverlaidontothefacility’s CADlayoutandLiDARpointclouds,revealingthatall walls,doors,and ixedobstaclesalignedwithinone gridcell(about0.05m)oftheirsurveyedpositions. Furthermore,therepeatedexecutionof“go‐to‐pose” commandstostoredwaypointsresultedinsuccessful navigationwithoutanyrecordedcollisions,thereby validatingtherobot’sabilitytoaccuratelyestimateits positionwithinthe60‐square‐metreworkspace.This convincingcorrespondence,inwhicheverystructural featureislocalizedinacentralmapinaccordancewith thereal‐world,providescon idenceinthenavigation stack’sabilitytoproduceanaccurateandreliablenav‐igationandsupportsreal‐timeprioritizationofthe identi iedhigh‐riskareasandtargeteddisinfection.
6.SubsystemIntegrationandValidation
Theresearchteamperformedexperimentsinthe facilitiesandlaboratoriesoftwouniversities,thereby facilitatingacomprehensiveexplorationofdifferent environments.
Figure7. a)LaboratoryatAristotleUniversityof Thessaloniki(70m2),showingaccuratereconstruction ofwalls,doorways,andfixedobstacleswithina0.05m resolutiongrid.b)ClassroomatInternationalHellenic University(60m2),demonstratingaconsistentmap qualityacrossdifferentindoorenvironments
Theexperimentswereconductedinaclassroom attheInternationalHellenicUniversityandinthe receptionareaoftheprofessors’of icesatAristotle UniversityofThessaloniki.Detailedmapsofthese premiseshavebeenprovidedforreference.Forexam‐ple,inFig. 6(b),theclassroom’ssettingsposedsig‐ni icantchallengesduetonumerousstaticobstacles, suchascabinetsandcomponents,anddynamicobsta‐cles,likehumans.Asillustrated,theexperimentaimed toevaluatetherobot’sabilitytomaptheenviron‐ment,detecthumanpresence,andautonomouslydis‐infecthigh‐riskareasbasedonreal‐timedata.After aninspectionperiod,thesystemidenti iedseveral high‐riskareas,asillustratedinFig.Thesystemaccu‐ratelydetectedhumanpresenceandtrackedindi‐viduals’movementstodistinguishconsistentlyoccu‐piedareas.Thewebinterfacedisplayedcolor‐coded circlestorepresentrisklevels:greencirclesindi‐catedlowmobilityandlowrisk,orangecirclesrepre‐sentedmediummobility,andredcircleshighlighted areasofhighmobility,classi iedashigh‐risk.Out ofthefourregionsdetected,twowereclassi iedas high‐risk,oneasmedium‐risk,andoneaslow‐risk. Therobotautonomouslydisinfectedthehigh‐risk areasbyapplyingmoredisinfectantwherecontamina‐tionriskwashigher,whilereducingdisinfectantusein low‐riskareas,therebyoptimizingresourceconsump‐tion.
7.DiscussionandConclusions
Inthisresearchwork,withintheEITHealth ResearchGrandproject,acustomizedrobothasbeen implementedtodisinfectindoorworkplaces.Thepro‐posedsolutionintegratesamachinevisionsystemto locatevisitorsandworkersinaspeci icarea.Italso integratesadecision‐makingsystemthatselectshigh‐riskareasfordisinfectionandadjuststhespraying volumebasedontherisklevel,withhigher‐riskareas receivingmoredisinfectant.Thedisinfectionprocess isinitiatedviaauser‐friendlywebinterfacethatpro‐videstherobotoperatorwithinformationabouthigh‐riskareasandtheirsize.
Figure8. Thefollowingillustrationdepictsthehuman detectionandnavigationprocess.Theupperdisplay depictsthemapoftheenvironmentwithdetected humanpositions,whilethelowerleftandrightwindows illustratereal‐timeobjectdetectionanddistance estimationforidentifiedindividuals
Figure9. Followingatwo‐hourinspection,thelocations identifiedrequiringfurtherinvestigationweremarked onthediagram.Thecircles’colorrepresentstherisk levelassociatedwitheacharea.Incontrast,thesizeof thecirclesindicatestheextentoftheareainwhich humanmovementswereobserved
Theinnovationofthesystemliesinthreekey aspects:(i)theintegrationofmachinevisiontomon‐itorareaswithhighhumanconcentration,(ii)the integrationofanintelligentdecision‐makingmecha‐nismthatselectshigh‐riskareasfordisinfectionand adjuststhesprayingvolumebasedontheestimated infectionprobability,withhigher‐riskareasreceiving moredisinfectants,and(iii)theselectionoftheshort‐estroutetocarryouttheprocesses.Theproposed roboticsystemoptimizestheamountofdisinfectant liquidrequiredtocoveranareaandthetimeneeded tocompletethedisinfectionprocessinlargebuildings andworkspaces.
Therobotwastestedinanareawithhighhuman presenceduringvalidation.Theperformancemetrics consideredweremapaccuracyandhumandetection ef iciency.Therobotsuccessfullymappedtheenvi‐ronment,accuratelyrepresentingthephysicallayout, andidenti iedthepointswiththehighesthumanpres‐enceandactivity.Thenitautonomouslynavigatedto thehigh‐riskareastoperformdisinfection.Thesys‐temdemonstratedaccuratedisinfectioncon irmingits practicalapplicationinreal‐worldsettings.
Originally,therobotuniformlysprayedtheentire 30‐square‐meterworkspaceofthe60‐square‐meter laboratory.IntegrationofmachinevisionandtheDSS resultedina33%reductionindisinfectantusage,as thesystemnowselectivelytargetsonlytenhigh‐risk 1m2 zonesfordecontamination,asopposedtothe previouspracticeofblanketsprayingtheentirearea. Futureresearchwillfocusonamendmentsonthe robotchassiswithimproved luidcapacityandbat‐teryautonomytosupportoperationsinlargerareas. Additionally,integratingmorenozzleswillallowthe robottosprayinmultipledirectionssimultaneouslyor toselectaspeci icdirectionbasedonthearealayout.
Whileourlabtrialsdemonstratedfeasibility,real‐worlddeploymentrequiresmaintenanceandadap‐tationstrategies.Weplanendurancerunstoassess batterylife—anticipatingrechargingevery2hours undercontinuousoperation—andtomonitornozzle cloggingorwear,schedulingtablet‐dropandsprayer‐nozzleinspectionsaccordingly.Tominimizedown‐time,theproposedroboticsystemwillfeaturea removablebatterypackandinterchangeable luid containersasspareparts.Wewillalsoimplement remotevehiclemanagement,loggingusageandmain‐tenancedata,andprovideon‐boardfunctionalitiesfor utilizingmultiplefacilitylayoutoccupancygridmaps. Furthermore,theconsortiumiscommittedtoevaluat‐ingtherobustnessofroboticvehiclesinvariousreal‐worldenvironments.Byexpandingtrialsbeyonduni‐versitylaboratoriestoincludeof icesuitesandmeet‐ingroomswithdifferingcrowddensities,theconsor‐tiumaimstoascertainthesystem’smappingef iciency ineachsetting.
Theconsortiumalsoplanstoparticipatein keyindustryconferencesandevents,suchasthe EuropeanDetergentsConferenceandtheWA DisinfectionandDisinfectionBy‐productsConference, toattractpotentialpartnersandexpandthesolution’s applicability.Anothercriticalstepisattempting topatenttheinnovativesolution.Thisapproach couldpavethewayforexclusivedistributionrights, additionalrevenuethroughroyalties,andcommercial salesundertheHi‐Gienbrand.
AUTHORS
GeorgiosKaramitsos∗ –Departmentof IndustrialEngineeringandManagement, InternationalHellenicUniversity,+306973913684, SindosCampus,Sindos,Greece,57400,e‐mail: yiorgoskaramitsos@gmail.com.
VasileiosSidiropoulos –Departmentof IndustrialEngineeringandManagement, InternationalHellenicUniversity,+306973289267, SindosCampus,Sindos,Greece,57400,e‐mail: billsidiropoulos27@gmail.coml.
EvangelosSyrmos –DepartmentofIndustrialEngi‐neeringandManagement,InternationalHellenicUni‐versity,+306970677707,SindosCampus,Sindos, Greece,57400,e‐mail:evangelossyrmos@gmail.com. AthanasiosSidiropoulos –Departmentof MechanicalEngineering,AristotleUniversityof
Thessaloniki,+306973289643,AristotleUniversity Campus,Thessaloniki,Greece,54124,e‐mail: thanossidiropoulos@gmail.com.
XenofonKaramanos –Departmentof MechanicalEngineering,AristotleUniversityof Thessaloniki,+306998519461,AristotleUniversity Campus,Thessaloniki,Greece,54124,e‐mail: xenakiskaramanos@gmail.com.
DimitriosVlachos –DepartmentofMechanical Engineering,AristotleUniversityofThessaloniki, +306943846468,AristotleUniversityCampus,Thes‐saloniki,Greece,54124,e‐mail:vlachos1@auth.gr.
DimitriosBechtsis –DepartmentofMechanical Engineering,AristotleUniversityofThessaloniki, +306974351301,AristotleUniversityCampus,Thes‐saloniki,Greece,54124,e‐mail:bechtsis@gmail.com.
∗Correspondingauthor
ACKNOWLEDGEMENTS
ThisresearchwaspartiallysupportedbytheEuro‐peanInstituteofInnovationandTechnology(EIT) Healthprojectentitled“AutonomousRoboticVehicle fordisinfectingworkplaces”.
Thecodeforourstudycanbefoundhere https: //github.com/xkaraman/higien
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THEDESIGNOF3D‐PRINTEDOPENBEARINGSFORHUMANASSISTINGROBOTS THEDESIGNOF3D‐PRINTEDOPENBEARINGSFORHUMANASSISTINGROBOTS
Submitted:24th April2024;accepted:10th September2024
PiotrFalkowski,BazyliLeczkowski
DOI:10.14313/jamris‐2025‐021
Abstract:
Wearabletechnologies,includingexoskeletons,signifi‐cantlyimpactsupportingthemotionofpeoplewithdis‐abilities.However,activatinginternal/externalrotations inextremitysegmentsrequiresplacingbodysegments insidebearings,astheirrotationaxesmustoverlap. Thishinderstheexoskeletonmountingprocessandeven excludessomemedicalcasesfromusingthedevices. Forthisreason,thedesignofinnovative3D‐printed openbearingswaspresentedinthispaper.Itconsists ofanthropometricmodelling,computer‐aidedmechan‐icaldesign,multibodydynamicssimulations,strength analysis,andparametricoptimizationtoobtainminimal masswhilecomplyingwiththestrengthrequirements. Thedesignprocessresultedinreducingtheoverallmass ofdesignby40%.Moreover,itprovedthatthepow‐deradditivemanufacturingtechniquescombinedwith thethinslidinglayersprintedwithFFF/FDMtechnology aremoresuiTablefortheintendedusethanmonoliths manufacturedwithFFF/FDMtechnology.Thepresented methodologyisuniversallyapplicabletootherrobots interactingwithhumans,whichrequiretheuseofopen bearingswithoutdrives,andalsoifmanufacturedsub‐tractively.
Keywords: additivemanufacturing,exoskeleton,finite elementsmethods,multibodysimulation,openbearings, rehabilitationrobotics,strengthsimulation
1.Introduction
1.1.Exoskeletons
Exoskeletonsareagroupofwearablerobotsthat serveashumanexternalexoskeletons.Hence,theyare abletosupportuserswithadditionalforceoreven fullybringbackthemotioncapabilities.Theyaredis‐tinguishedbytheirkinematicchainmappingonthe humanlimbanatomy.Thesedevicescombinesensory andcontroltechnologies,amongothers,andexhibit featuresofbionics,robotics,computerandcontrolsci‐ence,medicine,andotherinterdisciplinary ields[35]. Theysupporttheworkofasingleorseveralsegments ofauser.Duetothekinematicscorrespondingtothat ofthehumanlimb,exoskeletonsmakeitpossibleto preciselyapplytherequiredtorquetoaspeci icjoint oftheuser[27].
Exoskeletonscanservedifferentfunctions dependingonthe ieldinwhichtheyareapplied.
Themostcommonpurposesoftheexoskeleton’s interactionwiththeuserarepowerampli ication, assistanceandmotorfunctionsubstitution.Dueto thesedevices’widerangeofapplicability,theyhave beenfoundtobeusedin ieldssuchasthemilitary, rehabilitation,andindustry[5,19,20,31].Roboticsys‐tems,suchasexoskeletons, indincreasinguseinreha‐bilitationwithsimilarormarginallysuperiorresults comparedtothestandardrehabilitationperformedby thephysiotherapist[33].
Anessentialpartoftheexoskeletondesignisits numberofDegreesofFreedom(DOFs).Deviceswith DOFnumbersclosertothoseofthelimbtheysup‐portenableuserstoachievemorecomplexandnatu‐ralmovements.However,thisrequiresmorecomplex controlalgorithms[32]andahighermanufacturing costforsuchadevice.
ForfullywearableexoskeletonstobeascomforT‐ableaspossible,itisnecessarytoreducetheweight exertedontheuser[36].Inthecaseoffull‐bodyand lower‐limbexoskeletons,itispossibletocompensate fortheweightoftheexoskeletonbyusingappropriate actuators.Ontheotherhand,researchindicatesthat suchstructures’greatermomentofinertia[21]may affecttheuser’scomfort.
However,totalweightcompensationisnotalways possibleinupperlimbexoskeletons,primarilywhen theentireweightrestsontheuser.Thegreaterweight oftheexoskeleton,inadditiontothepotentialdis‐comfortofuse,isoftenassociatedwithgreaterenergy consumptionrelativetolighterdesigns,which,inthe caseofthelowerlimbandfull‐bodyexoskeletons,may impacttheirrange[12].
Inexoskeletons,alargeproportionofthemassis accountedforbytheweightoftheactuators.Intypical designs,ahighernumberofDOFsoftengoeshandin handwithahigherweightofthewholedevice.This resultsinaneedtobalancethenumberofDOFswhen designinganexoskeletonsothatitisnottooheavy whileallowingtherequiredrangeofmotion,alsofor patientswithreducedmobility[30].
1.2.Freedegreesoffreedom
Oneofthemaindesignchallengesforexoskele‐tonsistoreducetheirmasswithoutrestrainingthe mobilityofthemechanism.Themassofthedevices typicallyincreasessigni icantlywiththenumberof actuatorsandtheirpower[16].Hence,itresultsin lighterexoskeletonshavingfewerdegreesoffreedom. However,thisapproachleadstolimitingtheexoskele‐ton’sfunctionality.
Insomesolutions,wherethedeviceisintendedto assistwithasinglespeci ictypeofmovement,thismay notnecessarilybeabigproblem.Onthecontrary,the situationisdifferentforthedevicesusedforawide rangeofmotionpatternsbymultiplepeople[29].One suchapplicationisrobot‐aidedrehabilitation.
Reducingthemassofthedeviceswhilemaintain‐ingtheirmobilityispossiblebyusingfreedegreesof freedomintheirkinematics(passivejoints).Theseare movableonlywiththeuser’sforce.Thus,theyreduce thenumberofactuatorsinthestructure.Forsuch anapproach,freeDOFsshouldbetheonesrequiring relativelysmalltorquetobedriven(thisshouldbe signi icantlylowerthanpossibletobegeneratedby auserinacertainDOF).Moreover,theconstruction shouldhavearelativelylowmomentofinertiaregard‐ingthecorrespondingaxisofrotation[11].
Theuseoffreedegreesoffreedominthedevice’s kinematicswillnecessitatepredictivecontrol.Thisis causedbytheinabilitytocontrolsuchDOFs.There‐fore,realizingthetasksrequirescompensatingtheir con igurationbyotherDOFs.Suchcanbene itfrom involvingAI(Arti icialIntelligence)topredictthe user’smovements[15].Thealgorithmsaretypically basedoninformationaboutthemovementinthe freedegreesoffreedom.Nevertheless,theycanbe enhancedbyintroducingEMGmeasurements,re lect‐ingthemuscularactivityofauser[23].
1.3.AdditiveManufacturing
Additivemanufacturingtechnologiesnotedrapid developmentinrecentyears[40].Theyallowtheman‐ufacturingofcomplexgeometries,oftenimpossible toobtainwithsubtractivemanufacturingtechniques. Moreover,additivetechniquesaresuiTableforsmall batchproduction,thusallowinguser‐speci icdesigns tobemanufacturedatrelativelylowcost[3].This correspondstotheneedfordevice‐aidedpersonalized medicine.Especiallyforthepatientssigni icantlydif‐feringwithanatomy[9].
Additivemanufacturingtechnologieshavebeen appliedinthemanufactureofexoskeletons[6].Two techniquesareparticularlyusable–FFF/FDM(Fused FilamentFabrication/FusedDepositionModeling) printingforplastics[24]andSLSprintingtechnology forpowdersofplasticsormetals[22].
FFF/FDMprintingisthemostcommonadditive manufacturingtechnology.Itisbasedontheextru‐sionofsemi‐ luidthermoplasticmaterialsothatit isarrangedininterconnectedpathways,forminglay‐ersthat,whensuperimposedononeanother,create geometry[38].ModelsproducedwiththeFFFtech‐nologyoften induseinrapidprototypingprocesses andtheproductionofpersonalizedcomponentsfor aspeci icuser.Itisduetotherelativelylowcostof unitproduction[13].Thankstotherecentdynamic developmentofthistechnology,manymaterialswith differentstrengthparametersandphysicalproperties areavailableonthemarket[28, 34].However,this technologyhasseverallimitations,whichmustbecon‐sideredwhendesigningmedicalelements.
Themanufacturedcomponentscanbebrittleand donotbehaveintheisotropicway[10,39].Therefore, thedesignprocessforsuchpartsshouldincludetheir strengthsimulations.Anincreaseintheuseofthis technologyinthemedicalindustrytoproducepro‐totypesofmedicaldevicesandcomponents,suchas dedicatedorthoses,hasbeenobservedinrecentyears [26].
SLS(selectivelasersintering)printingisatech‐nologybasedonbondingpowderswithalaserbeam [4].AsinFFF/FDMprinting,thepartsmadeusing thistechnologyaremadelayerbylayer.Apartfrom thermoplasticmaterialsintheformofpowder,metals andceramicscanbeusedaswell[25].Thegeome‐triesobtainedwiththistechnologyusuallyhavea betterexternalsurfacequalitythanthoseobtained withFFF/FDMtechnology.Theirmechanicalproper‐tiesareorthotropic[8],butforsomecases,theyare veryclosetoisotropic.
1.4.OpenBearingsConcept
Freedegreesoffreedominexoskeletonscanbe realizedmechanicallybyusingbearings.However, withthestandardbearings,allowing360degrees ofrotationmaynegativelyaffectthedevice’sconve‐nience,especiallyduringattachingtothepatient’s extremities.Withtheenclosedbearings,ausermust puttheirbodysegmentsthroughthesealongthekine‐maticchainofthedevice.Hence,patientswithspas‐ticcontractionsoraffectedanatomycanbeunable tousesuchsystems.Therefore,itisadvantageous tointroducebearingswithasemi‐opendesignthat allowsrotationinthefreedegreesoffreedombyan anglecorrespondingtotheanatomicalhumanrange ofmotion.Asthesolutionblocksexcessiverotationof thedeviceinfreeDOFs(beyondtheuser’sanatomical jointrotationrange),itimprovesthesafetyofthe exoskeleton.Inaddition,suchadesigncanincorporate featuresthatallowtheexoskeletontobemountedon theuser,straporvelcroholders,andsoftpadding, amongothers.
Suchabearingshouldconsistoftwomainrel‐ativelyslidingcooperatingcomponents.Itmustbe lightweightandstrongandthesametime.Asthe designisnotenclosed,therollingelementsbetween thetwomaincomponentscannotbeused.Forthis reason,thesurfacesremainingincontactshouldbe madeofslidingmaterialsthataredurabletowear.
Additivetechnologiescanbeusedtomanufacture suchbearings.Theirusemayallowobtaininggeome‐triesthatwouldbedif icultorimpossibletoproduce withothertechnologies.Suchcanbetheresultsof numericaloptimizationtargetingoverallmassreduc‐tionwhilestillmeetingthestrengthandfunctional requirements.
Thestudyaimstopresentthedesignprocessof theinnovativeopenbearingstobeusedwithinthe exoskeletonssupportinghumanactivities.Thepro‐cessconsistsofanthropometricmodelling,mechani‐caldesign,parametricoptimization,andstrengthval‐idation.Thebearingspresentedinthepaperareded‐icatedtotherehabilitationdevice, ExoReha [14,15].
Theoutcomesoftheworksweremanufactured andimplementedinthedesign.However,suchstruc‐turesandtheirdesignmethodologyareapplicable tootherdevices,suchasend‐effectorrehabilitation robotswithexoskeleton‐likeattachmentsoftheeffec‐torsorassistiverobotsforsupportingactivitiesof dailyliving.
2.Methodology
Themodelpreparationandoptimizationprocess willproceedinthefollowingorder(unlessnotedoth‐erwise, AutodeskInventorProfessional2021 wasused forCADmodelling, MSCAdams2021.1 –fordynamic analysis,and Ansys2021R1 –forFEAanalysisand optimization):
‐ PreparationofaCADmodeloftheexoskeletonbased onthedevelopedkinematicsandanthropometric data,
‐ Preparationofasimpli iedsix‐bodymodelofthe exoskeleton,withsolidsconsistingofrigidlycon‐nectedelements,
‐ Dynamicanalysistoobtainequivalentforcesand momentsoccurringinthebearingsforthreecritical positionsofeachbearing,
‐ Preparationofafullyfunctionalgeometricalmodel ofthebearingfor initeelementanalysisinthe SpaceClaim moduleof Ansys2021R1 software,
‐ PreparationoftheFEAmodelwithhigh‐quality initeelementmeshandloadsre lectingthemost dangerouscasesfromthedynamicsimulation,
‐ Strengthvalidationofthemodelindifferentcon igu‐rationsofthebearingcomponentsrelativerotation,
‐ Numericalparametricoptimizationofthemodel underthemostdangerousloadcases.
‐ Redesigningofthebearingbasedontheoptimiza‐tionresultstomeetthefunctionalcriteria,
‐ Strengthvalidationofthe inalmodel.
2.1.CaseDescription
Withintheframeworkofthispaper,thefree degreesoffreedomcorrespondingtotheanatomical movementsoftheupperextremitywillbeconsidered. Theanalogicalmethodcanalsobeusedforlowerlimb exoskeletonswithfreedegreesoffreedom.
Theconceptofusingfreedegreesoffreedom inexoskeletonkinematicsthroughtheuseofopen bearingsisusedinthe„ExoReha”exoskeleton(CAD modelisshowninFigure 1),whichisadeviceused fortask‐orientedtherapyoftheupperextremity[14, 15, 17, 18].Itisdedicatedtorehabilitatingpost‐stroke,neurological,orthopaedic,post‐accidentand post‐surgicalpatients.Thekinematicsofthedevice (presentedinFigure2)consistsof ivedegreesoffree‐dom,threeofwhicharedriven(DOFscorresponding totheanglesmarkedas ��1, ��2,and ��4 inFigure 2). Thetworemainingones(DOFscorrespondingtothe angleslabelledas��3 and��5 inFigure2),correspond‐ingtoshoulderandelbowjointrotations,remainnon‐driven.
Preliminarygeometricalmodelsoftheopenbear‐ingshavebeendesignedasshowninFigure 3.They consistofaninnerandouterpart,slidinglyrelatively, andalockingelementtoenclosethebearinginner elementinsidetheouterandblockexcessiverotation. Allofthemareinitiallydesignedasmonolithsmadeof slidingmaterial(3D‐printedfrom IglidurI-190-PF).
Theotherexoskeletoncomponentsaremountedto thebearingswithscrewconnections–withthethru holesintheinnerpartandmetalinsertsmeltedinto theouterpart.Moreover,thelockingpartisassembled intothemetalinsertsplacedintheouterelement.
Figure1. CADmodeloftheExoRehaupperextremity exoskeleton
Figure2. ExoRehakinematicsmodel
Figure3. Initialopenbearingdesign
Exoskeletonmultibodymodelfordynamics analysis
Therefore,inthefollowinganalysis,itistreated asitsintegralpart.Theouterpartofthebearingis designedtoallowtheuser’sextremityattachment usingthestrapswithbuckles.
Thepreparedmodelhasthenundergonestrength analysisandparametricoptimizationtoreduceits weight.Inthefollowingsections,thebearingdesign processispresentedontheexampleoftheDOF ��3 showninFigure3.Nevertheless,theprocesswasana‐logicallyconductedfortheDOF��5
2.2.DynamicsSimulations
Thedynamicanalysisoftheexoskeletonwascar‐riedouttodeterminetheresultantforcesactingonthe bearingsduringoperation.Themultibodymodelused forthisprocessisvisualizedinFigure 4.Itisworth noticingthattheExoRehaexoskeletonhasanadjust‐ment,allowingto itauserwithanatomicalparame‐tersbetweentheonesforthe5th femalepercentileof thePolishpopulation[7](denotedhereafterasW5) andthe95th malecentileofthePolishpopulation (denotedhereafterasM95).Themodelchosenforthe dynamicanalysiscorrespondstothecon igurationof thedeviceadaptedtotheM95user,asitwillcause thegreatestpossiblereactionforces.Themultibody modelincludestheupperextremitymodelattached totheexoskeletoninthemountingpointsofthebear‐ings.ThemodelshowninFigure4isageometrically modi iedCADmodelofthedevice,inwhichrigidly connectedcomponentshavebeensimpli iedtoindi‐vidualsolids.Theupperextremitymodelconsistsof twosolidelements:onecorrespondingtothearmand aonecorrespondingtothecombinedforearmwiththe hand.
Allthebodieshaveindividualparameters assigned–masses,momentsofinertiawithrespect totherotationalaxesofthesolids(axesasshown inFigure 4),andthecentersofmass(COMs).These arepresentedinTables 1 and 2.Fortheexoskeleton model,thesedatawerecalculatednumericallybased onthedensityofthematerialswithin Autodesk InventorProfessional2021 software.Thedatafor theextremitysubmodelscomedirectlyfromthe anthropometricTablesorwerecalculatedbased onthem.Themultibodymodelhas ivedegreesof freedom.Hingejointswereusedtoconnectthebodies oftheexoskeletonasinreallife.
Table1. Massparametersofthemultibodymodel bodies(Iqq –maininertiamomentalongqaxis)
Table2. CoordinatesofCOMs(centersofmasses)ofthe elementsinthelocalcoordinatesystems(COMq –centerofmassalongqaxis)
Sphericaljointswereusedtoconnecttheupper extremitybodiestooneanotherandtotheground element.Inaddition,onedegreeoffreedomwastaken awayfromthemodelledelbowjoint.Theexoskeleton wasconnectedtotheextremitymodelatthreepoints using“lock”joints(whichtakeawaythepossibility ofrelativemovementofconnectedelements):atthe pointofcontactbetweenthehandandthehandleand atthecentersofbearingswiththearmandforearm. Theformerrepresentsgraspingthedevicehandle, whilethelatterrepresentsattachmentofthestructure bystraps.
Fortheanalysis,itwasassumedthatthehighest forcesandmomentsactingupontheopenbearings occurwhenthefollowingconditionsoccur:
‐ theexoskeletonisinthestretched(base)con igura‐tion(showninFigure4);
‐ everyDOFisrotatingwiththemaximumpossible velocity;
‐ allthedrivesactwithmaximumtorqueindirec‐tionsoppositetothemovementinthecorrespond‐ingDOFs.
TheEarth’sgravitationalaccelerationwassetalong thenegativeY‐axis(seeFigure4).Theangularveloc‐itiessetforthejointsarepresentedin3.Theirdirec‐tionsareasfortheliftingtask.Theseassumptions guaranteethattheforcesoccurringwithinrehabilitat‐ingindividualswith ExoReha willnotexceedthecalcu‐latedones,regardlessoftheactivitybeingperformed.
Figure4.
Table3. Maximumangularvelocitieswhichmayoccur inDOFs
Figure5. Analyzedbearingconfigurations;fromleft:‐90 deg,0deg,and90deg
Figure6. Theouterpartgeometrypreparedinthe SpaceClaim
Theforcesandmomentsactinginthebearingwere determinedforthethreecon igurationspresentedin Figure5.Thesecorrespondtothetwoextremebear‐ingswings(±90degreesfromtheaxisofsymmetry) andthepositionatthecenteroftherangeofmotion (attheaxisofsymmetryofthebearing).
Onlythe irststepofthesimulationwasconsidered forfurtheranalysis,asonlythereinwastheexoskele‐toninthecharacteristiccon iguration.To indthe mostsevereload,onlythemostdangerousloadcase wasusedforthestrengthanalysis.
2.3.StrengthAnalysis
Forfurtherstrengthanalysis,geometriesofthe twointerfacingbearingpartswerepreparedinthe SpaceClaim environmentbasedontheirinitialmodels. Theyarevisualizedin6and7.
Figure7. Theinnerpartgeometrypreparedinthe SpaceClaim
Table4. Parametersoffiniteelementsmodels
Basedonthegeometry,elementmesheswerepre‐paredforthese.Differentmeshgridsweretested,and theoneswiththebestminimalelementqualityindica‐torswereselected.Theirparametersarepresentedin Table4.The inalmeshgridswereconstructedusing mainlytetrahedralelements.
Themeshgrids’qualitywasassessedashighusing the”elementquality”criterion,embeddedinto Ansys 2021R1,andcalculatedaccordingtotheformula 1, wherethefollowingsymbolstateforthevariables: ‐ ����–elementquality, ‐ ��–constantfortheelementtype, ‐ ��–elementvolume, ‐ ���� –thelengthofi‐thelement’sedge.
Theoutcomewasconsideredsatisfactorywhen therewerenoelementswithaqualitylowerthan0.2. Theminimumelementqualitywas0.282offorthe innerpartand0.213fortheouterpart,whilethe averageelementqualitywas0.836fortheinnerpart and0.821fortheouterpart.
Thegeometryoftheouterpartwasconstrained, asshowninFigure 8,withthecorrespondingcon‐straints:
1) Abushing‐typeconstraintontheplanes,which simulatesaboltedconnectionbetweentheouter partofthebearingandthelockingelement;
2) Fixed‐support‐typeconstraintssetonthecylindri‐calsurfacesoftheholes,restrainingtheirmove‐mentsanddeformation,whichsimulatethescrew connectionoftheouterpartwiththenextpartof theexoskeleton(throughanon‐threadedhole);
Constraintsoftheouterpart
Figure9. Constraintsoftheinnerpart
Table5. MaterialpropertiesforFEManalysis
Figure10. Optimizationparametersset
Table6. FEMmodelparametersinitialvalues(input parameters:P1‐P5andMaterialmodel,output parameters:maximumstressesandmassesoftheparts)
3) A“frictionlesssupport”setontheplane,restrain‐ingrotationaroundtheaxesotherthanthosenor‐maltotheplaneandthetransitionalmovementin anout‐of‐planedirection,whichsimulatescontact withthenextpartoftheexoskeleton.
Thegeometryoftheinnerpartwasconstrained,as showninFigure9withthecorrespondingconstraints:
1) Fixed‐support‐typeconstraintssetonthecylindri‐calsurfacesoftheholes,restrainingtheirmove‐mentsanddeformation,whichsimulatethescrew connectionoftheinnerpartwiththepreviouspart oftheexoskeleton(threadedinsert);
2) A“frictionlesssupport”setontheplane,restrain‐ingrotationaroundtheaxesotherthanthosenor‐maltotheplaneandthetransitionalmovementin anout‐of‐planedirection,whichsimulatescontact withthepreviouspartoftheexoskeleton.
Followingthis,astrengthanalysiswascarried outtocomputethestressesanddeformationsunder themostdangerousloads.Initially,thegeometrywas assumedtobemadeentirelywiththeFFFprinting technologyfromthe Iglidurl190-PF material.Asthe analysisisintendedtovalidatethestrengthofthe devicewiththehighsafetyfactor,anaverageisotropic strengthcharacteristicofthematerialwasinvolved.
Thisdoesnotimplicateanysigni icantimpacton theresultsanalysis.Table5showsthematerialmod‐elsusedfor Iglidurl190-PF [2]and F3DNanoCarbon (PA12+CF) [1],consideredinthefurtherstagesofthe designprocess.
2.4.ModelModificationBasedontheParametricOpti‐mization
Inthenextstep,themodelwassubjectedtoRSO‐typeparametricoptimization.Thisisintendedto selectthemodel’sdimensionsandmaterialtoreduce thebearing’smasswhilemaintainingitsfunctional operation(i.e.,fromthepreconceivedranges).The responseplanesoftheGeneticAggregation”typewere createdbasedon300points[37].Forthesimulation resulttomeetthedesignassumptions,itwasassumed thatthesafetyfactorforthepartafteroptimization couldnotbelessthan1.3.
Thedimensionsthathavebeenparameterizedare markedinFigure 10 asP1–P5.ParametersP1–P3 arecommonforbothparts(innerandouter)within theonly ittolerancedifferences.Additionally,the materialmodelwassetasthediscreteparameter.In ordertoalloweasyattachmentofthebearingtothe user’sarm,theinnerdiameterdimensionremained unchangedat146mm.
Figure8.
Table7. ConsideredrangesordiscretevaluesofFEM modelparameters
P1[mm] 10–16
P2[mm] 15–20
P3[mm] 26–30
P4[mm] 48–60
P5[mm] 40–50
Materialmodel IglidurI190‐PF/F3DNanoCarbon
Themassesofbothbearingpartsandthemaxi‐mumstressesineachwereconsideredtheminimized parameters–formerwiththeweightof1andlatter withtheweightof0.1.Moreover,overshootingthe material‐dependentmaximumaveragestressdivided bythe1.3safetyfactorwasusedasastopcriterion. Theinitialvaluesofallparametersarepresentedin Table6,whiletheirconsideredrangesarepresented inTable7.
Duringtheoptimization,oneofthevariable parameterswasthematerialmodel.Thisallowedver‐i icationoftheinitialassumptionthatthebearing partsshouldbemadeasslidingmonoliths.Perhaps, basedonthecomputations,makingthemfromF3D NanoCarbon(PA12+CF) ilamentwithadditional slidingelementsbetweentheinterfacingpartswas morebene icial.
3.ResultsandDiscussion
3.1.DynamicsSimulations
Theresultingforcesandequivalentmomentsfor everyfreebearings’con igurationarepresentedin Table8.Eachofthedeterminedloadcasescanbeused forstrengthanalysis.However,basedonthecompu‐tations,thehigheststressoccurredforloadcase4. Hence,itwasusedforfurtherthissimulationand parametricoptimization.However,loadcases1and 8werealsovalidatedaspotentiallydangeroustothe multibodysystem.
3.2.InitialStrengthAnalysis
Thedeterminedstressdistributionsinthebearing partsarepresentedinFigures11and12,whilethedis‐placementdistributionsarevisualizedinFigures 13 and 14.Asexpected,thebiggeststressappearedin theregionsalongtheedgesconnectingthecylindrical surfacesofthebearingswiththesurfacesincontact withtheotherexoskeletoncomponents.Nevertheless, theirmaximumvaluesdonotcauserisksofdamaging thedesign.Thebiggesttotaldeformationsappearin theregionsremainingincontactwithinthecon igura‐tion–aroundthelockingpart.Nevertheless,theirval‐uescannotcauseblockingtherotationofthebearing.
Figure11. Outerelementaveragestressequivalent distribution
Figure12. Outerelementaveragestressequivalent distribution
Figure13. Outerelementtotaldeformationdistribution
Figure14. Outerelementtotaldeformationdistribution
Table8. Equivalentloadstatesfortheconsideredcombinationsofbearingarrangements(DOFcolumnrepresentsthe DOFforwhichtheparametersarepresentedwiththeconfigurationintheopenbearingbytherotationindegrees,Fq–forcealongqaxisoftheglobalcoordinatesystem,Mq–forcealongqaxisoftheglobalcoordinatesystem)
Figure15. Initialmodel(left)comparedwiththemodel afterparametricoptimization(right)inthesamescale
Table9. FEMmodelparametersfinalvalues(input parameters:P1‐P5andMaterialmodel,output parameters:maximumstressesandmassesoftheparts)
Table10. Parametersoffiniteelementmodelsfor validationofthedesign
3.3.ModelModificationBasedontheParametricOpti‐mization
Themodelobtainedasaresultoftheoptimization iscomparedwiththeinitialdesigninFigure15.Itis visiblysmallerthantheoriginalonewhilemeetingthe functionalandstrengthcriteria.Theparametervalues obtainedasaresultoftheoptimizationareshownin Table 9.Itisworthnoticingthatthedesignmaterial hasalsobeenchangedasaresultoftheparametric optimizationprocess.
Changingthematerialsigni icantlyreducedthe parts’weight.However,tomaintainthefunctionality oftheopenbearing,itwasnecessarytomodifythe resultingmodelsothatthecontactbetweenthebear‐ingpartsoccurredviaslidingelements.
Figure16. Finalbearingmodel
Figure17. Outerelementaveragestressequivalent distributionafterparametricoptimiation
Figure18. Outerelementaveragestressequivalent distributionafterparametricoptimiation
Figure19. Outerelementtotaldeformationdistribution afterparametricoptimiation
ThenewmodelisshowninFigure16.Two1‐mm widthslidinginsertswereaddedbetweentheouter andinnerparts,madeofIglidurI190‐PF.
Finiteelementmesheswereagaingeneratedfor thenewbearingmodeltovalidateitsstrength.The parametersofthemeshesarecollectedinTable 10 Thequalityofallgridswasassessedashighusingthe same„elementquality”criterion,wherethequalityof noelementislowerthan0.2.
Figure20. Outerelementtotaldeformationdistribution afterparametricoptimiation
Table11. FEManalysissummaryafterfinaldesign modifications
Theminimumelementqualityis0.217forthe innerpartand0.208fortheouterpart,whilethe averageelementqualityis0.803fortheinnerpartand 0.819fortheouterpart.
Thenewmodelwassubjectedtoanalogical strengthanalysis.Figures 17 and 18 showthestress distributionsoftheouterandinnerparts,respectively, whileFigures 19 and 20 presentthestraindistri‐butions.Table 11 showsmaximumvaluesofstress, strain,radialdisplacementsoftheslidingcylindrical surfaces,thedisplacementoftherearsurfacecooper‐atingwiththeblockingelementinthenormaldirec‐tion(fortheouterpart),andtheminimumsafety factor.Thereisalsoinformationonwhatmaterialthe elementwiththelowersafetyfactorismadeof.
Thestressanddeformationdistributions remainedthesameasbeforetheoptimization. However,theirvaluesincreased.However,they donotexceedassumedsafelimitsandenablesafe operation.Thisincludesvalidatingthecylindricality oftheinnersurfacesoftheouterpart,andtheouter surfacesoftheinnerpart.Similarvalidationwas performedforthecomponents’interfacingback planes.Thesedeformationsarecritical,astheycan causestackingrestrainingrotationofthebearings.
4.Conclusions
Theinvestigationprovedthatitisreasonable todesign3D‐printedopenbearingsforassisting robotswiththesupportofnumericaloptimization.It turnedoutthatpowder‐basedadditivemanufactur‐ingtechnologiestypicallyresultinahigherstrength oftheobject.However,combiningitwithFFF/FDM‐manufacturedthininsertsmatchesthestrengthofthe constructionwiththeslidingfunctionality.
Theanalysisshowsthatthehigheststressesoccur inthesameregionsbeforeandafteroptimization andforboth3D‐printingtechniques,alongthesharp edges.Thedeterminedcylindricaldeformationsdo notexceedtheassumedmaximumvalue.Theother designassumptionswerealsomet,exceptforthe expectedmassreduction.Thismeansthatthemodel hasbeencorrectlyredesigned,butfurtheroptimiza‐tioncanbecarriedouttoreduceitsmass,e.g.,byusing topologicaloptimization.Thisalsocon irmsthatthe bearingshouldnotexperienceexcessivewearduring operationandthattheaddedslidinginsert(made ofIglidurl190‐PFwithslidingpropertiesandhigh wearresistance)willworkcorrectlywiththerestof thebearing.
Itisplannedtocontinueresearchonpossible massreductionforthepresenteddesignwiththe hybridoptimizationapproach(multipleparametric andtopologyoptimizationcycles)andvalidatethe impactofusingaverageisotropicmodelsinsteadof theorthotropicone.Thedesignedbearingwas3D‐printedwiththepowdertechniqueandassembledto the„ExoReha”exoskeleton.However,itisplannedto furthermodifythedesignandreducethetotalmass oftheexoskeletonby50%.
Thepresentedmethodologyisalsoapplicableto theelementsdesignedforconventionalmanufactur‐ing.Moreover,itiseasilytransferabletootherrobots interactingwithhumans,whichrequiretheuseof openbearingswithoutdrives.Theseincludeawide varietyofmedicalrobots,home‐useservicerobots, andevenexoskeletonsforspeci icapplications.
AUTHORS
PiotrFalkowski∗ –ŁUKASIEWICZResearchNet‐work–IndustrialResearchInstituteforAutoma‐tionandMeasurementsPIAP,Al.Jerozolimskie202, Warsaw;WarsawUniversityofTechnology,02‐486, PlacPolitechniki1,Warsaw,00‐661,Poland,e‐mail: piotr.falkowski@piap.lukasiewicz.gov.pl.
BazyliLeczkowski –ŁUKASIEWICZResearch Network–IndustrialResearchInstitutefor AutomationandMeasurementsPIAP,Al. Jerozolimskie202,Warsaw,Poland,e‐mail: bazyli.leczkowski@piap.lukasiewicz.gov.pl.
∗Correspondingauthor
ACKNOWLEDGEMENTS
Thepaperisbasedontheresultsofthe“Development ofauniversalandlightweightconstructionofreha‐bilitationexoskeletonwithacontrolalgorithmdedi‐catedtoremote,homeandtask‐orientedrehabilita‐tion”–SmartEx‐Homeproject, inancedin2024–2026 (1,793,900PLN),inthescopeofscienti icresearch anddevelopmentworksbytheNationalCenterfor ResearchandDevelopment(LIDERXIV,contractnum‐berLIDER14/0196/2023).
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CONTROLAPPROACH SELF‐TUNINGCONTROLLERFORSCALARSYSTEMS:APRESELECTEDTIME
CONTROLAPPROACH
Submitted:9th August2024;accepted:28nd February2025
AliSoltaniSharifAbadi
DOI:10.14313/jamris‐2025‐022
Abstract:
Asingle‐inputsingle‐outputlinearsystemcanmodel variousphysicalsystems.Oneofthechallengesincon‐trollingpracticalsystemsisthatthesettlingpointand settlingtimecannotbeprescribedsimultaneously.This paperpresentsanovelself‐tuningcontrol(STC)algo‐rithmforscalarsystemsthatensuressystemstability whileallowingboththesettlingtimeandsettlingpoint tobepredetermined.Toevaluatetheeffectivenessof theproposedcontrolmethod,fourpossiblescenarioswill bedefined.Foreachscenario,threedifferentcaseswill beexaminedinthesimulationsection.Linearquadratic regulation(LQR)willbeusedforcomparison.MATLAB softwarewillbeemployedtotestandsimulatethese cases.ThesimulationresultswilldemonstratethatSTCis anoptimalsolutionforscalarlinearsystems,comparable toLQR,withthesignificantadvantageofguaranteeing theachievementofthedesiredsettlingpointwithinthe predefinedsettlingtime.
Keywords: self‐tuning,optimization,control,preselected time,preselectedstate,hamiltonian
1.Introduction
Controlmethodshavebeendevelopedtostabi‐lizepracticalsystems.Thecontrolproblemsinclude regulation(stabilization),tracking,andpathfollow‐ing.Linearquadraticregulation(LQR),(Proportional IntegralDerivative)PID,andmodelpredictivecontrol (MPC)arethemostpopularcontrolmethods.These methodshavesomeadvantagesandsomedisadvan‐tages.Oneofthemostessentialparametersincontrol systemsisde iningthesettlingtimeandsettlingpoint. Somealgorithmsaredevelopedtopredict,determine, andcalculatethesettlingtimeorsettlingpoint[1–4].Theprede inedtimealgorithmscanprovidethe upperboundofthesettling(stabilization)timebefore applyingthecontrolsignaltothesystem[5–9].But nomethodprovidesawaytode inethesettlingtime andsettlingpointsimultaneouslyanddeterminingthe accuratesettlingtimeisanotherchallenge.
Tuningthecontrolparametersisanotherchal‐lengeincontrolsystems.Thecontrolparameters shouldbetunedtosatisfythecontrolgoals.ThePID controllerisoneofthemostcommoncontrolmeth‐ods,butithasatuningcontrolparametersproblem. Therearesomemethodsoutlinedintheliteraturethat solvethisproblem[10–14].AnotherissueinPIDis
thattheusercannotde inethesettlingtimeandbe surethatthesystem’soutputwillreachthesettling pointattheprede inedsettlingtime.TheLQRtech‐niqueprovidesanoptimalsolutionbytuningthecon‐trolparameters.However,thesettlingtimeofthecon‐trolledsystemremainsanopenresearchchallenge.
Aself‐tuningcontrol(STC)approachhasbeen de inedasamethodthatpredicts/adjustscontrol parameters.Thesemethodsareknownas“parame‐tertuners.”Theparametertunersareoftwotypes: of lineandonline[15–17].Themaincontributionof theparametertunersisincreasingthecontrolperfor‐mance.Insomecases,theparametertunersarethe mainpartofthecontrolmethodwithinthecontrol system.Inthesecases,thecontrolmethodiscalledan STCmethod.OneofthechallengesintheSTCmethods isthesystem’sstability.Intheparametertuners,the system’sstabilityisnotaproblem,sincethesystem’s stabilityshouldbeguaranteedbythemaincontrol method.Fuzzylogicisoneofthemostcommonmeth‐odsusedtodesignthecontrollersastheparameter tuner[18].Themaincontrollerinthisstudyisanon‐singularPID inite‐timeslidingmodecontrol(FSMC). TheFSMCguaranteessystemstability,andthefuzzy logicsystemtunesthecontrolparameters.Inother studies[18–20],fuzzylogicisusedasthetuner,and themaincontrollerisPID.Instudies[21–24],other typesoftunershavebeenintroducedtoadjustthe controlparameters,whichcanbecategorizedasSTC methods.Theseworkshavedevelopedrelayfeedback systemsforparametertuning.
Thesettlingtimeisanimportantparameterin theperformanceofasystem.Differentstabilization methodscanguaranteevarioussettlingtimes[25–30]. Anasymptoticstabilizationmethodrequiresanin inite amountoftimetoguaranteestability.However,a inite‐timemethodprovidesstabilitywithalimited upper‐boundsettlingtime[31].Fixed‐timestabiliza‐tionmethodsareterminalmethodsthatprovidean upperboundonthesettlingtime,independentof thesystem’sinitialcondition[32, 33].Prede ined‐timestabilizationmethodsprovide ixed‐timestability, wherethesettlingtimeisacontrollerparameter[34]. Preselected‐timecontrolisde inedasamethodwhere thesettlingtimeischoseninadvance,ensuringthat thesystem’sstatereachesthepreselected‐stateatthe exacttime.Thetimeselectedinthepreselected‐time approachcanbeconsideredthesettlingtimewhenthe preselectedstate(point)ischosentobeverycloseto zero.
Inmostcasesincontrolsystems,itisneces‐sarytoknow/de inethesettlingpointandsettling timetogether.Somestudieshavebeenpublishedthat presentwaysofcalculating,determining,andde ining thesettlingtimeandsettlingpointseparately,but de iningthesettlingtimeandsettlingpointtogether isanexcellentfeatureforusers.Inthisstudy,anSTC methodwillbedesignedtotunethecontrolparame‐terofthescalarsystems.TheproposedSTCmethod providesthepossibilityofde iningthesettlingpoint andsettlingtimesimultaneously.TheHamiltonian conditionswillbeusedtoprovetheoptimalityofthe method.ThefeaturesoftheproposedSTCmethodare asfollows:
‐ Itispossibletoselectthesettlingpoint(preselected state)andsettlingtime(preselectedtime)simulta‐neously.
‐ ItusesaLyapunov‐basedstabilizationmethod.
‐ Itisapracticablemethodthatcanbeusedindiffer‐entapplications.
‐ TheproposedSTCmethodprovidesanoptimal solutionforsingle‐inputsingle‐output(SISO)linear (scalar)systems.
‐ Itisalinearprede ined‐timesolutionforlinearsys‐tems.
‐ Itprovidesfourpossiblescenarios.
‐ Itcanbeupdatedforthetrackingproblemand (Multi‐InputMulti‐Output)MIMOsystems.
‐ Itprovidesanexponentialsolutionwithoutany unwantedovershootandlowershootforscalarsys‐temswhere��=��
2.ProblemStatement
Asuitablecontrollerforpracticalsystemsshould havethefollowingfeatures.
ConsiderthefollowingSISOlinearscalarsystem:
̇��=����+���� ��=�� ,��(0)=��0, (1)
where ��∈ℝ isthesystem’sstate, ��∈ℝ isthe system’soutput,��∈ℝ,��∈{ℝ−{0}}arethesystem’s parameters,��∈ℝisthecontrolinput,and��0 ∈ℝis theinitialconditionofthesystem.Thecontrolinput shouldguaranteethesystem’sstabilityandsatisfythe discussedfeatures.Itisassumedthatthesystem’s stateisavailablefordesigningthecontroller.Onthe otherhand,thesystemusesthefeedbackofthestate.
Remark1: Inpracticalandcontrollablesystems, thesystem’sparameter��isnotequalto0.
TheSTCwillguaranteethatthesystem’sstate reachesaspeci icpointataprede inedtime,which willbeselectedbythesystem’suser.Thisspeci ic pointandprede inedtimewillbechosensimulta‐neously.Also,thesolutionwillbeoptimal,whichis provenbytheHamiltonianequations.Thenonoptimal solutionoftheSTCwaspublishedin[17]asanof line self‐tuningcontroller(OSTC).
InOSTC,twoperformancecriteria[integralof absoluteerror(IAE)andintegraltimeabsoluteerror (ITAE)]areconsideredforpreparingsomeformulas touseintuningthecontrolparameters.IntheOSTC method,somerulesareprede ined,andthecontrol parametersaretunedaccordinglybeforeapplyingthe controllertothesystem.However,inSTC(online) methods,thecontrolparametersareadjusteddynam‐icallywhilecontrollingthesystem.
Inthispaper,theHamiltonianequationswillbe usedtodesigntheoptimalsolutionofthecontroller. Consideringthesystem(1)andthefollowingcost function: ��= ����2 +����2����, (2)
where��∈ℝ≥0 and��∈ℝ>0 aretheweightparam‐eters.TheHamiltonianequationforthissystemand costfunctionisasfollows:
��=����2 +����2 +��(����+����), (3)
where��isthecostatevariable.TheHamiltoniancon‐ditionsarepresentedasfollows[35–37]:
TheSTCcontrolinputwillbedesignedbyusingHamil‐tonianconditions.
3.Self‐TuningControllerDesign
ConsideringtheSISOscalarlinearsystemofEqua‐tion(1)andthecostfunctionofEquation(2),inorder tohaveanoptimalself‐tuningsolutionforthesecon‐ditions,thefollowingequationisused:
1 �� (−����+��������)
������ =−����;��= ln ��0 ����
, (5)
where �� istheSTCparameterthatisapositivecon‐stantas��= ln ��0 ���� ���� ,where��0 istheinitialcondition ofthesystem’sstate, ���� isthesettlingpoint(which wecanchooseandwanttoreachattheprede ined settlingtime),and ���� istheprede inedsettlingtime. Figure1showstheblockdiagramoftheproposedSTC method.
Remark2: TheconceptoftheSTCmethodis thattheusercanchoosethesettlingpoint(position) andsettlingtimetogether.Thisisoneofthegreatest advantagesofthismethod.
Remark3: Asettlingpointisavaluewiththe samesignastheinitialcondition,lessthanapositive initialcondition,andgreaterthananegativeinitial condition.Thisfactcausesthesystemnottohaveany unwantedovershootorlowershoot.
Theorem1: Thescalarlinearsystem(1)willbe stabilizedasanoptimalsolutionconsideringthecost function(2)bytheself‐tuningcontroller(5).
Self-tuning Controller
Figure1. BlockdiagramoftheSTCmethod
Proof: ThecostfunctionofEquation(2)canbe writtenas
TheHamiltonianequationofsystem(1)andthecost function(6)isasfollows:
TheHamiltonianconditionsofEquation(7)canbe writtenas
SISO system
Afterasimpli ication,
TheSTCparameterwillbeachievedasfollows:
Asde inedpreviously,theSTCparameterisequalto
,andfromtheHamiltonian,itiscalculated
Theseconditionscanbesimpli iedasfollows:
Thisresultistheself‐tuningtoolthatallowsusto de inedifferentscenarios.Thesescenarioswillbedis‐cussedinthenextsection.
TheLyapunovtheoryisemployedtoprovethe stabilityoftheself‐tuningcontroller.Thefollowing Lyapunovfunctioncanbede ined:
Afterapplyingthecontrolinputtothesystem,wehave thefollowing:
where��1 =2��isapositivevalue.Therefore,thesta‐bilityofthesystemisprovenbytheLyaponuvstability theory[38].
Toprovethefactthattheself‐tuningcontroller guaranteesthatthechosensettlingpointwillbe reachedattheprede inedsettlingtime,wecansolve thesystem’sdifferentialequationasfollows:
Inthe irstscenario,theusershouldselectthe settlingpoint,settlingtime,andweightparameter �� inthecostfunction;thentheSTCwillcalculatethe controlparameter��andtheweightparameterof��.
4.2.SecondScenario
Thesecondscenarioissimilartothe irstone,but inthisscenario,theweightparameter �� shouldbe selectedbytheuser,and��and��willbecalculatedby theSTC.
Remark7: Ingeneral,theweightparametersof thecostfunctioncanbepositiveornegative,butin mostcases,apositivevaluefortheseparametersis required.Inordertohavepositivevaluesoftheweigh parameters(�� and��)inthe irstandsecondscenar‐ios,oneofthefollowingconditionsisnecessary:
Therefore,theorem1isproven,andthesettlingpoint willbereachedatthesettlingtimebyapplyingtheSTC controlsignaltothesystem.
Thecontrolledsystem’sresponseis ��(��) = ��0��−����,whichexhibitsexponentialbehaviorand ensuresstability,aslim��→∞ ��=0
Remark4: RelationsinEquation(18)showthe relationshipbetweentheprede inedsettlingtime,set‐tlingpoint,andSTCparameter.Theserelationscanbe usedtocalculatethepropervaluesoftheparameters byde ining(selecting)twootherparameters.
Remark5: AsevidentinEquation(18),thesys‐tem’sstateandcontrolsignaloftheSTCmethodwill changeexponentially.ItisprovablethatforeverySTC solutionoftheSISOlinearsystem,thereisanoptimal solutionwithaspeci iedcostfunction.Bythetermsof Equation(15),theweightparametersofthespeci ied costfunctioncanbecalculated.
Remark6: ThepresentedSTCmethodcanbe extendedtoMIMOlinearsystemsbydecouplingthe irst‐orderSISOsubsystemsasfollows:
4.3.ThirdScenario
Inthisscenario,theweightparametersofthecost function �� and �� andthesettlingpoint ���� shouldbe de inedbytheuser,andthesettlingtime���� andcon‐trolparameter��willbecalculatedbytheSTC.Inthis scenario,theweightparametersshouldbepositive.
4.4.FourthScenario
Thisscenarioissimilartothethirdscenario,butin thisscenario,thesettlingtimeandweightparameters shouldbeselected,andthecontrolparameterand settlingpointwillbecalculated.
Inallscenarios,thecontrolparameterwillbecal‐culatedbythede inedcondition(otherparameters); thenthecontrolparameterwillbeappliedtothesys‐tem(1).Intheprevioussection,thesystemstabilityof theSTCmethodwasproven.
5.Simulations
Inthissection,threepracticeswillbede inedand simulatedforeveryscenario.First,itisnecessaryto determinethesystem’sparametersandthedesired parameters;thentheSTCwillcalculatetherestofthe parametersandthevalueofthecostfunction.
MATLABsoftwarehasbeenusedtosimulatethe scenarioswiththeode4solver,andthesteptime equals0.01.Thecalculationshavebeendoneuptotwo decimalplaces.
4.DifferentPossibleScenarios
ConsideringEquation(15),fourscenarioscanbe envisionedfortheproposedSTCmethod.Inthissec‐tion,thesescenarioswillbediscussed.
4.1.FirstScenario
ThemaingoaloftheSTCmethodisthattheset‐tlingpoint(����)andprede inedsettlingtime(����)occur simultaneously.
Forallpractices,thevaluesofthecostfunctions fortheSTC,LQR,andproportional(P)controllersare presented,andtheresultsarecomparedwiththoseof theLQRandPcontrollerstunedusingthePIDblockin Simulink/MATLAB.Itisexpectedthatthecomparison resultsfortheSTCandLQRwillbethesame.
5.1.SimulationsfortheFirstScenario
Thedeterminedscalarlinearsystemisasfollows:
(0)=10. (21)
Table1. Parametersindifferentpracticesofthefirstscenario Practices
Figure2. Simulationresultsofthefirstpracticeofthefirstscenario
Figure3. Simulationresultsofthesecondpracticeofthefirstscenario
Figure4. Simulationresultsofthethirdpracticeofthefirstscenario
Table2. Parametersindifferentpracticesofthesecondscenario
Practices Parameters SelectedbytheUser ParametersCalculatedby theSTCMethod CalculatedValuesoftheCost Functions
3
Figure5. Simulationresultsofthefirstpracticeofthesecondscenario
Figure6. Simulationresultsofthesecondpracticeofthesecondscenario
Figure7. Simulationresultsofthethirdpracticeofthesecondscenario
Threepracticesarede inedtotesttheproposedSTC algorithm.Thesimulationresultsarepresentedin Table 1.Figures 2, 3,and 4 showthesimulation resultsofthedifferentpractices.Inthe igures,the
selectedsettlingpointandsettlingtimeareshown. ThePcontrollerhasbeentunedusingthePID blockSimulink/MATLAB.ThePcontrolleristunedas �������� =−������,where���� =15.3191forthisscenario.
Table3. Parametersindifferentpracticesofthethirdscenario Practices
Figure8. Simulationresultsofthefirstpracticeofthethirdscenario
Figure9. Simulationresultsofthesecondpracticeofthethirdscenario
5.2.SimulationsfortheSecondScenario
Thedeterminedscalarlinearsystemforthesec‐ondscenarioisasfollows:
(22)
Thesimulationresultsofthesecondscenarioarepre‐sentedinTable2.Figures5,6,and7showthesimu‐lationresultsofthedifferentpractices.Inthe igures, theselectedsettlingpointandsettlingtimeareshown.
Simulationresultsofthethirdpracticeofthethirdscenario
Table4. Parametersindifferentpracticesofthefourthscenario
3
Figure11. Simulationresultsofthefirstpracticeofthefourthscenario
Figure10.
Figure12. Simulationresultsofthesecondpracticeofthefourthscenario
Figure13. Simulationresultsofthethirdpracticeofthefourthscenario
ThePcontrollerhasbeentunedusingthePID blockSimulink/MATLAB.ThePcontrolleristunedas �������� =−������,where���� =15.3191forthisscenario.
5.3.SimulationsfortheThirdScenario
Theselectedscalarlinearsystemforthisscenario isasfollows:
(0)=1.5. (23)
ThesimulationresultsarepresentedinTable 3 Figures8,9,and10showthesimulationresultsofthe differentpractices.Inthe igures,theselectedsettling pointandsettlingtimeareshown.ThePcontrollerhas beentunedusingthePIDblockSimulink/MATLAB. ThePcontrolleristunedas �������� =−������,where ���� =15.3191forthisscenario.
5.4.SimulationsfortheFourthScenario
Thedeterminedscalarlinearsystemforthefourth scenarioisasfollows:
̇��=−0.1��−0.6��,�� (0)=−3. (24)
ThesimulationresultsarepresentedinTable 4.Fig‐ures11,12,and13showthesimulationresultsofthe differentpractices.Inthe igures,theselectedsettling pointandsettlingtimeareshown.ThePcontrollerhas beentunedusingthePIDblockSimulink/MATLAB. ThePcontrolleristunedas �������� =−������,where ���� =−0.3404252forthisscenario.
Forthefourpossiblescenarios,threepracticesare de inedandtestedundervariousconditions.Inall practicesacrossallscenarios,theselectedorcalcu‐latedsettlingtimeandsettlingpointareaccurately achieved.TheSTCiscomparedwiththeLQRandP controllers,andthecostfunctioncalculationsindicate thattheSTCachievesthesameoptimalresultsasthe LQRwhileperformingsigni icantlybetterthantheP controller.
6.Conclusion
Thispaperpresentsanewcontrolstrategynamed aself‐tuningcontroller.TheproposedSTCcansta‐bilizethescalarlinearsystem.Thismethodcanbe updatedforMIMOlinearsystems.Thesimulation resultsshowthepoweroftheproposedmethod.The STCiscomparedwiththeLQRmethod,andtheresults demonstratethatSTCprovidesanoptimalsolutionfor thesystem.Also,itcancontrolthesystemtoreachthe settlingpointattheprede inedsettlingtime.Future workscanfocusondevelopingaMATLABtoolboxfor theSTCmethodanddevelopingtheSTCforMIMO systemsandtrackingproblems.
Funding
Theauthorsdidnotreceivesupportfromanyorga‐nizationforthesubmittedwork.
Conflictsofinterest
Theauthorshavenocompetingintereststo declarethatarerelevanttothecontentofthisarticle.
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Submitted:30th September2023;accepted:15th December2023
ThangarajMeena,JampaniChandraSekhar,PerumalAnandan,GanesanVinothChakkaravarthy,MuthaiyanElumalai, BellarmineAnniPrincy,ThirumalaReddyVijayaLakshmi
DOI:10.14313/jamris‐2025‐023
Abstract:
Researchershaverecentlyobservedasignificantincrease intheuseofevolutionaryoptimizationintheconstruction ofdigitalFIRfiltersbasedonfrequencydomainspecifi‐cations.Alinear‐phasefinite‐impulseresponse(LP‐FIR) filter,utilizingHenrygassolubilityoptimization(HGSO) approaches,isdesignedinthisstudyforcreatinghigh‐pass,low‐pass,band‐passandband‐stopfilters.Thepro‐posedworkiscomparedwithexistingmethodssuchas DesignandAnalysisofLP‐FIRutilizingthewaterstrider optimizationalgorithm(DALP‐FIR‐WSOA)anddigitalpre‐detectionequalizer(DPE)usingaFIRfilterfieldpro‐grammablegatearray(FIR‐GOA).Itachievestheobjec‐tivecompetentlyusingreducedripplesathighfilter,as wellashigherattenuationatlowpassandaband‐pass filteratlowexecutionaltime.
Keywords: Henrygassolubilityoptimizationalgorithm, cutofffrequency,clockfrequency,errorfunction,signals
1.Introduction
Digital iltersarenowadaysutilizedalloverworld. Filtersareusedtoimprovethequalityofsignalsas wellasremovingnoisefromthem.Finite‐impulse response(FIR)andin inite‐impulseresponse(IIR) arethetwotypesof ilters.Recently,therehasbeen anincreaseindemandfromactivenoise‐cancellation systemmanufacturersindevelopingareduceddelay inFIR ilters[1].Low‐pass ilters(LPF)aremainly usedtorejecthigherfrequenciesofnoisethanan establishedcutofffrequencyinthesignal.InLPF,dif‐ferentiationisusedtoextractinformationfromthe signal[2].Thesetypesof iltersarebroadlyusedin communicationdevices,medicalequipment,electron‐ics,etc.Inthemedical ield,digital iltersareutilized forde‐noisingEEG,ECGandMRIsignals[3].TheFIR ilterprovideshigherstabilityandlessfeedback.The digital ilterconsistsofmorecoef icients,suchasthe windowmethodandtheequal‐ripplemethod.Low‐, high‐andband‐pass,aswellasband‐stop,aresome classi icationsusedforsignalprocessingimprove‐mentmethods.ThegroupdelayintheLP‐FIR ilter indsfrequencycomponentsbychangingthetime[4]. Nowadays,researchonthese iltersfocuseson speedingthemupwhileusingaminimumamount ofspace,andreducingcontrolparametersindigital ilters.Theresearchproposedhereisusedtoreduce
ripplesinhigh‐passandband‐pass iltersandquickly increaseattenuationinband‐pass ilters.AnLP‐FIR ilterwasdesignedusingHenrygassolubilityopti‐mizationalgorithm,anewtechnique.Manystudies havepreviouslybeenpresentedintheliteratureon thetopicofLP‐FIR ilters.Somerecentworksare reviewedhere.
Karthicketal.[5]havesuggesteddesignsandeval‐uationsfortheLP‐FIR ilterutilizingthewaterstrider optimizationtechnique.Theirstudyusedthewater strideroptimizationapproach,andanef icientlinear‐phaseFIR ilterwasdevisedandimplementedina programmedgatearray,providingmaximumdelay andminimumexecutiontime.
Nima[6]presentedadigitalpre‐distortionequal‐izerutilizinganFIR ilterthatwasappliedusing MATLAB.Thesuggestedmethoddescribesthedesign anddemonstrationofbothstaticanddynamicFIR digitalequalizercircuits.Itprovideshighmagnitude responseandlowdelay.
Seshadri[7]proposedanotherapplicationof fastdigitalFIRandIIR ilters.Theirstudyuses conventional‐moving‐average(MA)FIR ilters;fast MAFIR iltersusinglook‐aheadarithmetic;conven‐tionalIIR iltersusingacombinationofintegratorand combsections(CIC)techniques;andfastIIR ilters usinglook‐aheadarithmetic.Itsuggeststheconven‐tionalMAFIR ilters,fastMAFIR iltersutilizinglook‐aheadarithmetic,conventionalIIR iltersutilizinga combinationofintegratorandCICmethods,andfast IIR iltersusinglook‐aheadarithmetic.Thisallowsfor higherexecutiontimeandlowermagnituderesponse.
Wu[8]alsopresentedahigher‐speedfault‐tolerantFIRdigital ilterutilizingprogrammablegate arraystoimplementhardwarewithmaximumdelay andminimumexecutiontime.
Inthismanuscript,bydeducingthemagnitude responsefromaLP‐FIRresponse ilter,theerrorfunc‐tionsarereducedtopenetratingthehighestpeakrip‐plecompletelybyseparatefrequencyfunction.LP‐FIRisthendesignedusingtheHenrygassolubility optimization(HGSO)algorithmandexecutedusing MATLAB.Inthisway,HGSOisusedforcalculatingthe co‐ef icientoftheoptimal ilter.
Figure1. OverallworkingprincipleofLP‐FIRfilterusing HGSOapproach
Themaincontributionofthisworkissummarized below:
‐ AnLP‐FIR ilterwithHenrygassolubilityoptimiza‐tionalgorithm[9]isdesignedandimplementedin MATLAB.
‐ Subsequently,theHenrygassolubilityoptimization approachisusedinanLP‐FIR ilterforbetterresults withmaximumpassripplesandminimumpass‐bandattenuation.
‐ ThisexecutionofDesignandAnalysisofLP‐FIRuti‐lizingWaterStriderOptimizationAlgorithm(DALP‐FIR‐WSOA)inapassbandishighlyef icientand producesgoodoutput,withmaximumpassripples andminimumattenuationatthestopband.
‐ TheproposeddesignandanalysisofLP‐FIRutiliz‐ingHenrygassolubilityoptimization(DALP‐FIR‐HGSOA)iscomparedwithexistingmethods,such asDALP‐FIR‐WSOAanddigitalpre‐detectionequal‐izerusingaFIR ilter ieldprogrammablegatearray (DPE‐FIR‐GOA).
Part2ofthisstudyconsistsofProposedMethod‐ology,Part3consistsofresultsaswellasthediscus‐sions,andPart4concludesthemanuscript.
2.ProposedLP‐FIRFilterUsingHenryGasSol‐ubilityOptimizationTechnique
TodesigntheLP‐FIR ilter,somespeci icationsare needed: iltercoef icientregisters,adder,andmulti‐plier,aswellastheaccumulator.LP‐FIR iltersare designedbycollectingthespeci icationfromthe il‐ter[10].TheproposedLP‐FIRisemployedinMATLAB andthepresentation ilterisveri ied.Figure1shows totalwork lowoftheLP‐FIR ilterwithHGSO.
Practicalapplicationsoflinear‐phaseband‐pass FIR iltersutilizingtheHGSOmethodsincludetone control,frequencyselectionandechocancellation.
Intonecontrol,FIR ilterscanbeusedtocon‐trolthetoneofaudiosignals,adjustingtheemphasis ofspeci icfrequencyranges.Thisiscommonlyused inelectronicmusicproductionandconsumeraudio devicestocreatedifferenttonaleffects.
Infrequencyselection,FIR ilterscanbeused toselectspeci icfrequencyrangeswithinanaudio signal,allowingforfrequency‐speci icprocessingor
analysis.Thisiscommonlyusedinaudioeditingand spectrumanalysistoisolateandmanipulatespeci ic frequencycomponents.
Inechocancellation,FIR ilterscanbeusedtocan‐celechoinaudiosignals,reducingthedelayedre lec‐tionofsoundthatcanoccurinenclosedspacesor whenusingmultiplemicrophones.Thisisparticularly importantinapplicationsliketeleconferencingand audiorecording.
Theminimum‐phase ilter,alsoknownastheLP‐FIR ilter,satis iesphaseresponse,groupdelayand linearfrequency.TheequationofLP‐FIR ilteris below:
Where ���� isdenotedastheco‐ef icientofthe ilter and �� isdenotedasthepatternofthe ilter.Inthe FIR ilter,groupdelayisreferredtoasthenegative slope.ThefrequencyresponseofLP‐FIRisexpressed inequation(2).
Therefore, ��[��] denotesresponseofamplitude; ��∗ denotesphaseoffset;and��∗ isdenotedasgroupdelay. IntheFIR ilter,therearetwoconditionsfor inding LP—evensymmetryandoddsymmetry.LP‐FIR ilter isexplainedinEquation(3).
=0������,��∗ = �� 2 ������ ��(��)=��(��−��);������������������������ ��∗ = �� 2 ���� 3�� 2 ,��∗ = �� 2 ������ ��(��)=−��(��−��);������������������������ (3)
VarioustypesofLP‐FIR iltersarepresentedbelow. Inthismanuscript,high‐,low‐andband‐pass il‐tersareconstructedusingoptimizederrorcoef i‐cientsbasedontheHenrygassolubilityoptimization approach.Here,��indicatesphaseresponseoftheLP‐FIR ilter,asdenotedinEquation(4):
����������(��)=[(����������(��1)),(����������(��2))…(����������(����))]�� (4)
TodesigntheLP‐FIR ilter, ��������������(��) isderivedby Equation(5) ��������������(��)= 1;0≤��≤�������� 0;����ℎ������������ (5) where �������� denotesthecut‐offfrequencyoftheLP‐FIR.Thelinear‐phasehigh‐passFIR ilter��������������(��) isexpressedinEquation(6): ��������������(��)= 0;0≤��≤�������� 1;����ℎ������������ (6)
TheLPband‐passFIR ilter��������������(��)iscalculatedin Equation(7): ��������������(��)= 1;�������� ≤��≤��ℎ����ℎ 0;����ℎ������������ (7)
G[m]= y
jp��[��−��] (1)
Table1. TypesofLP‐FIRfilter Filtertypes
Hence,�������� denotesthelow‐edgefrequencyand��ℎ����ℎ denotesthehighedgefrequencyinLP‐FIR ilters.The linear‐phaseband‐stopFIR ilter��������������(��)iscalcu‐latedinEquation(8):
TheerrorfunctionintheLP‐FIR ilterisexpressedin Equation(9):
Where ��(��) theweightedfunctioninthefrequency banderror.The iltercoef icientisoptimizedbyreduc‐ingtheerrorfunctionsintheLP‐FIR ilter.TheLP‐FIR ilteriscreatedbyutilizingHenrygassolubilityopti‐mizationalgorithm(HGSO).These iltercoef icients areusedforconstructinghigh,lowandband‐passFIR ilters.TheHGSOalgorithmmethod,whichisbased onHenry’slaw,isthenused.Duetothechallenges posedbycompetitionaswellasthroughtheneed tosolvestructuraloptimizationissuesinproduct‐developmentprocesses,newtechniqueshavebecome increasinglynecessary.
2.1.Step‐by‐stepProcedureofHenryGasSolubility OptimizationUtilizingFIRFilter
HGSOisarobustoptimizationalgorithmthateffec‐tivelybalancesexplorationandexploitation,which arecrucialpartsofanyoptimizationprocess.The adaptivemodi icationofthesolubilitycoef icient allowsforadynamicbalance,exploringthewhole searchspaceandexploitingpromisingareas.The incorporationofopposition‐basedlearningenhances diversityinthesearch,preventingthealgorithm fromgettingstuckinlocaloptima.HGSO’sability toavoidlocaloptimaisattributedtoitswell‐tuned exploration‐exploitationtrade‐offandtheutilization ofopposition‐basedlearning.
Notably,HGSOexhibitsversatilitybybeingappli‐cabletoabroadspectrumofoptimizationproblems, encompassingcontinuous,discrete,andconstrained scenarios.Additionally,itsrelativeeaseofimplemen‐tationmakesitaccessibletoawideuserbase,con‐tributingtoitseffectivenessasaversatileandpow‐erfuloptimizationtool.TheHenrygassolubilityopti‐mizationapproachisusedtodeterminethestepwise procedureforobtainingthebestFIR iltercoef icients. Itde inesthelow‐solubilitygasesin luidsusingthis optimizationalgorithm.Themathematicalequationof thisstageisgivenbelowinEquation(10):
Wherethepopulation��,���� symbolizesthelocationof the����ℎgas;��representsachaoticnumberbetween0 and1;��������,�������� denotestheproblembounds;and (��) denotestheiteration.ForeachgasparticleI,the partialpressureofgas �� ingroup ��, ������ iscalculated, aswellasthegassolubility �� ingroup ��, ������,using Equation(11):
(11)
where ���� denotesgroup ��’sHenry’sconstantand ������ signi iesthepartialpressureofgas �� ingroup ��.An equationforFIR iltercoef icientsisequatedbelow in(12):
Where��standsfortemperatureandisspeci iedasa ixedquantityoftheFIR ilterwithavalueof298,and ���� showstheHenrygaslawcoef icientforeachgroup ��.Additionally, �������� symbolizestheoverallnumber ofiterations.Finally,anequationfortheestimation of iltercoef icientsofHenrygassolubilityisshown in(13):
Where����,�� isthecurrentstateofeachgas��thingroup ��; �� denotesdistributedthecountbetween0and1; ��max(��,��) and��min(��,��) arethealgorithm’sbounds;and ��isusedasadistributionwithintherange[0,1].
TheHGSOalgorithmemergedasapowerfuland versatileoptimizationtechnique,offeringenhanced convergencespeed,solutionquality,robustness,scal‐ability,andef iciencycomparedtotraditionalopti‐mizationalgorithms.Itsabilitytosolveawiderangeof optimizationchallengesmakesitausefultoolforboth scholarsandpractitionersinvarious ields.Inthis way,thebestFIR iltercoef icientisobtainedusingthe Henrygassolubilityoptimizationalgorithm.
3.ResultWithDiscussion
Thisanalysislooksforthebestcoef icientsofLP‐FIR ilterusingtheHGSOalgorithm.Theproposed methodwasstimulatedusingMATLABonaPCwith anIntelCorei5CPUoperatingat2.5GHz,using8GB ofRAM,andrunningWindows7.Toachievethebest outcomewithintheconstraintsofthealgorithmand the ilterspeci icationsineachattempt,thealgorithm wasrun50times.
3.1.PerformanceMetrics
Severalperformancecriteria,includingdelayand clockfrequency,wereevaluated.
3.1.1.Delay
Thedelayofa ilteristheamountoftimeittakes fortheoutputofthe iltertorespondtoachangeinthe input.Itistypicallymeasuredinsamplesorseconds.
TheformulaforthedelayofanFIR ilterisgivenin Equation(14):
����������=������(ℎ[��]) (14)
Whereℎ[��]denotes ith iltercoef icient.
3.1.2.ClockFrequency
Clockfrequencyisthenumberoftimesaclocksig‐naloscillatespersecond,measuredinhertz(Hz).The highertheclockfrequency,thefasteracomputercan processinformation.Theformulaforclockfrequency isevaluatedin(15):
(15)
Where��istheclockfrequencyinHzand��istheclock periodinseconds.
3.2.PerformanceAnalysis
ThesimulationoutputsofDALP‐FIR‐HGSO approacharedepictedinFigures 2 and 3.The DALP‐FIR‐HGSOapproachwasthencomparedto currenttechniques,includingLP‐FIR‐WSOAand DPE‐FIR‐GOA.
Fig.2presentsthedelayanalysis.Comparedtothe existingLP‐FIR‐WSOAandDPE‐FIR‐GOAmethods,the proposedDALP‐FIR‐HGSOmethodachieves,respec‐tively,17.82%and17.82%improvementindelayfor 100nodes;18.44%and20.23%improvementindelay for200nodes;and19.02%and33.29%improvement indelayfor300nodes.
Fig.3presentstheclockfrequencyanalysis.Com‐paredtotheexistingLP‐FIR‐WSOAandDPE‐FIR‐GOAmethods,theproposedDALP‐FIR‐HGSOmethod achieves,respectively,animprovementof23.53%and 19.82%indelayat1.5GHzclockspeed;55.44%,and 56.23%indelayat2.5GHzclockspeed;and51.02% and65.29%indelayat3.5GHzclockspeed.
3.3.DesigningaLow‐passFIRFilterwiththeHGSO Approach
The iltercoef icientsarerepeatedlymodi iedin thecontextofFIR ilterdesigntominimizethedis‐paritybetweentheactualandplannedfrequency
responses.Thealgorithm’sharmonymemory,pitch‐adjustment,andharmony‐updatingmechanismsare utilizedtoexplorethesolutionspaceef iciently.The designingprocessbeginsbyde iningthedesired ilter speci ications,includingthecutofffrequency,transi‐tionwidth,andripplelevel.Theseparametersdeter‐minethe ilter’sbehaviorandcapacitytoattenuate high‐frequencysoundswhileallowinglow‐frequency signalsto lowthrough.
Anumberoffactorsareneededtodesignthe linear‐phaselow‐pass inite‐impulseresponse ilter, includingacut‐offfrequencyof0.51,a ilterorder of20,and21successive iltercoef icients.Theerror functionsarecomputedthroughEquation(11)and(2) calculatesthelow‐passlinear‐phaseFIR ilter’sideal solution.
Table2presentsthe20th‐orderlinear‐phaselow‐passFIR inite‐impulse‐response ilter’soptimized il‐tercoef icients.
InTable 2,theproposedmethod,comparedto existingmethodssuchasLP‐FIR‐WSOAandDPE‐FIR‐GOA,provides,respectively,42.72%and38.99% lowermaximumpassripple;34.99%and41.09% lowermean;23.99%and33.11%lowervariance;and 33.01%and36.56%lowerstandarddeviation.
3.4.LPHigh‐PassFIRDesignUtilizingtheHGSO Approach
TheHGSOalgorithmisusedtocreatealinear‐phasehigh‐pass inite‐impulseresponse ilter.The HGSOtechnique,inspiredbymusicalharmony,facil‐itatestheexplorationofthesolutionspacebyiter‐ativelyadjusting iltercoef icientstominimizethe discrepancybetweentheactualandtargetfrequency responses.Inthecontextofahigh‐passFIR ilter, thealgorithmisemployedtoattenuatelow‐frequency componentswhileenablingthehigher‐frequencysig‐nalsto low,aligningwiththespeci ieddesigncriteria. Designinghigh‐passFIR iltersusingtheHenrygas solubilityoptimization(HGSO)approachisaneffec‐tivemethodforachievingprecisefrequency iltering andmaintainingaconstantgroupdelay.TheHGSO algorithm’sabilitytoef icientlybalanceexploration andexploitation,avoidlocaloptima,andadapttodif‐ferent ilterspeci icationsmakesitavaluabletoolfor designinghigh‐passFIR ilters.
Figure2. Performanceofdelayanalysis
��=1/��
Figure3. Performanceofclockfrequencyanalysis
Table2. Optimizedfiltercoefficientof20th‐orderlinear‐phasehigh‐passFIRfilter
��(��) LP-FIR-WSOA DPE-FIR-GOA DALP-FIR-HGSO(Proposed)
��(1)=��(21) 0.0263875931 0.0124583400 0.028588311
��(5)=��(17) 0.0250148761 0.0011367841 0.0302000547
��(10)=��(12) 0.4055010541 0.3838627550 0.5143459152
Table3. 20th‐orderlinear‐phaseband‐passfinite‐impulse‐responsefilteranalysisatpassband
Table4. Optimizedfiltercoefficientof20th‐orderlinear‐phasehigh‐passfinite‐impulseresponsefilter
��(��)
��(1)=��(21) 0.0213875951 0.0112583401 0.040585314 ��(5)=��(17) 0.0196448761 0.0226567841 0.0312000947 ��(10)=��(12) 0.3555012542 0.3598627250 0.5243449152
Table5. 20th‐orderlinear‐phasehigh‐passfinite‐impulseresponsefilteranalyticsatpassband
Forlinear‐phasehigh‐pass inite‐impulse responsetobedesigned,anumberoffactorsare required,includingacut‐offfrequencyof 0.51��. ErrorfunctionsarecalculatedbyEquation(8)as wellasEquation(4).Table 3 showsthe20th‐order linear‐phasehigh‐pass inite‐impulse‐response ilters optimized iltercoef icients.Table 4 showsthat theoptimized iltercoef icientforthe20th‐order linear‐phasehigh‐pass inite‐impulse‐response ilter.
InTable 5,theproposedmethod,comparedto existingmethodssuchasLP‐FIR‐WSOAandDPE‐FIR‐GOAprovides,respectively,11.77%and11.99% lowermaximum‐passripple;29.99%and26.09% lowermean;21.99%and27.11%lowervariance;and 32.01%and33.56%lowerstandarddeviation.
3.5.Linear‐phaseBand‐passFinite‐impulseResponse FilterDesignUtilizingHGSOApproach
TheHGSOalgorithmisusedtocreateaband‐passLP‐FIR ilter.Itscapabilitytoef icientlyexplore thesolutionspaceandconvergeonthebestsolu‐tionsmakesitidealfordevelopinglinear‐phaseband‐passFIR ilters.Thetechniqueiscapableofiden‐tifyingthebest iltercoef icientsforaccomplishing thedesiredpassbandcharacteristicswhilepreserv‐ingaconstantgroupdelay.Anumberoffactorsare requiredtodesigntheLPband‐passFIR ilter,includ‐ingthehighcut‐offfrequencyorderof20.Theerror functionsarecomputedbyEquations(8)and(4), whichcalculatetheband‐passlinear‐phaseFIR il‐teroptimalresponse.Table 6 showstheoptimized
iltercoef icientsfor20th‐orderlinear‐phaseband‐passFIR ilters:
InTable7,theproposedmethod,comparedtothe existingLP‐FIR‐WSOAandDPE‐FIR‐GOAmethods, provides,respectively,48.77%and49.99%lower maximumpassripple;35.99%and29.09%lower mean;27.99%and26.11%lowervarianceand 49.01%and39.56%lowertypicaldeviation.
3.6.Linear‐phaseBand‐stopFinite‐impulse‐response FilterDesignUtilizingtheHGSOApproach
TheHGSOalgorithmisusedtocreatethelinear‐phaseband‐stopFIR ilter.Foralinear‐phaseband‐stopFIRtobedesigned,anumberoffactorsare required,suchasacut‐offfrequencyof 0.35��,and ahighcut‐offfrequency 0.65�� is20th‐order.The errorfunctionsarecomputedinEquations(8)and (4)calculatethelinear‐phaseband‐stopFIR ilter’s optimalresponse.Table8showstheoptimized ilter coef icientsforthe20th‐orderlinear‐phaseband‐pass inite‐impulse‐response ilter.
Table9showsananalysisofthe20th‐orderlinear‐phaseband‐stopFIR.Comparedwithexistingmeth‐odslikeLP‐FIR‐WSOAandDPE‐FIR‐GOA,thepro‐posedmethodprovides,respectively,42.13%and 50.90%lowermaximumpassripple;31.95%and 21.16%lowermean;18.62%and23.12%lowervari‐ance;and45.93%and33.57%lowerstandarddevia‐tion.Figure 4 showsthesimulationwaveformofthe proposedLP‐FIR‐HGSO ilter.
Table6. Optimizedfiltercoefficientsfor20th‐orderlinear‐phaseband‐passfinite‐impulse‐responsefilters
��(��)
��(1)=��(21) 0.0253875951 0.0122583401 0.039585314 ��(5)=��(17) 0.0256448761 0.0016567841 0.0312000947 ��(10)=��(12) 0.4855012542 0.3298627250 0.5143449152
Table7. 20th‐orderlinear‐phaseband‐passfinite‐impulse‐responsefilteranalysisatpassband
Table8. Optimizedfiltercoefficientof20th‐orderlinear‐phaseband‐passfinite‐impulse‐responsefilter
Table9. 20th‐orderlinear‐phaseband‐stopfinite‐impulse‐responsefilteranalysisinpassband
Figure4. Simulationwaveformoftheproposed LP‐FIR‐HGSOfilter
4.Conclusion
Thismanuscriptproposessuccessivedesignsof linear‐phaselow‐,high‐,andband‐pass ilter‐impulse‐response iltersusingtheHenrygassolubilityopti‐mizationtechnique.TheproposedDALP‐FIR‐HGSOA waswell‐appliedinMATLAB.The ilterscontainthe idealresponseforcalculatingtheperfectvalues.Filter coef icientsarechosenforminimumerrorfunction andhighidealmagnituderesponse.Therefore,com‐paredwiththeexistingDALP‐FIR‐WSOAandDPE‐FIR‐GOAmethods,theperformanceoftheproposedDALP‐FIR‐HGSOAmethodattains,respectively,37.010% and29.021%lowerdelay,aswellas17.007%and 20.195%maximumclockfrequency.TheHGSOAalgo‐rithmisprimarilydesignedforunconstrainedopti‐mizationproblems.Whileconstrainedoptimization canbeaddressedusingpenaltyfunctionsorother
techniques,incorporatingconstraintsdirectlyintothe algorithmmayimproveitsef iciency.
AUTHORS
ThangarajMeena∗ –Assistantprofessor,Depart‐mentofComputerScienceandEngineering,Vela‐gapudiRamakrishnaSiddharthaEngineeringCollege (Autonomous),Kanuru,Vijayawada,AndhraPradesh, India,e‐mail:meenait3110@gmail.com.
JampaniChandraSekhar –Professor,Department ofComputerscienceandengineering,NRIInstitute ofTechnology,Guntur,AndhraPradesh,India,e‐mail: pro jampanichandras@hotmail.com.
PerumalAnandan –AssistantProfessor,Schoolof ComputerScienceandEngineering,VelloreInsti‐tuteofTechnology,Chennai,India,e‐mail:assperu‐malanandan@hotmail.com.
GanesanVinothChakkaravarthy –AssociatePro‐fessor,DepartmentofComputerscienceandengi‐neering,VelammalCollegeofEngineeringandTech‐nology,Madurai,India,e‐mail:profvinothchakkar‐avarthyg@hotmail.com.
MuthaiyanElumalai –AssociateProfessor, DepartmentofMathematics,St.Joseph’sInstitute ofTechnology,IndianOMR,Chennai,India,e‐mail: asselumalaimuthaiyan@hotmail.com.
BellarmineAnniPrincy –Professor,Departmentof ComputerandCommunication,Panimalarengineer‐ingcollege,ChennaiTamilNadu,India,e‐mail:profan‐niprincyb@hotmail.com.
ThirumalaReddyVijayaLakshmi –AssociatePro‐fessor,DepartmentElectronicesandCommunication Engineering,MahatmaGandhiInstituteofTechnology, Gandipet,Hyderabad,India,e‐mail:proftrvijayalak‐shmi@hotmail.com.
∗Correspondingauthor
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SUPER‐RESOLUTIONNETWORK SEGMENTATIONOFE‐COMMERCEUSERSONCARTABANDONMENTANDPRODUCT SUPER‐RESOLUTIONNETWORK
Submitted:15th March2024;accepted:20th May2025
PraveenKumarP,SugunaR
DOI:10.14313/jamris‐2025‐024
Abstract:
Anovelapproachnamed“SegmentationofE‐commerce usersonCartAbandonmentwithProductRecommenda‐tionusingDoubleTransformerResidualSuper‐resolution Network(SEC‐CAPR‐DTRSRN)”isproposed.Thisstudy commenceswiththecollectionofe‐commercedatafrom adiversemulti‐categorystore.Thepre‐processingphase usesFairness‐awareCollaborativeFiltering(FACF)tosug‐gestpersonalizeditemsorcontenttousersbasedontheir preferencesthroughbehavior.Followingpre‐processing, thedataundergoessegmentationusingtheGeneral‐izedIntuitionisticFuzzyc‐meansClustering(GIFCMC) techniquetocategorizeuserstotarget‐basedcustomer groups.Toenhancecarttransactions,DoubleTrans‐formerResidualSuper‐resolutionNetwork(DTRSN)is introducedforproductrecommendations.Theexplo‐rationofcartabandonmentidentifiespotentialdiscord stemmingfromamisalignmentbetweenconsumerper‐ceptionsanddigitalsiteexperiences,potentiallyleading tocartabandonmentduetouserannoyance.Whilethe DTRSNlacksanexplicitadoptionofoptimizationsys‐temsforcalculatingoptimalparameters,themanuscript proposestheintegrationofPolarCoordinateBaldEagle SearchAlgorithm(PCBESA).PCBESAisintroducedtoopti‐mizePCBESADTRSN,ensuringpreciseproductrecom‐mendations.Theproposed(SEC‐CAPR‐DTRSRN)method isimplemented,andtheirperformancesisrigorously evaluatedusingkeymetrics,includingmeansquare error,standarddeviation,andmeanreciprocalrank (MRR).Theproposedmethodgives12.78%,29.85%,and 17.45%lowermeansquareerrorand23.67%,28.86% and16.45%higherMRRwithexistingtechniqueslikeseg‐mentationofe‐commerceusersdependingoncartaban‐donmentwithproductrecommendationusingcollabo‐rativefiltering,suchasmoderatingtheeffectofexorbi‐tantpricing(SECU‐CAPR‐CF),newtop‐nrecommendation techniqueformulti‐criteriacollaborativefiltering(PR‐MCCF‐EC)andreinforcementlearninge‐commercecart targetingtoreducecartabandonmentine‐commerce (RL‐EC‐RCA)methods,respectively.
Keywords: E‐commerce,cartabandonment,product recommendation,doubletransformerresidualsuper‐resolutionnetwork,polarcoordinatebaldeaglesearch algorithm
1.Introduction
Overthepastdecade,theroleofe‐commercemar‐ketsareexceedinglycrucialintherapidlygrowing onlineeconomy[1,2].Theavailabilityof24/7shop‐pingplatformswithoutlimitationshasempowered consumerstopurchaseawidearrayofgoodsany‐timefromonlinemarketplaces.Accordingtoreports fromtheIndiaBrandEquityFoundation(IBEF),India standsoutasacountryexperiencinghighergrowth ine‐commercesales[3–5].Theprojectionsindicate thatrevenuesfromthissectorwereexpectedtosurge fromUSD39billiontoUSD120billionthrough 2021,markingtheworld’swildestgrowthrateatan annualincreaseof51%inincome.Variousaspectsof onlinemarkets,suchascustomerpreferences,usage behaviors,productevaluations,ratings,andshop‐pingcartabandonment,havebeenthoroughlyexam‐inedduetotheextensivedemandinthedigitalmar‐ket.Furthermore,withtheevolutionoftheInternet pavingthewayfornewapproachesinonlinecom‐merce,customerlifestyleshaveundergoneadigital transformation[6].Now,whencustomersvisitphys‐icalstores,it’sbecomeahabitforthemtocom‐parepricesbetweenphysicalandvirtualofferings. Thishabitincreasinglyleadscustomerstowarddigital shopping.Acomprehensivesurveyinvolvingapprox‐imately23,000consumersglobalrevealed54%of themcreateweekly/monthlypurchasesonline,with 60%emphasizingpriceasthemostcrucialfactor in luencingtheirproductchoices[7].
It’srecognizedthattheexperienceofbuyinga productonlinedifferssigni icantlyfromtraditional brick‐mortarshopping.Despitetheeaseofaccess‐inginformation,customersarereluctanttopaymore. Pricingisn’tsolelyameanstoboostsalesbutisalso apivotalfactorimpactingabusiness’smostcrucial KeyPerformanceIndicators(KPIs)[8,9].Conversely, whenapotentialcustomerinitiatesanonlinecheck‐outbutabandonsprocessaforecompletingtrans‐action,itresultsinonlineorderingdrop‐off[10]. Itemsaddedtoashoppingcartmay/maynoteven‐tuallybeboughtandcategorizedasitemsconsumer ’abandoned.’Onlineproductratingsplayacrucial roleinshapingpurchasingdecisions,withlower‐ratedproductsexperiencingdecreasedlikelihoodof beingbought[11].Elementslikeperceivedvalue, pricing,experientialattributes,symbolicvalue,and
purchasefrequencyindirectlyin luencecartabandon‐mentrates[12, 13].Theseelementsencompassan understandingofreductionmagnitude,distribution expensesandsalespromotion.Apparentcostsare determinedbasedononlinefeedbackandspeci ic metrics[14].Thisactofcartabandonmentresembles addingproductstocartduringanonlineshopping sessionwithoutcompletingthepurchase[15].
Inthispaper,byintegratingnovelDTRSNwith segmentationusingGIFCMC,theproposedmethod aimstoenhancetheaccuracyandeffectivenessofseg‐mentinge‐commerceusers.Theproposedapproach focusesonthenoveldeeplearningmethodtoenhance recommendationsystemsinE‐commerceplatforms, leadingtomoreeffectiveandpersonalizedproduct recommendationsforusers.
Themajorcontributionofthisworkis
‐ Inthismanuscript,thesegmentationofe‐commerce usersonCartAbandonmentandProductRecom‐mendation(CAPR)usingDTRSNisproposed.
‐ Here,Fairness‐awareCollaborativeFiltering(FACF) isproposedtosuggestpersonalizeditemsorcontent tousersbasedontheirpreferencesandbehavior.
‐ GIFCMCisintroducedtosegmentpreprocesseddata totarget‐basedcustomergroups.Thissegmentation facilitatespersonalizedrecommendationsbasedon theidenti iedcustomergroups.
‐ Forproductrecommendations,novelDTRSN enhancescarttransactionsandoveralluser satisfactionduringe‐commercetransactions.
‐ Toimproveproductrecommendations,PCBESAis proposedtoenhanceDTRSNweightparameters.
Theorganizationofthisstudyreviewstherelated workinPart2,proposedmethodologyinPart3,Part 4provesoutcomesanddiscussion,andPart5conveys theconclusions.
2.RelatedWork
Here,wereviewedsomepapersbasedonE‐CommerceUsers(ECUs)onCAPRusingdeeplearning asfollows:
Rifatetal.[16]haveintroducedaMLsystem designedtohelpmerchantsreducethecheckoutaban‐donmentratethroughinformeddecision‐makingand strategicplanning.Asakeycomponentofthissys‐tem,theyhaveconstructedarobustMLmodelcapa‐bleofpredictingwhetheracustomerwillproceedto checkoutafteraddingproductstotheircart,basedon theiractivity.Additionally,systemoffersmerchants theabilitytodelveintotheunderlyingfactorsdriving eachpredictionoutput,providingvaluableinsightsfor optimization.Ithasalowmeansquareerrorbuthasa highstandarddeviation.
KayaandKaleli,[17]haveexplainedtop‐nrec‐ommendationsinmulti‐criteriacollaborative iltering (MCCF).Thisrevolvesaroundtwokeyaspects,how likesestablishingrelationalstructureamongproducts andthroughexamininguserinclinationsalongside theiruniquepatternswithratingdeliveries.Todis‐cernratingdelivery,productrelationships,relation
rulemining,andentropymeasureswereemployed, andusers’attitudes,tendenciesthroughevaluations werescrutinizedusingintuitionisticfuzzysets.This hasahighmeanreciprocalrankbut(MRR)hasless accuracy.
Kumaretal.[18]havedevelopedthemultivari‐atepruningtechniqueofwebindexsearchingon e‐commercewebsitesusingtheKnuthMorrisPratt (KMP)algorithm,andtheyuseavarietyofwebana‐lyticsmethodsinconjunctionwithmachinelearn‐ing(ML)classi ierstoextractpatternsfromtransac‐tionaldata.Additionally,usinglog‐basedtransactional data,anevaluationtechniquebasedonMLwasused todeterminehowusablee‐commercewebsitesare. Thepresentedmethodseekstodeterminetheunder‐lyingrelationshipbetweenthepredictorelements andtheoverallusabilityofthee‐commercesystem byutilizingthreeMLapproachesandmultiplelin‐earregressions.Thepresentedmethodwasexpected tocontributetotheeconomicpro itabilityofthee‐commerceindustry.
Khanetal.[19]havepresentedFuzzy sets/QualitativeComparativeAnalysistoexplore therelationshipbetweenthesefactorsandshopping cartabandonment.Resultssuggestadavoidance mightserveasalearningdeviceforconsumerswhen theyencounterineffectivemessagesorcontent, potentiallyimpactingtheirperceptionofshopping cartabandonmentforaspeci icbrand.Ithaslowroot meansquareerrorandlowaccuracy.
Wangetal.[20]havepresentedastimulus‐organism‐responsemethodtoinvestigateelements impactingcustomers’inclinationtowardsonline‐storechanneladoption(OSCA)andtheirchoiceto purchasefromaphysicalseller.Dualstudieswere conductedtovalidatetheoriesposited,focusingon GenerationYconsumersinMainlandChina.Datawere gatheredconcerningtwoproductcategoriesacross distincttimeframes.Thishasalowsquarerooterror butalsohasalowMRR.
ChawlaandKumar,[21]havepresentedtheexist‐inglegalstructureinIndiaaimedatsafeguardingthe interestsofonlineconsumers.Thefreshlyintroduced regulationsappearrobustandcapableoffortifyingthe rightsofonlineconsumers,therebypotentiallyfos‐teringthegrowthofIndia’se‐commercesector.With asturdylegalframeworkandprotectivemeasures forconsumersinplace,thetrajectoryofe‐commerce appearspromising.Theoutcomesofaddvaluable insightstotherealmofe‐commerce,andcustomer rightsprotectionthroughsheddinglightonpivotal factorsin luencingcustomertrustandloyalty.This hasalowmeanandhashighrootsquareerror.
3.ProposedMethodology
Theproposedmanuscriptintroducesamethodol‐ogynamedSEC‐CAPR‐DTRSRN.Proposedmethodol‐ogydiagramisdisplayedinFigure1.Thedetailedpro‐cedureoftheproposedmethodologyisshownbelow;
E-CommerceUser Data
Product Recommendationby DoubleTransformer ResidualSuperresolutionNetwork (DTRSN) Button OptimizationbyPolar CoordinateBaldEagle SearchAlgorithm(PCBESA)
DataPreprocessingby Fairness-aware CollaborativeFiltering (FACF) Segmentationby GeneralizedIntuitionistic Fuzzyc-meansClustering (GIFCMC)
Figure1. ProposedMethodologydiagram SEC‐CAPR‐DTRSRN
3.1.DataCollection
Initially,thee‐commercedatagatheredfroma multi‐categorystore[22].Then,thedataareprovided tothepre‐processingphase.
3.2.DataPre‐processingbyFairness‐awareCollabora‐tiveFiltering(FACF)
Thepre‐processingstageinvolvestheapplication ofFACF[23]toprovidepersonalizeditemsorcontent tousersbasedontheirpreferencesandbehavior.Fair userembedding’sreachedbyattachingclassi ier��1 to infersensitivefromuserembedding’s.Likewise,item classi ier��2 toforecastssensitiveinformationhidden initems’embedding.Assumingeachitemssensitive labels��,presentFACF.Filtermoduleisputintouser‐items’embeddingutilizingclassicalCFmethod��.The ilteredembeddingspace,forecaststhatratinĝ�� ���� of theuser��foritem��isintendedin ilteredembedding spacenEquation(1)
(1)
where ���� denotesitem ��′�� iltereditemandpre‐dictedrating ̂�� ���� ofuser �� foritem �� intendedin ilteredembeddingspace.Dualadversarialmodules areimplementedtoremovethesensitiveinformation fromuser,items’embedding.Choose ilteredembed‐dinginput,userclassi iereffortstoforecastusers’sen‐sitivelabels,itemclassi iereffortstoforecastpseudo sensitivelabelsofitems.Describeoveralllossfunction inEquation(2)
��(����,����)−������1(����,��)−������2(����,��), (2)
wherethe irstphraseisaccuracyloss,andnextphrase isusers’sensitivecategorizationoutcomes,andthe thirdtermisoutcomesfrompseudoitemlabels.Here, the ��, �� denotesbalancingparameterscontrolout‐comes.While �� equalszero,outcomesisdisappear.
Here,theoptimizationoftheoverallfunctionusing minimalvalueisgiveninEquation(3) min ��,�� max ��1,��2 ��
(����,��
)−������1(��
,��)−������2(����,��), (3) where ����1(����,��) isoptimizesclassi iersand ����(����,����) denotesemployedtodevelop recommendationaccuratenessisgiveninEquation(4) ����(����,����)= 1
Pseudoitemlabelsareallocated,deliberatedesign oflossfunction ����2(����,��).TheFACFidenti ies andgroupsusersbasedontheirpreferencesand behaviours.Thisstephelpsincreatinguserseg‐mentsthatcanbeutilizedinsubsequentstagesofthe methodology.
3.3.SegmentationbyGeneralizedIntuitionisticFuzzy c‐meansClustering(GIFCMC)
TheGIFCMCextendstraditionalFuzzyc‐means [24]clusteringbyintroducingconceptionofanintu‐itionisticfuzzyset.Intuitionisticfuzzysetsaccom‐modatenotonlydegreeofmembershipbutalso thedegreeofnon‐membership,ahesitationdegree foreachdatapoint,offeringamorecomprehen‐siverepresentationofuncertaintyinthedata.The pre‐processeddataundergosegmentationutilizing GIFCMCtocreatetarget‐basedcustomergroups.First, thenumericalvalueistransformedintodiscreteval‐ues,thenthevaluesarecalculatedinEquation(5).
(5)
where(��������)�� denotesthedataset���� minimalvalue ofthedatasetinthe����ℎvolume,and(��������)�� denotes itshighestvalue.��isauserdataand��denotestheitem data; ����ℎ isthevolumeofthedataset ����.Thisstarts theintuitionisticfuzzi icationprocess.Thedistance betweeneachdata‐itemiscalculatedoncethedataset hasbeennormalizedto[0,1].Thedistancematrix forthedatasetthathasbeennormalizedisshownin Equation(6)
here,thedistanceofeachdata �� iscalculated.The normalizeddataset’sdistancematrixiscalled������.The clustermatrix’sreciprocationisprovidedinEqua‐tion(7).
1
(7) where,theclustervaluematrixforeachdataset���� is providedbythematrix ��,andreciprocationof ������ matrixisdenotedbyrecorddataset.Considerthe recordasacandidateruleifthefrequencyofthe recordexceedstheAU.Theclusteringcriterioncomes nextinEquation(8).
where, ���� =(����,����,����) istheclustermethodrepre‐sentationofthe����ℎ data‐point,whichhas��Dfeatures, witheachfeaturehavingclusterre‐presentation. Thesecandidatecriteriaareusedtocreatepositive andnegativeclusters;anyrecordthatdoesnot itthe candidateguidelineswillberegardedasanoutlier recordanditisshowninEquation(9)
where ������ membershipmatrixoforder ��,and ∑�� ��=1 isthesetofcancroidsofthese�� clusters.Lagrange’s stateofunknownmultipliersG‐IFCMisutilizedin ordertogrouptheheartdiseasepatientsrecordusing theformulagivenbelowEquation(10)
parametersduringtraining.Themathematicalrepre‐sentationisasfollows;
Themodulecanextractconcealedweightinfor‐mationinthespatialarea.Recombinespatialfeatures createfeaturevectorsthroughspatialsimilarityin accordancewiththecorrelationofthefeatures.Thus, itisgivenbytheEquation(11)
where,�� and�� indicatesembeddedpurposesoffea‐turethenglobalassociation.������ and������ representsthe relationshipbetween����,thusthepixelisgivenbythe Equation(12)
(12)
where���� ���� isthenumberofgroupsinCluster������ that havetheleadingclasslabel,���� denotestotalnumber ofclusters,��andsigni iesthenumberofexamplesin cluster.
The inaloutputisasetofclusters,eachcontaining datapointsassignedtoitbasedontheirmember‐shipdegrees.InthecontextoftheSEC‐CAPR‐DTRSRN methodology,GIFCMCisappliedtosegmentthepre‐processede‐commercedataintocustomergroups, helpingtoidentifypatternsandpreferencesthatcan beusedfortargetedproductrecommendationsusing thesubsequentDTRSN.
3.4.ProductRecommendationbyDoubleTransformer ResidualSuper‐resolutionNetwork(DTRSN)
TheDTRSN[25]isemployedtoenhancecart transactionsbyrecommendingproducts.Cartaban‐donmentmaystemfromdiscrepanciesbetweencon‐sumerperceptionsanddigitalsiteexperiences,lead‐ingtofrustrationandcartabandonment.TheDTRSN takesasinputthesegmentedandpre‐processed e‐commercedata,whichincludesinformationabout userbehaviors,preferences,andhistoricalinterac‐tionswiththeplatform.Theinputdataispassed throughanembeddinglayertoconvertcategorical variablesanduser_iteminteractionsintoacontinu‐ousvectorrepresentationsuitablefordeeplearning. ThecoreoftheDTRSNliesinitsDoubleTransformer architecture.TheTransformermodelisapowerful NeuralNetwork(NN)architectureoriginallyintended forNaturalLanguageProcessing(NLP)butadaptable tovarioussequence‐basedtasks.Remainingconnec‐tionsareengagedtosolvevanishinggradientissue,aid trainingofdeepnetworks.Suchconnectionspermit methodtolearnremainingmappings,makingiteas‐iertooptimizeandimprovethe lowofinformation throughthenetwork.TheDTRSNistrainedusinga suitablelossfunctionthatcalculatesthedissimilarity amongthepredictedrecommendationsandtheactual userbehavior(e.g.,purchasehistory).Theoptimiza‐tionalgorithmisemployedtooptimizethemodel’s
������(��,��) Indicatesthepixelvalueofsuper‐perseverance, �� isthefeaturemappingfunction, ��(��,��)denotesweightcalculationsegmentofpixel, ������ isthefeaturevectoroncorrespondingpixels. Projectionconversionfunction �� isexpressedusing Equation(13)
where,��denotesProjectionconversionfunction,and ��,�� denotesweightestimation.Eachbodyregion’s inalfeaturesareobtained,andthenwefeedthem intothelayer,whichconsistsoftwoentirelyassoci‐atedconnectionlayerswhicharegivenbytheEqua‐tion(14)
(14)
where,��and��denotethetotalnumberofrecognized samplesandsamplessets,���� representstheduallabel ofthesample, �� andindicatestheprobabilitypredic‐tion.
TheutilizationofDTRSNinthiscontextaimsto provideasophisticatedandpersonalizedapproach toproductrecommendations,withtheultimategoal ofreducingcartabandonmentandenhancingoverall usersatisfactionduringe‐commercetransactions.
3.5.OptimizationofDTRSNbyPolarCoordinateBald EagleSearchAlgorithm(PCBESA)
ThePCBESA[26]isanoptimizationmethodfor ine‐tuningtheparametersoftheDTRSNtoenhance itseffectivenessinmakingpreciseproductrecom‐mendations.PCBESAmethodisusedtoenhance weightsparameters [�� and ��] ofproposedDTRSN. BelowisageneraldescriptionofthePCBESAandits steps:
Step1: Initialization
TheinitialpopulationofPCBESAis,initiallygenerated byrandomness.Then,theinitializationisderivedas Equation(15)
where,��isthepoplar’sdiameterofthe��thinitializa‐tionposition.
Step2: Randomgeneration
Theinputweightparameter[��and��]isproducedat randomusingPCBESAmethod.
Step3: Fitnessfunction
Itcreatesarandomsolutionfrominitializedassest‐ments.Itisassesssedutilizingtheoptimizingparam‐eter.ThisiscalculatedusingEquation(16):
FitnessFunction = optimizing[����������] (16)
Step4: ExplorationPhase:
Intheinitializationphase,thePBESalgorithmmust alsoregulatetheborder,andeachindividualcanbe dispersedthroughouttheentiresearchspace.Thus, thepolarangle �� hasavaluerangeof (0,2��).In addition,boundariesmustbede inedforthepolar diameterinordertopreventthePBESalgorithm fromexceedingthemduringtheoptimizationprocess. ThentheexplorationisgivenasEquations(17),(18), and(19):
(17)
where,���������� denotestheareathatwasfoundtobethe greatestchoiceforthebaldeaglestochooseduring thepriorsearch; ���� indicateswherethebaldeagles arelocated;����,������ iswherethebaldeagleshaverelo‐cated;���������� denotespositionofbaldeagles’average distributionfollowingpreviousexploration;��1 and��1 symbolizearithmeticnormalizationof �� and ����+1 is the��thbaldeagles’mostrecentrevisedposition. ��1 = ��1 max(|��1|) (18)
where, ��1 symbolizethearithmeticnormalizationof ��;��1 denotedaseverybaldeagleslocationisupdated.
��2 =��������∗cos(��) (19)
where,��byrenewing,thespeci icpositionisupdate; ��2 denotedaseverybaldeagleslocationisupdated and��������isarandomintegerbetween0and1.
Step5: Exploitationphaseforoptimizing [�� and ��]:
Retentionandreplacementarethetwoscenariosthat exist.Proceedwiththe irstoperationifnovel itness valueisdeterminedtobebetterthanpresent it‐nessvalue;ifnot,proceedwiththesecondoperation. InsteadofusingtheCartesiancoordinatesystem,the PBESupdatesindividualpositionsinthepolarcoordi‐natesystem.Thelocationofpersonisderivedthrough updates.Individuals’updatespeedswillincreasesig‐ni icantlyasaresult,andconvergenceef iciencywill risebyEquations(20),(21),and(22):
areathatwasfoundtobethegreatestchoiceforthe baldeaglestochooseduringthepriorsearch;���� indi‐cateswherethebaldeaglesarelocated; �������� isa randomintegerbetween0and1;��2 and��2 needsto becomparedtooneanother’sbaldeagleand��1 and��2 aretheenhancementcoef icient,whichistakenbyall ofthemtobe2. ��2 = ��2 max(|��2|) (21)
where,��2 needstobecomparedtooneanother’sbald eagleand��2 isdenotedaseverybaldeagles,location isupdated.
(22)
where, ��1 isarandomintegerbetweenAU0; ��2 is denotedaseverybaldeagles’locationisupdatedand ��������isdenotedbyrenewing,thespeci icpositionis updated.Thenthespeci icpositionisupdatedisgiven asEquation(23):
here,��denotescoef icientofdisturbance,withvalues among0,2;��������isarandomintegerbetween0;����+1 thenewroleforeachindividualisestablishedand���� needstobecomparedtooneanother.
ThePCBESAaimstoef icientlyexplorethesolu‐tionspaceand indoptimalparametersfortheDTRSN, enhancingitsperformanceinthespeci ictaskofprod‐uctrecommendationine‐commerce.Thealgorithm drawsinspirationfromthebaldeagles’huntingbehav‐iorandtheirabilitytonavigateandsearcheffectively intheirenvironment.
4.PerformanceEvaluation
Theexperimentaloutcomeofthesuggestedtech‐niqueisdiscussedinthesection.Thesimulations werecarriedoutonWindows7,anIntelCorei5, and8GBofRAM.Thesuggestedmethodwastested usingperformancemetricsinMATLAB.Theproposed SEC‐CAPR‐DTRSRNmethodisimplemented,andtheir performanceisevaluatedutilizingmetricslikesMSE, standarddeviation,andMRR.Theobtainedoutcome ofsuggestedSEC‐CAPR‐DTRSRNanalyzedwithexist‐ingML‐MCA‐EC[16],PR‐MCCF‐EC[17],andML‐ARM‐EC[18]methods,respectively.
4.1.MSE
Itmeasuresaveragesquareddifferenceamong forecastedandactualvalues.Incontextofthepro‐posedmethod,MSEcanbeutilizedtoassessaccurate‐nessofproductrecommendations.Thisiscalculated inEquation(24),
(20)
where,����,������ iswherethebaldeagleshaverelocated; ���������� denotespositionofbaldeagles’averagedistri‐butionfollowingpreviousexploration; ���������� denotes
here,��signi iestotalnumberofdatapoints,���� implies actualvalue,and �� signi iesforecastvalue.
Figure2. MSEanalysis
4.2.StandardDeviation
Itisascaleofamountofvariationinasetofval‐ues.Incontextofperformanceevaluation,itprovides insightsintotheconsistencyoftherecommendations. ItiscalculatedbyEquation(25),
here,��denotestotalnumberofdatapoints,���� implies allindividualdatapoints,and signi iesmeanofdata.
4.3.MeanReciprocalRank(MRR)
MRRisametriccommonlyusedtoevaluatethe effectivenessofrecommendationsystemsinranking items.Itmeasureshowwellthesystemranksthe relevantitemshigherinthelist.ItisgiveninEqua‐tion(26),
here, |��| denotesnumberofqueries, ���������� implies rankof irstrelevantitemfor����ℎ query.
Figure 2 showsMSEanalysis.TheSEC‐CAPR‐DTRSRNgivesalowmeansquareof20.78%,19.67% and27.80%withexistingML‐MCA‐EC,PR‐MCCF‐EC, andML‐ARM‐ECmethods,respectively.Lowervalues arebetter,astheysignifyhigheraccuracyandconsis‐tencyintherecommendations.
Figure 3 showsstandarddeviationanalysis.The SEC‐CAPR‐DTRSRNgiveslowstandarddeviationsof 30.78%,25.67%and17.80%withexistingML‐MCA‐EC,PR‐MCCF‐EC,andML‐ARM‐ECmethods,respec‐tively.
Figure 4 displaysMRRanalysis.TheSEC‐CAPR‐DTRSRNgiveshighMRRof20.48%,23.57%and 19.80%withexistingML‐MCA‐EC,PR‐MCCF‐EC,and ML‐ARM‐ECmethods,respectively.
5.Discussion
TheSECU‐CAPR‐DTRSRNintroducesauniqueand advancedapproachtoenhanceuserexperienceand transactionsuccess.Segmentationisacriticalstage
inunderstanding,andcateringtodiversenecessi‐ties,andbehaviorofECU.Byfocusingoncartaban‐donmentpatterns,thesegmentationprocessaimsto detectdistinctusergroupswithcommoncharacter‐istics.TheintegrationofDTRSRNintheproposed systemsigni iesasophisticatedandstate‐of‐the‐art approach.Themodel’sabilitytocaptureintricatepat‐ternsandfeaturesinuserbehaviorenhancesthepre‐cisionofproductrecommendations.Byfocusingon cartabandonment,themethodologyacknowledges theimportanceofidentifyingandaddressingtheroot causesbehindthisbehavior.Understandingtherea‐sonsforabandonmentiscrucialforimplementing operativeapproachestoreduceit.Theultimategoal oftheproposedmethodologyistopositivelyimpact conversionratesbyreducingcartabandonment.A morepersonalizedanddynamicapproach,facilitated byDTRSRNandreinforcementlearning,holdsthe potentialtocreateamoreseamlessandsatisfying shoppingexperience.
6.Conclusion
TheSECU‐CAPR‐DTRSRNisproposed.Through GIFCMC,theuserbaseiseffectivelysegmentedinto target‐speci icgroups.Thisuser‐centricapproach enablesmorepersonalizedandtargetedinterven‐tions.TheutilizationoftheDTRSRNforproduct recommendationsdemonstratesacommitmentto employingadvanceddeeplearningtechniques.This
Figure3. Standarddeviationanalysis
Figure4. MRRanalysis
enhancesthesystem’sabilitytounderstanduserpref‐erencesanddelivermoreaccurateandrelevantprod‐uctsuggestions.Implementationandevaluationof theproposedmethodutilizingmetricslikesmean, MSE,standarddeviation,andMRRprovideaquan‐titativeassessmentofitseffectiveness.Suchmetrics enablecompleteunderstandingofsystem’saccurate‐ness,consistency,andrankingquality.
AUTHORS
PraveenKumarP∗ –DepartmentofComputer ScienceandEngineering,VelTechRangarajan, Dr.SagunthalaR&DInstituteofScienceandTechnol‐ogy,India,e‐mail:praveen.padigela@gmail.com. SugunaR –ComputerScienceEngineering,VelTech RangarajanDr.SagunthalaR&DInstituteofScience andTechnology,Chennai,Tamilnadu,India,e‐mail: drsuguna15@gmail.com.
∗Correspondingauthor
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ROBOTVISIONSYSTEM
Submitted:13th June2024;accepted:13th September2024
ThanhNguyenCanh,DuTrinhNgoc,XiemHoangVan
DOI:10.14313/jamris‐2025‐025
Abstract:
3DObjectLocalizationhasemergedasoneofthepiv‐otalchallengesinMachineVisiontasks.Inthispaper, weproposedanovel3Dobjectlocalizationmethod, leveragingablendofdeeplearningtechniquesprimarily rootedinobjectdetection,post‐imageprocessing,and poseestimationalgorithms.Ourapproachinvolves3D calibrationmethodstailoredforcost‐effectiveindustrial roboticssystems,requiringonlyasingle2Dimageinput. Initially,objectdetectionisperformedusingtheYouOnly LookOnce(YOLO)model,followedbyanR‐CNNmodel forsegmentingtheobjectintotwodistinctparts,i.e., thetopfaceandtheremainingparts.Subsequently,the centerofthetopfaceservesastheinitialpositioning reference,refinedthroughanovelcalibrationalgorithm. Ourexperimentalresultsindicateasignificantenhance‐mentinlocalizationaccuracy,showcasingthemethod’s efficacyinreducinglocalizationerrorsbroadlyacross varioustestingscenarios.Wehavealsomadethecode anddatasetsopenlyaccessibletothepublicat(https: //github.com/NguyenCanhThanh/MonoCalibNet)
Keywords: CameraCalibration,ObjectLocalization, Machine(Robot)VisionSystem,IndustrialRobotics
1.Introduction
Therapidadvancementofimagingsensorsover recentdecadeshaspavedthewayforaplethora ofintelligentperceptionalgorithms[1, 2].Leverag‐ingthesecapabilities,visiontechnologyhasmade signi icantstridesinvarious ields,includingspace robotics[3],robotmanufacturing,rapidobjectdetec‐tion,andtracking.IndustrialRobotVision(IRV), whichintegratescomputervisionintoindustrialman‐ufacturingprocesses,presentsanuancedapproach comparedtotraditionalcomputervisionmethodolo‐gies.Typically,robotvisionsystemsprioritizetasks suchasharvesting[4],human‐robotinteraction[5], androbotnavigation[6].Thesesystems indappli‐cationacrossaspectrumofareas,includingcomplex systempartidenti ication,defectinspection,Opti‐calCharacterRecognition(OCR)reading,2Dcode reading,piececounting,anddimensionalmeasure‐ment[7].Figure1illustratesatypicalindustrialrobot visionsystemcon iguration,comprisingfundamen‐talcomponentssuchascamerasandcontrolsystems (e.g.,Robots,PLCs).Additionalfeatureslikeillumina‐tion,userinteraction,datastorage,andremotecontrol
aregraduallyintegratedtoimprovesystemef iciency. Objectimagescapturedaretypicallysubjectedtopre‐processing,segmentation,andfeatureextractionona server.Controlledlightingconditionsand ixedcam‐erapositionsensuretheprominenceofcriticalfea‐tures,whilethecontrolsystemreceivestaskexecution instructionsfromtheserver.
Cameracalibrationisindispensableinrobot visionsystemstoensurepreciseobjectlocationand accuratemeasurements[8].However,theprocess ishighlysusceptibletoenvironmentalchanges, encompassingvariationsinlighting,temperature, andhumidity,potentiallyintroducinginaccuraciesby impactingintrinsicandextrinsicparameters.Despite effortstopreciselyestimatecameraparameters, real‐worldcomplexitiessuchaslensdistortionsand non‐linearitiesmaynotbefullyaccountedfor,leading tocalibrationinaccuracies.Notably,challengesarise whentheobjectisnotdirectlyunderthecamera, resultinginanincorrectpredictionoftheobject’s centerrelativetothereferencepoint.Tomitigate thesechallenges,twoprimaryapproachesare considered:i)optimizationofintrinsicparameters andii)recognitionof3Dobjectstoestimatethe centerpoint.Numerousalgorithmshavebeen developedtoobtainintrinsicparametersforimaging sensors[9–11].Intrinsiccalibrationtypicallyinvolves acamerathatobservesanchorpointsinacalibration pattern,withcommonlyusedpatternsincluding checkerboards[12],coplanarcircles[13, 14],and AprilTags[15].Traditionalcalibrationmethods,such asthosesupportedbyOpenCV[16]andMATLAB[17], havebecomecommonplace,leveragingtheadvantage ofcalibrationtoolboxes.However,deployingthese approachesinfactorysettingsproveschallenging,as theyaresusceptibletonoiseandartifactsthatcan degradecalibrationperformance.
Forindustrialvisionsystems,severaltechniques for2Dcameracalibrationhavebeenintroduced toachievepreciseobjectlocalization.Brown’s PlumbLinemethod[18],anearlynotableapproach, addressesthelensasymmetryissuesencountered duringmanufacturing.Thismethodrequiresthe determinationof10parametersandachieveshigh accuracy,withdeviationsaslowas ±0.5���� ata distanceof2��
Figure1. Overviewoftheindustrialrobotvisionsystem
InnovationsbyClarke,FryerandChen[19]have adaptedthismethodtousewithCCDsensors,enhanc‐ingef iciency.LuandChuang[20]utilizeda latmoni‐toronwhichtheydrewlinesandthenestimatedthe projectionbetweentheimageplaneandthemon‐itorplanethroughmultipleshotstocalibratethe camera.TheTwo‐Stagemethod[21–23]focuseson real‐timecalibrationusingblacksquaresonawhite background,achievinguncertaintiesaround±1����at 2��.DirectLinearTransformation(DLT)‐basedmeth‐ods[24–27]simplifycalibrationmodelsandhave beenwidelyadopted.However,theseapproachestend tofailinthecaseoflocalizing3D‐shapedobjects.Due totheir3Dnaturalshape,thelocationsdetermined bythesecalibrationmethodsarethelocationsoftheir projectionsontheimageratherthantheirtruespatial positions.Consequently,theerrordistancetothereal locationoftheobjectsremainssigni icant.Zhang’s technique[28],requiringonlyaplanarpattern,offers lexibilitywithquickerapplicationinindustrialcon‐texts,albeitwithslightlyhigheruncertainties.Beyond these,researchershavetailoredcalibrationmethods forspeci icapplications,suchashigh‐speedtensile testingmachinesandunmannedvehicleguidance, providinguniqueinsightsandexperimentalresults. However,theseapproachestendtofailinthecase oflocalizing3D‐shapedobjects.Buildinguponfoun‐dationalstudiessuchasSiddiqueetal.[29],who explored3Dobjectlocalizationusing2Destimates forcomputervisionapplications,ourworkseeksto advancetheseconceptsbyintegratingmoresophis‐ticatedcalibrationmethodsanddeeplearningtech‐niquesforimprovedaccuracyandef iciencyinindus‐trialsettings.
Duetotheir3Dnaturalshape,thelocationdeter‐minedbycalibrationmethodsisinfactthelocation oftheirprojectionsontheimageinsteadoftheirreal location.Therefore,theerrordistancetotherealloca‐tionoftheobjectsstillremains.Inaddition,Xiem HoangVanandNamDo[30]introducedamachine learning–regression‐basedmethodforimprovingthe accuracyof3Dobjectlocalization.Ourmethodiscre‐atedbasedonmathematicalmodelingof3Dobjects andtheirprojectedimageinthe2Dplaneandis followedbyaregression‐basedalgorithmtoachieve modelparameters.
Inthispaper,weproposedanovelapproach(M‐Calib)withthefollowingcontributions:
1) Wevalidatedtheproposedworkinrigorousexper‐imentsusingacheckerboard.Theresultsshow thatourapproachoutperformsthepreviousin estimationaccuracy.
2) Weproposeanef icient3Dlocalizationmethod designedtoaccuratelycalculatethetranslation vectorbetweenthecalibrationcentertargetand theinitializedcenterpointwithsub‐pixellocaliza‐tionaccuracy.Thismethoddemonstratesrobust‐nesstonoise,ensuringreliableperformancein variousconditions.
3) WeprovidethesourcecodeofM‐Calibtothe researchcommunity,offeringaneasy‐to‐usecali‐brationtoolboxspeci icallytailoredformonocular cameras.Thisresourceisopenlyaccessibleat: ht tps://github.com/NguyenCanhThanh/MonoCal ibNet,facilitatingfurtherresearchandapplication developmentinthe ield.
Theremainderofthispaperisorganizedasfol‐lows:Section2delvesintotheintricaciesoftheprob‐lemstatement,offeringacomprehensiveunderstand‐ingofthechallengesathand.
Figure2. Illustrationofindustrialrobotvisionsystem: thegreenpointistheinitializedestimatecenterpoint, andtheredpointistheactualcenterpoint
Weunveilournovelmethodforisometric lat 3Dobjectlocalization,elucidatingthedeeplearning methodologiesemployedandelucidatingtheproce‐duralstepsinSection3.Section4presentstheexper‐imentalsetupandevaluatestheperformanceofour proposedmethodusingrelevantmetrics.Finally,Sec‐tion5concludesthepaper,summarizingthekey ind‐ings,discussingpotentialfutureresearchdirections, andemphasizingthesigni icanceofourcontributions.
2.ProblemStatement
Theproblemaddressedinthisstudyliesatthe intersectionofmachinevisionand3Dobjectlocal‐izationwithinindustrialrobotvisionsystems.While conventional2Dcameracalibrationmethods,such asBrown’sPlumbLineMethodandTsai’sTwo‐Stage Method,haveproveneffectiveforachievinghighaccu‐racyinobjectlocalization,theirlimitationsbecome evidentwhenconfrontedwith3D‐shapedobjects.The inherentchallengearisesfromthefactthatthese methodsdetermineobjectlocationsbasedontheir projectionsontothe2Dimageplane,resultingininac‐curaciesinrepresentingthetrue3Dpositions.This discrepancyisespeciallypronouncedinindustrial contextswherepreciseobjectlocalizationiscrucialfor taskssuchasroboticautomation,andqualitycontrol. Figure2illustratesthechallengeswhenestimatingthe centerof3Dobjects.Underthein luenceofoptical projection,theinitialestimatedcenterposition(green point)oftentendstodeviatefromtheactualcenter (redpoint)position.Toaddressthisgap,weproposea novelapproach,M‐Calib,leveragingef icient3Dlocal‐izationtechniquestoovercomethelimitationsoftra‐ditional2Dcalibrationmethods.Theobjectiveisto enhanceaccuracy,particularlyinthelocalizationof isometric lat3Dobjects,therebycontributingtothe advancementofmachinevisionapplicationsinindus‐trialenvironments.
3.ProposedMethod
Figure 3 presentsavisualrepresentationofour proposedcalibrationmethodology,centeredaround thedeliberatechoiceofacheckerboardasthecalibra‐tionpatternfortwosigni icantreasons.
Firstly,thecheckerboardpatterndemonstrates robustnessagainstscenesthatareoutoffocus[31]. Secondly,thefeaturesextractedfromthechecker‐boardofferastraightforwardde initionoftheoriginal coordinate,contrastingwithasymmetriccirclepat‐terns,wherefeaturesaremoresuitableformotion determination.Thecheckerboardpatternplaysapiv‐otalroleinpreciselydeterminingtheobject’sposition inthecalibrationprocess.Asthemonocularcameras sweepthecalibrationpattern,knownas���� corner,we leveragetheYouOnlyLookOnce(YOLO)model[32], astate‐of‐the‐artobjectdetectionmodel,toidentify objectswithinthecamera’s ieldofview.Oncethe ixedoriginalcoordinateisde ined,sub‐pixellocal‐izationaccuracyiscrucialforextractingtheimage centersofthecalibrationtargetstooptimizesensor calibration.ThisprocessisdetailedinSection 3.1 However,owingtothedirectionoflight,theobject’s positionmaydriftawayfromtheactualcenter.To addressthis,weintroduceanovelcalibrationmethod comprisingtwoparts.Initially,wesegmenttheobject intotheupperplane(����)andthelowerplane(����),as discussedinSection3.2,utilizingtheBilateral iltering algorithmtoeliminatenoise.Subsequently,wedeter‐minethecenteroftheupperplane (����) andemploy anedgedetectionalgorithmtoextracttheedge (����) ofthelowerpart.Thisedge(����)isthendividedinto twomainborderlines:theupperline (����) andthe lowerline(����).Thetranslationvector(T)from(����)to (����)iscalculated,asdetailedinSection3.3.Finally,the estimatedobjectpositioniscomputedbyshiftingthe centeroftheupperpart(����)followingthetranslation vector(T)withamagnitudeof1/2.
3.1.ObjectDetection
Indeterminingtheprecisepositionoftheobject, weinitiatetheprocessbyestablishingreal‐world coordinatesthroughthecaptureofacheckerboard image,enablingtheidenti icationofitscorners.Sub‐sequently,foreachobjectpresentintheimage,we leverageanadvancedobjectdetectionmethodtodis‐cerntheirrespectiveimagecoordinates.Inthecontext ofdetectingcheckerboardcorners,weestablishthe correlationbetweentheimagecoordinatesandtheir correspondingreal‐worldcoordinates.Notably,the relationshipbetweendistancesinimagesandtheir counterpartsintherealworldisnotalwayslineardue todistortion.Figure4delineatesthesequentialsteps employedtoascertaintheinitialobjectposition:
1) DetectCheckerboardEdgesandCorners:Utilizing theHoughtransformation,weidentifychecker‐boardedgesandthecoordinatesoftheirintersec‐tions,namely,checkerboardcorners,asdepictedin Figure4a
2) SelectFixedReal‐WorldCoordinate:Choosea ixedreal‐worldcoordinateinpixelimagespace, denotedas���� = ��0 ��0 ��
3) EstimateObjectCenterPosition:Employingobject detection,estimatethecenterpositioninpixel imagespace,representedas��= ���� �� .
Figure3. Ablockdiagramofourproposedcalibrationmethod.Thetranslationvectorbetweentheinitializedestimate centerpoint(greenpoint),andthecalibrationcenterpoint(redpoint)iscalculatedbasedondeeplearning,andour novelcalibrationmethod
(a) Checkerboarddetection (b) Objectdetection (c) Initialobjectposition
Figure4. Theprogressofthecalculationoftheobjectpositioninthereal‐worldcoordinate
4) CalculateObjectPositioninReal‐WorldCoordi‐nates:Computetheobject’spositioninreal‐world coordinatesusingtheformula ���� =(��−����)��, where �� signi iestheaverageratiobetweenthe lengthinpixelsandthelengthintherealworldof eachcellinthecheckerboardpattern.
3.2.Objectsegmentation
Whileutilizingthecheckerboardcalibration methodtoestimatethelocationofobjectsprovesto bestraightforwardandreadilyapplicableinindustrial settings,itsef icacydiminishessigni icantlywhen dealingwith3D‐shapedobjects.Ininstancesinvolving suchobjects,theboundingboxgeneratedthrough deeplearningmethodsmaynotalignaccuratelywith thetrueobjectlocation.
Speci ically,thecoordinatesoftheboundingbox’s centerareunlikelytocorrespondtotheactualcen‐teroftheobjectwithintheresultantimage.It’scru‐cialtonotethattheboundingbox’scentercanaccu‐ratelyrepresenttheobject’scenteronlyiftheobject ispreciselypositionedatthecenterofthecamera’s projectionontothe loor.Toaddressthislimitation, weemployaconvolutionalneuralnetwork(CNN)‐basedobjectsegmentationapproachtodivideobjects, detectedinSection3.1,intotwodistinctplanes.This segmentationinvolvesusingtheupperplane ���� to establishtheinitialcenteroftheobject,followedby noisereductionandedgeextractionfromthelower plane.
TheinitialstepinvolvesapplyingaBilateral ilter‐ingoperation,whichcanbeexpressedmathematically as: ��′(��)= 1
where:
‐ ��′(��)isthe ilteredintensityatpixel��.
‐ ���� isthenormalizationterm.
‐ ��(��)istheintensityatpixel��
‐ ������ isthespatialGaussiankernelwithstandard deviation����.
‐ ������ istherangeGaussiankernelwithstandarddevi‐ation����.
‐ Ωisthespatialneighborhoodofthepixel��. Here,��isthesizeofthekernel,and��isthestandard deviationoftheGaussiandistribution.
Afterthat,theedgedetectorincludesgradient computation,non‐maximumsuppression,andedge trackingbyhysteresis.Themagnitudeofthegradient (��) andthegradientdirection (��) arecalculatedas follows:
where ���� and ���� arethepartialderivativesofthe image.Afterobtainingthegradientmagnitude,non‐maximumsuppressionisappliedtothintheedges. Finally,edgetrackingbyhysteresisinvolvessetting twothresholds,��ℎ����ℎ and��������.Anyedgepixelwitha gradientmagnitudeabove��ℎ����ℎ isconsideredastrong edge,andpixelsconnectedtostrongedgesandwitha magnitudeabove�������� areconsideredweakedges.
Thenwedividetheedgeintotwomainborder lines:theupperline(����)andthelowerline(����).The upperlineisthecontactlinebetweenthetwoplanes ���� and ����,andthelowerlineistheboundaryofthe lowerplane ����.Figure 5 illustratestheprogressof objectsegmentationandedgeextraction.
3.3.CalibrationMethod
Weintroduceacalibrationtechniquedesignedfor objectpositioncalibration.Uponcompletionofthe objectsegmentationandedgeextractionprocesses, weobtaincrucialcomponents:theinitialpositionof theobject(centeroftheupperplane ����),theupper line ����,andthelowerline ����.Thetranslationvector ������ isthencalculatedusingAlgorithm1topredictthe inalpositionoftheobjectbyshiftingtheinitialpoint accordingto ������.Inthisprocess,eachpointonthe upperline���� calculatesitsdistancetothelowerline ����,determiningthesmallestvectorlength.Thevisual‐izationresultsaredepictedinFigure6a.Subsequently, thetranslationvector������ isde inedasthevectorwith themaximumlengthwithinthesetofdistancevectors foreachpoint,asillustratedinFigure6b
Algorithm1: EstimateTranslationVector
Input: ���� =����1,����2,…,������ ���� =����1,����2,…,������ ��isthenumberofpointsinline���� ��isthenumberofpointsinline����
Output: Translationvector: ⃗ ������
Indexpointinline����:��������
Indexpointinline����
begin: ��←0;
; ▷Themagnitudeofthe translationvector while ��<(��−1) do ��
�� ←+∞; ▷Thedistancefroma pointtoaline while ��<(��−1) do
Calculatethedistancebetweentwo points ������ =(������,������
and
) basedon(4):
)2 (4) if
then ��
; end ��+=1; end if
then
end ��+=1; end return ⃗ ��
end
Thiscalibrationtechniquefacilitatesaccurate objectpositioningbyaccountingforthespatial relationshipsbetweentheupperandlower components. However,theef icacyofAlgorithm 1canbecompromisedbysuboptimalsegmentations. Tomitigatethisissue,weintroduceAlgorithm 2 asasolution.Inessence,ifthevector ������ derived fromAlgorithm 1 isaccurate,thenuponprojecting theupperline ���� alongthetranslationvector,the distancebetweentheresultantline���� andthelower line���� shouldbeapproximately,orequal,to0.
Leveragingthisconcept,weconstructthesetof neighboringvectors��bymaintainingtheinitialpoint ofthevector ������ unchangedandselecting �� neigh‐boringpointsfortheterminalpoint.Subsequently, weprojecttheupperlinefollowingeachtranslation vectorin �� andchoosethevectorthatresultsinthe smallestdistance.
Theprogressofobjectsegmentationandedgeextraction
Thisnovelalgorithmservestoenhancetherobust‐nessofthecalibrationprocessagainstsuboptimalseg‐mentations,ensuringmorereliableresults.
4.ExperimentalResults
4.1.ExperimentSetup
Toevaluatetheproposedmethodforestimating thelocationofobjects,weconductedexperiments usingavisionsystemwithacamerapositionedabove, paralleltothe loor,andatadistanceof 40����.The real‐worldcoordinateswerede inedusingachecker‐boardpattern,whereeachsquarewasmeasured3× 3����2.Furtherdetailsabouttheexperimentalsetup, includinghardwarespeci ications,areprovidedin Table1.Inourexperiments,weusedaspeci ictypeof objecttoevaluatetheperformanceofourlocalization algorithm.Theobjectselectedforthisstudyisastan‐dardelectricalcharger,commonlyfoundinhouse‐holdsandindustrialsettings.Thisobjectwaschosen duetoitswell‐de inedshapeandeasilyrecognizable features,whichfacilitateaccuratedetectionandseg‐mentation.Thedimensionsofthisobjectare4.5����× 3.0����×3.5����.Thedimensions,shape,andsharpness ofthelocalizedobjectsigni icantlyimpacttheperfor‐manceofthelocalizationalgorithm.Theobject’swell‐de inededgesanddistinctfeaturesenablethedeep learningmodelstoaccuratelydetectandsegmentit fromthebackground.Thesizeoftheobjectensures thatitisneithertoosmalltobeoverlookedbythe detectionmodel.
Therectangularshapewith latsurfacesandsharp edgesfacilitatespreciseboundarydetectionduring thesegmentationprocess.Theclearanddistinctcon‐toursoftheobjectenhancethesegmentationaccu‐racy,leadingtobettercalibrationresults.
Theevaluationmetricsemployedforacompre‐hensiveassessmentareIntersectionoverUnion(IOU) forobjectsegmentation,MeanAveragePrecision (mAP)forobjectdetection,andtheEuclideanmetric forgeometricaccuracy.
Metrics:Weutilizeasetofrobustmetricstoassess theperformanceofourproposedobjectlocaliza‐tionmethodthoroughly.TheIntersectionoverUnion (IOU)metric,pivotalintheobjectsegmentationphase, isde inedastheratiooftheareaofoverlap (������) betweenpredicted (����������) andgroundtruth (������) boundingboxestotheareaofunion(������):
Themeanaverageprecision(mAP)isutilizedfor theobjectdetectionphase,calculatedbyintegrating theprecision(��)overtherecall(��)andthenumber ofclasses��atvariousIOUthresholds:
(a) Inputimage (b) Segmentation (c) Bilateralfiltering (d) EdgeExtraction
Figure5.
(a) Pointtolinetranslationvector (b) Linetolinetranslationvector
Figure6. Illustrationoftheestimatedtranslationvector
Algorithm2: TranslationVectorCorrection
Input: ���� =����1,����2,…,������ ���� =����1,����2,…,������
��isthenumberofpointsinline���� ��isthenumberofpointsinline���� ⃗ ������,��������,�������� ←��������������ℎ��1
Output: Translationvector: ⃗ ������
begin:
▷Choose��neighboringpointsof������������
��←−��/2; ��←{}; ▷Setoftranslationvectors while ��<��/2 do ��←�������� +��; ��.������ℎ�������� ⃗ ������������������ ; ▷Pushback
theneighboringvectorsof ⃗ ������ into�� end
�������� ←+∞; for ��=0;��<��������(��);��++ do ���� ←���� +����; ▷Projectupperline followingthetranslationvector
▷Calculatethedistancebetween���� and���� ��←0; ��←0; ��←0; while ��<(��−1) do while ��<(��−1) do Calculatethedistance�� betweentwopoints ������ =(̄������,̄������) and ������ =(������,������) basedon (4); ��←��+��; ��+=1; end ��+=1; end if �������� ≥�� then �������� ←��; ⃗ ������ ←����; end end return ⃗ ������; end
Table1. Experimentsetupdetails Parameter
Process IntelXeonProcessorwithtwo cores@2.3GHz GPU NVIDIATeslaT4 RAM 13GB OS Ubuntu20.04LTS
Table2. Performancecomparisonofvariousobject detectionmodels
TheEuclideanmetricassessesgeometricaccu‐racybycalculatingtheEuclideandistance�������������������� betweenthepredicted (����������,����������) andtrue (������,������) objectcoordinates:
Datasets:Weacquiredthreedistinctdatasets, eachcorrespondingtoaspeci icphaseofourpaper. Intheobjectdetectionphase,weamassedacollec‐tionof400imagescapturedfromvariousobjectloca‐tions.Toensureacomprehensiveevaluation,wepar‐titionedthisdatasetintothreesubsets:atrainingset comprising60%ofthedatarandomlyselected,avali‐dationsetwith30%,andatestsetwiththeremaining 10%.Subsequently,intheobjectdetectionphase,we gathered5000imagesfromdiverseobjectlocations. Tomaintainarobustevaluationapproach,wesplitthis datasetintoatrainingset(70%ofthedatarandomly selected),avalidationset(20%),andatestset(10%). Lastly,fortheobjectlocalizationphases,wegathered 60images,distributedinto10folds,eachcontaining6 images.
4.2.ObjectDetectionandObjectSegmentationResults
Table 2 presentstheresultsofvariousdetection modelsevaluatedintermsofmeanaverageprecision–mAP,modelsize–MS(MB),precision–Pr,andrecall–Rc.TheYolov3[33]modelachievesamAPof 90.0% withamodelsizeof8.7MB,accompaniedbyprecision andrecallscoresof 85.9% and 84.6%,respectively. Incontrast,theFastR‐CNN[34]modeldemonstrates superiorperformancewithamAPof 97.0% despite alargermodelsizeof 12.9 MB,achievingprecision andrecallscoresof 93.4% and 42.1%,respectively. TheMobileNet[35]modeloffersamAPof94.8%with arelativelycompactmodelsizeof 4.6 MB,achiev‐ingprecisionandrecallscoresof 93.8% and 93.4%, respectively.TheYolov4[36]andRTMDet[37]models exhibitcompetitivemAPscoresof96.8%and96.9%, respectively,withlargermodelsizesof 60.0 MBand 52.3MB.TheYolov7[38]andYolov8[39]modelscan achievesuperioraccuracywithamAPof 97.1% and 97.8%,respectively,withaprecisionof 95.7% and 95.5%,andarecallof93.1%and94.4%,respectively. Ourproposedmodeloutperformstheotherswithan mAPof98.7%,precisionof98.6%,andrecallof97.0%.
Figure7. Visualizedexamplesofexperimentalresults:figure(b):theorangepointistheYolocenter,figure(d):darkredis theupperpartcenter.Thevectorcreatedbythebluepointsisatranslationvector;thelightbluepointisthecorrection center
Additionally,ourmodelexhibitsarelativelycom‐pactsizeof 7.0 MBcomparedtoothermodels,indi‐catingitsef iciencyintermsofmemoryusage.These resultsunderscoretheeffectivenessandef iciency
ofourproposedobjectdetectionmodelforaccu‐ratelydetectingobjectsinvariousscenarios,making itwell‐suitedforpracticaldeploymentinreal‐world applications.
(a) Inputimage (b) Objectdetection (c) Segmentation (d) Calibirationresult
Table3. Experimentalresultsevaluatethepositionerrorofouralgorithm(mm)
35.324.567.010.350.810.88 0.190.380.420.19 0.570.60
510.268.3613.230.920.921.302.280.762.40 0.571.141.27 66.2711.4013.011.471.632.191.902.853.43 1.331.331.88
Average 8.308.9612.541.431.862.341.381.151.92 1.120.941.55
Table4. Performancecomparisonofvariousobject segmentationmodels Algorithm
Acomparativeanalysisofvariousobjectsegmen‐tationmodelsispresentedin 4.Amongthemodels evaluated,Yolov5[40]emergesasastrongcontender, showcasinganotablemAP@0.5 scoreof 98.7%,a precisionrateof 97.1%,andarecallrateof 96.2% Thesemetricsindicateitsrobustabilitytoaccurately identifyobjectswithinimageswhilemaintainingarel‐ativelycompactmodelsizeof7.4MB,makingitanef i‐cientchoiceforresource‐constrainedenvironments. Inaddition,Yolov7[38]andYolov8[39]demonstrate acommendableperformancewithhighmAPscoresof 99.0%and99.2%,respectively,alongwithimpressive precisionandrecallvalues.However,whatsetsour proposedmodelapartisitsexceptionalperformance acrossallmetrics.WithanoutstandingmAP@0.5 scoreof 99.8%,precisionrateof 99.1%,andrecall rateof97.9%,ourmodelsurpassesallothersinterms ofsegmentationaccuracywhilemaintainingamoder‐atemodelsizeof 28.9 MB.Theseresultsunderscore theef icacyofoursegmentationmodelinaccurately delineatingobjectswithinimages.
Figure 7 visuallyillustratestheexperimental resultsofourproposedmethod,includingobject detection,objectsegmentation,andobjectcalibra‐tion.Thesevisualizationsprovideacomprehensive insightintotheef icacyandaccuracyofeachphase ofourmethodology.Objectdetectionshowcasesthe abilityofourmodeltoaccuratelyidentifyandlocal‐izeobjectswithinthescene,layingthefoundation forsubsequentprocessingsteps.Objectsegmentation highlightstheprecisionwithwhichouralgorithm delineatestheboundariesofdetectedobjects,ensur‐ingaccuratelocalizationandanalysis.Finally,object calibrationvisuallydemonstratesthere inementand optimizationofobjectpositionsbasedonreal‐world coordinates,validatingtheeffectivenessofourcali‐brationapproachinenhancingspatialaccuracy.
4.3.ObjectLocalizationResults
TheexperimentalresultsinTable 3 offerquan‐titativeinsightsintotheperformancecomparison betweenourproposedmethod,thetraditional approach,andtheRegression‐basedmethod[30],our previousmethod[30](Regression‐basedmethod). Acrossmultiplefoldsandsamples,ourmethod consistentlydemonstratessuperiorperformancein termsofpositionerrormetrics.
Table5. Processingtimeofourproposedmethod (milliseconds)
Phase ProcessingTime
ObjectDetection 15±2
ObjectSegmentation 40±5
ObjectCalibration 300±10
Forinstance,inFold1,Sample1,thetraditional methodyieldspositionerrorsof��=9.69mmand ��=5.51mm,whileourproposedmethodachieves signi icantlylowererrorsof��=0.38mmand��= 1.14 mmbeforecorrection,and ��=0.95 mmand ��=0.76mmaftercorrection.
Theaveragepositionerrorsacrossallfoldsand samplesfurtherhighlighttheeffectivenessofourpro‐posedmethod.Onaverage,ourmethodachievesposi‐tionerrorsofΔ��=1.12mmandΔ��=0.94mmafter correction,comparedto Δ��=8.30 mmand Δ��= 8.96mmforthetraditionalmethod,whichreducesthe positionerrorby 87.64%.Similarly,theregression‐basedmethodyieldsaverageerrorsofΔ��=1.43mm andΔ��=1.86mm,indicatinganoticeableimprove‐mentoverthetraditionalapproachbutstillinferiorto ourproposedmethod.
Thesequantitativeresultsunderscorethesignif‐icantreductioninpositionerrorsachievedbyour proposedmethodcomparedtobothtraditionaland regression‐basedapproaches.Thesuperioraccuracy andprecisionofferedbyourmethodareparticularly advantageousinapplicationswherepreciseobject localizationisparamount,suchasroboticmanipula‐tion,augmentedreality,andautonomousnavigation systems.
Theprocessingtimeforeachphaseofourpro‐posedmethodissummarizedinTable5.Intheobject detectionphase,ouralgorithmtakesapproximately 15±2millisecondstodetectobjectswithinthecam‐era’s ieldofview.Subsequently,duringtheobject segmentationphase,whichinvolvessegmentingthe detectedobjectsintoupperandlowerplanes,thealgo‐rithmalsorequiresaround40±5milliseconds.Finally, intheobjectcalibrationphase,wherethepreciseposi‐tionoftheobjectsisdeterminedbasedontheseg‐menteddata,theprocessingtimeremainsconsistent atapproximately300±10milliseconds.Thisef icient processingtimeacrossallphasesunderscoresthe real‐timeapplicabilityandpracticalfeasibilityofour proposedmethodforobjectlocalizationinindustrial visionsystems.
5.Conclusion
Inconclusion,wehavepresentedM‐Calib,acom‐prehensivemethodologyforpreciseobjectlocaliza‐tionandcalibrationleveragingadvancedcomputer visiontechniquesforindustrialrobotvisionsystems.
Throughtheintegrationofadvancedcomputer visiontechniques,includingobjectdetection,segmen‐tation,andcalibration,ourproposedapproachoffers arobustandaccuratesolutionfordeterminingthe real‐worldpositionsofobjects.Experimentalresults demonstratetheeffectivenessofourmethodinsig‐ni icantlyreducing87.65%positionerrorscompared totraditionalapproaches,therebyenhancingspatial accuracyinindustrialenvironments.Furthermore,the computationalef iciencyofourmethod,asevidenced byminimalprocessingtimes,underscoresitspractical viabilityforreal‐worlddeployment.Overall,ourpro‐posedmethodologyholdspromiseforawiderangeof industrialapplicationswherepreciseobjectlocaliza‐tionisessential,offeringareliablesolutiontooptimize operationalef iciencyandenhancingproductivity.In thefuture,ouraimistoexploremachinelearningtech‐niquesforautomaticcalibrationparameteradjust‐mentandextendourmethodologytosupportreal‐timedynamicobjectlocalization.
AUTHORS
ThanhNguyenCanh –DepartmentofRobotics Engineering,UniversityofEngineeringandTechnol‐ogy,VietnamNationalUniversity,XuanThuy,Hanoi, 10000,Vietnam,e‐mail:canhthanh@vnu.edu.vn.
DuTrinhNgoc –DepartmentofRoboticsEngineering, UniversityofEngineeringandTechnology,Vietnam NationalUniversity,XuanThuy,Hanoi,10000,Viet‐nam,e‐mail:ngocdu2105@gmail.com.
XiemHoangVan∗–DepartmentofRoboticsEngineer‐ing,UniversityofEngineeringandTechnology,Viet‐namNationalUniversity,XuanThuy,Hanoi,10000, Vietnam,e‐mail:xiemhoang@vnu.edu.vn.
∗Correspondingauthor
ACKNOWLEDGEMENTS
ThanhNguyenCanhwasfundedbytheMaster, PhDScholarshipProgrammerofVingroupInnovation Foundation(VINIF),codeVINIF.2023.ThS.120
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Submitted:1st April2023;accepted:16th May2024
AbderrahmaneKacimi,AbderrahmaneSenoussaoui
DOI:10.14313/jamris‐2025‐026
Abstract:
Thisresearchpresentsanewcontrolmethodforatwin‐rotorMIMOsystemthatmodelsthebehaviorofaheli‐copter.Thecontrolstrategycombinesfeedbacklineariza‐tionwithanon‐linearobservercalledtheThauObserver andtakesfulladvantageofthesystem’sstateinfor‐mation.Theproposedmethodistestedinbothsimu‐latedandreal‐worldexperiments,anditisevaluated foritsabilitytoperformregulationandtrajectorytrack‐ingtasks.Theresultsdemonstratetheeffectivenessand superiorperformanceoftheproposedcontrolmethodin controllingtwin‐rotorMIMOsystems.
Themainadvantageoftheproposedmethodisits nonlinearcontrol,whichhasmorepowerandusesmore precisephysicalparametersofthesystemthanthelin‐earizedmodel.
Keywords: TRMS,robotics,UAVscontrol,non‐linearcon‐trol,non‐linearobserver
1.Introduction
Feedbacklinearizationisawidely‐usedcontrol techniqueforaerodynamicsystems.Thismethodlin‐earizesnon‐linearsystemsglobally,whichprovidesa linearclosed‐loopsystemforcontrollingaerodynamic systems.Feedbacklinearizationhasbeenshowntobe effectiveincontrollingaerodynamicsystems,evenin thepresenceofnon‐linearitiesandcross‐couplings. Itspopularityinthe ieldofcontrolengineeringcan beattributedtoitsreliabilityandeaseofimplemen‐tation.Recentresearchhascontinuedtodemonstrate theeffectivenessoffeedbacklinearizationforcontrol‐lingaerodynamicsystems.Forexample,inastudyby Kimetal.[1],feedbacklinearizationwasappliedtoa helicoptermodeltoimproveitscontrolperformance. Theresultsshowedthatthefeedback‐linearization approacheffectivelyreducedsteady‐stateerrorand improvedthetransientresponseofthesystem.In anotherstudybyLi[2],feedbacklinearizationwas usedtocontrola lapping‐wingaircraft.In[3,4],there arepresentationsoftheresultsofcontrollingaerody‐namicautonomoussystemssuchasquad‐rotorsand helicopters.
TheTwinRotorMIMOSystem(TRMS)isawell‐establishedbenchmarkfor lightcontrolexperiments andthevalidationofcontroltheories.Thissystem simulatesthedynamicsofahelicopter,withtwo inputsandtwooutputsthatarecross‐coupled.The
TRMSprovidesachallengingplatformfortestingcon‐troltechniquesduetoitsnon‐linearitiesandcomplex‐ity.Itsclosecorrelationtoreal lightdynamicsmakes itanidealsystemforevaluatingtheperformanceof controlsystemsunderchallengingconditions.Itsuse asabenchmarksystemhasbeenwidelyrecognizedin thecontrolengineeringcommunity.
AnumberofrecentstudiesontheTRMShavealso focusedonimprovingitscontrolperformance[5–7], usingtovalidatetheaccuracyofimportantnon‐linear andhybridcontroltechniquessuchasbackstepping, adaptivefeedbacklinearization,androbustcontrol. Forinstance,inastudybyWangandcolleagues[8], ahybridcontrolmethodwasappliedtotheTRMSto achieveimprovedregulationandtrajectorytracking. AnotherstudybyZhangetal.[9]appliedamodel predictivecontrol(MPC)approachtotheTRMS,with theaimofimprovingitsregulationandtrackingper‐formance.
Thepresentworkmakesasigni icantcontribution tothe ieldoffeedbacklinearizationandthecontrolof aerodynamicsystems.Bycombiningthefeedbacklin‐earizationcontroltheorywiththeThauobserver,we wereabletoachievebettercontrolperformancethan inpreviousstudies.Theuseofthetwin‐rotorMIMO systemasabenchmarkallowedustovalidatethe effectivenessofourcontrolapproachinareal‐world scenario.Thesimulationandreal‐timeexperiments conductedinthisworkshowedpromisingresultsin bothregulationandtrajectory‐trackingtasks,demon‐stratingthepotentialofthiscontrolapproachinprac‐ticalapplications.
Thisproposednewmethodcanbeusedtocon‐trolrobotsystemsingeneralUsingthisapproachto controlrealhelicoptersmaybepossible,takinginto considerationthehelicoptersystem’sspeci ications.
Theremainderofthispaperisorganizedasfol‐lows.Section 2 presentsthemathematicalmodelof thetwin‐rotorMIMOsystem.Section3focusesonthe feedbacklinearizationcontroltheoryanditsmathe‐maticalproofofstabilityintheclosed‐loopsystem, includingthesystem,controller,andobserver.The resultsofboththesimulationandreal‐timeexper‐imentsarepresentedanddiscussedinSection 4. Finally,inSection 5,weprovideconclusionsand futureworksuggestionstofurtheradvanceour ind‐ings.Throughoutthepaper,weillustrateandanalyze theresultstoaidinacomprehensiveunderstandingof ourwork.
2.TheTRMSModel
Inthissub‐sectionwewillpresenttheTRMS model,wewillfollowaphysicalmodellingusingthe lawsofaerodynamics,mechanicsandelectricityto haveanon‐linearmodel.
‐ Asitisabeinganonlinearandmulti‐variablesys‐tem;thedynamicsoftheTRMScanbetranslated throughequationsdescribingthemomentsofforce andinertia.
‐ Themathematicalmodelisdevelopedbymaking somesimpli ications;wesupposethat:
‐ Motordynamicscanbedescribedby irst‐order differentialequationsasafunctionofthejoint variablesofthemechanismandvice‐versa.
‐ Thefrictioninthesystemisoftheviscoustype.
‐ Rotationcanbedescribedinprincipleasthe movementofapendulum.
Thesearesimplifyingassumptions,theyaremade tosimplifythemodelling,thesethreeassumptions presentedaboveareargued,bythefactofthechosen operatingrange,aswellaswhichslowoperatingmode chosen,withoutforgettingthemechanicalstructureof thesystemthatallowsustomakethe3rd hypothesis.
Modelingoftheplantusedherefollowsthesame methodasourprecedentworks[11,21];afterrear‐rangementofequationsofmomentsandforceswecan getthefollowingnon‐linearstaterepresentation:
Wehavethestatevector:
Where��and��arethepitchandyawanglerespec‐tively.
��1 and��2 arethetorquesofthetwomotorsofpitch andyawrespectively.
Table1. TheTRMSparameters–fromthe“feedback” manufacturer
Parameters
Values
I1 –mainrotormomentofinertia 6.8.10‐2Kg/m2
I2 –tailrotormomentofinertia 2.10‐2Kg/m2
a1 –nonlinearityparameters 0.0135
b1‐nonlinearityparameters 0.0924
a2‐nonlinearityparameters 0.02
b2‐nonlinearityparameters 0.09 Mg‐momentofgravity 0.32N.m
B1��–parameterofthefriction momentfunction 6.10‐3N.m.s/rad
B2��–parameterofthefriction momentfunction 1.10‐3N.m.s/rad
B1��–parameterofthefriction momentfunction 1.10‐1N.m.s/rad
B2��–parameterofthefriction momentfunction 1.10‐2N.m.s/rad
Kgy –gyroscopicmoment parameter 0.5S/rad
Thissystemisintheform
3.Input‐OutputFeedbackLinearization
3.1.Feed‐backLinearizationController
Theexactlinearizationofnonlinearsystemscon‐stitutesanaturalandpromisingmethod,makingit possibletoobtainalinearinput‐outputbehaviorby implementaloop.Subsequently,thewholelinearthe‐orycanbeapplied[10–12].Advancedcontrolmeth‐odsoftenincludeseveralloopsincludingafeed‐backlinearization.Input‐outputlinearizationplaysan importantroleina ieldlikerobotics,wherethecalcu‐latedtorquemethodisaspecialcaseofinput‐output linearization[13].
3.1.1.CaseofMulti‐variableSystems
Considerthefollowingnonlinearsysteminaf ine formasinput:
Figure1. TwinRotorMIMOSystem(TRMS)
With ��∈ℝ��;��∈ℝ�� and ��∈ℝ�� asthestate vector,inputandoutputsofthesystem,respectively. ��(��),��(��)andℎ(��)aresuf icientlyregularfunc‐tionsinadomain��⊂ℝ��;Applications��∶��→ℝ�� and ��∶��→ℝ�� callthevector ieldsinthedomainD;and theapplicationℎ∶��→ℝ�� istheoutputimmersion. ThesolutionforSISOsystemscanbeeasilygen‐eralizedtomultivariatesystems.Wethenobtainthe suf icientconditiongivenby[11].
3.1.2.DecouplingbyRegularStaticLooping
Giventhesystemintheformof(1),wetryto ind, ifpossible,aregularstaticstatelooping,suchas
��=��(��)+��(��)�� (2)
With��(��)inversible,suchas,forall��=1.....��,given:
(��)
������������ ����,������,…,����(��) �� ,��≥0 (3)
(��) �� ∉���������� {����} (4)
Let ��ℎ ������(��)=����ℎ(��) becalledtheLiederivative of h inthedirectionof f.Condition(3)representsthe decouplingstressitself,andcondition(4)guarantees thecontrollabilityoftheclosedloopoutput.
Thesolutiontothisproblemisgivenbyaresult similarto[11];however,theconditionherebecomes necessaryandsuf icient.
Let(��1,…,����)bethesetofin initezerosperrow ofthesystem.Rememberthatthesearede inedas follows:
(5)
Recallthat���� correspondstothe irstderivativeof����, whichexplicitlyshowsthecontrollaw u: ��(����) =������ �� ℎ(��)+��
Withthemultiplicativetermof u designatingthecon‐catenationoftheterms
LetΔ(��)bethematrixde inedby:
x)=
Thismatrixiscalledthesystemdecouplingmatrix. ThisconditiononΔ(x)beingsatis ied—thestate feedbackde inedbyequation(2)—decouplesthe systemΣ,suchthat:
forastabilizingcontrolthatguaranteesacertainlevel ofperformanceforthesystemaccordingtoaspeci‐ication.Loads[13].Inthispaperwehavecontented ourselveswithaplacementofpolesbylinearstate feedback.Thiscanalsobeadynamicoutputfeedback, whichusesthestatesofthephysicalsystemestimated bytheThauobserver.
3.2.ThauObserver
TheresultsobtainedbyThauweregeneralizedby Kouetal.[15]andBanks[16].Thismethoddoesnot constituteasystematictechniqueforthesynthesisof anobserver,butrathergivesasuf icientconditionof theexponentialstabilityoftheobservationerror[14].
Letusconsiderthenonlinearsystem,whichcanbe putintothefollowingform:
Moreover,theloopedsystemhasalinearinput‐outputbehaviordescribedby:
Thelinearsystemobtainedbythismathematical transformationisachainofintegratorswith���� poles attheorigin;itisthereforeunstable,hencetheneed
Where ��(��)∈ℜ�� representsthestateofthe system, ��(��)∶ℜ�� ⟶ℜ�� isadifferentiablevector ield. ��(��)∈ℜ�� isthecontrolvector. ��(��)∈ℜ�� istheoutputvector.
Thus,thesystem̂��=��̂��+����+�� ( )+��(��−��̂��) isanexponentialobserverofthestateofthesystem. Theproofofthistheoremisin[16].
Thelemmain[18]characterizestheexponential convergenceofthisobserver.
3.3.ApplicationonTRMS
GiventhefollowingnonlinearTRMSmodel(shown inthe2nd section):
Thestateandoutputvectorsaregivenby:
‐ Centralizedarchitecture
Westartwiththesuccessivederivationsofthe irst output ��,whichmakesthetermofthecommands appearinitsthirdderivative,Thisallowsustoknow itsrelativedegree,���� =3.Theexpressionscontaining thesignfunctionsarenotdifferentiable,sothatthey willbeconsidereddisturbancesandomittedfromthe nonlinearmodelforthesynthesisofthelinearization feedback.ThesynthesismodelisgivenbyEither
CalculationofthesuccessiveLiederivativesyield:
OnecaneasilyverifythatthedeterminantofΔ(x) isdifferentfrom0:
Withtheconditionthatthesumoftherelative degreesofthetwooutputsofthesystemequalto n=6(theorderofthesystem),thecontrolde inedby theequation(2),and(8)globallylinearizingandfully decouplingtheTRMSsystem(nodynamiczeros).
Thelinearsystemthusobtainedisintheformof twodecoupledtripleintegrators,describedby:
Withimplementedcontrolas:
Tostabilizeforthedesiredperformance,linearized statefeedbackbyinput‐outputlinearizationunder thestatedeliveredbytheThauobserverwithinte‐gralactionwillbeappliedtotheauxiliarycommand inputs.
3.3.1.Regulation
1) Linearizedstatefeedback
With:
The ������,or ��=1,…,6,isthestateofthelinearized systemobtainedbyaLuembergerobserverwiththe outputsofthesystemasandtheauxiliarycommands ��1 and ��2 ̂�� ����,or ��=1,….6,isthephysicalstateof thesystemestimatedbytheThauobserverwiththe outputsofthesysteasinputsandthecontrolsignal appliedtothesystems��1 and��2
‐ Forthepitchangledynamicssubsystem,we imposedclosed‐loopdynamicsbasedonthe followingspeci ications:
‐ Depreciation ��=0.53 and ���� =0.777 sas responsetime,and
‐ Twoauxiliarypoles, ��3 =−2 and ��4 =−6;the latterisdedicatedtotheintegralactiontoregulate thedynamicsoftherejectionofdisturbances.
‐ Fortheyaw‐angledynamicssubsystem,weimposed aclosed‐loopdynamicsbasedonthefollowingspec‐i ications:
‐ Depreciation ��=0.56 and ���� =1.0185 sas responsetime,and
‐ Twoauxiliarypoles,��3 =−1.5��������4 =−15;the latterisdedicatedtotheintegralactiontoregulate thedynamicsoftherejectionofdisturbances.
3.3.2.Tracking
Where��(3) ��1 and��(3) ��2 arethethirdderivativesofthe referencetrajectoriesofthepitchangleandtheyaw angle,respectively.
‐ Linearizedstate-feedback
‐ Forthepitch‐angledynamics(pitch)subsystem,we haveimposedaclosed‐loopdynamicsbychoosing thefollowingpoles:
1 =−6,��2 =−10,��3 =−2, and��4 =−8
‐ Fortheyaw‐angledynamicssubsystem(Yaw),we haveimposedaclosed‐loopdynamicsbychoosing thefollowingpoles:
��1 =−5,��2 =−15,��3 =−10, and��4 =−10.
3.3.3.ApplicationoftheThauobserver
Knowingthatinput‐outputlinearizationbystate loopingrequiresknowledgeofallthestatesofthe systemandthatinthecaseoftheTRMS,thisis notentirelyaccessible–thesynthesisofnonlinear stateobserversisimposed.Ourchoiceisdirected towardstheThauobserver,whichisconsideredan exponentialobserver,thiswillfacilitatetheestablish‐mentofthestabilityoftheglobalclosed‐loopscheme, somethingthatisfarfromeasywithanasymptotic observer.Inaddition,itissimpletoimplementand, effective.Aboveall,thenonlinearmodelofoursystem isputintheappropriateformforsynthesisbysuchan observer.
WeassumethattheperformanceoftheTRMSsen‐sorsisacceptablebecauseTRMSisagoodbenchmark forthefeedbacksociety.
TheformoftheThauobserveroftheTRMSis written
(21)
where A, B and C arethematricesofthesystem de inedintheEquations(17),(19)and(21),respec‐tively.
(22)
Inthiscase,theThauobserverisdescribedby:
)+��(��−��̂��) (23) where ��,�� and �� arethematricesgivenpreviously, and��( )isdescribedby:
(24)
Forthelinearpartoftheobserver,weplacethefol‐lowingpoles,whichcanverifythethirdassumption inThautheorem[14]andadjustthedynamicsofthe estimation:
PO =[−30;−29.5258;−0.0984;−0.6983; −2.6028;−0.4742].
Thiswillbeusedtocalculatethegain L ofthe observerbyamultivariablestatefeedbackcalcula‐tiontechniqueappliedtothedualsystemthroughthe matrices���� and����.Theinstruction“place”isusedin matlabtocalculatethegainofestimation L.
3.3.4.Analysisofthestabilityoftheglobaldiagramof theclosedloop
Thankstothenonlinearseparationprinciple investigatedbyVidyasagar[18],itispossibletoapply thisprinciple,termedweakenedseparationprinci‐ple[19],todeducethestabilityofaglobalscheme ofanonlinearcontrolinaclosedloopinthepresence ofanobserverwithexponentialconvergenceinthis loop,inparticularifthecontrolisexponentiallystabi‐lizing[17].Thisisthecaseresultingfromcontrolby linearizinginput/outputloopprovidedwithanauxil‐iarycontrolstabilizingbyfeedbackofstate.
Considerthenonlinearsystemde inedbythe equation ̇��=�� (��)+��(��)�� ��=��(��)
Then,theseparationprinciplecanbeappliedifand onlyif��(��)isbounded.Itcanthereforebeconsidered tobeadisturbanceforthesystem,andobserver‐based controlcanensuretheinternalstabilityofthesystem andtherewillbenoexplosionofthestateofthesys‐tem[20].
Letbethenonlinearsystemgiveninthe2nd sec‐tion.Ifthefollowinghypotheseshold:
‐ Thesynthesizedobserverisglobally,uniformlyand exponentiallystableobservationerror.
‐ Thereisacontrollawsuchthatthesystemwithout anobserverisgloballyandexponentiallystable. Then,theloopedsystemviaobserverisglobally andexponentiallystable[17].
Wenotethatthecontrolbythelinearizing input/outputloopprovidedwithastabilizingauxil‐iarycontrolbyreturnofloopedstatewithaThau obserververi iesthehypothesesgivenabove.Wecan thendeducethatglobalstabilityintheclosedloopis assured.
4.Simulation
Inthispartwewillapplythecommandtothe nonlinearmodelpresentedinsection2usingMatlab (solverode45):
‐ Regulation: Theinputforthisexperimentisastep signal,TheobtainedresultsarepresentedinFig‐ures2and4
‐ Figures3and5showanenlargedviewofthe irst5 secondsfromthecontrolsignals.
Inthe irstmodeofregulation(Figures 3 and 4), wenotethatthetransientstateisexcellentwithout overshoot,andhasameansquareerroroforder10‐4. Thecontrolsignalwasalsoexcellent;notethatthere arepeaksinthe irstfractionsofasecondinFigures3 and 5,whichisatypicalphenomenonofcontrolby feedbacklinearization.inpractice,theactuatordoes notevennoticebecausetheproblemisquicklycor‐rectedbythecorrector,andwethennoticeasignal freeofpeaksandnotnoisy,visiblefrombothangles.
‐ Trajectorytracking
Inthesecondsimulation,themodelisexcitedby asinusoidalinput.Theobtainedresultsarepresented inFigures6and7.
Figure2. Pitchanglecontrolbylinearizingcontrolin simulation
Figure3. Anenlargedviewofthefirst5secondsof Figure 2
Figure4. Yawanglecontrolbylinearizingcontrolin simulation
Figure5. Anenlargedviewofthefirst5secondsof Figure 4
Figure6. Trajectorytrackingforthepitchangle controlledbythelinearizingcontrolinsimulation
Figure7. Trajectorytrackingforyawanglecontrolledby linearizingcontrolinsimulation
Table2. Regulationerrorvalues
Feedback-lin
M‐Aoferror Pitch MAE =0.0100 Yaw MAE =0.0060
M‐Soferror Pitch MSE =6.6811e−04 Yaw MSE =4.4122e−04
Table3. Trackingerrorvalues
Feedback-lin
MA oferror Pitch MAE =0.0066 Yaw MAE =0.0023
MS oferror Pitch MSE =5.7529e−05 Yaw MSE =7.0992e−06
Thisistotestitsperformanceintrajectorytrack‐ing.Thissinusoidalsignalischaracterizedby:
‐ Forthepitch:amplitude:0.4,frequency:0.2,cen‐teredat0.2
‐ Foryaw:amplitude:0.8,frequency:0.2,centeredat 0.
ForthesecondmodeinFigures 6 and 7 –trajec‐torytracking–wenoticedatrackingerrortrending towardszero.Giventhatthesetpointcurveisexactly thesameastheresponsecurve,wecanhardlydif‐ferentiatethem;withanoptimalcontrolsignaland withoutnoise,itissuitablefortheactuatorswhile respectingthespeci icationsmentionedabove.
Belowaretwotablescontainingthequadratic errorandtheabsoluteerrorbetweenthesetpointand theresponseforthetwomodes.
Inthesimulation,weseethatthiscontrollerhas provenitseffectivenessonthissystem,althoughit iscomplexanddif iculttoimplementcomparedto
thelinearmethods.Infeedbacklinearizationcontrol, dif icultiesarisefromthecascadeoftwolawsofcon‐trol:theinnercontrol,whichlinearizesthesystemand dependsonthephysicalstateoftheofthesystem, andtheouterorauxiliarycontrol,whichstabilizesand providesperformanceintheclosedloop.Thiscontrol dependsonthemathematical(linearized)state;ifthe innercontrolfails,theoutercontrolcan’tstabilizeand givesatisfactoryperformanceintheclosedloop.
Thelimitationsofthisschemeare:
‐ Non‐robustness,becauseofthenaivetyofthiscom‐mandwhichisentirelybasedonthemathematical modelofthesystem.
‐ Instabilityofthedynamicsofzeros.
‐ Inapplicabilitytothenon‐linearizableclassofnon‐linearsystems.
Byapplyingthismethod,wenotonlyobtained thestabilityofthesystem,butalsotheperformances, whichwereveryexcellentinaccordancewiththe speci ications.
ExperimentalResults
Inthissubsection,wewillimplementthecontrol lawsdirectlyintherealsystemtoverifytheirrobust‐nessandef iciencyinarealapplication.
Noteatthebeginningthattheapplicationofthis nonlinearcontrolontheTRMSallowedustorunthe experimentsfromanyinitialsetofconditionsaslong astheybelongedtothebasinofattractionofthesys‐tem;thestabilityofthesystemwaspreserved,andthe performancesweresimilar.
WenotefromtheresultsobtainedinFigures 8 and 9 thatwecouldnotobtainsatisfactoryresults inthepursuit,andwewerethereforesatis iedwith theregulation.Thesameinputusedinthesimulation hasbeeninsertedintothesystem.Weappliedastep disturbanceoneachangletocheckitsperformance aswellasitsrobustnessindisturbancerejection.This disturbancewasappliedatthe50th second.
Figure8. DiagramoftheTRMS
Figure9. Pitchcontrolbylinearizingcontrolin experiment
Figure10. Experimentalyawcontrolusingthefeedback linearizingcontrol
WenoteinFigures9and10presentedabovethe resultsfortheregulationarequitesatisfactory,prov‐ingthestabilityofthesystem.
Theauxiliarycontrolleralsodiditsjobbyachiev‐ingtheperformancerequiredinthespeci ications.For example,wementionthattheresponsetimeisless than4secondsfortheyawangle,withanovershoot oflessthan10%,andforthepitchangle,theresponse timeis3secondswithanovershootof0%.
Wealsonotetherobustnessofthecontrolscheme intermsofrejectionofdisturbancesand,inparticu‐lar,performance.Intermsofspeedofrejection,itis approximately3seconds,withasmallovershootfor thetwoanglesandaclearperformancefortheyaw angle.Elsewhere,thesteadystateerrorisalmostzero, thusimprovingaccuracy.
5.Conclusion
Inthispaper,anonlinearcontrolbasedonglobal linearizationandstabilizationoftheclosed‐loopsys‐temwasdevelopedandappliedtoTRMS.Thisstrategy requiresaccessibilitytoallstatesofthesystem,which isnotpossibleinthecaseofTRMSbecausethisplat‐formhasonlytwosensorsthatmeasurepitchandyaw angles.Thismeansanobserverisrequiredinorder toimplementthiscontrol.Wehavechosenanonlin‐earobservertheThauobserver,foritssimplicityand ef iciency.Thishasbeenprovenbythesatisfactory
resultsobtainedinregulation.Alinear‐statefeedback systemwasusedasanauxiliarycontrolinorderto stabilizethesystemandobtaintherequiredperfor‐mance.
Itisconcludedthatthiscontrolyieldedexcellent resultsforthetwoobjectives:regulationandenslave‐ment.Theseresultswerequitesatisfactoryinreal timeforstabilityandregulation.Fortracking,however itneedstoberobusttoreinforcestability,improve performanceinregulation,andsucceedinpursuit. Thiswillbethemainmotivationforthenextwork. Innonlinearcontrol,toimplementanef icienttrack‐ingscheme,thecontrolshouldberobustbecausethe exactparametersusedinthemathematicalmodelof thesystemarenotknown.Themainmotivationfor futureworkistodeveloprobustfeedbacklineariza‐tion.
AUTHORS
AbderrahmaneKacimi –ResearchAssociateatUni‐versityofOran,InstituteofIndustrialSecurityMain‐tenance,Algeria,e‐mail:kdjoujou@yahoo.fr.
AbderrahmaneSenoussaoui∗ –Universityof MascaraMustaphaStambouli,Algeria,e‐mail: sabdorrahmene@gmail.com.
∗Correspondingauthor
References
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Submitted:8th May2024;accepted:9th June2025
IhorBuratynskyi,ArturZaporozhets
DOI:10.14313/jamris‐2025‐027
Abstract:
Thispaperpresentsanoptimizationmodelfordetermin‐ingthenominalcapacityofanenergystoragesystem thattransfersexcessamountsofelectricalenergyfrom solarpowerplantsaspartofagroupofdistributed generationpowerplants,basedonthecriterionofthe minimumcostofsupplyingelectricitytoendconsumers. Theuseofthedevelopedoptimizationmodelallowsone todeterminetheoptimalparametersoftheenergystor‐agesystemtoachieveaneconomicbalancebetween theexcessamountsofelectricenergyofsolarpower plantsthataretransferredandthenumberofrestrictions oninvertersthataresubjecttopayment.Basedonthe developedmethodandontheforecastlevelofelectric energyconsumptionandstatisticaldataonthelevel ofelectricenergyproductionatwindandsolarpower plantsfortheterritoryofUkraine,theinstalledcapacity ofthewind,solar,reservepowerplant,andthenominal capacityofthetwo‐hourenergystoragesystemwere determined,whichwillprovidetheminimumlevelized costofenergyofsupplyingtoconsumersduringtheentire periodofcommercialoperationofagroupofdistributed generationpowerplants.
Keywords: optimizationmodel,distributedgeneration, solarpowerplant,windpowerplant,backuppower plant,energystoragesystem
1.Introduction
TheLawofUkraine“OntheElectricEnergyMar‐ket”[1]de inespowerplantswithaninstalledcapac‐ityof20MWandbelowasbelongingtodistributed generation,whilethestatepolicyinthe ieldofelectric powershouldpromotetheintroductionofnewcapaci‐tiesofdistributedgenerationpowerplantsandenergy storagesystem.TheLawofUkraine“OnAlternative EnergySources”[2](amendedNo.3220‐IX,dated 30.06.2023)stipulatesthattheCabinetofMinistersof Ukrainemustapproveastateprogramtostimulatethe developmentofdistributedgeneration,speci icallyfor thosetypesofpowerplantsthatproduceelectrical energyfromalternativeenergysourcesandenergy storagefacilities,includingthoseinstalledatcritical infrastructurefacilitiestoincreasethereliabilityofthe electricitysupplytoconsumers.
Distributedgeneration,whichisusuallyconnected tothenetworksofthedistributionsystemoperator, hassomeadvantagesovercentralizedpowerplants ofmuchhighercapacity.Themainadvantagesofthe decentralizationofgeneratingcapacitieswiththedis‐persaloflesspowerfulpowerplantsinpowernodes aretheimprovementofthesecurityofthesupplyof electricalenergytoconsumers,ensuringtheappro‐priatelevelofoperationalsecurityevenintheevent ofsystemaccidentsinthepowersystem,reductionof lossesinpowertransmissionlines,andtheconver‐genceoffacilitiesthatproduceelectricitywithfacili‐tiesthatconsumeit.Inaddition,intheabsenceofan electricalconnectionwiththepowersystem,inpartic‐ular,intheeventofanemergencyinthepowersystem, mostmodernpowerplantsofdistributedgeneration canparticipateinthepowerislandmodeofoperation andperformautonomousstart‐ups,providingaser‐viceforrestoringtheoperationofthepowersystem aftertheoccurrenceofsystemaccidents.Atthesame time,followingtheprovisionsoftheTransmission SystemCode,technicalrequirementsforautonomous start‐upandparticipationintheislandmodeofoper‐ationaremandatoryforgeneratingunitswithan installedcapacityof20MWandabove[3].
Powerplantsofdistributedgenerationthatgen‐erateelectricalenergyfromalternativesourcesof energy,includingwindandsolarpowerplants,are superiortoothers,andthereisnoneedtosupplythe fuelfortheiroperation.Thisallowsforsigni icantly loweroperationalcostsequaltothoseofothertypesof powerplants.Inthiscase,accordingtotheresearchof thetransmissionsystemoperator[4],theimplemen‐tationofnewfunctionsofwindandsolarpowerplants mustbeaccompaniedbyincreasedmaneuveringpres‐suresandenergystoragesystems.
Accordingtothestatisticaldataofthetransmis‐sionsystemoperator[4]fortheterritoryofUkraine, theaverageannualcapacityfactorofwindpower plantsis36percent,which,withthesameinstalled power,willprovidegreatervolumesofelectricity production,unlikesolarpowerplants,forwhichthe capacityfactoris14percent.Theadvantageofsolar andwindpowerplantsisthattheyaresubjectto betterscalingduetothelowpowerofthepower‐generatingequipment(whichincludephotovoltaic modulesandconversioninverters);therelativeease ofimplementationofthistechnology;andtheabsence ofnoiseduringoperation.
Theinstalledcapacityofsolarpowerplantscan varyfromtensofkilowattstotensofmegawatts, dependingontheinstalledcapacityandthenumber ofconvertinginverters.
Toensurethereliabilityoftheelectricitysupply toconsumers,includingintheeventofanemergency, individualpowerplantswithasigni icantshareof windandsolarpowerplantsmusthavebackuppower plants,whichcanbemaneuverablegasturbineunits, gaspistons,ordieselgenerators.Atthesametime,the maximumpossiblenumberofhoursofoperationof thestandbypowerplantduringthedayisdetermined basedonthetechnicalcapabilitiesofthepowerplant, namely,thespeedofincreasing/decreasingpower, andthepossibilityoffrequentstops.Itstartsduring theday,withspeci icfuelconsumption.Theselection ofthecompositionofpowerplantsforimplementa‐tioniscarriedoutbyachievingabalanceofelectri‐calenergybetweenthedailyvolumeofconsumption andproduction,takingintoaccountlossesinpower transmissionlines.Thepro itabilityassessmentofthe implementationofnewpowerplantsiscarriedout basedoncapitalinvestmentcostsduringimplemen‐tation,constructioncosts,operatingcostsduringthe furthercommercialoperationofpowerplants,which consistofconditional ixedandconditionalvariable costs,andfuelcosts.
2.ProblemStatement
Implementationofenergystoragesystemsand implementationofdemandmanagementisagener‐allyacceptedapproachusedtoincreasetheshareof renewableenergysourceswithanunstablelevelof generationthatdependsonweatherconditionsindis‐tributionnetworks[5].Optimizingtheparametersof theenergystoragesystem,namely,itsnominalcapac‐ityandenergyintensity,functioningaspartofthe solarpowerplantasanoption,canbecarriedout throughthecomprehensiveoptimizationofeconomic indicators,inparticular,theinternalrateofreturn (IRR),netpresentvalue(NPV),andtheinvestment paybackperiod[6].
Inastudy[7]oftheoptimallocationofenergy storagesystemsinelectricenergynodesofthedis‐tributionsystem,the lowsofelectricenergyfrom hydroelectric,thermal,solar,andwindpowerplants weretakenintoaccount.Theobjectivefunctionof themodelistheminimizationofthecomponentcost ofelectricityproductionatpowerplants,thecostof unsuppliedelectricity,andthecostofstoringelectric‐ity,plusthepriceofcharginganddischarging.Itwas determinedthattheintroductionofenergystorage systemsensuresthereliabilityofelectricitysupplyto consumers,increasesthevoltagelevel,andallowsfor theminimizationofthecostsofelectricityproduction duetothepossibilityofincreasingtheshareofcapac‐ityofrenewableenergysources.
Studiesconducted[8]basedontheoptimization modelfordeterminingtheenergyintensityofthe introductionofanenergystoragesysteminthedis‐tributionnetworkofSaudiArabiatotransferelectric energyovertimeshowedthattakingintoaccount thecostoftransformersubstationsandpowertrans‐missionlinesthatmustbeimplemented,theeco‐nomicfeasibilityofimplementingstoragefacilitiesis achievedwhenreducingtheircapitalinvestmentcost byatleast ivetimes.
Theuseofstatisticaldataonthelevelofelectri‐calenergyproductionofrenewableenergysources allowsforhighaccuracyindeterminingtheoptimal capacityfornewimplementationwithoutanexcessive increaseincapitalcostsandwiththeachievementof electricalenergybalance[9].Atthesametime,the evaluationoftheeffectivenessoftheimplementation oftheenergystoragesystemiscarriedoutthroughthe determinationofthelevelizedcostofenergy(LCOE) forthecostofstoredenergy.
Thehourlybalanceofelectricalenergywithinone dayforaseparateenergynodeisprovidedbycharg‐inganddischargingtheenergystoragesystem.The technicalstructureoftheenergystoragesystemis determinedfromthenominalpoweroftheinverter equipmentandtherequirednominalenergycapacity, which,consideringthedepthofpossibledischarge, mustprovidethenecessaryrangeofelectricalenergy availableforcharginganddischarging,andtherange forfrequencyandactivepowerregulation,including inconditionswherethereisautonomousoperation inthepowerislandmodewithoutconnectiontothe powersystem.Foranenergystoragesystem,themain technicalindicatorsareratedpower(kW)andrated energycapacity(kWh).Theratiobetweenthenomi‐nalenergycapacityandpowercharacterizesthetime duringwhichtheenergystoragesystemcanrelease previouslystoredelectricalenergyintothenetwork.
Takingintoaccountthesigni icantcostofimple‐mentinganenergystoragesystem,itsconstruction withexcesscapacityleadstoanincreaseincapital investmentsand,accordingly,toanincreaseinthe costofsupplyingelectricitytoconsumers.Onthe otherhand,insuf icientcapacityoftheenergystorage systemleadstolimitationsofthelevelofgenerat‐ingcapacities,whichalsoincreasesthecostofelec‐tricityfortheendconsumerduetothedecreasein thevolumeofusefulelectricitysupply.Inaddition,if distributedgenerationpowerplantsareusedatfull capacity,theenergystoragesystemmustensurethe availabilityofreserveenergycapacitynecessaryfor frequencyregulationandactivepower,includingfor theoperationofdistributedgenerationpowerplants inenergyislandconditions.
Thepurposeofthisworkistodevelopanopti‐mizationmodelfordeterminingthenominalcapac‐ityofanenergystoragesystemthatcarriesoutthe transferofexcessamountsofelectricalenergyfrom solarpowerplantsaspartofagroupofdistributed generationpowerplantsaccordingtothecriterionof theminimumLCOEofsupplyingtoconsumersduring theentireperiodofcommercialoperationofagroup ofdistributedgenerationpowerplants.
3.Methodology
Thewell‐knownmethodologyfordeterminingthe LCOE[10]wasadoptedasthebasisforresearchingthe pro itabilityofimplementationandfurthereconomic functioningofpowerplants,accordingtowhichthe ratioofdiscountedcapitalinvestmentcosts(CAPEX) andoperatingcostsisfound(OPEX)tothediscounted volumeofelectricityproductionduringtheentirelife cycleofthepowerplant.
ItisadvisabletousetheLCOEmethodologyto assesstheinvestmentattractivenessoftheintroduc‐tionofnewpowerplantsoperatinginmarketcon‐ditions,asdiscountingmakesitpossibletoestimate thevalueofinvestedfundsinfutureperiods.When calculatingtheLCOEforwindandsolarpowerplants, itischaracteristicthatonly ixedcostsforoperation andmaintenance(O&M)ofequipmentaretakeninto accountinOPEX,sincesuchpowerplantsdonotneed fuel.Forastandbypowerplant,inadditionto ixed costs,OPEXalsoincludesvariablecoststhatdepend onthevolumeofelectricityproductionandfuelcost, whichdependsonthecostofpurchasingfuel(e.g., naturalgas).
Thewell‐knownmethodologyfordeterminingthe levelizedcostofstorage(LCOS)[11]wasadoptedas thebasisforconductingastudyonthepro itabilityof theimplementationandfurthereconomicfunctioning oftheenergystoragesystem,accordingtowhichthe ratioofdiscountedcapitalinvestmentcosts(CAPEX) andoperatingcosts(OPEX)tothediscountedvol‐umesofelectricalenergystorageduringtheentirelife cycleoftheinstallation.Foranenergystoragesystem, OPEXincludes ixedO&Mcosts.Atthesametime,to reducetheamountofcontingentand ixedcosts,it isadvisabletogenerateincomefromthemarketof auxiliaryservicesfortheprovisionoffrequencyand activepowerregulationservices.
TheLCOEmethodologyforthedevelopmentof anoptimizationmodelforminimizingtheweighted averagedailycostofelectricityproductionforasolar powerplantwasusedtodeterminetheoptimalratio oftheinstalleddirectcurrent(DC)powerofpho‐tovoltaicmodulesandalternatingcurrent(AC)of inverterequipmentbasedonthelevelofsolarradia‐tionintensity[12].Theoptimizationmodelformin‐imizingthelevelizeddailycostofenergyproduction wasdevelopedwiththeintroductionintothestruc‐tureofthesolarpowerplantanenergystoragefacility fortheaccumulationofexcesselectricalenergythat occurswhenthesetDCpowerisincreasedoverthe setACpower(i.e.,DC/ACoverloading)[13].
Theobjectivefunctionoftheoptimizationmodel istominimizetheLCOEofsupplyingtoconsumers (LCOES)duringtheentireperiodofcommercialoper‐ationofagroupofdistributedgenerationpower plants,
(1) where LCOES isthelevelizedcostofenergyof supplying(€/MWh); LCOE isthelevelizedcostof energy(€/MWh); LCOS isthelevelizedcostofstorage (€/MWh); W�������� isthevolumeofelectricityproduc‐tionatthewindpowerplantduringtheyear(MWh); W���� isthevolumeofelectricityproductionatthe solarpowerplantduringtheyear(MWh); W������ is thevolumeofelectricityproductionatthereserve powerplantduringtheyear(MWh);and W�������� is thevolumeofelectricalenergystorageinthebattery energystoragesystem(BESS)duringtheyear(MWh).
InadditiontotheLCOE,theLCOESalsotakesinto accountthepartoftheelectricitythatisstoredinan energystoragesystem,soLCOSistakenintoaccount.
Foragroupofpowerplantsofdistributedgenera‐tion(wind,solar,andreservepowerplants),theLCOE isdeterminedrelativetotheshareofthevolumeof releasedelectricalenergyforeachindividualpower plant,
(2)
where L�������� istheLCOEatawindpowerplant (€/MWh); L���� istheLCOEatasolarpowerplant (€/MWh); L������ istheLCOEatareservepowerplant (€/MWh); L�������� istheLCOEofcurtailmentatasolar powerplant(€/MWh);and W�������� isthevolumeof curtailmentatthesolarpowerplantduringtheyear (MWh).
Theproposedde initionofLCOEforagroupofdis‐tributedgenerationpowerplantsconsidersthecostof curtailmentatasolarpowerplant,whichisdifferent fromthecostofgeneratingelectricityatasolarpower plant.Thevolumeofcurtailmentatthesolarpower thatispartofadistributedgenerationgroupduring theyeararedeterminedtobethedifferencebetween excesselectricenergyandthedailystoragevolume usinganenergystoragesystem,
where D isnumberofdays d duringtheyear; W�� ������ isthedailyvolumeofexcesselectricalenergy(MWh); and W�� �������� isthedailystoragevolumeattheenergy storagesystem(MWh).
Surpluselectricitygeneratedduringthedayis determinedbythedifferencebetweenproductionand consumptionvolume,
where W�������� �� isthedailyvolumeofelectricityproduc‐tionatthewindpowerplant(MWh); W�� ���� isthedaily volumeofelectricityproductionatthesolarpower plant(MWh); W�� ������ isthedailyvolumeofelectricity productionatthereservepowerplant(MWh);and W�� �������� isthedailyamountofelectricityconsump‐tion,takingintoaccountlossesinpowertransmission lines(MWh).
Thedailystoragevolumeattheenergystorage systemisdeterminedfromthecondition,
Toensureproperprojectfunctioningoftheenergy storagesystem,whenimplementingthefacilityand calculatingcapitalinvestments,itisadvisabletotake intoaccounttheincreaseintheusefulenergycapacity ofchargingtheenergystoragesystembyafraction thatincludesthepossibledepthofdischargeofthe batteries,
where C�������� isthenominalenergycapacityofthe energystoragesystem(MWh)and�������� isthedepth ofdischargeoftheenergystoragesystem.
where C����������ℎ���� isusefulenergycapacityofcharging attheenergystoragesystem(MWh).
MinimizationoftheLCOESisdeterminedby achievingabalancebetweenthemaximumvalueof excesselectricalenergyandthetimeduringwhich theenergystoragesystemwilloperateatmaximum capacityduringtheday,
where x�� isthevariablecharacterizingthetimeduring whichtheenergystoragesystemwilloperateatmax‐imumcapacityduringtheday.
Constraintsareintroducedintotheoptimization modelbecausethenominalcapacityoftheenergy storagesystemshouldnotbelessthanthesmallest installedcapacityofthewindorsolarpowerplantand shouldnotbegreaterthanthetotalinstalledcapacity ofthewindandsolarpowerplant.Theminimumlimit wasintroducedsothatthecapacityoftheenergystor‐agesystemwassuf icienttocompensateforthepower levelofthepowerplantthatwassuddenlyoutoforder, forexample,becauseofanemergencyshutdownwhen thebackuppowerplantdidnothavetimetogain therequiredpower.Themaximumlimitisintroduced sothatthecapacityoftheenergystoragesystemis suf icienttoabsorbthetotalamountofelectricity producedbythewindandsolarpowerplantsinthe eventofasharpdecreaseinthelevelofelectricitycon‐sumption,forexample,intheeventofanaccidenton apowertransmissionline.Thus,thenominalcapacity oftheenergystoragesystem,expressedthroughthe ratiooftheusefulenergycapacityofchargingtothe nominalnumberofhoursofoperationoftheenergy storagesystem,islimitedto
(7)
where P�������� istheinstalledcapacityofthewind powerplant(MW); P���� istheinstalledcapacityofthe solarpowerplant(MW); P�������� isthenominalcapacity oftheenergystoragesystem(MW);and H�������� isthe nominalnumberofhoursofoperationoftheenergy storagesystemduringtheday.
4.InputDataandModelingResults
Thedailydistributionofelectricenergyconsump‐tionisbasedontheactualstatisticaldataonthe electricloadscheduleandthelevelofelectricenergy productionatwindandsolarpowerplantsintheIPS ofUkrainefortheyear2020[14].Theelectricload scheduleisadjustedtotheconsumptioncapacityof localconsumersofthelocalenergyhub.Themaxi‐mumdailyamountofelectricityconsumptionduring theyearatthelevelof96.0MWh(averageelectricity consumptionof4MWhduringeachhouroftheday) wasrecordedonDecember10;theminimumamount ofelectricityconsumptionduringtheyearatthelevel of57.2MWh(averageelectricityconsumptionof2.4 MWhduringeachhouroftheday)wasrecorded onJune7.Accordingtothestatisticaldata,thetotal amountofelectricityproductionrequiredtoprovide electricitytoconsumersatthelocalenergyhub,taking intoaccountthelossesinthepowertransmissionlines fortheyear,wasdeterminedtobe26,727.2MWh.
Theinstalledcapacityofthewindpowerplant waschosenbasedontheanalysisofstatisticaldata, accordingtowhichthemaximumpowerofgenerating electricityatthewindpowerplantduringanyday oftheyearshouldnotexceedtheminimumlevelof electricityconsumptionofthelocalenergynode.The installedcapacityofthesolarpowerplantwaschosen basedonthearithmeticmeanvalueofcoveringdaily amountsofelectricalenergyconsumption;therefore, withasigni icantintensityofsolarradiation,excess electricalenergywillbegenerated,whichispartially transferredovertimewiththehelpofanenergystor‐agesystem.Theoperationalgorithmoftheenergy storagesystemconsistsincarryingoutonecomplete cycleofcharging(withsigni icantintensityofsolar radiationduringtheafternoonhours)anddischarging (withthemaximumlevelofconsumptionduringthe eveningpeak)ofbatterieswithinoneday.Iftheuseful energycapacityoftheenergystoragesystemisinsuf‐icient,theexcesselectricalenergyofthesolarpower plantislimitedtoinverters(i.e.,theelectricalenergy producedisnotreleasedintothenetwork).During periodsoftimewhenthereisfreeenergycapacityof theenergystoragesystem,itisusedtoprovideaux‐iliaryservicesforautomaticregulationoffrequency andactivepower.
Thedailymodeltakesintoaccountthefactthatin theabsenceofasuf icientlevelofelectricityproduc‐tionatthewindandsolarpowerplanttocovercon‐sumptionneeds,agasturbinepowerplantisstarted, whichcansetthenominalpowerforaperiodnot exceeding15min.
Todeterminethediscountratethroughthe weightedaveragecostofcapital(WACC)duringthe researchperiod,thefollowingwasadopted:the shareofownedfundsis30.0percent,theshareof borrowedfundsis70.0percent,theincometaxrate is25.0percent,thecostofequityis12.0percent, andthediscountrateoftheNationalBankofUkraine is14.5percent[15](asofMarch15,2024).The calculatedWACC,accordingtothegenerallyaccepted approach,is11.21percent.Inaddition,duringthe researchperiod,thefollowingwasadopted:the termofconstructionofpowerplantsandenergy storagesystemis1year,thetermofcommercial operationis20.0years,theeuro‐to‐UAHexchange rateis41.0,theeuro‐to‐US‐dollarexchangerateis 1.08,andtheshareofconstructioncosts(EPC)is14 percentofCAPEX.Forasolarpowerplant,theannual degradationofphotovoltaicmodulesistakenatthe levelof0.7percent,andtheDC/ACratiois1.3.The costoflimitinggenerationatasolarpowerplantis setat219.5€/MWh,whichisroughlytwicethecost ofelectricityproductionatasolarpowerplant,based ontheassumptionthatthecurtailmentofelectrical energyneedstobepaidfor.
Fortheinstallationofanenergystoragesystem basedonlithium‐ionbatteries,whendeterminingthe nominalenergycapacity,thefollowingisaccepted: conversionef iciencyis98percent;thedepthofpos‐sibledischargeis80percent;andannualdegradation andthecorrespondingdecreaseintheabilitytotrans‐feramountsofelectricalenergyovertimeis3percent. Thecostofprovidingauxiliaryservicesissetatthe levelof22.9€/MWh,basedonashareof70percentof thecurrentmarginalpriceofprovidingauxiliaryser‐vicesforsymmetricprimaryregulationoffrequency andactivepowerinthepowersystem(FCR)[16]. Thedurationoftheprovisionoftheauxiliaryservice istakenatthelevelof12hduringeachday,based onthefreevolumeofenergycapacity,whichintotal duringtheyearisabout50percent.Speci iccapital investments,conditionallypermanentandcondition‐allyvariablefuelcostswereacceptedinUSdollars fromtheLAZARDstudy[17].
Table1showstheinputdatafordistributedgen‐erationpowerplants(wind,solar,andreservepower plants)withaninstalledcapacityof1MW.Foratwo‐hourenergystoragesystem(EES)withanominal capacityof1MW,theusefulenergycapacityofcharg‐ingistakenatthelevelof2MWhand,accordingly,the nominalenergycapacityis2.5MWh.
Theblockofcells“Modelingresults(beforeopti‐mization)”showstheinstalledcapacityofdistributed generationpowerplantsdeterminednecessaryto covertheconsumptionneedsoflocalconsumers.
Table1. Inputdataandmodelingresults
Modelingresults(beforeoptimization)
Modelingresults(afteroptimization)
Beforeoptimizingthepoweroftheenergystorage system,itsenergycapacitywasselectedbasedonthe totalinstalledcapacityofthewindandsolarpower plants,minustheaveragedailypowerconsumption.
Theblockofcells“Modelingresults(afteropti‐mization)”showsthenominalparametersofthe energystoragesystemdeterminedbythedeveloped optimizationmodel,whichwillensuretheminimum levelizedcostofsupplyingenergytoconsumersdur‐ingtheentireperiodofcommercialoperationofa groupofdistributedgenerationpowerplants.
Figure1. Thedailyamountofexcesselectricalenergyof thesolarpowerplant,theamountofelectricalenergy transferusingtheBESSbeforeoptimizationandafter optimizationforMarchandApriloftheyearstudied
Fromthesimulationresultsgiveninthetable, itcanbeseenthattheoptimizationofthenominal capacityofthetwo‐hourenergystoragesystemand, accordingly,itsnominalenergycapacity,providesa reductionintheLCOEofsupplyingelectricitytocon‐sumersduringtheentireperiodofcommercialopera‐tionofagroupofdistributedgenerationpowerplants by8.2percent(from147.9to136.7€/MWh)anda reductionofCAPEXintotalforthepowerplantand energystoragefacilitiesby44.2percent(from38.1to 26.4millioneuros).
Asaresultoftheoptimization,theamountof transferofexcesselectricalenergyofthesolarpower plantwiththeuseoftheenergystoragesystem decreasesfrom24.1percentto9.0percent,and accordingly,theamountoflimitationoninverters increasesfrom2.6percentto17.7percent.Before andafteroptimization,about73.3percentofthetotal amountofelectricityproducedatthesolarpower plantistransmittedtoconsumersatthesametimeas whenitisproduced.
Figure1showsthedailyamountofexcesselectri‐calenergyofthesolarpowerplant,theamountofelec‐tricalenergytransferusingtheenergystoragesystem beforeoptimization(withusefulenergycapacityat thelevelof32MWh)andafteroptimization(with usefulenergycapacityatthelevelof7.8MWh)for MarchandApriloftheyearstudied.
Itcanbeseenfromthe igurethat,becauseofthe optimization,theamountofelectricalenergytrans‐ferredusingtheenergystoragesystemissigni icantly reducedcomparedtotheamountbeforeoptimization. Atthesametime,theoperationoftheenergystorage systematthespeci iedenergycapacityisstabler,with smallerdaily luctuations,whichclearlydemonstrates theincreaseintheutilizationratioofthecapacity factoroftheenergystoragesystem(from31.6percent to48.5percentduringtheyear).
5.Conclusion
Whileensuringthestabilityofelectricitysupply toconsumerswiththehelpofdistributedgeneration powerplants(wind,solar,andreservepowerplants), itisnecessarytoimplementanenergystoragesys‐temthatisnecessaryfortransferringexcessamounts ofelectricalenergy.However,compliancewiththe conditionwiththetransferofallexcessamountsof electricalenergyproducedatthesolarpowerplant leadstoanexcessiveincreaseintheenergyintensityof theenergystoragesystem,which,takingintoaccount thecostoftheequipment,leadstoanincreaseincap‐italinvestments.Ontheotherhand,notensuringthe preservationofallexcesselectricalenergyleadstothe limitationofthelevelofgenerationand,accordingly, totheincreaseinthecostofelectricityproductionfor theendconsumer.Theproposedoptimizationmodel fordeterminingthenominalcapacityofenergystor‐agesystemsthattransferexcessamountsofelectrical energyofasolarpowerplantaspartofagroupof distributedgenerationpowerplantsallowsforthe minimizationofthecostofelectricityproductionfor theenduserthroughouttheentireperiodofcom‐mercialoperationofpowerplants.Accordingtothe developedoptimizationmodel,abalanceisachieved betweentheamountoftransferofexcesselectrical energyproducedatthesolarpowerplantusingthe energystoragefacilityandtheamountofrestriction oninverters.
Basedontheresultsoftheresearch,itwasdeter‐minedthatfortheterritoryofUkraine,ensuringthe maximumdailylevelofelectricityconsumptionatthe levelof96MWh(withanaverageelectricityconsump‐tionof4MWhduringeachhouroftheday)isachieved byimplementingawindpowerplantwithaninstalled capacityofatleast3.6MW,aninstalledcapacityof thereservepowerplantof3.7MW,andaninstalled capacityofthesolarpowerplantof14MW.Atthe sametime,basedontheoptimizationmodel,itwas determinedthatthenominalcapacityofthetwo‐hour energystoragesystemshouldbeatleast3.9MW,with ausefulchargingenergycapacityof7.8MWhanda nominalenergycapacityof9.7MWh.Thedetermined parametersoftheenergystoragesystemwillensure thetransferovertimeofabout9.0percentofthe totalamountofelectricalenergyproducedatthesolar powerplantandatthesametime,theamountoflim‐itationofexcesselectricalenergyatthesolarpower plantwillbeabout17.7percent.
AUTHORS
IhorBuratynskyi –GeneralEnergyInstitute ofNASofUkraine,Ukraine,e‐mail:buratyn‐skyi@ienergy.kiev.ua.
ArturZaporozhets∗ –GeneralEnergy InstituteofNASofUkraine,Ukraine,e‐mail: A.O.Zaporozhets@nas.gov.ua.
∗Correspondingauthor
ACKNOWLEDGEMENTS
Thisworkwassupportedbytheproject“Studyof theoperationofdistributedgenerationobjectswith energystoragesystemsbasedonmeteorologicaldata” (0124U002308,2024‐2025),whichis inancedbythe NationalAcademyofScienceofUkraine.
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Submitted:28th February2025;accepted:13th May2025
MichałKowalik,ErwinRogoża,AleksyFigurski,MateuszPapis
DOI:10.14313/jamris‐2025‐028
Abstract:
Thisstudypresentsthedevelopmentandkinematiceval‐uationofacompliantartificialkneejointprototypefab‐ricatedusingmulti‐material3Dprinting.Thedesigninte‐gratesarolling‐contactcompliantmechanism—derived fromtheCOREandD‐COREconcepts—intoaprosthetic kneeconstruction,aimingtoreplicatebiologicaljoint behaviorwhilereducingweight,mechanicalcomplexity, andfriction.Theprototypeunderwentiterativerefine‐ment,includinggeometricmodifications,materialselec‐tionforflexurebands,andstructuralasymmetrytomiti‐gateoverextensionandincreasedurability.Theresulting jointexhibitedhybridkinematiccharacteristics,blend‐ingfeaturesofbothsingle‐axisandpolycentricknee mechanisms,andachievedafunctionalflexionrange ofapproximately142degrees.Initialcyclictestscon‐firmedsatisfactorystiffnessandshaperecoveryofflexure bandswithoptimizeddimensions,althoughlong‐term fatigueperformanceremainsachallenge.Abasicspring‐dampersystemwasalsointegrated,potentiallyaligning theprototypewithK‐1/K‐2prostheticclassification.How‐ever,fullvalidationrequiresfurthermechanicaltesting inaccordancewithISO10328standards,aswellasopti‐mizationofthedampingsystemforcommercialviability. Thisresearchdemonstratesthefeasibilityandpotential ofcompliantmechanismsinlower‐limbprostheticswhile identifyingcriticalareasforfuturedevelopment.
Keywords: compliantmechanisms,prostheticlimbs, kneejointprosthetic,3Dprinting
1.Introduction
Compliantmechanismsrepresent lexibledevices withvariablestiffnessthatgaintheirmobility throughdeformation[1, 2].Compliantmechanisms aremechanicalsystemsthatachievemotionthrough theelasticdeformationof lexiblecomponents, ratherthanthroughtraditionalrigid‐bodyjoints. Thisfundamentaldifferenceenablesthecreation oflightweight,monolithicstructureswithreduced partcount,whichinturnminimizesfriction,wear, andtheneedforlubrication.Theseadvantages makecompliantdesignsparticularlyappealing inhigh‐precisionandbiomedicalapplications, wheresimplicity,reliability,andcompactnessare critical.Incontrasttoconventionalrigidjoints— typicallycomposedofmultiplehardmaterials, suchassteelortitanium,interactingthrough friction‐proneinterfaces—compliantjointsoperate
throughcontrolledmaterialdeformation.Whilethis resultsinquieterandlower‐maintenancedevices,it introduceschallengessuchaslimitedfatiguelifeand susceptibilitytooverextensionormaterialfailure. Carefulmaterialselectionandstructuraloptimization arethereforeessentialforensuringthatcompliant mechanismsmeetthemechanicalperformance standardsrequiredindemandingapplications,such asprecisionmechanics,biomedicalengineering,and robotics[2].
Astandardrotationalrigidjointtypicallycon‐sistsofthreeprimaryelements:Twobodiesthat areconnectedbyashaft.Eachoftheseelementsis fabricatedfromrigidanddurablematerialssuchas steel,aluminum,titanium,orbronze,chosenfortheir highstrengthanddurability.Theinteractionbetween thesecomponentsgeneratesfriction,whichcanlead toheatbuildup,wear,andeventualfailureifnotprop‐erlymanaged.Tomitigatefrictionandextendthe lifespanofthesejoints,lubricationsuchasgreaseis appliedregularly.Despitethesemeasures,thenature ofrigidjointsmeansthattheyarestillsusceptibleto mechanicalwearandef iciencylossesovertime.The needforregularmaintenanceandthepotentialfor mechanicalfailurearesigni icantdrawbacksinappli‐cationswherereliabilityandlongevityarecrucial.
Incontrast,acompliantjointiscomposedofa singleelementmadefromaspeci ic lexiblemate‐rial.Thismaterialisengineeredtodeformelastically, accommodatingmotionwithouttheneedformultiple interactingparts.Theabilityofthecompliantelement tobendand lexunderloadiswhatprovidesthejoint’s mobility.However,thisrelianceonmaterialdeforma‐tionalsointroduceslimitations.Therangeofmotion isconstrainedbythematerial’sproperties,andexces‐sivedeformationcanleadtofatigueandfailure.Conse‐quently,whilecompliantjointscanreducecomplexity andeliminatefriction,theyaregenerallylessdurable andhaveashorterfatiguelifecomparedtotheirrigid counterparts.Theselimitationsmustbecarefullycon‐sideredandaddressedinthedesignphasetoensure thatcompliantmechanismsmeettherequiredperfor‐mancestandardsintheirintendedapplications.
Whenconsideringthereplacementofrigidjoints withcompliantmechanisms,itiscrucialtothoroughly understandandmitigatetheweaknessesinherentin compliantdesigns.Rigidbodymechanismsgenerally surpasscompliantmechanismsintermsofdurability andfatiguelife[2].
Anunder‐designedcompliantstructuremay exhibitfragilityandareducedoperationallifespan, whichcanbeproblematicindemandingapplications. Therefore,carefulmaterialselection,design optimization,andthoroughtestingareessential toensurethatcompliantmechanismscanreliably replacerigidjointsinpracticalapplications.This understandingisvitalwhenintegratingcompliant jointsintostructurestraditionallydominatedbyrigid bodyequivalents,particularlyinscenarioswhere reliabilityandlongevityareparamount.
Arti icialprostheticlimbdesignisacontinu‐ouslyevolvingbranchofbiomechanicalengineering, focusedondevelopingprostheticsthatcloselyrepli‐catethemechanicalcharacteristicsofnaturallimbs. Theprimarygoalsofthis ieldaretoprovidecomfort, functionality,andindependencetousersthroughthe developmentofadvancedprostheticdevices.Compli‐antmechanisms,inspiredbythenaturalcompliance foundinbiologicaljoints,offerpromisingpotential inthisregard[3–5].Theincorporationofcompliant mechanismsintoprostheticlimbdesigncouldlead todevicesthatarenotonlylighterbutalsocapable ofmorenaturalandef icientmovement[6, 7].By mimickingthebehaviorofbiologicaljoints,compliant mechanismscouldsigni icantlyenhancetheperfor‐manceanduserexperienceofprostheticlimbs,mark‐ingasubstantialadvancementinthe ield.Compared totypicalprostheses,thereisnoharmfulmovement ofareasofthebodythatarenotnaturallyinvolvedin performingagivenmovementortask[8].Additional advantagesovertraditionalmechanismsincludethe eliminationoftheneedforlubrication,nonoiseor oscillations,andwearcausedbyjointclearances[9].
Advancesinadditivemanufacturingtechnolo‐gieshaveenabledthepreciseproductionofvar‐ioustypesofprosthetics[10, 11]andexoskele‐tons[12].Inparallel,progressincontrolsystems— suchasbrain‐computerinterfaces(BCIs)—shows promiseforenhancinguserinteractionwithpros‐theticdevices[13].Together,thesedevelopments highlightthegrowingconvergenceofmechanical innovationandneurotechnologyinmodernprosthetic design.
Thisstudyinvestigatestheintegrationofacom‐pliantrolling‐contactmechanismintothedesignofan arti icialkneejoint,drawingontheprinciplesofCORE andD‐COREjointarchitectures.Aseriesofproto‐typesweredevelopedusing3Dprinting,withsucces‐siveiterationsaddressingchallengesrelatedto lexure banddurability,rangeofmotion,andoverextension control.Thegoalwastocreateacompliantkneejoint capableofreplicatingthehybridkinematicsofboth single‐axisandpolycentricdesigns,whilelayingthe groundworkforafutureprosthesiswithreducedcom‐plexityandenhancedbiomechanicalperformance.
2.MaterialsandMethods
2.1.BiologicalKneeandArtificialJoints
Thehumankneejointisbuiltoutoffourbones, ive ligamentsandninemuscles.Themotionofthehuman
kneejointisacomplexoperationtobedescribed kinematically[14].However,whendesigningapros‐thetickneejoint,thekinematicsofthebiological kneecanbesimpli ied.Similarapproacheswereuti‐lizedinthekinematicmodellingofotherbiological structures,wheresimpli iedmechanismssuccessfully replicatecomplexmovementswhilepreservingstruc‐tural idelity[15].
Atabasiclevel,thekinematicmotionofthe humankneeisdescribedwiththefemur,tibiabones andcruciate,collateralligaments.Theligamentscre‐aterestraintsforthetibiaandfemur,de iningtheir basicmotionandlimits.Collateralligamentsserveto restrainthetibiafrommovinginasidewaysmotion inreferencetothefemur.Thecruciateligamentslimit theforwardandbackwardmovementsofthetibiain referencetothefemur.Additionally,thepositionsof thecruciateligamentsallowforthetibiaandfemurto constantlymaintaincontactduringthemovementof theknee.Thetibiarotatesaroundthetipofthefemur, whichcanbesimpli iedtoa2Dplaneasageometry consistingoftworadii:R1andR2.Theschemeis presentedinFigure1.
Arti icialprosthetickneejointsarebuilttoemulate thepreviouslymentionedkinematicmodelofabiolog‐icalhumankneejoint.However,somearti icialknee types,likesingle‐axiskneejoints,donotentirelyemu‐latethismodel.Becausesingle‐axiskneejointshave onlyoneaxisofrotation,theyrefertoanextremely simpli iedkneemodelwherethetrajectoryfollows onlyoneradius.Mostwidelydesignedpolycentric kneeshavefouraxesofrotation.
Figure1. 2DSchemeofkneejoint
Thesefouraxesareconnectedinpairswithtwo beamsofvariouslengths.Thisconstructionpresents arigidbodyanaloguetoacruciateligamentsystem. Becausethelengthsofthebeamsaredifferent,the rotationalmovementofthearti icialpolycentricknee canbeportrayedintworadii.
Themechanicalcomplexityofarti icialkneejoints canbeappropriatedtofourK‐levelfunctionality groups[16,17],and[18].K‐1andK‐2leveldevices aremeanttoservepatientswiththebasicneedof movementindoorsandminimumactivityoutdoorson latsurfaces.K‐3andK‐4leveldevicesaredesigned forpatientswithmosthighoutdooractivityinclud‐ingtrainingvarioussports.Asnotedinbothmarked trendsandliterature,K‐1andK‐2levelarti iciallimb constructionsmostusuallyconsistofasimplespring anddampermechanismwherethemovementiscom‐plementedwithastainlesssteelspringandtheexten‐sionofthejointisdampenedwithaviscoelastic material.K‐3andK‐4levelarti iciallimbsareusu‐allydesignedwithahydraulicorpneumaticspring anddampersystem.Thesesystemsallowdamping throughoutthewholecycleofmotionofanarti icial knee.Thisthende inesasmootheroperatingknee, allowingforlongerperiodsofintensewalkingorexer‐cise.
2.2.RollingContactCompliantRevoluteJointMecha‐nism(CORE/D‐CORE)
Theconceptofdesignofthecompliantprosthetic kneejointderivesfromtheCOREandD‐COREcompli‐antrevolutejointdesign[19,20].TheCOREcompliant jointrepresentsapotentialsubstitutetoarigid1DOF pin‐in‐holetypehingemechanism.Apin‐in‐holehinge generatesfrictionandwear.Thekinematicconceptof theCOREisoftwocylindricalbodiescreatingarevo‐lutemotionbyrolling,whichgenerateslesswearand friction.Thetwocylindricalcamsareconnectedwith lexurebandsthatconstrainthefreedomofmovement oftherigidcylindricalbodies,de iningthemovement inaspeci iedway.
Themovementbetweenthecylindricalbodiesof theCOREjointisillustratedinFigure2.Asthelower cylinderrotatesatanangleof��,pointPofthelower cylinderrotatesatanangleof2��.Tomaintaincontact betweenthecylindersandpreventslidingandfriction, additional lexurebandsareused.The lexurebands connectthetwobodiesandrestricttheirmovement. Moreover,the lexurebandsde inetherollingcontact motionbecauseofthejoint’sconstruction.
3.Results
3.1.PrimaryDesignConcept
Theprimarydesignconceptconsistedofamodi‐iedcompliantCOREdesign.Bydefault,thethickness ofthe lexurebandsoftheCOREissmall.Thealter‐ationinvolvedincreasingthethicknessofthe lexure bandswhichresultedinhigherstiffness.Theinitial thicknessofthebandswassetto2mmwhichin assumptioncreatedazeropositionforthejointwhich themechanismreturnedtoafteranykindofrotation.
COREjoint–movementbetweenthe cylindricalbodies
Giventhehigherstiffnessofthebandsincompari‐sontotheD‐CORE,acertaindistancehadtobeset betweentheupperandlowercylinderssothatthe jointwouldnotbecomerigidandlacktheneededrota‐tionalmovement.Thecontactpointsforbothcylin‐dershaven’tbeenaddedyetsincetheprimarydesign wasmeanttotesttherotationalmovementcapabili‐tiesofthejoint.ThemodelispresentedinFigure3
Themodelwasdesignedformulti‐material3D printingtopreventthe lexurebandsfromstickingto thewallsofthecylindricalbodiesduringfabrication. Forthepurposeofnotusingadditionalelementsthe connectionbetweenthe lexurebandsandthecylin‐dricalbodieswasestablishedinthemechanicaldesign bymergingthedoublematerialwallstogetherwhich resultedinthebandsstaying irminthecylindrical bodies.Thematerialofchoiceforthecylindricalcams wasPET‐G ilamentduetoitsdurabilityandlowcost. Forthe lexurebandsPA+GF(Nylonwithinfusedglass iberparticles) ilamentwasusedasitoffersfavorable lexibilityandresistancetodeformationinrelationto stiffness.Speci ically,PA12+GF15—acompositecon‐taining15%glass iberbyweightinapolyamide matrix—wasemployed.Duetothenatureofthismate‐rial,theprintspeedwasreducedtoimproveinterlayer adhesionandminimizethermalwarping.Allparts wereprintedusingastandard0.4mmnozzlewith a0.2mmlayerheight.Compliantcomponentswere printedsolid(100%in ill),withalltoolpathsaligned alongthelengthofthepart.
Aftertheprimarydesignconceptwasmanufac‐tured,thekinematicmechanicalcapabilitiesofthe modelweretested.Thejointwasdeformedtoitsfull extentandthenreleasedtocon irmthatthebands returntotheirinitialposition.Themodelshowed promisingresultsasthereactiontothedeformation ofthenylon lexurebandscon irmedtheassumptions. Theshapeofthebandsdidnotalterandeffortlessly returnedtotheiroriginalform.
Figure2.
Figure4. Modelafterfirststageofmodification–technicaldrawing
However,aftersomecyclesoftesting,thebands showedsignsofpossiblebreakingatthepointswhere theywere ixedtothecylindricalbodies.Theextent ofthedeformationdependingonthethicknessofthe lexurebandshadtobeanalyzed.
3.2.ResultsofTestsandModifications
Anewmodeldesignwasdevelopedfor lexure bandthicknessanalysis.Thedesignmadeitpossible toremoveandattachthe lexurebandstothecylindri‐calbodies.Thegoalwastoestablishanoptimal lexure bandthicknesswhichwascharacterizedbysuitable stiffnessandlonglifespan.Themodelcanbeseenin Figure4.
Therangeofthicknesstobetestedforthenylon bandswasbetween0.5mmand2.5mm.Inadditionto thickness,theimpactofthewidthofthe lexurebands wastested.Thewidthofthetestedbandsrangedfrom 8mmto15mm.
Similartestswereconductedastotheprimary designmodel.Resultsfromthetests(Fig. 5)indi‐catedthatthicknessesrangingfrom1mmto1.5mm exhibitedthemostpromisingcharacteristics‐the jointshowednosignsoffailureafterapproximately 300cyclesandthestiffnesscharacteristicsweresuf‐icientlyreturningthejointtothezeroposition.
Thenumberofcycleswereasatisfactoryresult, consideringthatthicknessof1.5mmto2.5mm showedsignsofbreakingafterapproximately70–100cycles.Elementswiththicknessof0.5mmto1 mmshowedgoodresiliencetobreaking,however,low stiffnessledtoinstabilityofthezeropositionofthe compliantjoint.Thewidthoftheelementsdidnot displayin luenceinbreakingresistance,butelements withwidthsofover10mmdemonstratedgoodresis‐tancetotwistingmovementsofthejoint.Toverify thefatiguestrengthofcompliantcomponents,tests conductedonatestingmachineundercontrolledcon‐ditionsareplannedaspartoffutureresearch.
Thethicker lexurebandsofthemodi iedCORE modeldisplayedsignsofoverbendingwhenrotat‐ingthejointtoanextentofminimum130degrees. Regardingastandardkneeprostheticdevice,themax‐imumangleofrotationisde inedas142degrees. Overextensionof lexurebandscouldleadtoalowlife cycleofsuchacompliantjoint,thusfurtheradjust‐mentsweremade.
Toreducetheextentofdeformationofthe lex‐urebands,thepositionofthecylindricalbodieswas changedfromsymmetrictoasymmetric—thelower cylinderanditsverticalaxispositionswereshifted upto15mmfromtheuppercylinder’sverticalaxis. Theshiftvalueof15mmwasdeterminedbasedon experimentaltesting.Thisasymmetricalarrangement createdtwomovementcharacteristicsforthe lexure bands,shortandlong.Thelongmovementdeforms the lexurebandsmorethanthepreviousmodeland createsalargerangleofoverextension.Incontrast, theshortmovementcharacteristicdeformsthe lex‐urebandsless,preventingoverextension.Becausethe movementofaprosthetickneejointisonesided,the sidethatcharacterizesinalargerdeformationofthe bandswasconsideredasthefrontofthejoint.Amod‐i icationwasmadetothemodeltorestrictitsforward movement.
Theasymmetriccon igurationofthecompliant jointminimizedthemaximumextentofitsrotation whichwasbelow142degrees.Anadditionalalter‐ationwasdonetothemodeltode ineitsrotationlimit toapproximately142degrees.Thiswasachievedby downscalingthediameterofthelowercylinderto¾of theuppercylinder’sdiameter.Thedesignisdisplayed inFigure6.
Figure3. Initialconcept–technicaldrawing
Figure5. Testsresults
Designofsecondstageofmodification–technicaldrawing
Thelastmodi icationofthemodelde inedthe inal constructionofthecompliantrotationaljointofthe prosthetickneedeviceprototype.Cyclictestswere conductedtoevaluatethekinematicsofthecompliant jointandtocon irmtheoptimizationappliedtothe model.
IncomparisontothesymmetricalD‐COREjointin theviewofanarti icialkneejointdesign,theasym‐metricaljointshowsamoredesirablestructuralchar‐acteristic.The lexureofthejointintheextentof142 degreesdoesnotshowsignsofoverextensionsonthe lexurebands.
3.3.FinalVersion
The inalversionofthekinematicallytestedcom‐pliantjointwasadaptedtoaprosthetickneejoint designconcept.Anelementknownasthepyramid adapterwasaddedtotheuppercylinderbody.This allowstheprostheticjointtobeproperlyalignedand attachedtothelegsocket.Forthelowerbody,atube adapterextensionwasadded.A25mmdiameter tubecouldbeattachedtoconnecttheprostheticknee devicewithaprostheticfoot,completingthewhole assembly.Apyramidadaptercanalsobedesignedfor thelowerbodysinceitisauniversallinkingelement usedinlowerlimbprostheticconstruction.Thedesign ofthe inalversionispresentedinFigure7
Asimplespring‐dampermechanismwasdesigned forthe3D‐printedcompliantprostheticjoint.This couldpossiblyclassifythekneejointasK‐1,K‐2level. However,tofullyclassifytheprosthetickneejoint furtherstudiesandoptimizationhavetobedoneto thespring‐dampermechanismsincethisstudydoes notcoverit.Thespring‐dampersystemconsistsof aviscoelasticbandconnectingtheupperandlower bodycylindersanddampers,3DprintedoutofTPU
ilament,whichmitigatetheimpactwhenthejoints returntothezeroposition.Theprintedprototypeof thekneejointispresentedinFigure8.Thesummaryof thedesignprocessandperformedtestsarepresented inTable1.
4.Discussion
Theintegrationofarotationalcompliantmecha‐nismwithastandardprosthetickneejointconstruc‐tionresultedinakinematicprototypeofapolycentric compliantprosthetickneejoint.Thecompliantjoint, constructedfromcylinderswithaconstantradius, doesnotfullyreplicatethekinematicsofafour‐axis polycentrickneejoint.Instead,thekinematicsofthe compliantjointcanbedescribedasahybridbetween asingle‐axisandafour‐axispolycentricknee.This hybridnatureprovidesacompromisebetweenthe simplicityofsingle‐axisdesignsandthemorecomplex motionofpolycentricjoints.
Figure6.
Figure7. Finalversion–technicaldrawing
Figure8. Printedkneejointprotype–photo
Table1. Summaryofthedesignprogressofthecompliantjoint
Designversion Rotationextent Testtype
Primarydesign 180to180deg Manualfullextent deformationandrelease
Primarydesignsecond iteration(band thicknesstest)
Seconddesign (asymmetric)
Finaldesign
Finaldesignwithspring anddampermechanism
180to180deg
Cyclicmanualfullextent deformation
101to144deg
0to142deg
0to142deg
Cyclicmanualfullextent deformation
Cyclicmanualfullextent deformation,staticload test(74kginprimary position)
Cyclicmanualfullextent deformationandrelease
Therangeofmotionoftheprostheticjointreaches thestandardapproximate142degreesofrotation, whichalignswellwiththetypicalrangerequiredfor functionalkneemovement.Thefragilecompliantele‐mentofthejointisprotectedfromoverextensionand beingoverloaded.Moreover,asimplespring‐damper systemideawasintroducedintothemodeltoclassify theprototypeasK‐1,K‐2functionalitylevel.However, thisresearchcoveredonlythekinematicsofthispro‐totype.Tocon irmthepossibleusabilityandclassi‐icationsoftheprototypecompliantjoint,themodel mustundergostressandfatiguetests.Additionally, thespring‐dampermechanismhastobeclassi iedand optimizedforcommercialuse.
5.Conclusion
Thestudysuccessfullyintroducedacompliant arti icialprosthetickneejointprototype,integrating theprinciplesofcompliantmechanismswithconven‐tionalkneejointdesigns.Thisprototypedemonstrates ahybridkinematicbehaviorthatcombineselements ofbothsingle‐axisandpolycentrickneejoints.Iteffec‐tivelyachievesarangeofmotionofapproximately 142degrees,aligningwellwiththemovementrange typicallyrequiredforfunctionalkneeprosthetics.
Theuseofcompliantmechanismsinthisproto‐typeoffersnotablebene its,includingreducedweight andmechanicalsimplicity,whichcontributetoamore streamlinedandpotentiallycost‐effectiveprosthetic design.However,theresultsalsorevealsomelimita‐tions.Speci ically,the lexurebands,whilefunctional, exhibitedsignsoffragilityandpotentialwearafter cyclictesting.Thissuggeststhatwhilethecompli‐antdesignoffersadvantages,italsorequiresfurther re inementtoimproveitsdurabilityandperformance underrepeateduse.
Testresults
Jointreturnstoitsprimaryposition,novisible signsofshapealteration,visiblesignsof structuralbreakingafterrepeatedtests
Thickerbands(1.5mmto2.5mm)showbetter stiffnessbutbreakquickly(after70–100 cycles),thinbands(0.5mmto1mm)don’t break(>300cycles)butareunstable.Optimal thicknessisbetween1mmand1.5mm (breakingoccursatapprox.300cycles)
Nosignsofbreakingafter>300cycles,joint returnstoprimarypositionafterrepeated cyclictests
Nosignsofbreakingafter>300cycles,no signsofbandsbreakingduringstatictest,no instabilityduringstatictest.Furtherstructural testingisneeded
Nosignsofbanddeformationafter>300 cycles,springanddampermechanismaidsthe returnofthejointtotheprimaryposition. Dampingeffectneedstobetested,spring stiffnessneedstobetestedandadjustedfor differentweightsofarti icialfootprostheses
Additionally,theintegrationofasimplespring‐dampersystemintothedesignproposesaclassi ica‐tionwithintheK‐1orK‐2functionalitylevels.Never‐theless,thisaspectoftheprototypewasnotthepri‐maryfocusofthecurrentstudyandrequiresfurther optimizationtofullymeetthenecessarycriteriafor theseclassi ications.
Tocon irmthepracticalapplicabilityandlong‐termviabilityofthiscompliantkneejoint,subsequent researchshouldincluderigorousstressandfatigue testinginaccordancewithISO10328standards[5]. Thesetestswillbecrucialinverifyingthejoint’sability toendurethedemandsofregularuse.Moreover,addi‐tionalworkisneededtooptimizethespring‐damper systemtoenhancetheoverallfunctionalityandcom‐mercialpotentialoftheprostheticknee.
Insummary,whilethecompliantkneejointpro‐totyperepresentsasigni icantstepforwardinpros‐theticdesign,furtherdevelopmentandtestingare essential.Thisresearchunderscoresthepotentialof compliantmechanismstoimproveprostheticlimb technology.
AUTHORS
MichałKowalik –InstituteofAeronauticsand AppliedMechanics,WarsawUniversityofTechnology, Warsaw,Poland,e‐mail:michal.kowalik@pw.edu.pl. ErwinRogoża –AutomotiveIndustryInstitute, ŁukasiewiczResearchNetwork,Poland,e‐mail: erwin.rogoza@pimot.lukasiewicz.gov.pl.
AleksyFigurski –DoctoralSchool,Warsaw UniversityofTechnology,Warsaw,Poland,e‐mail: aleksy. igurski.dokt@pw.edu.pl.
MateuszPapis∗–InstituteofAeronauticsandApplied Mechanics,WarsawUniversityofTechnology,Warsaw, Poland,e‐mail:mateusz.papis@pw.edu.pl.
∗Correspondingauthor
References
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[3] A.H.J.Slocum,“RollingContactOrthopaedicJoint Design,”PhDThesis,MassachusettsInstituteof Technology,2013.
[4] C.HuxmanandJ.Butler,“ASystematicReviewof CompliantMechanismsasOrthopedicImplants,” J.Med.Device.,vol.15,no.4,2021,040802,doi: 10.1115/1.4052011.
[5] “ISO10328:2016.Prosthetics—StructuralTest‐ingofLower‐LimbProstheses—Requirements andTestMethods,”InternationalOrganization forStandardization,2016.
[6] M.Qiuetal.,“DesigningProstheticKneeJoints withBio‐InspiredBearingSurfaces,” Tribol.Int., vol.77,2014,pp.106–110,doi:10.1016/j.triboi nt.2014.04.025.
[7] P.G.Kulkarnietal.,“OvercomingChallengesand InnovationsinOrthopedicProsthesisDesign: AnInterdisciplinaryPerspective,” Biomed.Mater. Devices,vol.2,no.1,2024,pp.58–69,doi:10.100 7/s44174‐023‐00087‐8.
[8] A.Demofontietal.,“DesignofaModularand CompliantWristModuleforUpperLimbPros‐thetics,” Anat.Rec.,vol.306,no.4,2023,pp.764–776,doi:10.1002/ar.24911.
[9] D.Stojiljkovićetal.,“Simulation,Analysis,and ExperimentationoftheCompliantFingerasa PartofHand‐CompliantMechanismDevelop‐ment,” Appl.Sci.,vol.13,no.4,2023,p.2490,doi: 10.3390/app13042490.
[10] M.Kowaliketal.,“CanineHindlimbProsthetic ResearchanditsManufacturingwiththeHelp ofAdditiveTechnology,” MaterialsResearchProceedings,2023,pp.91–99.doi:10.21741/97816 44902578‐13.
[11] A.R.Gutierrez,“ExploringtheFutureofProsthet‐icsandOrthotics:HarnessingthePotentialof3D Printing,” Can.ProstheticsOrthot.J.,vol.6,no.2, 2024,doi:10.33137/cpoj.v6i2.42140.
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[14] J.Victor,“KinematicsoftheNormalNativeKnee,” SoftTissueBalancinginTotalKneeArthroplasty, S.Matsuda,S.Lustig,andW.vanderMerwe,eds., SpringerBerlinHeidelberg,2017,pp.29–37,doi: 10.1007/978‐3‐662‐54082‐4_3.
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AHEALTHRECOMMENDERSYSTEMFORSLEEPAPNEAUSING
Submitted:30th April2024;accepted:26th August2024
MubashirKhan,YashpalSingh,HarshitBhardwaj
DOI:10.14313/jamris‐2025‐029
Abstract:
Inhealthcare,thereisagrowinginterestonbuilding recommendationsystemsforsleepapneamanagement. Thesesystemsusedatafromavarietyofsources,includ‐ingpatient‐reportedoutcomesandelectronichealth records,toassesssleepquality,breathingpatterns,and medicaltreatmentadherence.Leveragingartificialintel‐ligence(AI),machinelearning(ML),theInternetofThings (IoT),andcloudplatforms,thesystemanalyzesthese datatouncoverpatternsandcorrelations.Itthencreates individualizedpatientprofilesthatincorporatedetails aboutdiet,medicalhistory,andsleephabits.Basedon theseprofiles,customizedrecommendationsaregener‐atedtoenhancesleepapneamanagement.Theserec‐ommendationsmayencompasstreatmentoptionsand lifestyleadjustments,Yoga,exercise,etc.toimprove treatmenteffectivenessandoverallwell‐beingforindi‐vidualswithsleepapnea.Thisreviewarticlediscusses availableliteratureonsleepapnea,itsdiagnosis,andthe roleplayedbyMLanddeeplearningclassifiersinthe predictionandclassificationofthedisease.Thearticle alsopresentsacomparativeanalysisonperformance measuresforthesemethods.Thisarticlehighlightsthe researchscopeforincorporatingtechnologiessuchasAI, theIoT,andcomputationalintelligenceinimprovingthe diagnosis,remotemonitoring,andtreatmentofsleep apnea.
Keywords: sleepapnea,healthrecommendersystem, InternetofThings,sleep‐disorderedbreathing,deep learning,machinelearning
1.Introduction
Arecommendationsystemutilizespatientpro iles andanalyzeddatatogeneratetailoredrecommenda‐tions.Recommendationssuchaschangesinlifestyle thatcanimprovesleepquality,suchasbetterhygiene practices,managingstress,eatinghealthily,exercising regularly,andavoidingcertainsubstances(suchas alcoholortobacco)aresometimesrecommended.
Thesystemcanprovidesleepexercisesrecom‐mendationstoimproveone’ssleepenvironment,seta sleepschedule,trainrelaxationtechniques,andother strategiestoimprovesleep.Recommendationsys‐temscanencourageconsistentuseofprescribedtreat‐mentsandinterventionsbymonitoringpatientcom‐plianceandprovidingremindersandfeedback.Feed‐backandinteractionbetweensystemandpatientscan
beestablished,whereausercanrespondtosugges‐tionsprovidedbythesystemthroughuserinteraction. Therecommendersystemcontinuouslylearnsfrom newdataandpatientfeedback,re iningitsalgorithms andrecommendationstoadapttoindividualpatient needsandpreferences.Thisiterativeprocessensures thatthesystemremainsup‐to‐dateandrelevant.
Anotherpopularwaytodealwithsleepapnea (SA)istodiagnosethisdiseaseatanearlystagewith machine‐learning(ML)anddeep‐learning(DL)meth‐ods.Signalsrecordedfromsuspectedpatients’body likeelectrocardiogram(ECG),SpO2,andEEGareana‐lyzedthroughthesetechniquestomakepredictions abouttheseverityofthedisease.Figure 1 showsa detailedwork lowforSAdiagnosisatsleepcenters.
Thisreviewarticlediscussesvariousapproaches todiagnosesleepapneaandtheiradvantagesand drawbacks.Thisarticlealsocomparestheeffective‐nessofMLorDLalgorithmsintermsofaccuracy, precision,andrecall.Attheend,weproposearecom‐mendersystemforSApatients.
1.1.DataSearch
WehaveexploreddatabasessuchasPubMedand IEEE‐Xploreto indtheinteractionbetweenthehealth andbiologicalsciencesliteraturewiththecomputer scienceandengineeringliterature.GoogleScholarand NCBIwerealsousedtomanuallyscreenpapersfrom variousjournalsandconferencesbasedontitleand abstract;seeTable 1.Inthisreviewarticle,wehave included/excludedarticlesbasedonsomecriteria; thoseareshowninTable2
2.LiteratureReview
2.1.PrevalenceandRiskFactorsofSA
Theavailableliteraturesuggeststhattheoccur‐renceofSAandfactorsthatcontributetoobstructive sleepapnea(OSA)inIndiaareincreasingurbaniza‐tion,astressfullife,andlifestylechanges.Indiais expectedtofaceanobesityepidemic,whichishighly associatedwithOSA[1].OSAisthemostcommon breathingdisorderworldwide.Whileobesityremains amajorcauseofOSAinAsians,factorslikeage, bodymassindex(BMI),smoking,andalcoholcon‐sumptionmaycontributemoretoOSAdevelopment; seeFigure 1 fortypes,causes,andconsequencesof
Figure1. Workflowofsleepapneadiagnosisprocess
Table1. Databasesearchandselectioncriteria
Electronicdatabase 1.PubMed
2.GoogleScholar
3.IEEEXplore 4.NCBI
Inclusioncriteria
1.Articlesondevelopingor validatingasleepapnea predictionmodelusingvarious datasources,suchas individualpatientdataor electronichealthrecords.
2.Wearabledevicedata, physiologicalprocessing,or physicalmovement measurementsdatacanbe usedtoclassifysleepdisorders byML.
3.Allthesignalsmeasuredin anyformat,suchascontinuous, binary,ordinal,multinomial, andtime‐to‐event.
Exclusioncriteria 1.ResearchemployingMLto classifynon‐physiologicaldata, suchasquestionnaireratings.
2.Studiesthatonlystudy physiologicalrelationships withsleepapneaasamethod ofinformationdiscovery.
3.Reviews,conceptpapers, andabstracts‐onlyarticles.
SA.Researchhighlightstheneedforpublicaware‐ness,earlydiagnosis,andeffectivetreatmenttotackle SA[2].
ThefollowingresearcharticlesshowthatSAis highlyprevalentinIndiaandinotherpartsofthe world.Thedataset“Sleep‐Cohort‐StudybyWiscon‐sin”discussestheoccurrenceofsleep‐disordered breathing(SDB)fortwodistincttimeframesinthe US:1988–1994and2007–2010.The indingsreveal asigni icantincreaseintheprevalenceofmoderate‐to‐severeSAoverthepasttwodecades.Therelative
Table2. Searchstrategy
Population Studiesusingphysiologicaldatato buildsleepapneaclassi ication algorithms
Comparison Differentmodelsandtheirutilityfor clinicalintervention
Outcome Abilitytodetectorpredictsleep apnea,sleeparousals,respiratory eventsduringsleep
Studytype Quantitativestudy
Keywords Sleepapnea,recommendersystem, polysomnography,machinelearning, arti icialintelligence
increasesinvarioussubgroups(byage)rangefrom 14percentto55percent[3].Adecadeago,Suripio‐neeredworkonsleepmedicineinIndia,whichled totheestablishmentofmultiplesleepcentersacross thecountry.Thearticleunderscorestheneedfor educationalinitiatives,localproductionofaffordable sleepanalysistools,andintegratingsleepmedicine intomedicaleducation.Thearticleadvocatescollab‐orationswithpremierengineeringinstituteslikeIIT‐Madrasfordevelopingcost‐effectiveequipment’sfor SAdiagnosis[4].
TypesofSA: Theexistingliteraturesuggeststhree categoriesofSA:OSA,centralsleepapnea(CSA),and mixed/complexsleepapnea;seeFigure 2 formore details.Ofthese,OSA)ismostprevalent.Individuals withOSAcommonlyexperiencerepeatedinstances ofpharyngealairwaynarrowingorcollapseduring sleep,ashighlightedbyCampanaetal.[5].
OSA ischaracterizedbyrepeatedcollapseofthe upperairwayduringsleep,leadingtodisruptedsleep, hypoxemia,andincreasedriskofconditionslike hypertensionandcardiovasculardisease(CVD).Fig‐ure3showsacomparisonbetweenvariousbreathing patternsassociatedwithbreathingdisorders.Witha globalprevalenceof2percentto10percent,riskfac‐torsincludeage,gender,obesity,genetics,craniofacial
anomalies,smoking,andalcoholconsumption.Iden‐ti iablesymptomsincludeloudsnoring,observed apneas,anddaytimesleepiness[6].
Sleep-Disordered-Breathing(SDB) Recognizedasa signi icanthealthissueinyoungchildren,SDBhas estimatedprevalenceratesof1percentto4percent, withcontributingfactorsbeinganarrowairwayand reducedneuromusculartone.Childrenwithcondi‐tionslikeDownsyndromeareathigherrisk.SDB symptomsincludesnoring,frequentarousal,enuresis, andhyperactivity,andifuntreated,itcanleadtolearn‐ingchallenges,stuntedgrowth,andincreasedrisksof hypertensionandcardiovascularproblems[7].
SinceSAissleep‐relateddisorder,knowledgeof sleepstagesisimportantbecauseithasbeenobserved throughtheliteraturethatSAoccurswhenapatient goesintodeepsleep.Therearetwomaintypesof sleepstages:the irstoneisnonrapideyemovement (NREM)sleepandthesecondoneisrapideyemove‐ment(REM)sleep.
NREMissubdividedintostagesN1,N2,andN3. ThecharacteristicsofREMsleeparerapideyemove‐ments,muscleatonia,anddesynchronizedbrainactiv‐ity[8].
RiskFactorsofOSA:Obesity:Theliteratureana‐lyzedheresuggeststhatpatientswithhighBMIvalue isverylikelytodevelopSA.Kandalaetal.[9]inves‐tigatedOSAin30participantswithsnoringhistory andahighEpworthsleepinessscalescores.Basedon BMI,23patientswerediagnosedwithOSA(AHI>5); outofthese,13wereobeseand10werenonobese. Obeseindividualsexhibitedlowermeanoxygensat‐urationlevels(SpO2)andexperiencedreducedtotal sleeptime,sleepef iciency,N3stage,andREMstage comparedtononobesepatients.Thesamethingis highlightedbyReddyetal.[10];theyhaveassessed OSAoccurrenceandcontributingfactorsinanurban Indianpopulationaged30to65,estimatinga9.3per‐centpopulationprevalenceforOSAand2.8percentfor OSAsyndrome.Malegender,highBMI,andabdominal obesitywereassociatedwithOSA,withobesityfound tobeamajorriskfactor;theynotedassociationswith hypertension,whiletheleastsigni icantriskfactors weresmokinganddrinking.Theirstudyalsohigh‐lightedthefactthatOSAisacommonconditionthat causesinterruptedbreathingduringsleep,affectsvar‐iousagegroups(prevalence:2percentto14percent), andleadstofragmentedsleepanddaytimesleepiness. Linkedhealthissuesincludehypertensionandheart disease,withpredictivefeatureslikesnoringandobe‐sity.Diagnosisinvolvespolysomnography(PSG),and theprimarytreatmentisthecontinuouspositiveair‐waypressure(CPAP)machine,withbariatricsurgery consideredforobesepatients.
2.2.ConsequencesofSA:SALeadingtoOtherDiseases IfSAisleftuntreated,itsconsequencescanbefatal. Someofthefollowingarticlesdiscusslinksbetween SAandotherdiseases.AccordingtoGurubhagavatula etal.[11],OSAcancausedaytimesleepinessandcog‐nitiveimpairments,affectingvigilance,memory,con‐centration,andexecutivefunction,thusincreasingthe
riskofaccidentsanddiminishingoverallqualityoflife. TreatmentofOSAhasdemonstratedimprovementsin theseareas.ResearcherslikeMartinetal.[12]high‐lighttheimpactofOSAduringpregnancy,linkingit toadverseoutcomessuchaspreeclampsiaandges‐tationaldiabetes.Fatimaetal.[13]emphasizethat OSAisprevalent,affectingabout20percentofUS adults,withahigherincidenceinobeseindividuals andmales.Homestudiesrevealthat7.5percentof middle‐agedIndianmenhaveOSA.Theconnection betweenOSAandCVDisofinterestduetotheirpoten‐tialmechanisms,buttheimpactofOSAtreatmenton cardiovascularriskremainsuncertain.
ManyresearchersdiscussSAandkidneydiseases. Ankeretal.[14]highlightthecommonoccurrence ofSDBinCVDanditsimpactonoutcomes.Itdis‐cussesthetwomainSDBtypes,diagnosticconsid‐erationsusingPSGorportabledevices,andeffective treatmentslikeCPAPforOSA.Theoptimaltreatment forCSAinheartfailureisuncertain,withemerging therapieslikephrenicnervestimulationunderexplo‐ration.Targaetal.[15],intheirstudy,exploredthe linkbetweenOSAeventsandtheirimpactonsleep patterns,Alzheimermarkers,andcognitivedeclinein 116patients(medianage:76,AHI:25.9).Obstruc‐tiveapneaswererelatedtosleepdisruptions,while hypopneaswerelinkedtoincreasedarousal,andboth mixedandcentralapneasaffectedsleepstructure.At the12‐monthfollow‐up,hypopneaswerethemost signi icantpredictorofgreatercognitivedeteriora‐tion,andOSAwasconnectedwithraisedneuro ila‐mentlightlevels.Mavanuretal.[16]showedthatSDB iscommoninadvancedchronickidneydisease(CKD), affectingover50percent.Itleadstoupperairway blockageduringsleep,causingphysiologicalreactions andincreasedcardiovascularrisks.Treatmentslike renaltransplantationandspecializeddialysismeth‐odsshowpromiseinreducingSDBseverityinCKD patients.
3.MaterialandMethods
3.1.DiagnosisofSleepApnea
FordiagnosisofSA,sleepexpertsusuallymonitor ECG[17–21],EEG[22],SpO2 [23],snoringsound,and variousotherbodyparametersofthepatient.Sharma etal.[24]emphasizedthatduetolackofawareness aboutOSAinIndia,theMinistryofHealthandFamily WelfareestablishedINdianinitiativeonObstructive sleepapnoea(INOSA)guidelines.Theseguidelines recommendasleepassessment,particularlyforindi‐vidualsshowingsymptomslikesnoringanddaytime sleepinessorthosewhowereconsideredhigh‐risk cases.PSGisthestandarddiagnosticmethod,and positiveairwaypressure(PAP)therapyistheprimary treatment,withoralappliancesandbariatricsurgery consideredforspeci iccases.
3.1.1.ECG/EEG/SpO2 SignalsforSADiagnosis
Inlinewiththis,Huttunenetal.[25]showedthat, byutilizingpolysomnographicdatafrom877partic‐ipants,thismodelenhancestheassessmentofSA
Figure2. SAsymptoms,causes,andconsequences
Figure3. Breathingpatterns bytakingintoaccounteachindividualsleepstage. Usingpulseoximetrydata,itimprovestheaccuracy ofdistinguishingbetweenapneaandhypopnea,and itsabilitytoestimateAHIduringREMandNREM sleepmakesitvaluableforOSAscreeningandtreat‐ment.Korkalainenetal.[26]proposedaneffective DL‐basedautomaticsleepstageclassi icationmethod thatshowsreliableresultsforsubjectswithvarying
degreesofOSA.Thisapproach,especiallywhensingle orfrontalEEGchannelsareused,isacost‐effectiveand accuratealternativetoOSAdiagnosis.
Manyresearcharticlesunderlinetheapplication ofECGsignalsforSAdiagnosis.Pomboetal.[18] investigatedtheuseofclassi ierstoidentifyepisodes ofSAfromminute‐to‐minuteECGsignals.ECG‐derived respiration(EDR),heartratevariability(HRV)arethe
Table3. Subjectdemographics
Author Data
Peppardetal.[3] 1520 – –
2000–2015 PSG
Hanetal.[27] 4014 2841 1173 53 2014–2021 PSG,ESS questionnaire
Shietal.[28] 1493 1269 224 – 2019–2021 PSG
Targaetal.[15] 116 52 64
Zareietal.[29] 25 21 04
2015–2019 PSG
2011 PSG
Huttunenetal.[25] 877 480 396 44–65 2015–2017 PSG
Pomboetal.[18] 70 57 13 27–63 – ECG
characteristicsusedinastudytoexaminetheaccuracy andperformanceofvariousclassi iers.Thehighest accuracyattainedwas82.12percent,accompanied by88.41percentsensitivityand72.29percentspeci‐icity.
3.2.DataExtractionandAnalysis
Table3showsvarietyofdatausedbyresearchers acrosstheworldtoaddressresearchquestions concerningSAclassi ication.Thedatacomponents encompasssubjectdemographics,datasetsofECGsig‐naldata,EEGsignals,andSpO2 relatedtoSA.Datasets werealsoobtainedthroughvariouskindsofwearable sensorslikesmartwatches,pulseoximeters,SArings, smartbodysensors,andnasalcannulas.
3.3.TreatmentOptionsAvailableforSA
Alargevolumeofliteratureisavailablethatshows howtheCPAPmachineiseffectiveinSAtreatment. CPAPisthe irstchoiceofmedicalexperts.Someof thefollowingliteraturehighlightedtheuseofCPAP. Jané[30]highlightedthatstandardtreatmentinvolves CPAPtherapy;theirresearchfocusesonadaptive pressurealgorithmsandemergingtrendsaimedat enhancingpatientengagementthroughmobileapps andwebplatformssuchm‐HealthandTele‐Health. Similarly,authorslikeSenavongseetal.[31]discuss theaffordabilityissueofCPAPmachinesfortreat‐ingOSAandpresentastudydesigningafunctional prototype.Theprototype,demonstratingaccurate measurementsandpotentialimprovements,shows promiseforclinicaltrialsinaddressingOSAandsnor‐ing.Amrullohetal.[32]presentedanon‐demand CPAP(OCPAP)controllerasanalternativeSAtreat‐ment,adaptingairpressurebasedonrespiratory needsforenhancedcomfortandupperairwaymuscle training.DevelopedwithLabView,themodeldemon‐stratedpromisingresultsinperformancetests,offer‐ingpotentialforalow‐costtreatmentoption,partic‐ularlyinIndonesia,toreducedependenceontradi‐tionalCPAPsystems.
SomeauthorshavediscussedadvancesintheCPAP machineandtheiruseinSAtreatment.Boisteanu etal.[33]comparedautomaticCPAP(APAP)toa ixed‐pressureCPAPinmoderatetosevereOSApatients; thestudysuggeststhatAPAPisaseffective,offering aslightlylowereffectivepressure.IntelligentCPAPs withremote‐monitoringcapabilitiescanreducecosts
anddoctorvisits,makingthemapotentialchoice forlong‐termtreatment.Penzeletal.[34]investi‐gatedhowOSAaffectscardiovascularandrespiratory regulationduringdifferentsleepstages,focusingon patientswithOSAandnormalbloodpressure,OSA andhypertension,andnormalcontrols.
Researchershavediscussedotherpopulartreat‐mentoptionsaswell,suchasthemandibularadvance‐mentdevice(MAD).Dagaetal.[35]assessedsleep qualitybeforeandafterusinganMADandparticipat‐inginyoga.WhiletheMADgroupshowedimmediate improvementswithcomplianceissues,theyogagroup demonstratedsustainedbene itsoverthelongterm, indicatingtheeffectivenessofyogaandpranayama practicesinlong‐termmanagementofOSA.
TheliteratureavailableonSAsuggeststheuse ofadvancedtechnologicaloptionssuchasadaptive servo‐ventilation(ASV)forCSAtreatment.Aurora etal.[36],accordingtoarecentsystematicanalysis, showedthatASVenhancedleftventricularejection fraction(LVEF)andnormalizedtheapnea‐hypopnea index(AHI)inpatientswithCSAassociatedwithcon‐gestiveheartfailure.Websteretal.[37]proposed anovelSAtreatmentdevicecomprisingamask, hose,andCO2 chamber,thatautomaticallyadjusts rebreathedairtoreduceapneaswithoutPAP,offering apotentiallymoreeffectiveandcomfortabletreat‐mentfortheover25millionAmericansaffectedbySA.
Inconclusion,theavailableliteraturesuggeststhat therearecontinuousimprovementsgoingontomake CPAP,MAD,ASV,andSAmonitoringdevicesbetterand morepatient‐friendly.Thereisfutureresearchscope inthis ieldtoincorporatearti icialintelligence(AI) andadvancedMLandDLalgorithmstomakethese devicesintelligent,withautomatedpressuresettings.
3.3.1.PhysiotherapyTreatmentofSA:Yoga,Asanas, Pranayama’s
Physiotherapytreatmentslikeyoga,asanas,and oralexercisehaveproveneffectiveinSAtreatment; seeTable 5 fornoninvasivetreatmentoptionsfor SA.Kumaretal.[38]studiedindividualssuffering withmild‐to‐moderateSAandsnoring;theyrecom‐mendedphysiotherapywithdifferentyogapostures. Athree‐monthyogaprogramdemonstratedpositive impactsonbreathingpatterns,oropharyngealmus‐culature,andrespiratoryconcerns,providingsymp‐tomaticreliefforthe23participants.Bankaretal.[39]
Table4. TreatmentoptionsforSA
Author Treatment
Boisteano,etal. 2009[33] ixedCPAP,ACPAP
Penzeletal. 2011[34] CPAP
Jané,2014[30] CPAP,adaptivepressure algorithm,M‐Health, Tele‐Health
Auroraetal. 2016[36] ASVforCSApatients
Senavongseetal. 2017[31] Alow‐costfunctional prototypeisdesigned.
Websteretal. 2018[37] NovelSAtreatmentdevice consistingofmask,hosepipe, CO2 chamber.
Amrullohetal. 2019[32] OCPAPcontrollerdeveloped usingLabViewsoftware
Observations
ACPAPeffectivelylowers pressure.Itisalong‐term treatmentoption.
OSAaffectscardiovascular, respiratoryregulationduring sleep
OSAdisruptsair lowduring sleep;SpO2 isalsoreduced.
Cardiacmortalityrateishigh forLVEF>=45%, moderate‐severeCSA.
ModernCPAPmachineisnot affordabletoeveryone nowadays.
Deviceautomaticallyadjusts rebreathedairtoreduce apneas.
OCPAPadaptsairpressure basedonrespiratoryneeds
Improvements
IntelligentCPAPwithremote monitoringcanreduce frequentdoctorvisits,reducing overallcost.
CPAPaffectscardiovascular couplingduringdeepsleep; barore lexsensitivityresponse variesacrosssleepstages.
Standardtreatmentoptionis CPAP,advancedCPAPwith adaptivepressuresettings.
ASVsuggestedforpatients withLVEF>45%and mild‐moderateCSA.
Thefunctionalprototype demonstratesaccurate measurementsandimproves OSA,snoringtreatment.
NoneedforCPAP
Low‐costtreatmentoptionthat reducesdependencyonCPAP. Dagaetal. 2021[35] MADandyogaexercise Sleepqualityisassessedbefore andafterMADsurgery.
MADgroupshowedimmediate improvementswhiletheyoga groupshowedsustained improvementsoveralongtime period.
showedthatincomparisontothecontrolgroup,the yogagroupscoredhigheronquality‐of‐lifecompo‐nentsandhadaminimizedPittsburghSleepQual‐ityIndex(PSQI)sleepqualityvalue.Yogapartic‐ipantsreportedfewersleepdisturbances,shorter sleeplatency,reducedrelianceonsleepmedications, andbettersubjectivesleepqualityandhabitualsleep ef iciencyscores.Regularyogapracticeappearedto positivelyin luencesleepqualityandoverallwell‐beingintheelderly.Researchershaveemphasized regularlydoingyoga,asanas,andexercisescanhelp overcomeillnesseslikeSA;seeTable 5 foracom‐parativestudy.Khalsaetal.[40]comparedKundalini yogatosleephygieneforinsomnia;bothinterventions improvedsleep,butyogashowedlargereffects,sug‐gestingthatself‐careyogainterventionscanprovide lastingimprovementsinsleepqualitybeyondtradi‐tionalapproaches.
Kanchibhotlaetal.[41]studiedSudarshanKriya Yoga(SKY),abreathingexercise,involving473par‐ticipants;theyfoundthatregularSKYpracticepos‐itivelyimpactedsleepquality,withtheextentof improvementvaryingbasedonage,gender,andprac‐ticefrequency;theyemphasizedapositivecorrelation betweendailySKYpracticeandsubstantialenhance‐mentsinsleepquality.
Manyresearchershaveexploredtheuseofhomeo‐pathicmedicineforSAtreatment,asshownbyauthors likeBroadwayetal.[42].Theyproposedafuzzylogic methodbasedontheInternationalPhysicalActiv‐ityQuestionnaire(IPAQ)toclassifyphysicalactivities
performedbypatientsofOSA;themethodimproved precisionovertraditionalassessmentsandallowed forbettermonitoringofchangesinphysicalactivity andtheeffectivenessofCPAPtreatmentinrespira‐toryclinics.Nakanekaretal.[43]proposedtreatment methods,includingAbhyanga,Utsadan,oralmedica‐tions,andBasti,withafocusonbitterherbs;there werepositiveeffectsonrespiratorypatternsduring sleep.Bloodsugarlevel,weight,bellysize,BMI,waist‐to‐hipratio,andcategoriesontheBerlinSnoring QuestionnaireallimprovedwhenBastiwasused.
3.4.MLApplicationinSADiagnosis
Anampleamountofliteratureisavailableonthe applicationofMLinSAdiagnosis;seeTable 6 fora comparativestudy.Hanetal.[27],intheirstudy,eval‐uatedMLtechniquesforOSASseverityassessment usingdemographicandquestionnairedatafrom313 patients.Forclassi ication,randomforestandsupport vectormachine(SVM)modelsperformedbest,yield‐ingthehighestaccuracyof44.7percent,withmisclas‐si icationobservedinonly5.7percentofcases.Lin‐earregressionandtheSVMmodelperformedwellin predictingtheAHI,withregressionmodelsachieving aminimumRMSE=22.17.Similarly,Alvarezetal.[44] usedregressionandSVMtechniques,discoveringthat intermsofforecastingtheAHI,thedual‐channeltech‐niqueperformedbetterthanindividualoximetryand air low,showcasinghighcomplementaryvalue,and signi icantlyimprovingaccuracyforef icientat‐home screeningofOSA.
Table5. PhysiotherapytreatmentforSA
Author SampleSize Treatment Improvements
Kumar,2019[38] 23 Yogaprogramfor3monthsfor mild‐to‐moderateSAandsnoring issues
Bankar,2013[39] 2groups
Khalsa,2021[40] 2groups
Kanchibhotla,2021[41] 473
Positiveimpactonbreathingpattern, oropharyngealmusculature, respiratoryconcerns.
TwogroupsofSApatientsformed; controlgroupandyogagroup Yogagroupscoredhigherqualityof lifePSQIvalue,reducedsleep disturbances,shortersleeplatency.
Twogroupsofinsomniapatients formed:Kundaliniyogaandsleep hygiene Kundaliniyogagroupshowed improvedsleepquality
SudarshanKriyayogaandbreathing exercise
Kwiatkowska,2008[42] – Fuzzylogic‐basedtreatmentmethod toclassifyphysicalactivities performedbyOSApatientsbasedon IPAQ
Khobarkar,2022[43] – AbhyangaUtsadana,Basti,oral medicationwithbitterherbs
ResearchershavefoundthatMLalgorithms,along withbodyparameterslikeSpO2,canbeusedforSA diagnosis.Shietal.[28],intheirstudyinvolving1493 OSApatientsand27variables,includinghyperten‐sion,learnedthatMLalgorithms,andparticularly,the gradient‐boostingmachine(GBM),tobethemostreli‐ableinpredictinghypertensionassociatedwithOSA (AUC=0.873,accuracy=0.885,sensitivity=0.713). Theidenti iedkeyvariables,includingage,minimum arterialoxygensaturation,BMI,andpercentageof timewithSaO2 <90percent,ledtothedevelopment ofanonlinetoolforclinicians[28].Researcherslike Liuetal.[45]emphasizetheimportanceofdetecting non‐apnea‐relatedarousalsduringsleepforassessing sleepquality.Theproposedalgorithmtrainedand testedonPSGdatautilizingconvolutionalneuralnet‐works(CNNs)andarandom‐forestmodule,achieved anAreaUnderthePrecision‐RecallCurve(AUPRC)of 0.552.Whileeffective,themethodmayhavelimita‐tionsforcertainpatients.
AuthorshavediscussedtheuseofMLforjudg‐ing/monitoringtreatmentprovidedtoSApatients. Mitrietal.[46]discussedtheuseofCPAP,applying airpressureforconditionslikeSAandpreterminfants, withafocusonanomalydetectionaidedbyMLusing theNumentaAnomalyBenchmark(NAB)andHier‐archicalTemporalMemory(HTM).Anexperiment usinginfantbreathingpatternsdemonstratedeffec‐tiveanomalyprediction,emphasizingthepotential ofHTMinanomalydetection,thoughitsimmaturity limitsprogress,suggestingtheneedforfuturework tosolidifyitscompetitivenessinMLresearch.Fal‐lamnnetal.[47]comprehensivelyreviewedtechno‐logicaladvancementsinsleepmonitoring,addressing sleepbehaviorcharacterization,assessmentmethod‐ologies,monitoringtechniques,andanalysismeth‐odswithinpersonalizedsmarthealthcare,emphasiz‐ingthepotentialfordata‐driventechniquestobridge thegapbetweenclinic‐basedandhome‐basedsleep
Positiveimpactonsleepquality. Improvementvariedamongpatients basedonage,gender,yogapractice frequency.
Improvesmonitoringofeffectiveness ofCPAPtreatment,physicalactivities performed.
Improvementshowninbloodsugar level,BMI,waist‐to‐hipratio, categoriesofBSQI.
assessments.Rao[48]exploredwearablesensorsfor respiratoryandpulsemonitoring,emphasizingtech‐nologieslikeheartratemonitoring,GPS,GSM,IoT,and infrared‐basedbreathsensors,aimingtoenableself‐monitoringofhealthparametersandimprovehealth caretechnologythroughMLtechniquesandaninno‐vativesystemleveragingIoTandGSMplatforms.
TheaccuracyofMLmethodsappliedforSAdiag‐nosiscanbeimprovedbyconsideringcombinationof signalsinsteadofindividualsignals;ECG‐SpO2 [54], ECG‐nasalpressure,SpO2‐EEG[44],ECG‐EEG,ECG‐chest‐abdomensignalcombinationscanbetried.Lim‐itationswithstandaloneMLalgorithmsincludethe lackoffeatureextraction/optimalfeatureselection ability;hence,hybridcombinationsMLmodelswith optimizationalgorithmsshouldbetested[e.g.,particle swarmoptimization(PSO),geneticalgorithms(GAs), bluewhale(BLO),andgraywolf(GWO)].Inorder toenhanceperformancemeasuresofMLapproaches, researchershavetriedhybridapproacheslikeCNN‐LSTM,PSO‐SVM,andHRV‐LDA[52].
3.5.DLApplicationforSADiagnosis
DLhasshownverypromisingresultsindiagnosis andprocessingofsignalsreceivedfromSA‐suspected patients.Featureextractionandoptimalfeatureselec‐tionwerethekeypointsofDLalgorithmslikeCNNs andrecurrentneuralnetworks(RNNs).Wehavepre‐sentedacomparativestudyofvariousDLmethods appliedinSAprediction;seeTable 7.Sunetal.[55] presentedaclassi icationofsleepstages,atwo‐stage neuralnetworkstrategythatusesanRNNfortempo‐ralinputprocessingandfeaturelearning,alongwith apretrainingproceduretoaddresssampleimbalance. Testsonsleepdatabasesdemonstratesuperiorper‐formancecomparedtoadvancedmethods,achieving signi icantF1scoresandKappacoef icients.
ResearcherslikeKristiansenetal.[51]have investigatedtheuseofdataminingmethods,such
Table6. MLalgorithmsforSAdiagnosis
Author Biosignal MLAlgorithm
Sharmaetal., 2023[49] EEG K‐NN, ensemble baggedtrees (EbagT)
Mencaretal., 2020[50] Questionnaire baseddata SVM,RF,LR 44.7
Álvarezetal., 2020[44] SpO2,BP,HR LR,SVM 81.3Kappa coef icient= 0.71
Shietal., 2022[28] BP,SpO2 GBM,XGBOOST 88.5
Kristiensenetal., 2018[51] ECG RF,KNN,SVM, ANN
Pomboetal., 2020[18]
Schraderetal., 2000[52] ECG,HRV LDA
Linetal., 2006[53] ECG DWT,ANN –
Xie&Minn, 2012[54] SpO2,ECG KNN
Table7. DLalgorithmsforSAdiagnosis
Author Bio Signal DL Algorithm
Huttunen,2023[25] SpO2,PR,ECG CNN,RG –
Classi ication
AHIprediction
0.873 prediction, hypertension
classi ication
classi ication
classi ication
predictionand classi ication
Typeof Classi ication
Sharmaetal., 2022[49] SpO2,PR CNN 93.4% – – detection
Strumpfetal., 2023[56] SpO2,HR ANN 91% 0.83 0.76 multiclass classi ication
Hemrajanietal., 2023[57] ECG RNN,LSTM, GRU. 89.5%RNN; 90%LSTM; 90.5%GRU – – classi ication
Korkalainenetal., 2021[26]
EEG,SpO2 CNN,RNN hazardratio =1.14 (p = 0.39) formildOSA
hazard ratio = 1.59 (p < 0.01) for moderate OSA hazard ratio = 4.13 (p < 0.01) forsevere OSA estimation
Liuetal.,2020[45] EEG,SpO2 CNN,RF AUROC = 0.953 AUPRC= 0.552 – detection
Mitrietal.,2017[46] Nasalpressure, CPAPpressure readings HTM,NAB – – – anomaly detection
Sunetal.,2019[55] EEG RNN – – – binary classi ication
Yungetal.,2020[58] ECG 1D‐CNN 89% – – detection Zareietal.,2021[29] ECG CNN‐LSTM
Abbreviations:GRU,gatedrecurrentunit;PR,pulserate.
asdecisiontrees,randomforests,SVMs,K‐nearest neighbor(KNN),andarti icialneuralnetworksto examinephysiologicalsignalsforthepurposeof detectingOSA,utilizingdatasetsfromtheMIT‐BIH andApnea‐ECGdatabases[51].Otherauthorslike Yangetal.[58]utilizeda1D‐CNNmodelonone‐channelEEGdatawithsleep‐stageannotations, demonstratinghigheraccuracyforintrapatient
insomniaidenti ication,particularlyleveragingREM andSWSepochs,comparedtobaselinemethods, while indingnosigni icantdifferencesininterpatient identi ication.
Manyresearchersstressedtheuseofensembled ML/DLalgorithmsasKwonetal.[59]have;they presentedanovelmethodusingIR‐UWBradar andDLalgorithmsforreal‐timeapnea‐hypopnea
identi icationinSAandhypopneasyndrome, achievinghighperformancewithastrongassociation betweenestimatedandreferenceAHIs.Zarei etal.[29]introducedanautomatedapproach utilizingECGsignalsandacombinationofCNNs withLSTMnetworksforSAdetection,achieving impressiveresultswithhighersensitivity(94.41 percent),speci icity(98.94percent),andaccuracy (97.21percent)onApneicandUCDDBdatasets.The LSTM‐CNNmodeloutperformstraditionalmethods, providingaccurateper‐segmentandper‐recording classi ications,therebyenhancingSAdiagnosisfor physicians.
Researchershavealsopresentedtheuseofpre‐trainedneuralnetworksinSAdiagnosis.Hemra‐janietal.[57]presentedMobileNet‐V1,LSTM,and GRUnetworksforidentifyingsingle‐leadECGsignals inundiagnosedOSAcases,achievingaccuracyrates of89.5percent,90percent,and90.29percenton authenticcases.Sharmaetal.[49]workpresented anautomatedtechniquethatusespulse‐oximeter‐recordedSpO2 andPRdatatoidentifyepisodesof SA.Forepoch‐basedapneadetection,theDLmodel obtainedatestperformanceof90.4percentarea undertheROCcurveanda58.9percentareaunder theprecision‐recallcurveafterbeingtrainedonahet‐erogeneouscohortofpatients.
3.6.IoTApplicationforSAMonitoringandDiagnosis
TheIoT,alongwithhealth‐monitoringdevices,has averywidescopeinthe ieldofhealthcaremon‐itoring.Kwonetal.[60]introducedaportableat‐homesolutionthatuseswearableelectronicswith embeddedMLandwirelesssleepsensorstosolve theproblemofundetectedsleepdisorders.Clinical testingdemonstratesacomparableperformanceto PSGincapturingbrain,eye,andmusclesignals.The wearablesystemaccuratelyidenti iesOSAwith88.5 percentprecision.Steblinetal.[61]introducedan IoT‐basedsolutiontoimprovethetreatmentofOSA. ToassistpatientswithOSAandprovidefeedbackto lungspecialists,thesuggestedtechnologytransmits patientdatatothecloudforanalysis.
Manyresearchershavetriedtoemphasizethe importantroleoftheIoTandML/DLcombinations inSAdiagnosis.Abdel‐Basitetal.[62]exploredthe challengesindetectingandtreatingOSAandhigh‐lightedthepotentialofAI‐drivenIoTtechnologiesfor remotepatientmonitoring,providinganoverviewof developmentsfrom2016to2019inbigdata,cloud computing,ML,smartdevices,andfogcomputing.
3.7.RecommenderSystemsforSA
Recommendersystems(RSs)giverecommenda‐tionsbasedonuserpro ile.Here,inthecaseof SAtreatmentrecommendations,authorshavepro‐posedvariousapproachesofRSsincollaborationwith ML/DLalgorithms;seeTable8.Nanehkaranetal.[63] introducedamedicalrecommendationsystemuti‐lizingIoTdevices,employingKNNclassi icationfor diseaseidenti icationandcollaborative ilteringfor treatmentrecommendation.Theapproachshowshigh
precisionindiagnosingchronicdiseasesandrecom‐mendingtreatments,surpassingpreviousmethods. Otherauthors,likeCasal‐Guisandeetal.[64],pre‐sentedanintelligentsystemfordiagnosingOSA.The systemcombinespatienthealthdataandsymptom informationtogenerateriskindicatorsforOSA.The earlytestingofthesystemshowedpromise,butfur‐therclinicalvalidationandimprovementsareneeded beforeitcanbewidelyusedinhospitals.
Wehaveanalyzedresearcharticlesontheapplica‐tionofRSinthehealthcaredomainutilizingelectronic healthrecords(EHRs).Razaetal.[65]introduceda two‐stagerecommendersystemforclinicaldecision‐makingwiththehelpofEHRs.The irststageretrieves candidateitemsbasedonpatientrecordsusingadeep neuralnetworkandalanguagemodel.Thesecond stageranksandrecommendsrelevantitemsconsid‐eringpatienthistoryandcontext.Pinionetal.[66] proposedafederatedlearningarchitectureforhealth recommendersystems(HRSs)inprecisionmedicine, addressingprivacyconcernsandenablingarealfed‐eratedHRSwithoutcompromisingcon identiality.In thisresearch,theyevaluatedanHRSdevelopedfor theTeNDER‐project,whichprovidespersonalizedrec‐ommendationsbasedonmonitoringdevicedata.The noti icationscoveredvariousaspectsofdailylife.
However,otherauthors,likedelRioetal.[67],have proposedarecommendationsystemthatsuggestsa healthylifestylescheduletomitigateSAseverity.A probabilisticMarkovmodel(PMM)guidesactivities basedonpatienttimeallocation,aimingtoreduce apneacyclesandimprovesleeppatterns.Thesystem usesahiddenMarkovmodelforcondition‐directed recommendations,focusingon lexibilityanduser preferences.
Figure 4 showsaproposedHRS.Itinvolvespro‐cesseslikefeatureengineeringandselection,ini‐tialstagesofHRSsweneedtoidentify,andrele‐vantfeatures(e.g.,SpO2,bloodpressure,sleephabits, patientdemographicssuchasage,gender,BMI,and neckcircumference.Datashouldbepreprocessed (i.e.,cleanedandnormalized)beforefeedinginto anML/DLalgorithm.Beforealgorithmselection,we needtoinvestigatevariousMLalgorithms.HRSsmay requireDLtechniques(CNNsandRNNs)forbetter predictionresults.Thereisaneedtooptimizehyper‐parameters(learningrate,regularization).Ensem‐blemethodscanbeusedbycombiningpredictions frommultiplemodels.Performanceevaluationmet‐ricssuchasaccuracyandrecallcanbeconsidered,and cross‐validationmethodslikek‐foldcross‐validation canbeusedtoimproveHRSperformance.Domain‐speci icknowledge,suchascollaborationwithsleep medicinespecialists,isessential.Understandingclini‐calimplicationsisalsoveryimportant.
Todemonstrateitsef iciencyandeffectivenessin thehealthcareindustry,thestudy[71]presentsa HealthcareMonitoringSystem(HMS)thatcombines IoTandMLtechnologies.Itdoesthisbyusingwear‐ablesensorsforreal‐timemonitoringandamedical
Figure4. WorkflowforanHRSforSA
Table8. RecommenderSystemforSA
Author Disease Prediction
RecommenderSystem
ML/DL Algorithm
DataSetUsed
Nanehkaran, 2022[63] ChronicDisease collaborative iltering K‐NNclassi ier PhysioNetdata repository
Razaetal. 2023[65] SA two‐stagerecommender system; precision=89%, macro‐averageF1score =84% – MIMICdataset
Kaneriyaetal.[68] SA Markovdecision‐based recommendersystem HiddenMarkov Model –
Pinonetal., 2023[66] – federatedlearning recommendersystem – historicaldisease‐drug interactionsanddrug data
delRioetal., 2023[67] ChronicDisease – restricted Boltzmann machine wearablesensors connectedonpatient’s body
Casal‐Guisande etal.,2023[64] OSA personalized recommendation MLclassi ierwith fuzzyexpert system datasetwith4400 patientsfromtheÁlvaro CunqueiroHospital (Vigo,Galicia,Spain)
Torres‐Ruizetal., 2023[69] COVID‐19 collaborative iltering – –
Chinyereetal., 2023[70] Hospital Recommendation collaborative iltering – datacollectedthrough mobile/webapplication
decisionsupportsystemforthedetectionandanalysis ofhealthissues.
3.8.AIforSADiagnosis
Researchersacrosstheworldhaveexploredthe ieldofAIforSAdiagnosisandtheroleofAIinassist‐inginSAtreatment.Inlinewiththis,Kaneriaetal.[68] developedanautomatedDLmethodcalledDOSED todetectsleep‐breathingeventsinPSGrecordings, whichareusedtodiagnoseOSA.Theperformanceof themethodwascomparedtotheprecisionofhuman sleepexpertsindiagnosingtheseverityofOSAand detectingindividualbreathingevents.Furthermore, Thoreyetal.[72]reviewedpublicationsfrom1999to 2022toexploreAI’sroleinimprovingOSAtreatment. AIcanpredicttreatmentoutcomes,evaluatecurrent treatmenteffectiveness,andenhanceunderstanding
ofOSAmechanisms.Strumpfetal.[56]havedesigned Belun‐Ringandtesteditsperformance,involving84 participantsandcomparingtheBelun‐Ringresults within‐labPSG.TheyfoundthattheBelunRingwith BSP2algorithmsaccuratelydetectedOSA,classi ied itsseverity,andclassi iedsleepstages.
3.9.ChallengesandAvailableDataSetsforSA
SAdetectionusingMLandDLapproachesis stronglyreliantonhigh‐qualitydata.Researchersface numerousissueslinkedtodataavailability,privacy, andsecrecy.Herearethemainissues:
1) ObtaininglabeledSAdataischallengingowingto thespecializednatureofthestudyandtheneces‐sityforexpertcomments.
Table9. VariousDatasetsavailableforSA
UCDDBdataset/St.Vincent UniversityHospital,Dublin[73]
(SHHS)[75,77]
2) Researchersfrequentlyusepubliclyavailabledata setstoconstructandtesttheirmodels.These databasesarecriticaltodevelopingSAresearch.
3) Dataprivacyandcon identiality.Sleep‐related information,includingphysiologicalsignals (electroencephalography,electrocardiography, andbreathingpatterns),issensitiveandpersonal. Maintainingpatientprivacyandadheringto ethicalrulesarecritical.Researchersmustkeep dataanonymousandsecure.
4) NationalSleepResearchRepository(NSRR).The NSRRisanexcellentresourceforSAresearchers.It hostsavarietyofsleepproblemdatasets,includ‐ingSA.Researcherscanexaminemanysortsof data,includingPSGrecordings,actigraphydata, andclinicalinformation.
Table 9 containsinformationaboutspeci icdata setsimportantforSAresearch.
4.Conclusion
SAisasleep‐relateddisorderthathasseverecon‐sequencesifnottreatedontime.TodetectSAatan earlystage,MLandDLmethodsarecrucial.These methodscanbeappliedtosignalscollectedfroma patient.SignalssuchasECG,EEG,andSpO2 arevery usefulindiagnosis,buttheavailabilityofsuchreal‐timedataisbighurdlethatneedstobeaddressed. Thereisalotofscopeforfutureresearchinthedirec‐tionofoptimalfeatureselectionfromthesesignals andthetestingofensembleML/DLtechniquestoele‐vatepredictionaccuracies.AnHRScanrecommend somelifestylechanges,treatmentrecommendations, oradoctororhospitalrecommendationtopatients sufferingfromSA.Thesetechnologieshelptodiagnose andeffectivelytreatpatientswithSA.Inparallel,SA patientscandoregularoropharyngealexercise,yoga, andpranayamawhichhaveprovedtobelong‐term, effective,andnoninvasivetreatments.
AUTHORS
MubashirKhan∗ –ResearchScholar,Departmentof CSE,ASET,AmityUniversity,Rajasthan,India,e‐mail: khan.mr24@gmail.com.
YashpalSingh –AssociateProfessor,ASET, AmityUniversity,Rajasthan,India,e‐mail: yashpalsingh009@gmail.com.
HarshitBhardwaj –ASET,AmityUniversity,Noida, UP,India,e‐mail:hb151191@gmail.com.
∗Correspondingauthor
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