Journal of Automation, Mobile Robotics and Intelligent Systems, vol. 17, no. 4 (2023)

WWW.JAMRIS.ORG pISSN 1897-8649 (PRINT)/eISSN 2080-2145 (ONLINE) VOLUME 17, N° 4, 2023

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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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Pablo Estévez (University of Chile)

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Fernando Gomide (University of Campinas, Brazil)

Aboul Ella Hassanien (Cairo University, Egypt)

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Ching-Teng Lin (National Chiao-Tung University, Taiwan)

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Krzysztof Malinowski (Warsaw University of Technology, Poland)

Andrzej Masłowski (Warsaw University of Technology, Poland)

Patricia Melin (Tijuana Institute of Technology, Mexico)

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Zbigniew Nahorski (Polish Academy of Sciences, Poland)

Nadia Nedjah (State University of Rio de Janeiro, Brazil)

Dmitry A. Novikov (Institute of Control Sciences, Russian Academy of Sciences, Russia)

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Lech Polkowski (University of Warmia and Mazury, Poland)

Alain Pruski (University of Metz, France)

Rita Ribeiro (UNINOVA, Instituto de Desenvolvimento de Novas Tecnologias, Portugal)

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Leszek Rutkowski (Czestochowa University of Technology, Poland)

Alessandro Saffiotti (Örebro University, Sweden)

Klaus Schilling (Julius-Maximilians-University Wuerzburg, Germany)

Vassil Sgurev (Bulgarian Academy of Sciences, Department of Intelligent Systems, Bulgaria)

Helena Szczerbicka (Leibniz Universität, Germany)

Ryszard Tadeusiewicz (AGH University of Science and Technology, Poland)

Stanisław Tarasiewicz (University of Laval, Canada)

Piotr Tatjewski (Warsaw University of Technology, Poland)

Rene Wamkeue (University of Quebec, Canada)

Janusz Zalewski (Florida Gulf Coast University, USA)

Teresa Zielińska (Warsaw University of Technology, Poland)

Publisher: All rights reserved

Journal of Automation, Mobile Robotics and Intelligent Systems

VOLUME 17, N˚4, 2023

DOI: 10.14313/JAMRIS/4-2023

Contents

1

Matrix Transposition Algorithm Using Cache Oblivious

Samuel Guzmán López, Adolfo Javier San Gil Santana, Jorge Alberto Cuba Alonso del Rivero, Sonia Pérez Lovelle, Humberto Díaz Pando

DOI: 10.14313/JAMRIS/4‐2023/25

8

On Various Types of Soft Ground – A Case Study on Various Types of Soft Ground – A Case Study

Maciej Trojnacki, Przemysław Dąbek

DOI: 10.14313/JAMRIS/4‐2023/26

17

The Overview of Challenges in Detecting Patients’ Hazards During Robot‐Aided Remote Home Motor Rehabilitation

Julia Wilk, Piotr Falkowski, Tomasz Osiak

DOI: 10.14313/JAMRIS/4‐2023/27

28

Binary Shuffled Frog Leaping Algorithm for Optimal Allocation of Power Quality Monitors in Unbalanced Distribution System

Ashkan Doust Mohammadi, Mohammad Mohammadi

DOI: 10.14313/JAMRIS/4‐2023/28

40

Lyapunov‐L Lasalle Based Dynamic Stabilization for Fixed Wing Drones

Jean Sawma, Alain Ajami, Thibault Maillot, Joseph el Maalouf

Doi: 10.14313/JAMRIS/4‐2023/29

49

New Robust Model for Stability and H∞ Analysis for Interconnected Embedded Systems

Amal Zouhri

DOI: 10.14313/JAMRIS/4‐2023/30

56

Wimax Network Optimization Using Frame Period with Channel Allocation Techniques

Mubeen Ahmed Khan, Awanit Kumar, Kailash Chandra Bandhu

DOI: 10.14313/JAMRIS/4‐2023/31

68

Extended State Observer Based Robust Feedback Linearization Control Applied to an Industrial CSTR

Ali Medjebouri

DOI: 10.14313/JAMRIS/4‐2023/32

79

Implementing Visual Assistant Using YOLO and SSD for Visually‐Impaired Persons

Ratnesh Litoriya, Kailash Chandra Bandhu, Sanket Gupta, Ishika Rajawat, Hany Jagwa

DOI: 10.14313/JAMRIS/4‐2023/33

MATRIXTRANSPOSITIONALGORITHMUSINGCACHEOBLIVIOUS MATRIXTRANSPOSITIONALGORITHMUSINGCACHEOBLIVIOUS MATRIXTRANSPOSITIONALGORITHMUSINGCACHEOBLIVIOUS

Submitted:11th January2023;accepted:18th March2023

DOI:10.14313/JAMRIS/4‐2023/25

Abstract:

TheParallelandDistributedComputinggroupbelonging totheIntegratedTechnologicalResearchComplex(CITI). hasbeenengagedinthecreationofgeneral‐purpose componentsthatsupporttheprocessingoflargevolumes ofinformationthatcharacterizetheproblemsinvolvedin parallelcomputing.

Usingtheobliviouscachemodel,whichworksinde‐pendentlyofthecomputerarchitecture,andthedivide andconquerprinciple,analgorithmformatrixtrans‐positionisimplementedtoreducetheexecutiontime ofthisalgebraicoperation.Thealgorithmensuresthat mostofthedatacontentisloadedtothecacheforfast processing,andmakesthemostofitsstayinthecache tominimizemissedreadsandachievegreaterspeed.

Theworkincludesconclusionsandstatisticaltests carriedoutfromexperimentsoncomputerswithdifferent architectures,reflectingthesuperiorityofthealgorithm thatusesobliviouscachefromanorderofmatrixdeter‐minedaccordingtothecharacteristicsofeachPC.

Keywords: Cacheoblivious,Matrixtransposition,Missed readings

1.Introduction

TheIntegratedTechnologicalResearchComplex (CITI)wascreatedasacoordinationprojectbetween the TechnologicalUniversityofHavana(CUJAE)and theMinistryofInterior(MININT).Thisentityis designedtohostthemostadvancedtechnologies beingworkedwithworldwide[1].

CITI’smissionistodeveloptechnologiesto enhancethesecurityandinternalorderofthe country.Itsvisionistobeacreative,innovative andbenchmarkorganizationinhumancapital management.Inaddition,tobeareferencein theapplicabilityoftheresultsobtainedinthe developmentofsystems,technologiesandinnovative integratedapplications,withimpactonsecurityand internalorder,forwhichitwillbaseitsworkonthe integrationofhighlyquali iedprofessionalswith talentedstudents[1].

AtCITIthereareprojectsinwhichmatrixtranspo‐sitionisintensivelyused,sothistaskwasassignedto theParallelandDistributedComputinggroup,which isdedicatedtoreducetheexecutiontimeofvari‐ousalgorithmsbyemployingparallelismandrecur‐rencetechniques.Thistime,thetechniqueselectedby thegroupwasthecacheoblivious,arecurrenttech‐niqueaboutwhichthereissomeliteratureandimple‐mentationtestedanddocumentedbyotherauthors [2–4].Thismethodwasusedbytheauthorsina researchworkonmatrixmultiplicationobtaining goodresults[5].

2.CachingAlgorithms

2.1.Cache‐awareAlgorithms

Cache‐awarealgorithmstakeintoaccountthe hardwarearchitectureonwhichtheyarerunning, mainlythecachearchitecture,i.e.thenumberofcache levelsandthesizeofeachlevel.Theyarespeci ically developedtoperformaswellaspossibleintheenvi‐ronmentforwhichtheywerecreated.

Thisposesaproblemwhenchangingtheenviron‐ment,sinceifacache‐awarealgorithmisexecuted outsidethearchitectureforwhichitwasdesigned, itwillnotperformwell.Tocounteractthisproblem, cacheobliviousalgorithmswerecreated,ablework ef icientlyonanyarchitecture[6].

2.2.CacheObliviousAlgorithms

Cacheobliviousalgorithmshaveadesignthatwill alwaysbe“cache‐optimal”,regardlessofthecache hierarchy.In1996,theideaofrealizingalgorithms thatdonottakeintoaccountthearchitectureofthe computerwheretheyareexecutedwasconceivedby CharlesE.Leisersonandcalledcacheobliviousalgo‐rithms.Thistopicwas irstpublishedin1999byHar‐aldProkopinhismaster’sthesisattheMassachusetts InstituteofTechnology[4].Theuseofthecache obliviousmodelhasawidevarietyofapplications suchas:matrixmultiplication,matrixtransposition, Bioinformatics(RNAsecondarystructureprediction), ShortestPathAlgorithmwithorderO(n),dynamic programmingoftheGaussiansolution(Numerical Mathematics).

Theuseofthecacheobliviousmodelaimsto decreasemissedreadsorcachemissessincethese algorithmsusethedivide‐and‐conquerprincipleto dividetheproblemintosmallsubproblemsuntila cache‐ ittingsizeisreached,regardlessofthesizeof thecache.

SamuelGuzmánLópez,AdolfoJavierSanGilSantana,JorgeAlbertoCubaAlonsodelRivero,SoniaPérezLovelle, HumbertoDíazPando

Byreducingthenumberofmissedreadsorcache misses,executiontimesaresigni icantlyreduced, resultingingreateref iciency.

Oneofthefeaturesbywhichitoutperformsthe traditionalcacheisself‐tuning.Intypicalcachealgo‐rithms,thealgorithmsrequiretuningtovariouscache parametersthatarenotalwaysavailablefromthe manufacturerandareoftendif iculttoextractauto‐maticallywhichhinderscodeportabilitywhereasin cacheobliviousalgorithmsnosuchtuningisrequired, asinglealgorithmshouldworkwellonallmachines withoutanymodi ication[3,4,7–9].

2.3.MatrixTransposition

Matrixtranspositionisafundamentaloperation oflinearalgebraandothercomputationalprimitives suchasthemultidimensionalFastFourierTransform; itisalsoappliedinnumericalanalysisineconomics, imageandgraphicsprocessing,aswellasbeingused incryptographicmethods[10].

Thisseeminglyinnocuouspermutationproblem lacksbothtemporalandspatiallocalityandisthere‐foredif iculttoimplementef icientlyformatriceswith alargevolumeofdata.Infact,thereisnotemporal localitytoexploit,sinceeachelementofthematrixis accessedatmostonce[10].

Asfarasspatiallocalityisconcerned,thematrix elementswaps(i,j)and(j,i)implicitinthetranspose semantics,whentranslatedintomemoryaddresses usingcanonicalrow‐majororcolumn‐majorordering, equalsthememorylocalitiesni+jandnj+i.Depending onthevaluesofiandj,thesemaybecloseorfar apartintermsofcachesetsormemorypages.Care‐fulschedulingoftheseswapoperationsisrequired togainanyadvantagefromthesemultiwordcache lines[10].

Explicittranspositionofanarrayintomemorycan oftenbeavoidedbyaccessingthesamedatainadif‐ferentorder.Forexample,softwarelibrariesforlinear algebra,suchasBLAS,generallyprovideoptionsto specifythatcertainmatricesshouldbeinterpretedin transposedordertoavoidtheneedfordatamove‐ment[10].

Describingthealgebraicoperationassuch,atrans‐posedmatrixistheresultofrearrangingtheorigi‐nalmatrixbyexchangingrowsforcolumnsinanew matrix(seeFigures1and2).

Inotherwords,thetransposedmatrixistheaction ofselectingrowsfromtheoriginalmatrixandrewrit‐ingthemascolumnsinthenewmatrix.

Examples:

2.4.TranspositionofBlockMatrices

Themanipulationofmatriceswithalargenum‐berofrowsandcolumnsinvolvesbigproblems,even whentheyarehandledwithacomputer.Therefore, itisofteninterestingtoknowhowtodecomposea problemusinglargematricesintosmallerproblems, i.e.,usingsmallermatrices[11].

Thepossibilityofdecomposingamatrixinto smallermatriceshasmanyapplicationsincommuni‐cations,electronics,solvingsystemsofequations,tak‐ingadvantageofthevectorstructureofsomecomput‐ers,andsoon.And,especially,itgivesthepossibility ofwritingamatrixinamorecompactway[11].

Theblocksareobtainedbydrawingimaginaryver‐ticalandhorizontallinesbetweentheelementsofthe matrix.Theirdimensiondependsonthesizeofthe cacheblocksandaimstostoreasmuchinformation aspossible.

3.AlgorithmImplementation

3.1.DescriptionofOperation

Thefundamentalideaistoreducethetransposeof amatrixtothetransposeofsmallsubmatrices.Thisis achievedbydividingthematricesinahalfalongtheir largestdimensionuntilonlyonematrixtransposethat itsinthecacheneedstobecarriedout(intheory, onecouldfurtherdividethematricesdowntoabase caseofsize1×1,butinpracticealargerbasecaseis used,e.g.,16×16,inordertoamortizetheoverhead ofcallingrecursivesubroutines)[12].

3.2.DescriptionoftheImplementation

Insection 2,allthetheoreticalfoundationsthat supporttheimplementationofamatrixtransposition algorithmusingthecacheobliviousmodelwerepre‐sented.Algorithm 1,adaptedfromtheonefoundin https://es.stackoverflow.com,wasused.

Thisalgorithmhasfourintegersandapointeras parameters,ofwhichthe irstandthirdarefunda‐mentaltodividetheoriginalmatrixintosmallsub‐matrices.Thesecondandfourthrefertothenumber ofrowsandcolumnsrespectively,whilethepointer referstotheresultmatrix.

Figure1. Exampleoftranspositionofasquarematrix andanotheroforder2x3(takenfrom[11])

Figure2. Exampleoftranspositionofamatrixoforder 3x7(takenfrom[11])

Table1. Computercharacteristics

Characteristics

PC1 PC2 PC3 PC4 PC5 PC6 PC7

Processor Intel(R)Core (TM) i3‐5020UCPU @2.2GHz 2.2GHz

RAM 4,00GB

Single‐Channel DDR3 @798MHz

Intel(R) Celeron(R) CPUG3900@ 2.8GHz 2.8GHz

4.00GB

(2.95GB utilizable) DDR4‐2133

Intel(R) Celeron(R) CPUG1840@ 2.8GHz 2.8GHz

2,00GB

Single‐Channel DDR3 @665MHz

Intel(R)Core (TM) i3‐7130UCPU @2.7GHz 2.7GHz

8.00GB (7.95GB utilizable) DDR4‐2400

Intel(R)Core (TM)i3‐4130 CPU@ 3.4GHz

Intel(R)Core (TM) i7‐1165G7@ 2.8GHz 2.8GHz

8.00GBDDR3 16.2GB (15.8GB utilizable) DDR4‐3200

Intel(R) Pentium(R) CPUG4560@ 3.50GHz 3.50GHz

8.00GB (7.95GB utilizable) DDR4‐2400

Typeof system Windows64 bits Windows64 bits Windows64 bits Windows64 bits Linux64bits Windows64 bits Windows64 bits

Motherboard ASUSTek COMPUTER INC.X540LA

Gigabyte Technology Co.,Ltd. B85M‐DS3H

Gigabyte Technology Co.,Ltd. B85M‐DS3H

voidcachetranspose(int rb, int re, int cb, int ce, Matrix*T)

{int r=re-rb,c=ce-cb; if (r<= 16 &&c<= 16){ for (int i=rb;i<re;i++){ for (int j=cb;j<ce;j++){

T->data[j*rows+i]=data[i*columns+j];}}} else if (r>=c){

cachetranspose(rb,rb+(r/2),cb,ce,T); cachetranspose(rb+(r/2),re,cb,ce,T);} else {

cachetranspose(rb,re,cb,cb+(c/2),T); cachetranspose(rb,re,cb+(c/2),ce,T);}}

Algorithm1. Recursivematrixtranspositionalgorithm usingcacheoblivious

4.Experiments

Forthedevelopmentoftheexperimentsitwas necessaryapreviousstudyofseveralalgorithms(tra‐ditional,blocksandblocks_for_squared_matrices)to establishacomparisonwiththoseusingthecache obliviousmodel(forsquareandnon‐squareorders). Theseexperimentsconsistofrunningeachalgorithm 5timesonorderswithdifferentcharacteristics(see Table1).Fromtheresultsobtained,astatisticalanaly‐sisisperformedtodeterminewhetherthealgorithms usingthecacheobliviousmodelaresuperior(interms ofexecutiontimeandmissedreads)tothosethatdo notusethismodel.

4.1.Results

Inthissectionwepresentdiagramsshowingthe averageexecutiontimeandthemissedreadings(the latteronlyinPC5),foreachofthealgorithmsanalyzed.

Inthosecases,wherenon‐squaredmatriceswere tested,thesewere illedwithzerosinordertousethe blocks_for_squared_matricesalgorithmforthecorre‐spondingcomparisons.

DellInc. 02DG7R (U3E1)

VersiónA00

Gigabyte B85M‐DS3H HPSpectre 14‐EA GigabyteGa‐H110m‐S2h

AscanbeseeninFigure3,forthecomputeriden‐ti iedasPC1,theblocks_for_squared_matricesalgo‐rithmisfasterthantherestofthoseanalyzedfor orderslowerthan14000,fromwhichthealgorithm usingcacheobliviousstartstobesuperior.

Figure4showsthatforthecomputeridenti iedas PC1,thealgorithmusingcacheobliviousissuperior intermsofexecutiontimetothetraditional,block andblock_for_squared_matricesalgorithmsforallthe ordersanalyzed.

Figure3. BehaviorofthealgorithmsinPC1forsquare orders

Figure4. BehaviorofthealgorithmsinPC1for non‐squareorders

ItisevidentfromFigure5 that,forthecomputer describedasPC2,thealgorithmusingcacheoblivious issuperiorintermsofexecutiontimetothetradi‐tionalandblockalgorithmsforallorders,whilethe blocks_for_squared_matricesalgorithmhasloweror similartimestotheoneusingcacheobliviousupto order10000,fromwhichthecacheobliviousalgo‐rithmpresentslowervalues.

Figure6showsthat,forthecomputeridenti iedas PC2,thealgorithmusingcacheobliviousissuperior intermsofexecutiontimetothetraditional,block andblock_for_squared_matricesalgorithmsforallthe ordersanalyzed.

Figure 7 showsthat,forthecomputeridenti‐iedasPC3,thealgorithmusingcacheobliviousis superiorintermsofexecutiontimetothetradi‐tionalandblockalgorithmsforallorders,whilethe blocks_for_squared_matricesalgorithmhaslowerexe‐cutiontimesthantheoneusingcacheobliviousup toorder6000.Between8000and12000theresults aresimilarandfromthelatter,thecacheoblivious algorithmstartstohavelowervalues.

Figure8showsthat,forthecomputeridenti iedas PC3,thealgorithmusingcacheobliviousissuperior intermsofexecutiontimetothetraditional,block andblock_for_squared_matricesalgorithmsforallthe ordersanalyzed.

non‐squareorders

Figure 9 showsthat,forthecomputeridenti‐iedasPC4,thealgorithmusingcacheobliviousis superiorintermsofexecutiontimetothetradi‐tionalandblockalgorithmsforallorders,whilethe blocks_for_squared_matricesalgorithmhaslowerexe‐cutiontimesthantheoneusingcacheobliviousuntil order12000,whentheystarttohavesimilarvalues.

Figure10showsthat,forthecomputeridenti ied asPC4,thealgorithmusingcacheobliviousissuperior intermsofexecutiontimetothetraditional,block andblock_for_square_matricesalgorithmsforallthe ordersanalyzed.

Figure11showsthat,forthecomputeridenti ied asPC5,thealgorithmusingcacheobliviousissuperior intermsofexecutiontimetothetraditional,block andblock_for_squared_matricesalgorithmsforallthe ordersanalyzed.

Figure12showsthat,forthecomputeridenti ied asPC5,thealgorithmusingcacheobliviousissuperior intermsofexecutiontimetothetraditional,block andblock_for_squared_matricesalgorithmsforallthe ordersanalyzed.

ItisevidentinFigure 13 that,forthecomputer identi iedasPC6,thealgorithmusingcache

Figure5. BehaviorofthealgorithmsinPC2forsquare orders

Figure6. BehaviorofthealgorithmsinPC2for non‐squareorders

Figure7. BehaviorofthealgorithmsinPC3forsquare orders

Figure8. BehaviorofthealgorithmsinPC3for non‐squareorders

Figure9. BehaviorofthealgorithmsinPC4forsquare orders

Figure10. BehaviorofthealgorithmsinPC4for

Figure17. Performanceofthealgorithmsintermsof missedreadingsonPC5forsquareorders

Figure18. Performanceofthealgorithmsintermsof missedreadingsonPC5fornon‐squareorders

obliviousissuperiorintermsofexecutiontime tothetraditionalalgorithms,byblocksand blocks_for_squared_matrices,startingfromthe order10000x10000.

Figure14showsthat,forthecomputeridenti ied asPC6,thealgorithmusingcacheobliviousissuperior intermsofexecutiontimetothetraditional,block

andblock_for_squared_matricesalgorithmsforallthe ordersanalyzed.

Figure15showsthat,forthecomputeridenti ied asPC7,theblocks_for_squared_matricesalgorithmis superiortotheothersanalyzedanditcanbeobserved thatthealgorithmusingcacheobliviousobtainsa certainparityfromtheorder14000x14000.

Figure11. BehaviorofthealgorithmsinPC5forsquare orders

Figure12. BehaviorofthealgorithmsinPC5for non‐squareorders

Figure13. BehaviorofthealgorithmsinPC6forsquare orders

Figure14. BehaviorofthealgorithmsinPC6for non‐squareorders

Figure15. BehaviorofthealgorithmsinPC7forsquare orders

Figure16. BehaviorofthealgorithmsinPC7for non‐squareorders

Table2. ResultsobtainedinPC1forsquareorders

Algorithms traditional blocks blocks_for_squared_matrices

Table3. ResultsobtainedinPC1fornon‐squaredorders

Algorithms traditional blocks blocks_for_squared_matrices

Table4. ResultsobtainedinPC5formissedreadingsinsquareorders

Algorithms traditional blocks blocks_for_squared_matrices

Table5. ResultsobtainedinPC5formissingreadingsinnon‐squareorders

Algorithms traditional blocks blocks_for_squared_matrices

Figure16showsthat,forthecomputeridenti ied asPC7,thealgorithmusingcacheobliviousissuperior intermsofexecutiontimetothetraditional,block andblock_for_squared_matricesalgorithmsforallthe ordersanalyzed.

4.1.1.Missedreadings

ThePAPI(PerformanceApplicationProgramming Interface)library,developedattheUniversityofTen‐nessee,wasusedtoaccountformissedreads.Itsmain purposeistoprovideaccesstothePMCs(Perfor‐manceMonitoringCounter)ofadiversecollectionof modernprocessors[13].PAPIprovidesanabstraction layerthatallowsdeveloperstoaccessPMCs.Instead, thedeveloperusescallstothePAPIAPI(Application ProgramingInterface),makingthecodeportable,i.e. itcanbeusedonanyarchitecturesupportedbythe librarywithoutmodifyingaccesstoPMCs[14].

ThemissingreadingswerecountedonthePC5 computer,whichhasaLinuxoperatingsystem becausethelibraryused(PAPI)hasnotprovidednew updatessincetheXPversionofWindows.

Figure17showsthat,forthecomputeridenti ied asPC5,thealgorithmthatusescacheoblivioushasthe lowestnumberofmissedreadings.

Figure18showsthat,forthecomputeridenti ied asPC5,thealgorithmusingcacheoblivioushasfewer missedreadings.

5.StatisticalAnalysis

TheWilcoxonnonparametrictestwasusedforsta‐tisticalanalysis.Itwasselectedsinceitwasproven thatthedatadonotfollowanormaldistributionand duetothesmallsamplesize.Itisexpectedthat,when thetestisrun,itwillreturnap<∝value,ifthisoccurs H0 isrejectedanditisconcludedthattheexecution timeofthecacheobliviousalgorithmislessthanthat ofthetraditionalalgorithm.

Severalsignedranktestswereappliedwhenthe sampleswerepaired,oneforeachofthelastthree ordersofthealgorithmsoneachcomputerdescribed.

ThefollowingaretheresultsobtainedonPC1in termsofexecutiontimeandonPC5intermsofmissed readings:

ItisevidentintheresultsofTable 2 thatthe blocks_for_squared_matricesalgorithmisfasterthan therestoftheanalyzedalgorithmsfororderslower than14000,fromwhichthealgorithmusingcache obliviousstartstobesuperior.

TheresultsinTable 3 showthesuperiorityin termsofexecutiontimeofthealgorithmusingthe cacheobliviousmodelforalltheordersanalyzed.

Table 4 showsthesuperiorityintermsofmissed readingsofthealgorithmusingthecacheoblivious modelforallordersanalyzed.

Table 5 showsthesuperiorityintermsofmissed readingsofthealgorithmusingthecacheoblivious modelforallordersanalyzed.

Thetestwasperformedwiththestatisticalsoft‐wareR.Afterthetestitwasdemonstratedthatthe matrixtranspositionalgorithmusingthecacheobliv‐ious,dependingonthearchitectureofthecomputer whereitwasusedandfromacertainorder,willbe betterthantheotheralgorithmsanalyzed.

6.Conclusion

Underthecomputationalconditionsusedforthe experiments:

1) OnacomputerwithaWindowsoperatingsystem, inthematrixtranspositionoperation,forsquare ordermatricesitisnotfeasibletoemploythealgo‐rithmusingthecacheobliviousmodelforanorder lessthan14000x14000.

2) Regardlessofthecomputerarchitecture,itwas shownthatfromorder6000x8000fornon‐square ordermatrices,thematrixtranspositionalgorithm usingcacheobliviousisfasterthantherestofthe algorithmsstudied.

3) Theblocks_for_squared_matricesalgorithmhasa lowerperformancewhenusedfornon‐square matricessincethesemustbecompletedwithzeros untiltheirorderissquareandthereforethealgo‐rithmincreasesitsexecutiontime.

4) Forlargevolumesofinformation,theexecution timeisindirectcorrespondencetothemissed readings.

5) Algorithmsthatusethecacheobliviousmodelfor largevolumesofinformationhavefewermissed readingsthantherest.

AUTHORS

SamuelGuzmánLópez∗ –TechnologicalUniversity ofHavanaJoséAntonioEcheverría,Cuba,e‐mail: samuguzmanlopez97@gmail.com.

AdolfoJavierSanGilSantana –TechnologicalUni‐versityofHavanaJoséAntonioEcheverría,Cuba, e‐mail:asang@ceis.cujae.edu.cu.

JorgeAlbertoCubaAlonsodelRivero –Techno‐logicalUniversityofHavanaJoséAntonioEcheverría, Cuba,e‐mail:jcuba@ceis.cujae.edu.cu.

SoniaPérezLovelle –TechnologicalUniversity ofHavanaJoséAntonioEcheverría,Cuba,e‐mail: sperezl@ceis.cujae.edu.cu.

HumbertoDíazPando –TechnologicalUniversityof HavanaJoséAntonioEcheverría,Cuba,e‐mail:hdi‐azp@ceis.cujae.edu.cu.

∗Correspondingauthor

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SIMULATIONRESEARCHOFMOTIONOFLIGHTWEIGHTWHEELEDMOBILEROBOT

SIMULATIONRESEARCHOFMOTIONOFLIGHTWEIGHTWHEELEDMOBILEROBOT ONVARIOUSTYPESOFSOFTGROUND–ACASESTUDY

Submitted:13th October2023;accepted:27th November2023

MaciejTrojnacki,PrzemysławDąbek

DOI:10.14313/JAMRIS/4‐2023/26

Abstract:

Aproblemofinfluenceofthreetypesofsoftground onlongitudinalmotionofalightweightfour‐wheeled mobilerobotisconsidered.Kinematicstructure,main designfeaturesoftherobotanditsdynamicsmodel aredescribed.Anumericalmodelwaselaboratedto simulatethedynamicsoftherobot’smulti‐bodysystem andthewheel‐groundinteraction,takingintoaccount thesoildeformationandstressesoccurringonthecir‐cumferenceofthewheelintheareaofcontactwith thedeformableground.Numericalanalysisinvolvingfour velocitiesofrobotmotionandthreecasesofsoil(dry sand,sandyloam,clayeysoil)isperformed.Withinsim‐ulationresearch,themotionparametersoftherobot, groundreactionforcesandmomentsofforce,driving torques,wheelsinkageandslipparametersofwheels werecalculated.Aggregatedresearchresultsaswellas detailedresultsofselectedsimulationsareshownand discussed.Asaresultoftheresearch,itwasnoticed thatwheelslipratios,wheels’sinkageandwheeldriving torquesincreasewithdesiredvelocityofmotion.More‐over,itwasobservedthatwheels’sinkageanddriving torquesaresignificantlylargerfordrysandthanforthe otherinvestigatedgroundtypes.

Keywords: Lightweightwheeledmobilerobot,Longitudi‐nalmotion,Deformableground,Dynamicsmodel,Tire‐groundinteraction,Wheelslip,Wheelsinkage,Simula‐tionstudies

1.Introduction

Lightweightwheeledmobilerobotsareversatile vehiclesthatworkinbothindoorandoutdoorenvi‐ronments.Thelargestgroupofsuchvehiclesare lightweightmobilerobots,anexampleofwhichare robotsforspecialapplications.Suchrobotsmoveon avarietyofsurfaces,bothpaved[1]andunpaved[2].

Atthestageofdesigningrobotstructuresand controlsystems,itisbene icialtoknowtherobot dynamicsmodel[3,4].Theformoftherobotdynamics modelisfundamentallyin luencedbyitskinematic structure[5],whichdependsontheareaofapplication oftherobot.Suchamodelcanbedevelopedusingclas‐sicalmethods,e.g.,usingtheNewton‐Eulerformalism orLagrangeformalism[6].

Alternativemethodsmayalsobeusedinwhichthe dynamicsmodelcanbebuiltusingsystemidenti ica‐tionthroughmeasurementsoftheinputandoutput signalsofthesystem[7].Thisprocesscanbecar‐riedoutbothof line[8]andonline,dependingonthe method.Italsomayormaynotrequiretheknowledge oftherobot’smodelstructure.Arti icialintelligence methodscanalsobeused[9],e.g.,basedonarti icial neuralnetworks[10],toapproximateunknownnon‐linearfunctionsinthedynamicsmodel.

Regardlessoftheadoptedmethodofcreating thedynamicsmodel,itisimportantthatittakes intoaccountthewheel‐groundinteraction.Forthis purpose,tiremodelsareintroducedinthedynam‐icsmodel.Tire‐groundinteractioninthecaseof lightweightmobilerobotsmovingatrelativelyhigh speedsshouldtakeintoaccountthepossibilityof wheelslippage.Ifrobotmotionoccursondeformable ground,theninadditiontowheelsliptheground deformationhastobeconsideredaswell.Modeling theinteractionofwheelswithunpavedgroundisthe subjectofterramechanics,thebasisofwhichwasfor‐mulatedinthework[11].

Theproblemofmotionondeformablegroundis ofcriticalimportanceinthecaseofoutdoorwheeled mobilerobotsusedforreconnaissanceincivilandmil‐itaryscenariosandisrelatedtotheproblemofrobot mobility.Inthiscase,thequestionsofhowtheground typeanddesiredrobotvelocityaffectwheelslips,soil deformation(orwheelsinkage)anddrivingtorques shouldbeanswered.Examplesofstudiesofmotion ofvehiclesondeformablegrounds,especiallytracked andwheeledones,are[11,12]and[13].Themajority ofworksisfocusedonmannedvehicles;however, onecanalso indworksconcerningwheeledmobile robots,forinstance[14],andinparticularplanetary rovers[15,16].Heavyoff‐roadvehiclestypicallyuse pneumaticwheels.Apartfromthetread,theirdriving propertiesaredeterminedbytirepressure,aswellas wheeldiameterandwidth.Theresearchresultsinthis areaaredescribed,amongothers,inworks[11,12]. Inturn,lightweightvehicles,suchasmobilerobots forspecialapplicationsoftenhavenon‐pneumatic wheels.Therefore,intheircase,themechanicalprop‐ertiesofthewheel illingsusedareimportant.

Theaimofthispaperistostudythein luence ofthreetypesofdeformablegroundonthemotion parametersofalightweightwheeledmobilerobot duringitslongitudinalmotion.Theanalysisiscar‐riedoutfortherobotmovingwithvariousdesired velocitiesonthreedifferenttypesofsoftground,i.e., drysand,sandyloamandclayeysoil.Inthepresent work,thenumericalanalysisonlyispresented,but asimilarstudywithexperimentalveri icationwas carriedoutfordrysandinpaper[17].Inthepresent article,theissueoftheinteractionofthewheelwith thesoftgroundisalsodescribedinmoredetail.Inpar‐ticular,thedistributiononthewheelcircumference ofsoildeformationsandstressesinthecontactarea ofthewheelwiththegroundisanalyzed,whichis verydif iculttoperformatthestageofexperimental research.

2.RobotandItsModel

Withinthispaper,thePIAPGRANITEfour‐wheeledmobilerobotwithnon‐steeredwheelsis analyzed.Therobot’swheelsarenon‐pneumatic,i.e., theyare illedwithstiffeningfoam.Thisrobotisa platformdedicatedtoresearch(Fig. 1a).Therobot’s kinematicstructureisillustratedinFigure1b,where theparticularsubsystemsaredistinguished,i.e.:0–body,1–4–wheels,5–6–optionaltoothedbelts.

Therobotcanbecon iguredtoworkinseveral versions,i.e.:1.thefrontorreardrivecanbedecou‐pledandonlytheremainingwheelscanbedriven; 2.onlythefrontorrearwheelscanbedriven,but additionaltoothedbeltscanbeusedtotransferdrive totheremainingwheels;3.allwheelscanbedriven independently.Inthecaseanalyzedinthispaper,the toothedbeltswereremoved,andindependentdriveof allwheelswasused.

Inthecaseoftherobotmovingonsoftground, doublewheelswereusedbecausetheuseofstandard‐widthwheelsresultedintoomuchwheels’sinkageon sand,makingtherobotunabletomove.Thefollowing designationsofgeometricparametersoftherobot wereintroducedinFigure1b: L –wheelbase, W –track width(��1��3 =��2��4 =��,��1��2 =��3��4 =��),����,���� –respectivelyradius,andwidthofthe i‐thwheel,where ��=1,…,4

Thevelocityofthepoint R oftherobotwas assumedasthegivenparameteroftherobot’smotion, thatis �������� = ����������.Theleftsuperscript O means thatthedesiredvelocityisexpressedinthestation‐arycoordinatessystem.Iftherobotisinlongitudinal motion,thevelocitiesofthegeometriccentersofthe wheelsareequaltothevelocityofpoint R,i.e., �������� = ���������� = ��������

Withregardtodesiredangularvelocitiesofwheel spins������,iftherobotmoveswithoutslip,theycanbe determinedbysolvingtheinversekinematicsproblem forthemobileplatform,thatis,fromtherelationship:

���� = ��������/���� (1)

Figure1. PIAPGRANITErobotduringtestsinacontainer filledwithsand(a),kinematicstructureoftherobot(b)

However,wheelslippagemayoccurwhilethe robotismoving.Themeasuresofthatslippageare instantaneouslongitudinalslipratios ���� andmean longitudinalslipratio���� (longitudinalslipratioofthe wholerobot).

Thoseslipratiosaregivenwiththeformulas:

–wheelcircumferentialvelocity,

–distancetraversedbypoint R oftherobotinlon‐gitudinaldirection,�������� –desireddistancetraveledby point R whenrollingwithoutslip.

Forthepresentinvestigations,thefollowing assumptionsareadopted:

‐ wheelsaretreatedasrigidbodies, ‐ theso‐calledmulti‐passeffect(inwhichafollow‐ingwheelissubjecttosmallerrollingresistance, becauseitmovesinarutmadebyaleadingwheel) arenotconsidered,

‐ treadblocksoftiresareneglected.

Amulti‐bodydynamicsmodelwasderivedforthe robot.Itwasassumedthatontherobotacttheground reactionforces,i.e., ��F���� =[����������, ����������, ����������]�� (��= 1,…,4)andgravityforce ��G =���� ��g (Fig.2a),where ���� isrobottotalmass, ��g =[������, ������, ������]�� the vectorofgravityacceleration,andtheleftsuperscript R meansthatmentionedvectorsareexpressedinthe movingcoordinatesystemattachedtotherobot.

Thefollowingindexesareintroducedforindivid‐ualpairsofwheels: f –frontwheels(��=1,2), b –rear wheels (��=3,4).Oneachwheel,apartfromforce ofgravityandforcesfollowingfromtheinteraction withtheground,actdrivingtorque ��T�� =[0,����,0]�� andmomentofmotionresistance��M���� =[0, M����,0]�� (Fig.2b).

Asaresultofthereductionofforces ��F���� tothe axesofrotationofwheels,theforces ��F���� = ��F���� = [����������, ����������, ����������]�� areobtained.

Themulti‐bodydynamicsmodelisbasedonthe followingequationsofdynamicsforthewholevehicle andforindividualwheels(associatedwiththeirspin):

Θ and ���� = ���� –angularaccelerationsofrotationof respectivelymobileplatformandwheelaboutmen‐tionedaxes, ���������� and ���������� –componentofthe linearaccelerationoftherobotmasscenter.

Thedevelopedmodelenablesthesolutionofthe forwarddynamicsproblemfortherobot.According tothismodel,inasingletimestepofsimulation,the followingquantitiesaredetermined:

1) Instantaneousslipratiosforwheels���� (��=1,…,4) andfortherobot���� fromequations(2)and(3).

2) Geometricquantitieslikemaximumwheelsinkage ��0�� andanglesofwheel‐terraincontact ��1�� and ��2�� =����2��1�� (Fig.3a).

3) Soilsheardeformation ����(��1��)accordingto[13] andwheelsinkage ����(��1��) intherangeofwheel‐terraincontactanglesfrom −��2�� to ��1�� basedon dependencies:

����(����)=����((��1�� −����)−(1−����)(sin��1�� sin����)), (8) ����(����)=max(��0�� −����(1−cos����),0). (9)

4) Pressure����(��1��)accordingtoBekker[11]:

����(����)=��(����(����))�� = ���� ���� +���� (����(����))�� , (10) where: ����(����)–cohesive(frictional)modulusof terraindeformation, n –terraindeformationexpo‐nent.

where: ������ =��/2−��������, ������ =−��/2−��������, �������� and �������� –robotmasscentercoordinates, �������� –robotmassmomentofinertiaabouttheaxisparallel to ���� andpassingthroughrobotmasscenter, �������� –wheelmassmomentofinertiaaboutitsspinaxis,E=

5) Normalstress����(��1��)≈����(��1��),maximumshear stress ����������(��1��),basedonmodi iedMohr‐Coulombfailurecriteria[18](Fig. 3b)including thecaseofmovingtiresurfacewithrespecttosoil: ����������(����)=min(��������(����),��+����(����)tan��), (11) thatistakingintoaccountsoilcohesion c,internal frictionangle��andcoef icientofstaticfriction���� forthewheel‐terrainpairaccordingto[19].

Figure2. Illustrationofforcesandmomentsofforceactingontherobotanditswheels

6) ShearstressesaccordingtoJanosi‐Hanamoto hypothesis[12]intherangeofwheel‐terrain contactanglesfrom−��2�� to��1��:

where K isthesheardeformationparameter.

7) Forcesandmomentsofforcelike:staticnormal load����,tractionforce����,motionresistanceforce ������ andmomentofmotionresistance������ basedon theknownstressdistributionoverwheelcircum‐ference,accordingtoformulasin[13],i.e.,basedon equations:

and inally,resultantforces:longitudinal ���������� = ���� +������ andnormal ���������� =���� +������,which includescomponentforceresultingfromthetire‐groundsystemdamping������ =������ 0��sgn(��0��).

8) Linearandangularaccelerations,i.e.: ����������, ����������, Θ and ���� (��=1,…,4),forthemulti‐body systemoftherobotbasedontheequationsof dynamics(4)–(7).

Itshouldbenoted,thatvelocities ������, ����������, ���� necessaryfordeterminationofslipratios ���� and ���� inthe irststageofthealgorithmdescribedabove, coordinatesofcentersofwheelsnecessaryforcalcu‐lationofwheels’sinkage��0�� andangles��1�� and��2�� in thesecondstageofthatalgorithmaretakenfromthe previoustimestepofcalculations.

3.ResultsofNumericalStudies

NumericalstudieswereconductedintheMat‐lab/Simulinkenvironment.

Aspartofthepreliminarysimulationtests,a numericalveri icationofthewheel‐groundinterac‐tionmodelwascarriedout.Inthesestudies,theprevi‐ouslymentionedparametersofthismodelweretaken intoaccount.

Inthecalculations,itwasassumedthatthechange oftheangle���� ∈⟨−��2��,��1��⟩willbeimplementedwith astep Δ��=��/180 rad.Moreover,itwasassumed that ��2�� =����2 ��1��,where ����2 =0.4.Calculations wereperformedforthefollowinginputdata: �������� = 0.0815 m, ���������� =1 m/s, ���� =14 rad/s, ���� = 1Nm.Theassumedangularvelocityofthewheelsis themaximumfortheGRANITErobotandcorresponds tothecircumferentialvelocityequalto������ =1.4m/s.

Figure4showsthestressdistributions����(����)and ����(����)onthewheelcircumference,theresultingforces ����������, ���������� andmomentofforce M���� aswellasthe inputandoutputdatafortheanalyzedtest.

Illustrationofthedistributionofstresses ����(����) and ����(����) onthewheelcircumferenceaswellas theresultingforces ��F������, ��F������ andmomentof force M����

������ =−����(����)2 ��1�� −��2�� ����(����)d����, (16)

Figure3. Modelofaninteractionofthewheelwith deformableground(a), ��������(��) dependencyaccording to[13](b)

Figure4.

Itshouldbenotedthattheobtainedvalueofthe groundnormalreactionforceisequalto ���������� = 105.2N.Inthecaseoftheanalyzedtire,suchaforce wouldcauseitsradialdeformationequalto Δ���� = 0.0026m,whichissmallincomparisonwiththemax‐imumgrounddeformation��0�� =0.015m.

Inturn,Figure5presentsdistributionsofdeforma‐tionsofthegroundandstressesonthewheelcircum‐ferenceasafunctionoftheangle���� fortheanalyzed case.

Accordingtothepreviouslygivenformulas,after integrationofstresses w��(����), r����(����), f��(����), f����(����) and����(����),theresultantforcesandmomentofforce, areobtained,i.e.: W��, R����, F��, F���� and M����.

Itcanbenoticedthatthevalueoftheforce F���� is signi icantlyin luencedbythestressdistributionin therearpartofthetireinrelationtothedirectionof movement.

Inparticular,stress r����(����)hasnegativevaluesin therange ���� ∈(0,��1��) whilstpositivevaluesinthe range ���� ∈(−��2��,0),whilestress f��(����) haspositive valuesintherange���� ∈(−��2��,��1��),withthelargestin therange���� ∈(−��2��,0).

Aspartofthemainsimulationstudiesforthe entirerobot,thelongitudinalmotionfordesiredmax‐imumvelocities ������ from0.2m/sto0.7m/swas analyzed.Desiredmaximumacceleration���������� dur‐ingspeedingupandbraking,aswellasdesiredtotal distance���� tobetraveledwerechosenindividuallyfor theparticularcaseofmotion.Desiredparametersof robotmotionaresummarizedinTable1

ThevaluesofthebasicparametersofthePIAP GRANITEmobilerobotusedinsimulationstudiesare showninTable 2.Soilparametersrequiredbythe adoptedmodelandbasedonwork[14]arepresented inTable3

Theaggregatedresultsoftheresearchareshown inFigure 6.Itcanbenoticedthatthesmallestslip ratiosarefordrysandandthelargestforsandyloam andthattheslipratiosincreasewithdesiredvelocity. Thelargestwheelsinkageoccursfordrysand,andfor theotheranalyzedgrounds,itismuchsmaller.The wheelsinkageincreasesslightlywithrobotvelocity.

Inthecaseofdrysand,wheelsinkageismuch largerincomparisontoradialdeformationofthetire, whichwouldoccuronrigidground.Tireradialdefor‐mationwouldbe2–3mmbecausetheradialstiffness ofthetireis������ =40,000N/m[17].Fortheremaining typesofground,wheelsinkageisofcomparableorder tothisdeformation.Thedrivingtorquesincreasewith velocity,i.e.,torquesincreasenearlytwotimeswhen comparingresultsfor0.2m/sand0.7m/scasesof desiredrobotvelocity.

InFigures7–10,detailedresultsforrobotmotion withdesiredvelocity �������� = 0.5m/sondrysand, sandyloamandclayeysoilareillustrated.

Figure5. Distributionsonthewheelcircumferenceof soildeformations:tangential ����(����) (a)andnormal ����(����) (b),aswellasstressesresultingfromthem: tangential ����(����) (c),normal ����(����) (d)andresultants: w��(����), r����(����), f��(����), f����(����)= r����(����)+ f��(����) (e–h)

Table1. Desiredrobotmotionparametersforthe investigatedcases

Table2. BasicparametersofthePIAPGRANITEmobile robotusedinsimulationstudies

Dimensions ��=0.425m, ��=0.59m, ���� =0.0965m, ���� =2⋅0.064m

Massesofthebodies ��0 =36.54kg, ���� =1.64kg

Robotmasscentercoordinates �������� =−0.012m, �������� ≈0m, �������� =0.06m

Massmomentsofinertia ������ =0.016kgm2 , �������� =0.51kgm2

Tireparameters ������ =40000N/m, ������ =1000Ns/m

Table3. Soilparametersassumedfortheresearch[14]

Figure6. Influenceoftypeofsoilanddesiredmotion velocityon:longitudinalslipratiosfortherobot(a), wheelsinkage(b),drivingtorques(c)

InparticularinFigure7,timehistoriesofdesired andactualrobotvelocitiesaswellascircumferential velocityresultingfromwheelspinarepresented.It canbenoticedthatduringsteadymotion,valueof theactualrobotvelocity �������� isnoticeablysmaller withrespecttodesiredvelocity ��������.Thisisbecause therobotdoesnotachievethedesiredacceleration, especiallyintheinitialstageofmovement.

This,inturn,resultsfromthehighvaluesofthe longitudinalslipratiosofthewheels ���� occurring especiallyduringtheaccelerationoftherobot.The robot’sactuallongitudinalvelocity �������� isclosestto thedesiredvelocity �������� forthecaseoftherobot movingondrysand.Inallcases,itcanbeseenthat themaximumcircumferentialvelocityofwheels���� is reachedwithadelay,whichresultsfromtheinclu‐sionofthedynamicsofthedriveunitsinthemodel, describedinpaper[17].

InFigures 8–9 thetimehistoriesoflongitudinal slipratiosandsinkageforfrontandrearwheelsare shown,respectively.Thetimehistoriesoflongitudi‐nalslipratiosaresimilarforfrontandrearwheels. However,adifferencecanbenoticedinthecaseof wheels’sinkage,duetothefactthatthecenterof massislocatedintherearpartofthevehicle.For thisreason,highervaluesareobtainedfortherear wheels.Similartothevelocity,thetimehistoriesofthe longitudinalslipratiosaresimilartoeachotherforthe

analyzedgroundcases,butduringaccelerationthey areapparentlythesmallestforthemovementondry sand.However,therearelargedifferencesinthetime historiesofwheels’sinkagefortheanalyzedtypesof theground.De initelythehighestvaluesofwheels’ sinkageoccurfortherobot’smovementondrysand. Inturn,thesmallestvaluescanbeseeninthecaseof clayeysoil.

Finally,inFigure 10,thetimehistoriesofdriving torquesforfrontandrearwheelsareillustrated.Dur‐ingacceleration,thehighestvaluesofdrivingtorques areachievedwhentherobotmovesondrysand.Inthe caseofothergrounds,similarresultswereobtained, moreover,thedrivetorquesforthefrontandrear roadwheelsarelessdifferentiatedinrelationtothe movementondrysand.

Simulationstudieswerealsocarriedouttoanalyze theimpactofwheelgeometricparametersonlongitu‐dinalslipratios,wheelsinkageanddrivingtorques.

Inthisresearch,inrelationtostandardcon igura‐tionoftherobot,thefollowingwheelsolutionswere analyzed:

1) wheelswithwidthreducedby50%,

2) wheelswithadiameterincreasedby50%.

Theresultsofsimulationresearchindicatethat fortheanalyzedrobotmotionvelocities,changing thegeometricparametersofthewheelshasasmall impactonthedrivingtorques.

Figure7. Timehistoriesofdesiredvelocity ��v���� and actualvelocity ��v���� oftherobotaswellas circumferentialvelocityofwheels ���� obtainedin simulationoftherobot’smovementwiththemaximum velocity ������ =0.5 m/son:drysand(a),sandyloam(b) andclayeysoil(c)

Figure9. Timehistoriesofsinkageforfrontandrear wheelsobtainedinsimulationoftherobot’smovement withthemaximumvelocity ������ =0.5 m/son:drysand (a),sandyloam(b)andclayeysoil(c)

Figure8. Timehistoriesoflongitudinalslipratiosfor frontandrearwheelsobtainedinsimulationofthe robot’smovementwiththemaximumvelocity ������ =0.5 m/son:drysand(a),sandyloam(b)and clayeysoil(c)

Figure10. Timehistoriesofdrivingtorquesforfrontand rearwheelsobtainedinsimulationoftherobot’s movementwiththemaximumvelocity ������ =0.5 m/s on:drysand(a),sandyloam(b)andclayeysoil(c)

Whenwheelswithasmallerwidthwereused, slightchangesinlongitudinalslipratiosandasignif‐icantincreaseinwheelsinkagewereobserved.The changeinwheelsinkagecanbeseenfromthecom‐parisonoftheresultsshowninFigure6bforwheels withalargerwidthandinFigure11forwheelswith asmallerwidth.Thisobservationisconsistentwith theeffectsofpreliminaryexperimentaltestsforthe PIAPGRANITErobotandwasthereasonfortheuse ofwheelswithlargerwidth.

Theresultsofsimulationstudiesalsoindicatethat theuseofwheelswithadiameter50%largerleads toareductioninwheelsinkage,butthischangeis notsigni icant.However,theuseoflargerdiameter wheelsleadstoasigni icantreductioninlongitudinal slipratios,especiallyathighervelocities.Thiscanbe seenbycomparingtheresultsshowninFigure6afor wheelswithasmallerdiameterwiththeresultsin Figure12forwheelswitha50%largerdiameter.

4.ConclusionandFutureWorks

Withinthispaperthesimulationstudiesofin lu‐enceoftypeofdeformablegroundonlongitudinal motionoflightweightwheeledrobotwascarriedout.

Investigatedcasesincludedfourdesiredvelocities ofmotion,i.e.:0.2m/s,0.3m/s,0.5m/sand0.7m/s andthreetypesofground:drysand,sandyloamand clayeysoil.

Forallthosecases,aggregatedresultsofwheelslip ratio,wheelsinkageandwheeldrivingtorquewere

presented.Detailedresultsforthecaseof0.5m/s velocityonallanalyzedtypesofsoilwerealsoshown. Thefollowingmainconclusionscanbedrawnfrom theconductednumericalresearch.

Ifalightweightwheeledmobilerobotmovesona deformableground,then:

‐ longitudinalslipratiosigni icantlyincreaseswith desiredvelocity;

‐ wheelsinkageincreaseswithdesiredvelocity–in caseofmotionondrysand,wheelsinkageismuch largerthanradialdeformationoftirewhichwould occurforcomparablewheelloadonrigidground;

‐ wheeldrivingtorquesincreasewithvelocityand reachthelargestvaluesforrobotmotionondry sand;

‐ changingthewheelwidthsigni icantlyaffectswheel sinkage,i.e.,itishigherfornarrowerwheels;

‐ changingthewheeldiametercauses,inturn,a changeinthelongitudinalslipratios,i.e.,they decreaseasthewheeldiameterincreases.

Thescopeoffurtherresearchmayinclude:

‐ modelingthedynamicsofbothlightweightand heavyvehiclesusingwheelswith illingsofvarious mechanicalproperties;

‐ simulationstudiestakingintoaccounttiredeforma‐tion,treadblocksandmulti‐passeffectintiremodel;

‐ experimentalstudiesoftherobotmotiononsandy loamandclayeysoil;

‐ simulationandexperimentalstudiesofrobotturn‐ingandrotationinplaceforvarioustypesofthe ground.

AUTHORS

MaciejTrojnacki∗ –WarsawUniversityofTechnol‐ogy,FacultyofMechatronics,InstituteofMicrome‐chanicsandPhotonics,Boboli8,02‐525Warsaw, Poland,e‐mail:maciej.trojnacki@pw.edu.pl.

PrzemysławDąbek –ŁUKASIEWICZResearch Network—IndustrialResearchInstitutefor AutomationandMeasurementsPIAP,Al. Jerozolimskie202,02‐486Warsaw,Poland,e‐mail: przemyslaw.dabek@piap.lukasiewicz.gov.pl.

∗Correspondingauthor

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THEOVERVIEWOFCHALLENGESINDETECTINGPATIENTS’HAZARDSDURING

THEOVERVIEWOFCHALLENGESINDETECTINGPATIENTS’HAZARDSDURING

ROBOT‐AIDEDREMOTEHOMEMOTORREHABILITATION ROBOT‐AIDEDREMOTEHOMEMOTORREHABILITATION ROBOT‐AIDEDREMOTEHOMEMOTORREHABILITATION

Submitted:13th September2022;accepted:6th March2023

JuliaWilk,PiotrFalkowski,TomaszOsiak

DOI:10.14313/JAMRIS/4‐2023/27

Abstract:

Minimally‐supervisedhomerehabilitationhasbecome anarisingtechnologicaltrendduetotheshortages inmedicalstaff.Implementingsuchrequiresproviding advancedtoolsforautomaticreal‐timesafetymoni‐toring.Thepaperpresentsanapproachtodesigning thementionedsafetysystembasedonmeasurements andmodellingtheinterfacebetweenapatient’smuscu‐loskeletalsystemandarehabilitationdevice.Thecon‐tentcoversthesegmentationofpatientsregardingtheir healthconditionsandassignsthemsuitablemeasure‐menttechniques.Thedefinedgroupsaredescribedby thehazardswithwhichtheyaremostendangeredand theircauses.Eachcaseiscorrelatedwiththeappropriate datatypethatmaybeusedtodetectpotentialrisk. Moreover,aconceptofusingpresentedknowledgefor trackingthesafetyofbonesandsofttissuesaccordingto thebiomechanicalstandardsisincluded.Thepaperforms asetofguidelinesfordesigningsafetysystemsbasedon measurementsforrobot‐aidedhomekinesiotherapy.It canbeusedtoselectanappropriateapproachregarding aspecificcase;whichwilldecreasecostsandincreasethe accuracyofthedesignedtools.

Keywords: Biosignals,Biomechanics,Homerehabilita‐tion,Kinesiotherapy,Minimally‐supervisedtreatment, Rehabilitationrobotics

1.Introduction

Kinesiotherapyistreatmentwithmotiondesigned torestoremaximumfunctionalityofpatients.Itspur‐poseistorecoverfromdiseasesofthemusculoskele‐talsystem.Duringkinesiotherapyofextremities,a physiotherapistinteractsphysicallywiththepatient’s limbsinaspeci icwaytoregaintheirmobility[61].

Bringingbackmaximumfunctionalityisessen‐tialforbasicdailyactivities(ADL).Themotortreat‐mentoftenrequiresalotofprofessionalphysical engagement,whichmaybeovertakenbyrehabili‐tationrobots.Moreover,workingwithpeoplewho donothavetheabilitytositorstandthemselves oftenrequiresuprightstandingwiththehelpofup tothreephysiotherapists[21].Inaddition,theageing societyrequiresmoreintensiveandfrequenttreat‐mentwhilethenumberofmedicalpersonnelongo‐inglydecreases.Hence,themostsigni icantproblemis

aninsuf icientnumberofphysiotherapistsandcare‐giversinnursinghomes[50].Itispossibletoreduce theparticipationofprofessionalsinthetherapyeven whilebeingdependentonfamilymembers.However, thisrequiresthedevicestosupportperformedexer‐cisesinapreciseandcontrolledway[53].Research indicatesadvantagesofprovidingstrokepatientsand peoplewithparesis,whorequirepermanentrehabili‐tation,withtransportable,lightweight,andwearable devices.Suchmaybeinvolvedinthepost‐discharge homerehabilitation[60].

DuetotheCOVID‐19pandemic,patientsneeding constanttherapywereseverelydisadvantaged.This wascausedbypandemicrestrictionsinhumanmeet‐ings[25],overcrowdingofhospitals,andtheshortage ofhealthcaremembers.Toavoidsuchsituations,it iscrucialtodevelopwell‐validatedtoolsforremote homerehabilitation[26].

Consideringthementionedconditions,adapting rehabilitationdevicestohomeself‐useisanarising needandchallengeformedicalrobotics.Asthether‐apistmaybenotprovidedwithhapticfeedbackdur‐ingremotehomerehabilitation,developingarobust safetysystemiscritical[80].Suchshouldanalyse dynamicsoftherehabilitatedbodysegmentandaddi‐tionalmeasurementstoassessthesafeoperationof auserwithoutinvolvingaphysiotherapist[23].The followingpaperpresentsanapproachtomodelling patients’physicalloadstodetectpotentialpainor discomfortautomatically.Thisispossibleforpartic‐ularcasesbymeasuringandinterpretingbiosignals ordynamicparameters.Thepaperclassi iespatients accordingtotheirdisorderslevel.Basedontheselev‐els,potentialhazardsduringkinesiotherapyarelisted andmatchedwiththecorrespondingmeasurements. Thesemaybeusedtobuildamodelenablingcontinu‐oushuman‐lesssafetymonitoring.

2.Methodology

Basedonaliteratureoverview,thepaperconsists ofasystematicanalysisofthepotentialautomatic detectionofhazardoussituationsduringremotehome treatment.Thisincludesdiseasecasesegmentation, possiblecausesofinjuries,andmeasurementmeth‐ods.Withthese,amultibodymodelmaybecreated andusedtoassessthesafetyofthetreatment.

TheScopus,ResearchGate,GoogleScholar,and PubMeddatabaseswereanalysedtocreatethis paper.Thefollowingkeywordswereused:home telerehabilitation,kinesitherapy,stroke,paresis, spasticity,extremityexoskeleton,paindetection, measurablebiologicalsignals,ROMmeasurement, OpenSim.92articleswerereviewedwiththe limitationofbeingpublishedin2016orlater,of which37wereconsiderednottocontributemuch tothispaper.Papersdescribingtheexactconcept ofspeci icrehabilitationdeviceswererejected. However,itisworthnoticingthatmostofthem assumetheconstantpresenceofaphysiotherapist nexttothepatientorpriorlimitingjointsrangeof motion(ROM),whichaffectsthedevice’sworking area.Papersmainlydealingwiththepharmacological treatmentofstrokes,spasticity,orparesiswerealso rejected,asthisisnotrelevantfortheuptakentopic.

3.ResultsandDiscussion

3.1.SegmentationofCases

Thepatientsweresegmentedinto ivegroupsto assignthemcorrespondingpotentialrisks.Thanksto this,thenumberofmeasurementtechniquesneeded forsafetymonitoringislimitedforeverycase.The de inedgroupsare:

1) Patientswithsensationaftermechanicaltrauma (e.g.,fractures)orlightmusculoskeletaldisor‐ders(e.g.,jointcalci ication)andpost‐surgical patients–withapossiblecompletereturntopre‐injuryperformance

2) Patientswith laccidmuscles,deprivedofsensa‐tion

3) Patientswith laccidmuscles,withsensation

4) Spasticpatients,deprivedofsensation

5) Spasticpatients,withsensation

Thepatientswithmuscle laccidityareunderstood astheoneswithmissingconnectionsbetweenthe brainandspinalcordcircuitsessentialforvolun‐tarymovement[22].Spasticityisamotordisorder characterizedbyavelocity‐dependentexaggerationof stretchre lexesresultingfromabnormalintraspinal processingofprimaryafferentinput.Suchmalfunc‐tioningimpliesincreasedmuscletone,enhancedten‐donre lexes,andextendedre lexzones[14]andis usuallytheresultofstroke[8].Tocorrectlyreferto individualcasesinthepaper,theyareassignedwith thenumbersoftheabove‐proposedsegments.

Thedivisionaboveincludescasesofpatientseli‐gibleforrobotichomerehabilitationandreferstothe partofthebodyrehabilitated(e.g.,whileperforming kinesiotherapyofthelowerlimbofapatientwiththe laccidlowerhalfofthebodyandsensation,theyare treatedasthegroup3–eventhoughtheirupperhalf ofthebodymaybenotaffectedbyanydisorder).For everygroup,thesignalswhichcanbemeasuredfor paindetectionpurposeswereselected.Theproposed approachtodetectriskpriortopatients’injuriesby theroboticrehabilitationsystemsispresentedbelow.

3.2.MethodologyofMeasurements

Selectionoftheappropriateapproachto measurementspriortoandduringkinesitherapeutic robot‐aidedsessionsiscriticaltoautomatingthe process.Themethodsmaybecombinedandused alongwitheachothertoimprovethereliabilityof thesafetysystemofthedevice.Currently,themost commonsensorsforrehabilitationdevicesareIMU, encoders,pressuregauges,andEMGsensors.The irst twoareusedtoobtaininformationonthedevice’s kinematicscon iguration,whiletheothersarefor biofeedback[19, 72].Thissubsectionpresentsan overviewoftheconsideredtechniquesandcorrelates themwiththesegmentspresentedbefore.

Measurementofthepatient’srangeofmotion

Measurementofthepatient’srangeofmotion(ROM) isconnectedwithactivelyexercisedjoints.The resultedvaluesdescribetheoperationalspaceofthe individualbodysegment,wheretheexercisemay beperformedwithoutpainoranyriskoftrauma. Suchmeasurementmayberealisedmanuallywith goniometersorwitharehabilitationdeviceitself, e.g.,bytheSFTRmethod[31].Beforestartingthe actualtreatmentsession,thedeviceshouldlauncha measuringmoduletodeterminethepatient’sROM andadjusttheexercisespace.

Thereisnocertaintythatstayingwithin singlejointlimitswillensurethepatient’ssafety duringcomplexmovements.Inotherwords, thedecompositionofacomplexmotionintothe appropriatecomponentsinthefundamentalplanes: sagittal,frontalandtransverse,doesnothave tocorrespondtothesumofthesemovements intermsofthemuscleloads.Moreover,sucha measurementshouldtakeplaceseveraltimesthe duringrehabilitationprocesstoconsiderpotential ROMincreaserelatedtotheconvalescenceprocess[2]. However,thistime‐consumingprocessdoesnotfully safeguardfurtherautomatickinesiotherapy.Ifsucha calibrationistobeperformedwithoutanadditional operatorofthesystem,eitherintelligentalgorithms havetosensemotionlimitsorthedevicemust receiveequivalentinformationfromapatient.The irstapproachisdif iculttoimplementforpatients withsevereneuraldiseases.Ontheotherhand, con irmingtheendofpossiblemotionrequiresthe user’scapabilityofphysicalinteractionwiththe human‐machineinterface(HMI)orimplementation ofvocalcommands.Thisimpliestheneedforan excellentcommandandsoundrecognitionsystem, potentiallywithanadvancedneuralnetwork[37]. Theserequirementsalsoaffectthenumberofpatients whomayusethedevice.

PulseandECGmeasurement

TomeasurepulseorECG,thedevicehastobe equippedwiththededicatedsensors.Asthesevere stressrelatedtopainsensationscausesthechange inreadings[71],thistechniquecanbeusedto detectemergencystatesoftherehabilitation

system.However,thevaluesofrestingheartrate andthemeasurementsduringexercisingvaryfor individuals[78].Additionally,theabnormalitiesmay beregisteredtoolatefortherobottoreactbefore harmingthepatient.Moreover,theexpectedaccuracy ofaround60–80%andnodistinctionbetweenpain levelsmaynotbeenoughreal‐timepainrecognition forrobot‐aidedkinesiotherapy[56].

Estimatingthestrengthparametersoftissues

Thesafetyalgorithmscanbebasedonthemultibody modelofthecooperatingdeviceandmusculoskeletal system.However,thisapproachrequirescomparing computedresultsofloadswithinindividualtissues withtheirstrengthparametersdifferentforeveryper‐son.

Themostvulnerabletoinjuriesaretendonsand ligaments[42].Forthisreason,machinesshouldnot exceedthestrengthlimitsofthesetissues.Itispartic‐ularlychallengingtoobtaindataontheirparameters, suchasYoung’smodulus.Thecorrespondingexper‐imentaltrialsareusuallycarriedoutonanimals[7] ortissuesfromthedeceased[34],whichdonotfully correspondtothetissuesofalivehumans.Moreover, tissuepropertieschangewithage,gender,andexperi‐encedillnesses[59].

Topreventhazardoussituations,estimatingthe tensilestrengthismostcriticalforindividualsoft tissues,astheyaremostvulnerabletodamagein thisdirection[3].Beforethetreatment,theirvalues maybeobtainedwithaspeci icdevicesuchas MyotonPRO[5].Themeasurementmethodconsists ofregisteringthedampednaturalvibrationsofsoft biologicaltissueintheformofanaccelerationsignal andthencalculatingthedesiredparameters.Such technologyenablesmeasuringthetone,stiffness, lexibility,relaxation,andcreepoftissues[5].The proposedsolutioncouldalsobetransferredto therehabilitationrobotbyequippingitwitha dedicatedsensorysystem.Nevertheless,thereare alsolimitationstothismeasurementtechnique,e.g., theresultsarelessaccurateforobesepatientsaswell asthedeeplylocatedandtoothintissuesaredif icult toworkwith[1].

EDAmeasurement

EDAiselectrodermalactivity,demonstratedtobe effectiveinarousalestimation[73].Asapatient’s sweatingchangesattimesofseverestress[32], analysingcorrelatedEDAsignalscancontributeto detectingincreasingpain.Thistechnologyisbeing continuouslydeveloped,anditdoesnothavemany validatedapplicationsyet[4].Thereareserious doubtswhetheremotionssuchasjoyorstresscaused byprovidingtreatmentbyarobot,notahuman,will notcauseexcessivesweating[64].Suchaneffectcan leadtoconfusionofhazardsituationswitharegular operationofthedevicebytheautomaticsafety monitoringsystem.Forthisreason,implementing EDAwithinareal‐timesystemfordetectingrisksin homerobot‐aidedtreatmentisnotsuggested.

EEGmeasurement

EEG,electroencephalography,isanon‐invasive methodofanalysingbrainelectricalactivitybased ontherecordingsfromthescalp.Asapatient’s intentionsaredetectablewiththismeasurement[46], arehabilitationrobotcanuseEEGsignalsfor predictivecontroltointeractwithauserandnot exceedtheirrangeofmotion[80].However,not everyintentionofmotionresultsinthemovement–itsimagemaybeenoughforthecorresponding areaofthebraintobecomeactive[49].Onthe otherhand,researchersprovedthatphysicalpain, particularlyacute[70],canbedetectedbasedon EEGwithanaccuracyofalmost95%andusedfor real‐timere lexinprostheses[75].Thisimplies theapplicabilityofthetechniqueforrobot‐aided rehabilitation.Nevertheless,usingadvancedEEG systemsisrelativelyexpensiveandrequiresprecise placementoftheelectrodesonapatient’sscalpto providerepetitiveresults[12].Thesemightbethe mainbarrierstousingsuchforhometherapy.

EMGmeasurement

EMG,electromyography,maybeeitheraninvasive ornon‐invasiveinvestigationoftheelectrical activityofmuscleunitsorwholegroups.Registered signalsprovideinformationregardingthetemporal behaviourandmorphologicallayoutofactivemotor unitsduringmusclecontraction[68].Thismaybe usedtoestimateinternalstressinthesetissues andcomparethemwiththeirbiomechanicallimits. Thesafetysystemmustreacttosuddenpeaksin theregisteredsignals.Thesemayeitherberelated tothenociceptive lexionre lexcausedbypain stimuliorthespasticre lexcausedbyasudden noise,unexpectedtouch,orstress[13].Thetwo mentionedhavetobedistincted.Hence,theEMG maybeuselessfordetectinghazardoussituations forspasticpatientsinspasticity‐relatedsituations. Theresearchersalsopresentthemethodofdetecting painbasedonEMG‐registeredfacialexpressions. However,thisrequiresnon‐affectedfacialmuscles andgeneratessimilarproblemsasforEEG,including preciseplacementoftheelectrodes[39].The valuesregisteredwithEMGcanbeusedtoestimate temporarymuscletension[58].However,thesurface EMG,theonlyapplicablewithinrobot‐assistedhome kinesiotherapy,isvulnerabletonoisesfromelectrical devices,othermusclegroups,andfatlayers[77].

Selectionofmethodsforcases

Inordertoproposethesolutiontailoredtothecapa‐bilitiesofaspeci icgroupofpatients,adecisiontree formeasurementselectionispresentedinFigure 1. The irststepistoassesswhetherapatienthasphysi‐calsensations.Itisassumedthatpost‐traumapatients meetthisrequirement–ifnot,theyareassignedto groups2or4.

Moreover,patientswithspasticityhavetobemed‐icallyquali iedforrobot‐aidedexercising.Thisdeci‐siondependsontheseverityoftheproblemaccording tooneofthescalessuchasAshworthscore,modi ied Ashworthscore,Tardieuscale,ormodi iedTardieu scale[74].Theoneswiththedegreeofspasticity exceedingacertainthresholdcannotworkoutby themselvesduetotheirspastic,uncontrolled,intense musclecontractions[14].Suchapre‐treatmentmed‐icalassessmentshouldbebasedonseveraldoctors’ independent,expertopinions[35].

Ontheotherhand,patientsdeprivedofsensation oftensufferfromexcessivesweating[33].Theyare unabletoidentifytheirownpainailments[33],and thus,theiravailablerangeofjointmobility.

AsmaybeobservedinFigure 1,patientsfrom groupnumber1aresuitableforallthemeasurement methods.Themostchallengingtaskistomeasure biologicalsignalsforgroup2becauseitisnotpossible togatherdatarelatedtotheirmuscletensionortheir senseofmotionlimits.

Moreover,thereisadifferenceintheapplicability ofEMGmeasurementsbetweennon‐spasticandspas‐ticpatients.Forthe irstgroup,thesensedelectrical signalsmaybecorrelatedwiththemuscularforces andthenanalysedregardingbiomechanicallimitsfor safeguardingpurposes.Whenitcomestothesecond group,theiruncontrolled,rapid,andseveremuscle contractionsmayturnEMGsignalsunabletobeused asdescribedabove.However,signi icantchangesin themeasuredsignalscanbeassignedtotheemer‐gencystopoftherehabilitationdevice(markedin Figure 1 asEMG*).Thismaycounteractthehazard ofmusclerippingduringtheinvoluntary,disease‐relatedcontraction.Furthermore,forpatientswithout sensation,theROMrangecannotbemeasuredasthey cannotfeeltheirphysicallimits.

Besidesthementionedabove,itisnecessarytobe awarethatforindividualcasesfallingintooneofthe proposedsegments,assignedmeasurementsmaynot giveexpectedresults.Therefore,thepatientshouldbe treatedas ittinganothergroup,eventhoughtheydo notmeetitscriteria.

3.3.HarmfulSituationTypes

Apartfromavoidingauser’sdiscomfort,theauto‐maticsafetysystemforrehabilitationrobotsshould preventsituationscausingphysicaldamagetotissues. Thismayberealisedbymodellingthecausesofpar‐ticularhazardsandcomparingtheirreal‐timevalues withestimatedthresholds.Table1containssegmen‐tationofthese.Iftheriskofaparticularcauseoccuring istypicallyneglectableduringrobot‐aidedtreatment, the“high‐riskgroups”cellislabelledas“lowrisk”.

Thebone‐relatedtraumasaretypicallyhazardous forthepatientsrehabilitatedaftersimilartraumas. Regardingsegment1ofpatients,itissimilarforthe injuriesofmuscles,ligaments,andtendons.Therefore, high‐riskgroup1*referstothepersonaftersimilar fracturesordamagetothesofttissues.Onthecon‐trary,B4traumamayonlyappearduringlong‐time forceappliedtotheextremity’ssegment,whichis noticeableasapainstimulusbypatientswithunaf‐fectedsensation.Thedevicemaybestoppedimme‐diatelyinsuchasituationandnotcauseanyharm. Onlygroups2and4arenotabletonoticesucha casethemselves.Therefore,anadditionalsafetysys‐temmonitoringcontinuousloadshastobeprovided.

Figure1. Segmentationofcaseswithcorresponding measurementtechniques

Trauma Symbol Cause High-riskgroups Measurementtechnique(otherthan trackingdevice’sdynamicparameters)

Transversebonefracture

Impactedbonefracture

Thedevicehastoreacttotheriskofbonefractures beforeanactualdangeroussituationappears.There‐fore,nopain‐basedmeasurementswillbehelpful. Instead,theoverallsystemshouldbemonitoredbased onitsmultibodymodelsuppliedwiththemeasured dynamicparameters.Moreover,greenstickfractures andsimilar,morecomplexvariants(B4,B7,B8)may appearwhileexceedingnaturalROM.Therefore,this shouldalsobeimplementedforsafeguardingsuch cases.

Asthestrainsandcontusionsarelessseverethan othertypesoftraumarelatedtosofttissues,theymay bedetectedwithpain‐basedmethods.Moreover,they typicallyappearprecededbynoticeablephysicaldis‐comfort.Therefore,thedevicemaybestoppedbefore harmingtheuser.Formuscletearsandligamentor tendonruptures,thesystemhastoreactpriortothe contusion.Hence,apredictionbasedonthemulti‐bodymodelandmeasureddynamicparametersofthe deviceissuggested.

Moreover,asthemajorityofmuscles’andliga‐ments’traumas(notM3)arerelatedtotheforcegen‐eratedinthecorrespondingmuscles,theyarerelevant onlyfornon‐ laccidpatients.Furthermore,theirrisk maybetrackedwithEMG.Forthepatientswithno sensation,anadditionalsystembasedonthemulti‐bodymodelandthedevice’sdynamicsparametershas tobeprovided.

Thedamagetosofttissuesmayalsobecausedby exceedingtheindividual’sanatomicallimits.There‐fore,constantmonitoringofthedevice’scon iguration relatedtothemeasuredROMshouldberealised.

Apersonassignedtooneofthesegmentspre‐sentedbeforehandshouldbeassignedtothepoten‐tialrisksbasedonthe“high‐risk”columninTable 1 Subsequently,asensorysystemandamathematical modelshouldbebuilttodetectandreacttohazardous situations.Thankstosuchanapproach,arehabilita‐tiondevicemayimplementitsemergencyroutines whenriskappearstopreventharmtoauser.Asmay beobserved,detectingeverypossibletraumarequires trackingthedevice’sdynamicsparametersandbuild‐ingatleastasimplemultibodymodelofaphysical interfacebetweenamachineandahuman.

3.4.ApplicabilityofResults

Themeasurementsproposedintheprevious section,alongwiththedynamicsparametersofthe device(drives’torquesandencoders’positions),can beusedtobuildamultibodymodelofthesystem. Suchcanbeusedtoestimateinternalforces,torques andstressesoccurringinthebodysegmentsduring atreatmentsession.Thesevaluesshouldremain belowtheacceptablethresholds,whichmayvary forindividualcases.Assumingcorrectestimations regardinganatomy,comorbidities,andapatient’s medicalhistoryregardingavailablebibliography sourcesenablesthebuildingareliablesafetysystem. Thefollowingsectionpresentstheindividualtissue strengthparametersforvariouscases.

Methodologyoftesting

Generally,inmaterialengineering,theleadingtest carriedouttoidentifythestrengthpropertiesofa materialistheuniaxialstatictensiletest.Themajor challengeistoselectthetestingsampleshape.This isduetothefactthatsofttissuesarepreparedpost‐mortem(tissuesofbloodvesselsandskintissues, amongothers)and,hence,theyarepre‐tensioned. Therefore,theirsusceptibilitytodeformationmakes itchallengingtopreparetheappropriate ittingof asample.Forthisreason,softtissuesareusually examinedintheformofabar[47].

Bones

Thereisastrongcorrelationbetweenanindividual’s gender,age,orbonetypeandthetissue’sstrength.For example,loadingawoman’sradiusorhumeruswitha torqueofapproximately61Nmwillcauseafracture witha50%probability[63].Thedifferencesinthe criticalvaluesmaybeassigni icantas100Nmforthe criticalbendingmomentofthehumerus,depending onthegender.Analysingshearforceinthisbone, itscriticalvalueis1.7kNforwomenand2.5kNfor men[63].

Table1. Segmentationoftissuesdamages

Itismuchmoredif iculttodamagethelowerlimb. Theprobabilityofaninjuryincreasesoutstandingly whentheforceof5kNisexceeded[63].Withinthe lowerlimbs,the ibulaisthemostvulnerablebone. Itstensilestrengthisuptotentimeslessthanthe femur’s[63].Formanyapplications,thecriticalbone resultantstresscanbetakenas150MPa[20]and shouldbescaledaccordingtotheindividualcase. Moreover,extraordinaryattentionshouldbegivento theweakestboneoftheexercisedbodypart.

Muscles

Thereisacorrelationbetweenthedirectionofmuscle tensionanditsforce.Moreover,harmtothesetissues istypicallycausedbythetendons’force,orexcessive strain[11].Forthisreason,musclesareoften analysedwithtendonsasuniformbodiesofaverage strengthproperties[41].Correlatedstress‐strain curvespresentthatastrainover0.4leadstoarapid increaseinstressashighas200kPa[63].Moreover, themaximumforceappliedtothemusclemaybe calculatedasthemultiplicationofPCSA,andestimated tetanictension,e.g.,22.5N/cm2 formammalian muscles[51].Thisrequiresmeasurementofthe initialmusclelengthsandmonitoringkinematics oftheextremityduringexercises.Hometreatment shouldberealisedwithalowereffortforthepatient’s safety.Aspresentedintheliterature,monitoring offorceoccurringinthissofttissuecanberealised bybuildingacomputationalmultibodymodelor analysingtheirmeasuredexcitation[15].Hence, apotentiallydangeroussituationresultingfrom exceptionalmuscletensioncouldbedetectedas therapidincreaseoftheEMGsignal,whichleadsto reachingbiomechanicalthresholds.

Tendonsandligaments

Thestrengthandstiffnessofligamentsandtendons dependonapatient’sageandlevelofphysicalactivity. Themaximumforcethatcanloadthesetissuesfora young,athleticpersonisestimatedas6.1kN,while foranolderpersonwithastaticlifestyle–only4.6 kN[16].About10%–15%extensionofthetendon causesstressbeyondtheelasticlimit[63].Thiscre‐atesstressofapproximately50kPaandresultsin adeformationof4mmonaverage[52].Theforce generatedinthetissueisthencloseto200N[20]. Forelderlypeople,Young’smodulusofligamentsand tendonsincreases.Theyaremoredif iculttostretch andbecomeless lexible.Nevertheless,theelastic‐ityofthesetissuesguaranteestheirproperfunction‐ing[20].

Moreover,theworkstateofthetissueisalsoacriti‐calfactorforestimatingsafetythresholds.Contracting tissuesgeneratemorestressandaremoreexposedto thedamagethantheextensingones[20].Ingeneral, Young’smodulusofthetendonmaybeestimatedas 0.9–1.4GPa[20].

3.5.ModelProposal

Asmentionedbefore,thepropertiesoftissuesdif‐feramongindividuals.Thesolutiontopredictthe effectsofagivenexerciseforaspeci icpersonisto

createadigitaltwinofthepatientandarehabili‐tationdevice[27,80].Itispossibletobuildsucha mathematicalmodelinopensoftware,e.g.,OpenSim. Thegeometricalparametersofthefreemodelsmay bemodi ied,aswellasthestrengthparametersofthe tissues[65].

Modellingthephysicalinterfacebetweenareha‐bilitationdeviceandauserenablesthepredictionof thesystemdynamicsinreal‐time.Hence,hazardous situationsmaybemitigatedbeforetheyoccur[25]. Moreover,thismaycontributetooptimisingtherapy effects.

Internalforcesinthetissuesmaybeanalysed regardingtheexternalloadsapplied[62],alsoinan externalenvironmentastheexportedtimeseries[44]. Thankstothis,itispossibletosimulatetheresultsof themostdangerousmovementsforpatientswithpar‐ticulardiseasesandacertainage.Basedonthesesim‐ulations,thepatientmaybequali iedonlyforlimited accesstothedevice’sfunctionality.Thus,thehome treatmentremainssafe.Moreover,theregisteredEMG signalscanbeincludedinthemodelasadditional validationofthesimulations[55].However,inEMG‐basedcontrol,themajorchallengeissigni icantsignal noise[66].Duetotheneedto ilterthisout,almost real‐timeprocessingishindered.Inaddition,themea‐suredparametersvarybetweenindividuals.More‐over,thistypeofcontrolcanonlybeusedbypeople capableofgeneratinganelectricalactivityexceeding acertainthreshold[48].Therefore,theEMGmeasure‐mentsshouldnotbeconsideredastand‐alonetoolfor automaticpainmonitoring.

Withinthepresentedmethodology,buildingan accuratemodelofthepatientandthedeviceiscritical forprovidingthesafeoperationoftherehabilitation robot.Themodel’sgeometryshouldre lectareal‐life patient’sanatomy,whilethesimulatedtissueshaveto beprovidedwithadequatematerialparameters.The researchersprovethattheready‐madeopenhuman bodymodelsmaybeeffectivelyenhancedbyadding rigidmultibodymodelsoftherehabilitationdevices andusedasproposedinthepapers[40,62,65].

4.Conclusion

Mostoftheexistingrobot‐aidedrehabilitationsys‐temsneedthephysicalpresenceofaphysiothera‐pist[79].Forthisreason, indingavalidatedcontext forthepresentedproblemisdif icult.Moreover,the methodsofreal‐timesafetymonitoringbasedonmea‐surementsarenotthesameforallpatients.

Duringthetreatment,physiotherapistsmanu‐allyrecognisesoft(muscular)andhard(bone)resis‐tance[9].Theyknowhowmuchtoexceedthesoft resistancetoimproveapatient’sconditionwhile notexposingthemtoinjury.Thishapticfeedback withaprofessional’sexperienceneedstobetrans‐ferredintomachinealgorithms.Existingpainscales suchastheVisualAnalogueScale(VAS),theVerbal RatingScale(VRS),andtheNumericalRatingScale (NRS)[38]aresubjective.Moreover,theyaremainly basedonapatient’spreviousexperiencecomparedto thepresent[43].

Onthecontrary,theproposedsegmentation allowsfocusingonindividualdiseaseentitiesand developingdetectionmodelssuitableforspeci ic cases.Inthebeginning,therobot’saimshouldbe de ined.Thiscaneithersupportpeopleafterlighter injuries[17]orserveforagradualrecoveryofmotor activitiesforpeoplewithsevereimpairment[6].

Forthesecondcase,thedevicemaynotevencor‐rectinaccuratemovementsinitiallytoregainbasic mobilitywithoutthepain.Suchshouldbeincludedin therulesforhazardsdetectionalgorithms.

Arti icialintelligencecanbeusedforthesepur‐poses,asitincreasestheaccuracyoftherapists’and doctors’decisions.Moreover,theneuralnetworkscan contributetooptimalsearchamongthepossibleail‐mentscausesandtreatmentoptions.Inaddition,this approachiseasilyscalable.Therefore,itcanbeusedto thoroughlyanalyselargedatasetsonthecourseofthe diseaseandthepatient’streatment[19].

Furthermore,rehabilitationdevicescanbebet‐tersuitedtospasticpatientsbyprovidingthemwith awarming‐upmoduleinvolvingsimple,low‐speed motions.Thiswillnotonlymentallyfamiliarisea patientwiththerobotbutalsorestrainmusclecon‐tractionswithinthemainsession[14].

Thecurrentchallengesinthesafetymonitoringof robot‐aidedkinesiotherapydependonbothsoftware andhardware.Theformerincludesthespeedofreal‐timedataandtheautomaticselectionofaccurately restrainedROM.Thesystemsenablingthesehavenot beenimplementedinanydeviceyet.Thelattercon‐sistsofthemechanicaldesignrequirementstosuit peopleofdifferentanatomyandphysicallylimitthe excludedROM[24,36].

Therefore,whiledesigningthesystemforreal‐timehazardsmonitoringduringthehomerobot‐aided therapy,thefollowingshouldbevalidatedexperimen‐tally:

‐ howcanamuscletensionincreasedtothepainlimit affectthemeasuredsignals;

‐ isthechangeinthesignalrelatedtothehazard confusablewithothersafesituations;

‐ howbigisthesignal‐registrationanddevice‐processingdelay;

‐ whatarethetypicalvaluesofthemeasuredsignal fortheindividual.

Onlyselectingthemeasuringtechnique,whichpro‐videsdetectionofpotentialriskswithhighaccu‐racyandlowdelay,enablesreal‐timemonitoring safetyduringhomerobot‐aidedkinesiotherapy.As describedinthepaper,themethodsmaybecombined, alsowithamultibodymodelofthedeviceandthe user.Suchanapproachmaybecomethebaseforthe computingpredictionofemergenciesandpreventing them.

AUTHORS

JuliaWilk∗ –ŁUKASIEWICZResearchNetwork

IndustrialResearchInstituteforAutomationand MeasurementsPIAP,Al.Jerozolimskie202,02‐486 Warsaw,WarsawUniversityofTechnology,Plac Politechniki1,00‐661Warsaw,Poland,e‐mail: julia.wilk@piap.lukasiewicz.gov.pl.

PiotrFalkowski –ŁUKASIEWICZResearchNetwork

IndustrialResearchInstituteforAutomationand MeasurementsPIAP,Al.Jerozolimskie202,02‐486 Warsaw,WarsawUniversityofTechnology,Plac Politechniki1,00‐661Warsaw,Poland,e‐mail: piotr.falkowski@piap.lukasiewicz.gov.pl.

TomaszOsiak –ŁUKASIEWICZResearchNetwork

IndustrialResearchInstituteforAutomationand MeasurementsPIAP,Al.Jerozolimskie202,02‐486 Warsaw,TheJózefPiłsudskiUniversityofPhysical EducationinWarsaw,Marymoncka34,00‐809 Warsaw,CenterofFunctionalRehabilitation,Orthos, Kobylańska30,02‐984Warsaw,Poland,e‐mail: tomasz.osiak@awf.edu.pl.

∗Correspondingauthor

ACKNOWLEDGEMENTS

Thepaperisbasedontheresultsofthe“Smart exoskeletonforremoterehabilitationwiththedigital twintechnology”–SmartEx‐Twinproject, inancedin 2021‐2023(265,800EUR),inthescopeofscienti ic researchanddevelopmentworksbytheNational CenterforResearchandDevelopment(funding programme5thCallforProposalsPoland‐Turkey, contractnumberPOLTUR5/2022/81/SmartEx‐Twin/2023).”

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Abstract:

BINARYSHUFFLEDFROGLEAPINGALGORITHMFOROPTIMALALLOCATIONOF POWERQUALITYMONITORSINUNBALANCEDDISTRIBUTIONSYSTEM

BINARYSHUFFLEDFROGLEAPINGALGORITHMFOROPTIMALALLOCATIONOF

BINARYSHUFFLEDFROGLEAPINGALGORITHMFOROPTIMALALLOCATIONOF POWERQUALITYMONITORSINUNBALANCEDDISTRIBUTIONSYSTEM

Submitted:23rd May2021;accepted:7th February2023

AshkanDoustMohammadi,MohammadMohammadi

DOI:10.14313/JAMRIS/4‐2023/28

Thispaperdealswithoptimaldetectionofnumberand bestlocationsofpowerqualitymonitors(PQMs)inan unbalanceddistributionnetworkbasedonthemonitor reachareaconcept.Theproposedmodelusesbinary string,representingtheinstallationmodeofPQMs(Yes orNo)ineachbusofthenetwork.Inthispaper,the binaryversionofshuffledfrog‐leapingalgorithm(BSFLA), becauseofhavingtheabilitytoimprovethesearch capabilitywithafastconvergencerate,isutilizedfor theoptimizationprocess.Theoverallcostfunctionis formulatedtooptimizethetwoindices,whicharethe monitoroverlappingindexandsagseverityindex.The onlyoptimizationconstraintinthisproblemisthatthe numberofmonitorsthatcandetectvoltagesagsdueto afaultataspecificbusmustnotbezero.Inthisstudy, DIGSILENTsoftwareisutilizedforfaultanalysiswhilethe optimizationproblemishandledbytheBSFLA.Toverify theproposedalgorithm,theIEEE34Busunbalanced distributionnetworkisconsideredasacasestudyand resultsarecomparedtosimilarinvestigationssoasto illustratetheeffectivenessoftheproposedalgorithm.

Keywords: Binaryshuffledfrog‐leapingalgorithm,Topo‐logicalmonitorreacharea(TMRA),Powerquality,Power qualitymonitoring

1.Introduction

Activepowerdistributionsneedtobemonitored online.Thismustbeperformedcorrectlyfromthe pointofviewofvariouspowerqualityindices.Har‐monic,voltagesag,voltageswingandotherpower qualityindicesmustbemeasured.Voltagesagsmoni‐toringanditsassessmentgivesinformationaboutthe actualcauseandsourceofvoltagesagsthatcanhelp powerengineersmitigatesuchdisturbances.Thus,to accuratelymonitortheoverallsystem,powerquality monitors(PQM)needtobeinstalledatallbusesina powersystem,whichisverycostlyanduneconomical planning[1].Therefore,newoptimalplacementmeth‐odsarerequiredtodeterminetheminimumnumber andthebestlocationsofPQMstoensurethatthrough anef icientallocationapproach,anyeventthatleads tovoltagesagiscaptured.Afewoptimalallocation techniquesofPQMshavebeenreportedinthelast

fewyears.Generally,thevoltagesagmonitorplace‐menttechniquescomprisefourfundamentalmethods, namely,monitorreacharea(MRA),coveringandpack‐ing(CP),graphtheory(GT),andmultivariableregres‐sion(MVR)[2].DongandSeungproposedanewGT‐basedalgorithmtomonitorthevoltagesaginapower systemwhichrepresentsthepowersystemnetwork usingasimplegraphwithanincidencematrixand analyzedthesysteminanetworkmatrixframe[3]. TheGT‐basedtopologicaltechniquebasedoncover‐agematrixwasutilizedforPQMplacementbyDong andSeung[4].In[5],anovelpowerqualitymonitor‐ingallocationalgorithmbasedontheCPmethodwas discussed.In[6],acombinatorialproblemoftheCP methodwiththeIntegerLinearProgramming(ILP) techniquewasemployedtominimizethecostofPQMs. In[7],amethodwaspresentedbyauthorsforthe optimalplacementofPQMsthatisplannedbasedon theCPapproachandthatusedGAMSsoftwaretosim‐ulatethefaultsonthesystem.TheCPmethodhastwo drawbacks.Oneisevaluatingthesystem’sconnectiv‐itytoanalyzesystemobservabilitybasedonKirch‐hoff’scurrentandOhm’slaw,andthesecondisconsid‐eringsteadystateinformationincomparisonwiththe actualinformationofvoltagesagasconstraintsofthe optimizationproblem.In2011,anewmethodbased ontheMVRmodelwaspresentedintheplacementof PQMs[8].AnovelPQMplacementtechniqueusingCp andRpstatisticalindicesforpowertransmissionand distributionnetworkswasanalyzed[9].Recently,the MVRmethodwascombinedwithCpandRpstatistical indicesandusedforoptimalPQMplacement[10]. Inrecentyears,theheuristicsapproacheshavebeen mixedwiththeCpstatisticalindexapproachto ind thebestlocationandimprovetheaccuracyofthe solution.Forexample,optimalpowerqualitymoni‐torplacementintransmissionnetworksusinggenetic algorithmandMallow’sCpwasaddressedby[11]. Also,asimilarstudybythesameauthorswasreported aboutoptimalpowerqualitymonitorplacementusing theGA_Cpmethodfordistributionnetwork[12].In 2003,Olguinetal.proposedamonitorreachareaor MRAconcept‐basedmethod,whichgivestheareaof thenetworkthatcanbeobservedfromagivenmeter positionbyconstructingabinarymatrix.Accordingto theirproposedmethod,ifafaultoccursinsideMAR, thentheeventwilltriggerthePQM,while,forfaults outsideit,noPQMwastriggered[13].

Thus,theMRAsofallpossiblelocationsusingthe binaryMRAmatrixthroughnetworkfaultslocated alongtheelectricallinesaredeterminedtoestab‐lishandformulatetheoptimizationproblem.InMRA‐basedmethods,theheuristicsoptimizationalgo‐rithmsareemployedtodeterminethenumberof PQMsandbestlocationsthroughoptimizingobjective function,whichisformulatedbaseontheMRAmatrix. ManystudieshavebeenreportedthatusedtheMRA methodcombinedwithheuristicsalgorithmsforopti‐malplacementofPQMs.In[14],authorspresented amethodbasedontheconceptoftheMRAandthe sagseverityindexfortheplacementofPQMswhich usedGAtosolvetheoptimizationproblem.Inthe recentlyreportedstudy,theconceptoffuzzy,which wasusedin[15]isutilizedforfuzzymonitorreach area(FMRA)tolocatePQMsinlargetransmission network.Theimprovedadaptivegeneticalgorithm (IAGA)waspresentedby[16]foroptimalallocation ofPQMsbasedontheMRAandMRMmatricesand redundantvectorconcepts.AlthoughthePQMsloca‐tionintransmissionsystemsusingtheMRAmatrix techniqueisasimpleperformance,theMRAmatrix isgenerallynotsuitableforapplicationinradialdis‐tributionsystems,asitoftenyieldsonePQMplace‐mentsolution.Thus,in2011,AhmadIbrahimpro‐posedthenewconceptoftopologicalmonitorreach area(TMRA)anduseditforoptimalplacementof PQMsindistributionsystems[17].Thementioned paperusedtheDIGSILENTsoftwareforfaultanalysis, whiletheoptimizationproblemwashandledbythe GA.TheTMRAwasproposednotonlytomakeobserv‐abilityapplicablefortransmissionsystems,butalso forradialdistributionsystems.InTMRA,toensure more lexibilityofthesearchalgorithmsinconsenting tosensitivityandeconomiccapability,thealphaasthe monitorcoveragecontrolparameterisimplemented andaddedtoMRAmethod.Authorsin[18]solvedthe optimalpowerqualitymonitorplacementinpower systemsbasedonTMRAusingparticleswarmopti‐mization(PSO)andanarti icialimmunesystem(AIS). Thequantuminspiredparticleswarmoptimization (QPSO)wasintroducedbythesameauthorsforPQM placement[19].TheadaptiveQPSO(AQPSO)was alsoaddressedforPQMplacementbasedonMRA approach[20].The irstinnovationofthisstudyis usingtheDIGSILENTsoftwarecombinedwiththe MATLABprogramfortheunbalancedshortcircuit process.Thistechniqueincreasesthespeedrunof simulation.Thesecondinnovationusesthebinary formatoftheshuf ledfrog‐leapingbasedoptimiza‐tionalgorithmtosolvethisproblem(PQMplacement). Thisaspectofthestudywasnotperformedbythe others.

Themainsectionsofthispaperarelistedasfol‐lows:

Section 2:PowerQualityMonitor/Meters(Func‐tionsandInstallation)

Section3:Fundamentalconceptsabouttheresid‐ualfaultvoltagematrix,monitorreacharea,system topologyandtopologymonitorreacharea.

Section 4:Objectivefunction,illustratethemini‐mizingthenumberofrequiredmonitors(NRM), minimizingthemonitoroverlappingindex(MOI) andmaximizingthesagseverityindex(SSI).

Section 5:Optimizationtechniques,imperialist competitiveapproachanditsbinaryversion.

Section6:SimulationandResults

Section7:Conclusion

2.PowerQualityMonitor/Meters(Functions andInstallation)

ThePQMisanidealchoicewhencontinuousmon‐itoringofathreephasesystemisrequired.Itprovides meteringforcurrent,voltage,realandreactivepower, energyuse,costofpower,powerfactorandfrequency. InFigure 1,theschematicandinstallationofseveral typesofPQMispresented.PQM’sapplicationandthe monitoringandmeteringfunctionofatypicaltypeare listedasfollows:

‐ Applications

1‐Meteringofdistributionfeeders,transformers,gen‐erators,capacitorbanksandmotors

2‐Mediumandlowvoltagesystems

3‐Commercial,industrial,utility

4‐Flexiblecontrolfordemandloadshedding,power factor,etc.

‐ MonitoringandMetering

1‐Harmonicanalysisthrough63rdwithTHDandTIF 2‐Eventrecorder, 3‐Waveformcapture/4‐Datalogger

Figure1. SchematicandinstallationofPQM

3.FundamentalConcepts

ThemainstructureoftheoptimalPQMplace‐mentproblemusingtheproposedapproachisto understandthemonitorobservabilityconcept.This structureisneededtoexplainthefollowingconcepts, whicharediscussedearlierinsections3.1to3.4:

‐ ResidualFaultvoltagematrix

‐ Monitorreacharea

‐ Systemtopology

‐ Topologymonitorreacharea

3.1.FaultVoltage(FV)Matrix

IntheMRA‐basedapproachofPQMplacement, theresidualvoltagesateachbusofasystemforall typesoffault(singlelinetoground(SLG),twophases toground(LLG),threephasefaults(LLL))andfor allfaultcasesarerequired.Inshortcircuitanaly‐sis,alltypesoffaultsaresimulated,generallyusing theDIGSILENTsoftwareateachbuswithzerofault impedancetoformtheFVmatrix.

Itiscleartheworstfaultwithsevereandcritical resultsisthefaultwithminimumimpedance.Inthe singlephasetogroundandthreephasestoground faults,iftheimpedanceofthepointfaulttoground experimentisthezerovalue,thelargestcurrentfault willbeachieved.Therefore,itisbettertodesignthe systemundertheworstfaultwiththelargestfault current.ThedesignofsystemwithPQMsunderthis conditioncanguaranteethegoodperformanceofthe systemforotherconditionsoffault.Thisnoteisillus‐tratedintherevisedpaper.Intheunsymmetrical faultsforexampleinthesingletogroundfault(SLG), wehave:

Inwhich,XF denotesthefaultimpedance(reac‐tance)atthefaultpoint(faulttoground)and X+ th,Xth andX0 th denotethepositive,negativeandzero sequencesequivalentTheveninimpedancesfromthe faultpointwhichaffectedbytopologyofsystem.The smallertheXF,thehigherthepositiveandnegative sequencefaultcurrentsI+ F,IF,andsowehavehigher faultcurrentsofphasesa,bandc(IF A,IF B andIF C).

Theresidualvoltageateachbusisvaluableinfor‐mationintheformationofthemonitorreacharea (MRA).Therefore,itisnecessarytostoretheresid‐ualvoltagesinamatrixcalledtheFaultVoltage(FV) matrix,wherethematrixcolumnsrepresentthebus numberandthematrixrowsrelatetothesimulated faultposition.Then,theMRAmatrixcanbeobtained bycomparingalltheFVmatrixelementsforeach phasewithathresholdvalue.EachelementoftheMRA matrixis illedwith1(one),whenthebusresidual voltagegoesbeloworequalto �� p.u.inanyphase andwith0(zero)otherwise.Inthestepoftheshort circuitprocessaboutfaultanalysis,itisnecessaryto simulateallthevariouskindsoffault.Thisstepis performedgenerallyateachbususingtheDIGSILENT softwarewithoutfaultimpedance(i.e.,zeroamount forit)toformandconcludetheFVmatrix.Finally,the residualvoltagesoftheFVmatrixarekepttoemploy inMRAformulation.(SeeFigure11forsimulationof theshortcircuitanalysiswithDIGSILENTsoftware andcalculatetheFVmatrix).

Finally,theresidualvoltagesasFVmatrixarekept toemployinMRAformulation.IntheFVmatrix,the matrixcolumn(j)isrelatedtobusnumbersofresidual voltages,anditsrow(k)iscorrelatedtothepositionof thesimulatedfaultforaspeci icfaulttype[17,21].To betterunderstandtheconceptofFV,considerasimple powersystemshowninFigure2

Duringaspeci icfaultatbus3,thevoltagereadings ateachbusofthesystemarecomputedusingDIGSI‐LENT.Thesevoltagevaluescorrespondtothe3rdrow oftheconstructedFVmatrixforthesystem,whichis reportedforacompletefaultanalysisofthesystemas inFigure3

3.2.MonitorReachArea(MRA)Matrix

TheconceptofMRAcanbeexplainedasanarea ofthenetworkthatanyfaultthatleadstovoltagesag canbecapturedbyaspeci iedmonitorlocation[22]. ThisMRAisabinarymatrixwheretheMRA(j,k)= 1,signi iesthatpointkisseenandcoveredbythe installedPQMatbusjwhereasMRA(j,k)=0 iden‐ti iesthatpointkisoutsideofthecoverageareaof theinstalledPQMatbusj.AnyelementoftheMRA matrixcanbeobtainedbycomparingalltheFVmatrix elementsforeachphasewithathresholdvaluewhich isrepresentedby��parameter.

Figure2. Asimpleradialdistributionsystem

Figure3. AnexampleoftheFVmatrix

IfthebusresidualvoltageoftheFVmatrixisless thanorequalto��p.u.inanyphase,thenMRA(j,k)= 1,andotherwise,i.e.,residualvoltageofFVmatrixis morethan�� p.u.atallphases,thenMRA(j,k)=0as expressedfollows:

MRA(j,k)=

1 ifFV(j,k)≤��p.uatanyphase

0 ifFV(j,k)>��p.uatallphases (3)

TobetterunderstandtheconceptoftheMRA matrix,considerthesimpleradialdistributionsystem asshowninFigure 2 anditsFVmatrixobtainedin Figure3.Inthisexamplecase,thethresholdissetat ��=0.9p.u.,theformationoftheMRAmatrix‐based equation(3)andtheyieldsMRAmatrixasshownin Figure4.

3.3.SystemTopologyMatrix(T)

LiketoMRAandFVmatrices,theTmatrixcolumn isrelatedtobusnumberanditsrowcorrespondswith faultlocation.Whenthereisapathfromgeneratorbus toaparticularbusinthesystem,thematrixis illed with1(one)andotherwise illedwith0(zero)[23]. Whenafaultoccursinaparticularbus,namelya faultedbus,itbecomesacutvertexthatsplitsintovar‐iousverticesofthesamecomponentasmanyadjacent edges.SomeexamplesofaparticularrowinaTmatrix forasinglefedradialsystem,adoublyfedradialsys‐tem,andaringsystemarepresentedinFigure5.For instanceduringfaultatbus3,dependingonthenum‐beroffeedersconnectedtothisbus,thesystemgraph willbeseparatedintoseveralsections.Bychecking theconnectivitystatusbetweengeneratorbusandthe otherbusbasedonmentionedcriteriatheTmatrix elementsarethen illedwith‘1’or‘0’.Asshownin Figure 5,(a)thesystemhasonlyonepowersource atbus1.Clearly,thereisapathfromthegenerator bus(bus1)tobuses1,2,and3butnotfortherest. Therefore,Tmatrixelementsare illedwith‘1’up tocolumnthreeand‘0’fortherest.Asindicatedin Figure5(b),inthiscase,thebusnumbers4and5have beenconnectedtothesecondpowersourceandthus, theTmatrixis illedwith‘1’uptocolumn5.Inthe lastcase,aringsystem,asshowninFigure5(c),gives all‘1’sfortheTmatrixcolumnbecauseofconnec‐tionsbetweenthegeneratorbus(bus1)andtheother buses.Theseexamplesaredesignedwithafaultonly atbus3,anditneedstobesimilarlyrepeatedonall

busestogivetheinformationaboutsystemtopology throughacompleteTmatrix.

3.4.TopologyMonitorReachAreaMatrix(TMRA)

Thetopologicalmonitorreacharea(TMRA)is introducedtomakeitapplicableforbothdistribu‐tionandtransmissionsystems.TheTMRAmatrixis acombinationofMRAmatrixandsystemtopology (T)matrixbyusingoperator‘AND’asexpressedin (4)[17].

TMRA(j,k)=MRA(j,k)•T(j,k) (4)

4.ProblemFormulation

Thethreemainpartsofatypicaloptimization problemaredecisionvector,objectivefunctionand constraints.Therefore,eachitemhasbeenillustrated inregardtooptimalsolutionofPQMplacement.

Figure4. AnexampleoftheMRAmatrix

Figure5. Exampleofrow3inTmatrixfordifferent systemtopologies[22]

4.1.DecisionVector

ThedecisionvectorthatrepresentstheMonitor Placement(MP)vectorisintroducedasabinarydeci‐sionvectorinbitsintheoptimizationprocess.

Eachbitindicatesthepositionsofmonitorsthat areinstalledornotinpowersystemnetwork.If MP(n)=1,itindicatesthatasagmonitorshouldbe installedatbusnwhereasavalue0meansthatno monitorneedstobeinstalledatbusn.ThisMPvector canbedescribedasfollows[20]:

1 ifmonitorisrequiredatbusn

0 ifmonitorisnotrequiredatbusn (5)

4.2.ObjectiveFunction

ThePQMoptimizationproblemdiscussedinthis studydealswiththreeobjectivefunctionsthatare addressedfollows.

1.Minimizingthenumberofrequiredmonitors (NRM)

The irstobjectivefunctionistominimizethenum‐berofrequiredmonitors(NRM),whichcaneasilybe obtainedasexpressedin(6),andthisparameterneeds tobeminimized.

bus

NRM=

=1 MP(n) (6)

2.Minimizingthemonitoroverlappingindex (MOI)

Monitoroverlappingindex(MOI)isintroducedto assessthebestmonitororganizationinapowersys‐tem.Overlapsofmonitorcoverageareasfordifferent arrangementsaretheissueofPQMplacementina powersystem.Here,itisessentialtoconsiderthat theseoverlapsrepresentthenumberofsagmonitors thatreportthesamefaulthappeninginapowersys‐tem.Thus,theseoverlapsshouldbeminimized.The overlapscanbedeterminedbymultiplyingtheTMRA matrixandthetransposedMPvector.Ifalltheele‐mentsintheobtainedresultsare1,itsigni iesthat thereisn’tanyoverlapofthemonitors’coverage.A lowerMOIindexrepresentsabetterorganizationof PQMsinapowersystem[19].

TheMOIisgivenby:

MOI= ∑(TMRA∗MPT)

NFLT (7)

WhereNFLTindicatesthetotalnumberoffault locationsconsideringalltypesoffaults.

3.Maximizingthesagseverityindex(SSI)

Ifseveralmonitorcon igurationshavethesameMOI values,thenintheevaluationstepofmonitorplace‐ment,theuseofanotherindex,whichiscalledthe SagSeverityIndex(SSI),willbenecessary.Thisindex signi iestheseveritylevelofaparticularbusregarding voltagesagwhereanyfaultthathappensatthisbus willmakeaseriousdropinvoltagemagnitudeinmost busesofthesystem.

Thus,itisneededtocalculatetheseveritylevel (SL) irst.TheSListhetotalnumberofphasesfaced withvoltagesags(NSPB)withmagnitudesbelowt p.u.consideringthenumberofphasesintotalforthe system(NTPB)theSLisextractedasbelow[23]:

Finally,theSSIisdeterminedbyweightingcoef‐icientswhichappliedfordifferentseveritylevels.It isnotablethatthelowesttvalueisappointedwith themaximumweightingfactorandviceversa.Inthis study, ivethresholdsareconsidered;0.1,0.3,0.5,0.7 and0.9p.u.

Finally,thecomputedSSIvaluemustbestoredin amatrixformwherethematrixcolumniscorrelated tothebusnumber,andthematrixrowiscorrelated tothetypeoffault(F).AhighervalueofSSIindi‐catesabetterplacementofthemonitor.Thehighest valueofSSIataparticularbusimpliesthatthebus isthemostin luentialbusthatcausesvoltagesagin apowersystem,andtherefore,thisbusneedstobe givenpriorityininstallingaPQMcomparedtoother buseswithlowerSSIvalues.Inordertocombinethe MOIandSSIindices,bothofthemshouldhavesame optimalcriteriaofeithermaximumorminimum.In ourstudy,theSSImatrixshouldberevisedtoconclude minimumvalueinoptimizationasthecaseofMOI.It isworthtonotethatthehighestvalueofSSImatrix elementsisequalto1.SO,thesuitableindexcanbe extractedbytheuseofcomplementarymatrixofSSI. Asaresult,anegativeseveritysagindex(NSSI)ispro‐posedtoassessthebestplacementofPQMs.TheNSSI canbedeterminedbymultiplyingofcomplementary ofSSImatrixwithtransposedMPvectorwithconsid‐eringthenumberoffaulttypes(NFT)asexpressed follows[9].ThenalowerNSSIvalueconcludesabetter organizationofPQMs.

Sincethethreementionedobjectivefunctionshave thesameoptimalcriteria,withcombinationofthem, thesingleobjectivefunctionforminimizationofthe proposedproblemisextractedasfollows:

=(NRM∗MOI)+NSSI (11)

4.3.OptimizationConstraint

Theonlyoptimizationconstraintinthisproblem isthatthemonitoringtimesofthespeci icfaultpoint mustnotbezero.Itisimportanttonotethatthe numberofmonitorsthatcandetectvoltagesagsdueto afaultataparticularbuscanbeobtainedbythemul‐tiplicationoftheTMRAmatrixbythetransposedMP matrix.Sohisconstraintisformulatedasfollows[22]:

5.ShuffledFrog‐LeapingAlgorithm

5.1.ClassicalApproach

TheSFLAwasoriginallyintroducedasa population‐basedmeta‐heuristicbyM.Eusuff andK.Lansey[24].Thisalgorithmisinspiredbythe frog’slifeasagroupwhenthefrogsareinsearchof food.Ashuf lingstrategyprovidesthemechanism toexchangeinformationbetweenlocalgroupsfor thepurposeofmovingthesolutiontowardsaglobal optimum[25].ThetermfroginSFLAissimilarto chromosomeinGeneticAlgorithm(GA)orparticlein ParticleSwarmOptimization(PSO)approach.InSFL, thepopulationofthefrogs(solutions)isdividedinto differentgroupsreferredtoas memeplexes

Thestepsofthealgorithmareasfollows:

Initializingthepopulation: Createaninitialpopula‐tionof P frogsgeneratedrandomly,P={X1,X2,…,XP} whichfor z‐dimensionalproblems(z variables),the positionof ith froginthesearchspaceisrepresented asx�� =[xi,1,xi,2,…,xi,z].A itnessfunctionisde inedto evaluatethefrog’sposition.Thefrogsarethensorted indescendingorderinaccordancewiththeir itness.

Partitionfrogsintomemeplexes: Dividethefrogs into m�� memeplexeseachholding n�� frogssuchthat ��=���� ×����.Thedivisionisdonewiththe irstfrog goingtothe irstmemeplex,thesecondonegoingto thesecondmemeplex,the i���� froggotothe i���� meme‐plexandthe (i+1)���� frogbacktothe irstmemeplex.

Localexploration: Inthisstep,aprocessisappliedto improveonlythefrogwiththeworst itness(notall frogs)ineachcycle.Foreachmemeplex k,thefrogs withthebestandworst itnessareidenti iedas x��������,�� and x����������,�� respectively.Also,thefrogwiththeglobal best itness x���������� isidenti iedamongallthememe‐plexes.Forthememeplex k atthetimeoriteration t,theworstfrog x����������,�� leapstowardthebestfrog x��������,�� andthepositionoftheworstfrogisupdated basedontheleapingrule,asfollows:

xt worst,k =xt−1 worst,k +dt k (13)

dt k =rand(xt 1 best,k xt 1 worst,k) (14)

Where t isthecurrentiterationnumberand d�� = [dk,1,dk,2,dk,3,…,dk,z]with −�������� ≤����,�� ≤��������, which D������ isthemaximumallowedchangeoffrog’s positioninonejump.Ifthisprocessproducesabet‐tersolution,itisreplacedfortheworstfrog.Oth‐erwise,thecalculationsinequations(13)and(14) arerepeatedbutwithrespecttotheglobalbestfrog (i.e. x��������,�� isreplacedby x����������).Ifnoimprovement ispossible,thenanewsolutionisrandomlygener‐atedtoreplacetheworstfrog.BasedonFigure6,the evolutionprocessiscontinuedforaspeci icnumber ofiterations[30].ThestepsofFigure 6 arelistedas follows:

‐ Continuethecalculationofstep3foraspeci icnum‐berofiterations

‐ Reshuf iethefrogsandsortthemagain.

‐ Returnbacktostep2,iftheterminationcriterionis notmet,elsestop.

Accordingly,themainparametersofSFLare:num‐beroffrogs, P;numberofmemeplexes m��;numberof frogsineachmemeplex, n��;numberofgenerationsfor eachmemeplexbeforeshuf ling, g;numberofshuf‐lingiterations;numberofshuf lingiterations, t������ InFigure 7,the lowchartoflocalsearchasapartof Figure6,ispresented.

Figure6. FlowchartoftheBSFLalgorithm

5.2.BinaryShuffledFrog‐LeapingAlgorithm(BSFLA)

Indiscretebinarysearchspace,everypositionvec‐torcantakeonly0or1.Themovementmeansthat thecorrespondingvariablevaluechangesfrom0to 1orviceversa.Inordertoproposeabinaryversionof theSFL,itisrequiredtomodifythesomefundamental conceptsofSFL.Theleapingruleofthefrogsmaybe consideredsimilartothecontinuousalgorithm(11).

Figure8. Probabilityfunction

ThemainaspectthatdistinguishesthebinarySFL (BSFL)fromclassicalSFListhatinthebinaryversion, themakingupdateoftheworstpositionmeansthe switchingbetween‘0’and‘1’values.Thisswitching shouldbeperformedinaccordwiththeleapingrule. Theideaistomakethepositionupdateinsucha waythattheBSFLchangesthecurrentbitwitha probabilityvaluewhichisdeterminedinaccordwith theleapingrule.Thismeansthat,BSFLupdatesthe leapingruleandconsidersthenewworstpositionto beeither1or0withagivenprobability.Tointroducea suitabletransferfunctiontomakearelationbetween theleapingruleandtheprobabilityupdatingofworst position,twobasicconceptsmustbeconsidered.

†Whenthecurrentpositionoftheworstsolution isnotpropersoagreatabsolutejumpisneededto arrivethebestpositionandasaresultchangingthe positionoftheworstsolutionmustbeprovidedwith ahighprobability.

†Whenthecurrentpositionoftheworstsolution isclosetothebestpositionsoasmallabsolutejumpis neededtogetthebestpositionandasaresultchang‐ingthepositionoftheworstsolutionmustbeprovided withalowprobabilityclosetozero.Thusconsidering abovepoints,forasmall|dt k|,theprobabilityofmove‐mentxworst,kmustbenearzeroandforalarge|dt k| theprobabilityofchangingxworst,kmustbehigh.To overcomethisproblemthefunctionS(dt k) basedon absolute“tanh”transformationtothecomponentof absolutejumpispresentedasfollows[26].

S(dt k)squashesabsolutejumpintotherangeof[0,1] andincreaseswithincreasing |dt k| asshowninFig‐ure8.OnceS(dt k)iscomputed,themovementoffrogs willbedoneasfollows:

Togetapleasantconvergencerate,thefrogsjump mustlimitas |dt k|≤ Dmax whichbasedonexperi‐ments,Dmax isbettersettobe6.

Figure7. Flow‐chartofthelocalsearchintoeach memeplex

5.3.BSFLAforOptimalPQMPlacement

UsingtheBSFLA,analgorithmfortheoptimal placementofPQMscanbeobtained:

Step1: Power lowandshortcircuitanalysesare implemented.

Step2: SLiscalculated,andanSSImatrixis formed.TheMRAmatrixisconstructedsimultane‐ouslybasedontheshortcircuitresults.

Step3: The T matrixisdevelopedfromthenet‐workcon iguration,andtheTMRAmatrixiscon‐structed.

Step4: AllentriesoftheMPvectors(frog’sposi‐tions,xij)inthesystemarerandomlyinitialized.

Step5: IftheMPvectorsdon’tful illthementioned constraints,theentriesofeachMPvectoraremanipu‐latedtoful illtheconstraints.

Step6: AllthePQMplacementevaluationindices, namely,NRM,MOI,andNSSI,areobtained.

Step7: TheperformanceofeachMPvectoriseval‐uatedwiththeformulatedobjectivefunction(f )based ontheobtainedindices.The itnessvaluesforeach frog, f��(t),arerecorded.

Step8: Thefrogsarethensortedindescending orderinaccordwiththeir itness.

Step9: Partitioningfrogsintomemeplexeswas performedusingdividethefrogsinto m�� memeplexes eachholding n�� frogs.

Step10: Localexplorationasaprocessisapplied toimproveonlythefrogwiththeworst itness(notall frogs)ineachcycleandthepositionoftheworstfrog isupdatedbasedontheleapingrule.

Step11: EachMPvectortoanewpositionis updatedwithcriteriapresentedin(Eq. 13)and (Eq.14).

Step12: Steps5–12arerepeateduntilconver‐genceisobtained,wherethebest itnessvalueisequal totheworst itnessvalue.Uponconvergence,the optimalPQMplacementisobtained.

TheoverallprocedureintheoptimalPQMplace‐mentmethodusingBSFLAisshownina lowchartin Figure9.

6.SimulationandResults

TheIEEE34Bustestsystemisanunbalanceddis‐tributionsystem.Thesystemconsistsof34nodes interconnectedby34linesandthetestsystemdatais providedin[27].TheFVanalysisresultsinamatrix andisextractedwiththeproposedmethodinaDIGSI‐LENTenvironmentasindicatedinFigure10

AlltheoptimizationparametersofBSFLAarestan‐dardizedwherenumberoffrogs,P;numberof memeplexes mp;numberoffrogsineach memeplex,nf;num‐berofgenerationforeach memeplex beforeshuf ling g;numberofshuf lingiterations;numberofshuf ling iterationstmax.Theselectedparametersare:P=60, mp=10,nf=6,g=5andtmax=50respectively.Inthis paper,thebestvaluesfortheaforementionedparam‐etersareobtainedbyrunningtheBSFLAalgorithm 100times.

Table 1 showstheoptimalnumberofPQMsand thecomputationaltimesintheIEEE34BUSsystemat different �� valuesbyBSFLAandarecomparedwith QBPSOandAQBPSOby[20]tovalidatetheoptimal solutions.Ascanbeseeninthistable,intermsofcom‐putationaltime,theBSFLAisfasterthantheQBPSO

Figure9. ImplementationofBSFLAforoptimalPQM placement

Figure10. ShortcircuitanalysisintheDIGSILENT environmenttoformFVmatrix

Table1. TheoptimalnumberofPQMsandelapsedtimeon34Bussystematdifferent �� values

Table2. TheoptimalarrangementofPQMswithoptimalfitnessvaluesatdifferent �� values

andaswellasAQBPSOasthe �� valuedecreases. Althoughforthe��valuegreaterthan0.55perunit,the computationaltimesbyQBPSOandAQBPSOarecom‐parable;howeverbydecreasingthe��value,thecom‐putationaltimesbyBSFLAisuniformityincreased.

Table2showstheoptimalPQMplacementatopti‐malbusesofthesystemofBSFLAwithrelatedoptimal itnessvalue,and inally,resultsarecomparedwith AQBPSOandQBPSOby[20]tovalidatetheresult. Theresultsshowedthatthebuslocationsforplacing thePQMsinthe34Bussystemarenearlysimilarfor BSFLAandbothAQBPSOandQBPSO.

Theterm‘N.R’inTable 2 meansthatthecor‐respondingvalueisnotreportedbythatreference.

Table3showstheperformancesofvariousalgorithms intermsofconvergencerateandqualityofsolution afterperforming20runsat ��=0.25.Ascanbe

Figure11. Thebestperformancecharacteristicsof BSFLA,AQBPSOandQBPSOinsolvingPQMplacement for34Bussystemwhen ��=0.85

seenintheTable,allmethodshaveobtainedasame optimalsolution.However,BSFLAshowsgoodopti‐malsolutioninaverageandmoreaccuratebasedon rangeofsuboptimalsolutionsbetweenthebestand theworstvaluesasindicatedbytheaveragevalues incomparedwithAQBPSOandQBPSOby[20].Based onthestandarddeviation(��),allofthealgorithms provideaprecisesolution.Intermsofcomputational times,BSFLAisfasterthanAQBPSOandismuchfaster thanQBPSO.TheresulthasalsoillustratedthatBSFLA convergefasterthanAQBPSOandQBPSOinwhichit hassolvedtheoptimizationproblemin6iterations comparedtotheAQBPSOin7iterationsandQBPSO in8iterations.

Table3. PerformanceofBSFLAandotherreferenceson 34Bussystemfor �� at0.25P.U

Figure 11 showsthebestcharacteristicofeach algorithminobtainingoptimalsolutionfortheIEEE 34Bussystemwhen ��=0.85.Accordingtothis igure,BSFLAhasdemonstratedafasterconvergence thantheAQBPSOwhereasQBPSOgivestheworst performanceintermsofconvergencerate.Although, AQBPSOdoesnotconvergefast,ithasprovidedabet‐teroptimalsolutioninaverageascomparedtoQBPSO.

Hence,BSFLAhasshownthebestperformance oftheoptimizationtechniques,butitdoesnotshow asigni icantdifferentbetweenthemsincethebest obtained itnessvaluesaresame,anditrequirestotest onlargescalesystems.

Inordertofurthervalidatetheplacement,100 faultsatdifferentlocationsarerandomlysimulated. Fromall100simulatedfaults,60%singlephasefaults, 30%twophasefaultsand10%threephasefaults areconsidered.ThePQMswillbetriggeredifone ofthephasevoltagemagnitudesdropsdowntothe thresholdlevel0.75,andtheeventwillberecorded bytheparticularPQM.Table 4 showsasummaryof thefaultdetectionactivityby3PQMsatthesuggested locations.Accordingtothetable,for ��=0.75,all thesimulatedfaultsaredetectedandrecordedbyat least1PQM.Inotherwords,referringtotheresults inTable 4,foralphaequals0.75,novoltagesagwas incorrectlymonitored,whereasforalphaequals0.85, 5twovoltagesagswereincorrectlymonitored.Forthe voltagesagsmonitoredbythreePQMs,20faultsthat resultedinvoltagesagsweremonitoredmorethan onceat��=0.75,whereas10faultsweremonitoredat ��=0.85.However,amoreaccuratePQMmonitoring ofvoltagesagsisachievedat��=0.75comparedwith ��=0.85.Thus,itisproventhattheobtainedPQM placementsarecapableofobservingandcapturing anyfaultoccurrenceinthewholesystem.

7.Conclusion

Inthispaper,duetothediscretebinarysearch spacenatureforPQMsplacement,inwhicheveryposi‐tionvectorcantakeonly0or1,thebinaryversion oftheshuf ledfrog‐leapingalgorithm,BSFLA‐based method,wasintroduced.Theabsolute“tanh”trans‐formationtothecomponentoftheabsolutejumpis presentedandsquashesabsolutejumpintotherange of[0,1].Theobjectivefunctionbaseontheminimum numberofPQMs,alongwiththeminimizingmonitor overlappingindexandthemaximizingsagseverity index,isformulatedandoptimizedusingBSFLA.In thispaper,theresultsofshortcircuitanalysisusing DIGSILENTsoftwareareimportedtotheoptimization mediathatishandledbyBSFLA.Thealgorithmwas appliedtoIEEE34BUSunbalanceddistributionsys‐tem.Fordifferentvoltagesagthresholds,theoptimal

numberandcon iguration,aswellastheMOIand SSIindices,areanalyzed.Theeffectofthethreshold ofthevoltagesagsontheMOIandSSIindicesare evaluated.Thus,thelowerthethresholdofthevoltage sags,thesmallertheMOIandthehigherthenum‐berofmonitorsrequired,whichavoidsoverlappingin themonitoringscheme.Whenthevoltagethreshold reducesfrom0.85to0.25,theMOIindexdecreases from1.132to1.004.

AlsoFitnessvalues,convergencetimeanditer‐ationnumbersaredeterminedandcomparedwith QBPSOandAQBPSO,whichwereutilizedinprevious studies.ResultsdepictthatBSFLAproducesthebest solutioncomparedtotheotheroptimizationmethods. OtheradvantagesofBSFLAincludefastconvergence, smallruntime,capabilityof indingglobaloptimum andnearlyzerostandarddeviation.

AUTHORS

AshkanDoustMohammadi –Department ofElectricalEngineering,BorujerdBranch, IslamicAzadUniversity,Borujerd,Iran,e‐mail: ashkan.doustmohammadi@gmail.com.

MohammadMohammadi∗ –Department ofElectricalEngineering,BorujerdBranch, IslamicAzadUniversity,Borujerd,Iran,e‐mail: mohammadi.m.84@gmail.com.

∗Correspondingauthor

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LYAPUNOV‐LASALLEBASEDDYNAMICSTABILIZATIONFORFIXEDWINGDRONES LYAPUNOV‐LASALLEBASEDDYNAMICSTABILIZATIONFORFIXEDWINGDRONES LYAPUNOV‐LASALLEBASEDDYNAMICSTABILIZATIONFORFIXEDWINGDRONES

Submitted:2nd March2022;accepted:20th March2023

DOI:10.14313/JAMRIS/4‐2023/29

Abstract:

ThemarketofUnmannedAerialVehicles(UAVs)forcivil applicationsisextensivelygrowing.Indeed,theseair‐planesarenowwidelyusedinapplicationssuchasdata gathering,agriculturemonitoringandrescue.TheUAVs arerequiredtotrackafixedormovingobject;thus,track‐ingcontrolalgorithmsthatensurethesystemstability andthathaveaquicktimeresponsemustbedeveloped. Thispapertacklestheproblemofsupervisingafixed targetusingafixedwingUAVflyingataconstantaltitude andaconstantspeed.Forthatpurpose,threecontrol algorithmsweredeveloped.Inallofthealgorithms,the UAVisexpectedtohoveraroundthetargetinacircular trajectory.Moreover,thethreeapproachesarebased uponaLyapunov‐LaSallestabilizationmethod.Thefirst trackingalgorithmensuresthattheUAVcirclesaround thetarget.However,thepaththattheUAVfollowsin ordertojointhispatternisnotstudied.Inthesecondand thirdapproach,twodifferenttechniquesthatallowthe UAVtointerceptitsfinalcircularpatterninthequickest possibletimeandthusfollowthetangenttothecircular patternarepresented.Simulationresultsthatshowand comparetheperformancesoftheproposedmethodsare presented.

Keywords: UAV,Stabilisation,Lyapunov‐LaSalle

1.Introduction

UnmannedAerialVehicles(UAVs)arenowwidely usedinnumerouscivilapplicationsincludingfor searchandrescue,humanoranimalsurveillance,agri‐cultureandindustrialmonitoring, ire ighting,etc.For thesepurposesmanytypesofUAVaredeveloped, suchasMulti‐Rotordrones,SingleRotorHelicopters, ixedwingdronesandhybridVTOL(VerticalTake‐OffandLanding).SingleandMulti‐rotorUAVsbene it frombeingeasytomanufacture,relativelycheapand easytocontrol.ThesetypesofUAVscantake‐offand landverticallyandcan lywithaspeedequaltozero. However,theysufferfromsomedisadvantages,infact, theseUAVsarerelativelyslow(limitedspeedrange), theyhavelimited lyingtimeandrange,theyarenot ef icientastheyspendahugeamountofenergyto ightgravityand inallytheyhavealimitedpayload. Fixedwingdronesaretotallydifferentinthesense theybene itfromhavingalong lyingtime,longrange, highef iciencyandhighervelocitybutsufferfrom beinghardtocontrol.Indeed,theseairplanesstallat lowspeedandthusareusuallycontrolledby ixingor minimallyvaryingtheirlinearspeed.

Finally,hybridVTOLcombinesthebene itsof singleandmulti‐rotorUAVsalongwith ixedwing dronesbutsufferfrombeingexpensiveandhardto manufacture.

InalmostallUAVapplications,theobjectiveisto tracka ixedormovingtarget.Thispaperfocuses on ixedtargettrackingalgorithmsusing ixedwing UAVsforlongrange, ixedaltitudeapplications.The dronesusedinsuchapplicationsarealsocalledHigh AltitudeLongEndurance(HALE)typeUAVswith ixed wings.Since,asmentionedpreviously,theseUAVs couldnotdropbelowaminimumlinearspeed.Thus, thecontroltrackingalgorithmsappliedtotheseair‐planesarechallenging.Infact,unlikesingleandmulti‐rotordrones, ixedwingsUAVsarenotcapableof reachingandmaintainingthetarget’sposition.Thus, thesedronesshouldfollowaspeci icpathinorder totrackthenhoveraroundthetarget.Consequently, pathplanningandre‐planningbasedtrackingcontrol algorithmsareused[8,14].

Themodelusedinthisarticleisinspiredbythe Dubinsmodel[12, 24]and[9].Ithasbeenexten‐sivelystudiedforthemodelingofvehiclesand ixed wingdrones,especiallyinregardstotrajectoryopti‐mality[2, 7, 18]and[16].Theauthorsin[1, 4, 22] and[21]provideareviewofUAVpathplanningandre‐planningtrackingalgorithms.In[5]and[3],theprob‐lemofdynamicoutputstabilizationofcontrolsystems intheunobservablecasefor ixedwingsdronesis treated.

TheLyapunovmethodhasbeenusedbyseveral authors,indifferentways,suchasin[10,13,15,17] and[19].Lyapunovstrategiespresentedinthelit‐eraturearenotalwayscompletelysmoothandthe inalcurvatureisabitsmallerthanthemaximum curvature.

In[6,18]and[23]theauthorsprovidedadetailed studyofpathplanningUAVtrackingalgorithms usingLyapunov‐LaSallebasedstabilizationandtime‐optimalstabilizingsynthesis.Theproposedmethods havebeenusedtotrackacirclepatternusingaDubins vehicle.

Thepaper[18]presentsthreecontrolalgorithms for ixedtargettrackingusinga ixedwingUAV lying ataconstantaltitudeandaconstantspeedandcom‐paresthemtoaminimum‐timepathplanningalgo‐rithm.Inordertoconsiderthetargetreached,theUAV hastomaintainahoveringpatternaroundthetarget. Theproposedtrackingalgorithmsuseacircleasa hoveringtrajectory.Thiscirclehasthetargetasits center.The irsttrackingalgorithmpresentedherein

JeanSawma,AlainAjami,ThibaultMaillot,JosephelMaalouf

isbasedonaLyapunov‐LaSallestabilizationmethod andhasbeenstudiedin[18].Thisresultisgivenforthe self‐consistencyofthispaper.Thismethodensures thattheUAVisreachingandmaintainingthehovering pattern.Inthetwostabilizationmethodspresented herein,theUAVusesthetangenttothecircularpattern asitstrajectoryguidetogettoitsdestination.The performancesoftheproposedmethodsaresimilar; However,thecalculationtechniquesaredifferent.In fact,thesecondtechniqueiscomputedinanewrotat‐ingreferenceframe,whilethethirdoneisperformed inthestationaryreferenceframe.

Therestofthepaperisorganizedasfollows:Sec‐tion 2 presentsthekinematicalmodelofthe ixed wingsUAV.InSection3,thepresentationofthemajor results[18]isexplored.The irsttrackingalgorithm consideredinthispaperandthetime‐optimalsyn‐thesisareusedascomparison.Section 4 presents thesecondandthirdtrackingalgorithms.Simulation resultsandalgorithmscomparisonareaddressedin Section5

2.ProblemUnderConsideration

Thissectiondevelopsthekinematicalmodelofa ixedwingHALEUAVusedhereinforbothsimulation andcontrolpurposes.ThekinematicsofaroughHALE dronearesupposedtobegovernedbythestandard Dubinsequations[11,24]:

̇��=�� 0 cos(��) ̇��=�� 0 sin(��) ��=�� (1)

where (��,��,��)∈ℝ2 ×��1 isthestate. (��,��)∈ℝ2 isthedrone’sinertialpositioninaconstantaltitude planeand �� istheyawangle(theanglemadebythe aircraftdirectionwithrespecttothe��‐axis).��0 ∈ℝ∗is thelinearspeedand��∈[−��������,��������]isthecontrol drivingUAVkinematics.

Equation(1)expressesthedronesmovementsin the(��,��)‐plan.ThealtitudeoftheUAVisconsidered constantthusthealtitudecomponentisomittedin Eq.(1).Moreover,thespeedofthedrone��0 isconsid‐eredconstant.Theboundontheyawangularveloc‐ity(��)modeledtheUAVkinematicsrestrictiononits turningradius,whichisgivenby��= ��0 ��������

Asmentionedpreviously,inordertotracka ixed point(target),thedronehastohoveraroundthis targetusingacircularpatternofradius ��.This inal circularpatternisdenotedby��andhasthefollowing characteristics:

‐ ��centeristhetarget.

‐ ��radiusis��= ��0 �������� .

�� couldalsobeseenasthemaximumcurvature patternthatcanbeachievedbytheUAVandcouldbe representedbythefollowingequation:

��={(��,��,��)∣��=��sin��,��=−��cos��}. (2)

3.LyapunovandMinimalPathPlanning

In[18],theauthorsstudiedtwocontrolstrategies fortheproblempresentedpreviously.The irststrat‐egyreliesonaLyapunov‐LaSallestabilizationmethod. Thesecondstrategywasconstructedusingthetime‐optimalcontrolsynthesisfortrackingacirclebya Dubinsvehicule.Inthissection,onlytheprincipal resultsof[18]usedinthispaperareaddressed.

3.1.Lyapunov‐basedStrategy

ThesystemmodeledwithEq.(1)canbesimpli‐iedbywritingitinamoving‐frame.Thisnewframe isstickingtotheUAVandthusrotatingwithit.The systemmodelinthenewmoving‐framecouldbecal‐culatedbyapplyingthefollowingtransformation: = cos�� sin�� sin��

AndthusthesystemEq.(1)couldberewrittenas:

(3)

(4)

Thesysteminequation(4)possessestwoequilib‐riumpointsfor ��=��max and ��=−��max,namely ��1 =(0,−��)and��2 =(0,��).Theycorrespondtothe target��beingcirculatedcounter‐clockwiseandclock‐wise,respectively.Inthefollowing,theequilibrium point��1 isthepointattheendofthemissionwhere theUAVwillhover�� counter‐clockwise.Itshouldbe mentionedthatpoint��2 couldalsobechosenwithout modifyingthecontrolalgorithmperformances.

Havingchosen ��1 asanequilibriumpoint,itis possibletoswitchtoanewrotatingreferenceframe (̄��,̄��)wheretheequilibriumpointis(̄��=0,̄��=0) Thetransformationform(̃��,̃��)to(̄��,̄��)isgivenby:

̄��=̃�� ̄��=̃��+�� (5)

Reachingtheequilibriumpoint (̄��=0,̄��=0) in thisnewrotatingframeisthesameascirclingthe hoveringpattern �� counter‐clockwiseinthe (��,��)‐plane.Thesystemmodelcouldbewritteninthenew (̄��,̄��)frameas:

̄��=�� 0 +��̄��−���� ̄��=−��̄�� (6)

The ixedtargetthattheUAVshouldtrackiscon‐sideredtobelocatedattheoriginofthe ���� ixed referenceframe (��=0,��=0).TheUAVstartsits trackingmissionfromaninitialposition(��=��0,��= ��0)andwithaninitialangle(��=��0)andhasto ind itspathtointerceptandmaintainacircularhovering patternthathasaradius �� and ���� originascenter. SincethespeedoftheUAVisconstantequalto ��0, theonlyparameterthatcouldbemodi iedtomeetthe controlobjectivesis ��= ��,theUAVangularspeed. Itshouldbementionedthat,accordingtoEq.(1),the inputiswithintheinterval[−��������,��������].

Knowingthisinformation,letEq.(7)beaLya‐punovfunctioncandidate.

��(̄��,̄��)=̄��2 +̄��2 (7)

Afterderiving ��(̄��,̄��) andcombiningitwith Eq.(6),thefollowingequationiscomputed:

��(̄��,̄��)=2̄��(1−����) (8)

Inorderfor��(̄��,̄��)tobeaLyapunovfunction,the followingrulesshouldbeapplied:

‐ ��(0,0)=0

‐ ��(̄��,̄��)shouldbepositive.

‐ ��shouldbenon‐positive.

The irsttworulesaresatis ied.However,to ensurethethirdoneisveri ied,someconditionson ��areneeded.In[18],theauthorsshowedthat,ifthe control��isequaltoaanysmoothfunction��∶ℝ2 → [−��������,��������] thatveri iesEq.(9),then �� isnon‐positive.

��=��(̄��,̄��)= �������� if̄��≥0 −�������� ≤

if̄��<0 (9)

Moreover,accordingtoLaSalle’sprincipleand since �� isaproperfunction,allthetrajectoriesof system(6)withfeedbackcontrol ��(⋅) convergeto thelargestinvariantsetcontainedintheset ��= {(̄��,̄��)| ��(̄��,̄��)=0} whichhasbeenprovedin[18] tobetheequilibriumpoint(0,0).Consequently,there existsanexplicitfeedbackcontrolfunction ��(⋅) that hasthefollowingpropriety:thepattern�� isaglobal asymptoticallystableattractorfortheclosed‐loopsys‐temasaresultsofapplying��(⋅).Forexample,wemay considerthefollowingequationwhichsatis ies(9) andsteersasymptoticallysystem(1)to��. ��=

�� if̄��≤−��

��max−�� 1+��1/(��+��)+1/�� +�� if̄��∈(−��,0)

��max if̄��≥0, (10) where �� isapositiverealnumberand �� issuchthat −�������� ≤��<��������.

Inotherwords,thefeedbackcontroller(10)turns theUAVwiththeextremalauthorizedcurvatures(��= �������� or ��=��)whenevertheUAVismovingaway fromthetarget(̄��≥0 or ̄��≤−�� ).Thus,thedrone willturnuntilitgetsbackontrack.Wheneverthe UAVisontrack,itwillturnwithanangularspeed equalto+��hoppingtogettoits inalcircularpattern withitsminimumturningradius(��=��������).The UAVangularspeedwillvaryaccordingtoFigure 1 duringthisapproach(when ̄��∈[−��,0[ )inorderto ensureasmoothtransitionfrom��=�������� to��=�� andreducethechatteringeffectofthiscontroller.The irsttrackingcontrolalgorithmconsideredhereinis obtainedinapplyingthefeedbackcontrolde inedin Eq.(10).

Inordertoverifytheperformancesofthiscon‐troller,theUAVissimulatedinclosed‐loopusingMAT‐LAB.TheUAVparametersusedinnumericalsimula‐tionsaregiveninTable1,andthecontrolparameters are��=0.2������/��and��=10��.

Figure1. Shapeofthefeedbackcontroller ��(̄��,̄��)

Table1. UAVparameters

Figure2. ThepathfollowedbytheUAVusingLaSalle’s principlebasedplanification

ThestartingpositionoftheUAVis(��0,��0,��0)equal to(100��,60��,0������/��).

Figure 2 showsthepathfollowedbytheUAVto reachitstargetpatterncenteringattheorigin.

OnthisFigure,thepathusedbytheUAVseemsto notbetime‐optimal.Indeed,theUAVisdoingloops beforereachingandmaintainingthe inalpattern.

3.2.Time‐optimalSynthesisBasedStrategy

Anotherstrategywaspresentedin[18]inorder to indasolutiontotheproblempresentedinSection 2.Herein,theminimumtimeproblemforSystem 1 isaddressed,andasummaryofthissecondmethod basedonantime‐optimalcontrolsynthesisispre‐sented.

Figure3. Theoptimalsynthesis.Alloptimaltrajectories startat ��0 withcontrol −1.Thedashedblackcurveis theswitchingcurve,thepurplecurveisthesingular trajectoryandthegreencurvesarecutloci.Noticethat theminimum‐timefunctionisnotcontinuousalongthe bluedashedcurve[18].

Inordertosimplifythetreatmentuptoadilation inthe (��,��)‐planewemayassumewithoutlossof generalitythat ��0 =1 and [−��max,��max]=[−1,1] Thus,weconsiderthefollowingproblemdenoted(P).

(P) Forevery (��0,��0,��0)∈ℝ2 ×��1 indthepair trajectory‐controljoining(��0,��0,��0)to��,which istime‐optimalforthecontrolsystem

̇��= cos�� ̇��= sin�� ��=��,��∈[−1,1].

(11)

TosolveProblem(P),areducedsystemindimen‐siontwoiscomputedusingEq. 3:theproblemcon‐sideredisthereforerewritteninthefollowingform denoted(P′).

(P′) Forevery(̃��0,̃��0)∈ℝ2 indthepairtrajectory‐controljoining (̃��0,̃��0) to ��0 =(0,1),whichis time‐optimalforthecontrolsystem

̃��=−��̃��+1

̃��=��̃�� ,��∈[−1,1].

Thetime‐optimalstabilizingsynthesisisthecollec‐tionofallsolutionto(P′)forevery (̃��0,̃��0) [20]. In[18],authorsstatedthistime‐optimalstabilizing synthesisandconstructedFigure3,whichisrelatedto theinversedynamicoftheproblem.Thetime‐optimal stabilizingsynthesisof(P′)isobtainedsimplyby invertingthearrowsofthetrajectoriesrepresented.

Thesolutionstoproblem(P)canbededucedfrom thesolutionstoproblem(P′),obtainedthanksto thetime‐optimalstabilizingsynthesisrepresentedin Figure3.Figure4,showsapairofplotsshowingasolu‐tionofproblem(P′)(Figure4a)anditscorresponding solutiontoproblem(P)(Figure4b).

(a)

(b)

Figure4. Abang‐singular‐bangoptimaltrajectory solutiontoproblem(4a)andthecorrespondingoptimal solutiontoproblem(4b)

4.ImprovementoftheLyapunov‐LaSalle BasedStabilizationMethod

Theobjectiveofthissectionistoproposetwo trackingcontrolalgorithmsthatresolvetheproblem presentedinSection 2 withashorterpaththanthe oneobtainedwiththe irstLyapunov‐basedmethod statedabove.Theproposedmethodsapproachthe performancesoftheoptimaltechniquebutarecom‐putationallylessdemanding.Thissectionisdivided intotwosubsectionsdetailingthetwomethodsfor computingthesealgorithms.

4.1.AFirstShorterStabilizationMethod

A irsttechniquethatallowsthe ixedwingUAV toslideontothetangenttowardthecircularpattern targetisdetailedinthissubsection.Itisestablished inthesamewayasinSection3;however,inthiscon‐troller,theparameter��usedinEq.(10)isconsidered afunction��2 ∶ℝ∗− ×ℝ→[−��������,��������[.Thus,the

Figure6. ThepathfollowedbytheUAVtotrackthe targetusingtheminimumtimestrategyfor ��=0.2��������, ��=0.5�������� and ��=0.9�������� controllerequation(10)isrewrittenasfollows:

��=��(̄��,̄��)=

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

��2(̄��,̄��) if̄��≤−��

��max−��2(��,��)

1+��1/(��+��)+1/��

+��2(̄��,̄��) if̄��∈(−��,0)

��max if̄��≥0,

(12)

commandshaveless luctuation.Itshouldbemen‐tionedthatahighervalueof�� leadstheUAVtoslide ontoatangenttowardthehoveringpattern.

4.2.ASecondSimplerComputationStabilization Method

Inthissubsection,anothermethodforcomputing atrackingcontrolalgorithmthatresolvestheprob‐lempresentedaboveisestablished.Thisalgorithm iscomputedusingthestationarycoordinates (��,��) insteadofusingarotatingreferenceframe(̄��,̄��).The stabilizationofthissystemisperformedusingthe sameLyapunov‐LaSalletechniqueasinSection 3.As previously,theparameter �� inEq.(10)isreplaced byafunction ��3 ∶ℝ2 →[−��������,��������[.Thusthe controllerEq.(10)canberewrittenas:

��=��(̄��,̄��)=

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

��3(̄��,̄��) if̄��≤−�� ��max−��3(��,��) 1+��1/(��+��)+1/��

+��3(̄��,̄��) if̄��∈(−��,0)

��max if̄��≥0,

(13)

Considering ̄��<0 ,let ��= arctan(̄��/̄��) bethe angularcoordinateoftheUAVinthe (̄��,̄��)‐planeas representedinFigure5.Let��2(̄��,̄��)=��sin(��)with ��suchthat0≤��<��������.Thus,−�������� ≤��2(̄��,̄��)< ��������,andthecontrollerde inedinEq.(12)veri ies theconditions(9)andstabilizesthesystem(1)toward theconsideredpatternasstatedinSection3

Figure6showstheperformancesoftheplanning algorithmusingthecontrolequation(12)for ��= 0.2��������, ��=0.5�������� and ��=0.9�������� and ��=10��.TheUAVstartingpointis (��0,��0,��0)= (100��,60��,0������/��),anditsparametersaregiven inTable 1.Byincreasingthevalueof ��,thetime neededtojointhepatternisdecreased(quickertime response),andbydecreasingthevalueof��,theUAV

A irststepforcalculating ��3(��,��) istocompute thetangentequationsofthecircularpatterninthe���� stationaryframe.Let(��0,��0)bethecoordinatesofthe UAVinthe����frame.Anylinethatpassesthroughthe UAVhasthefollowingequation:

��=��(��−��0)+��0 (14)

where��,��∈ℝand��istheslopeofthelinetobecal‐culatedinthefollowing.Inordertobeatangenttothe circularpatternEquation(14)mustalsosatisfythe circularpatternequation(��2 +��2 =��2).Combining bothequationsleadstothefollowing:

(15)

with

2 Thesolutionsofequation(15)arethelinesthatlinks theUAVtothecircularpattern.Eachlinecutsthecircle intwodifferentpoints,exceptforthetangent,which onlycutsthecircleatonepoint.Thus,equation(15) doublerootscanhelpcalculatingthetangentequa‐tionsasfollows.

(16)

Solvingequation(16)resultsincalculatingthetwo slopesofthetwotangents ��1 and ��2 (Figure 7).It shouldbementionedthatifnorealsolutionexists,the UAV(��

Figure5. ThefixedwingUAVinthe ���� and ̄��̄�� frames

Knowingtheequationsofthetwotangents,the UAVshouldslideononeoftheminordertoreachits inalcircularpattern.Indeed,Afterthecomputation ofthetwotangentslopes ��1 and ��2,itispossibleto calculatethetwoslopeangles��1 and��2 (Figure7)by applyinganarctanfunctionasfollows:

��1,2 =arctan

with:

−8��0��0 ±√Δ′

−8��2 0 +8��2 (17)

Δ′ =��″2 −4��″��″

Inordertohavevalidslopeangles, Δ′ shouldbe positiveorequaltozerowhichmeansthefollowing equationshouldbesatis ied:

��2(��2 0 +��2 0 −��2)≥0

ThisequationmeansthattheUAVshouldbeoutside thehoveringpattern.

ItshouldbementionedthattheUAVposition (��0,��0)couldbewrittenasfunctionof̄�� and̄�� using thefollowingtransformation:

��0 =̄��cos(��)−(̄��−��)sin(��)

��0 =̄��sin(��)+(̄��−��)cos(��) (18)

Thetangentthathasthelowestvalueoftheslope angleistheonetobechosensinceitleadstohov‐eringaroundthecircularpatterncounterclockwise. Theothertangentwiththehighervalueoftheslope

angleleadstohoveringaroundthecircularpattern clockwise.Inthefollowing,wewilleitheruse��1 or��2 anddenotedthechosenangle��.

Aftercomputingtheangle��,theangle��=��/2−�� iscalculated(Figure7).��shouldbewithintheinterval [−��;��].Having��,itispossibletocompute��3(��,��)as follows:

��3(��,��)=�������� tanh(����) (19)

Where ��>0 isaproportionalregulationconstant. Whenincreasing ��,thetimeneededinorderto convergetowardsthetangent,willbedecreased.By applyingequation(19),itisensuredthattheUAV willslidetothehoveringpatternusingtheshortest possiblepath(thetangent).Itshouldbementioned that��3(��,��)satis iestheconditionsexpressedinSec‐tion 3 andensurestheconvergenceofacontroller basedontheonegiveninEquation(10)towardsthe circularpatternconsidered.

Finally,theproposedcontrolleralgorithmissum‐marizedbythefollowingsteps:

‐ Compute��1 and��2 then��1 and��2

‐ Choosethetangentthatleadstohoveringthecircu‐larpatterncounterclockwise

‐ Compute��

‐ Compute��3(��,��)usingequation(19)

‐ ComputetheinputtobeappliedtotheUAV(equa‐tion(13))

Figure8showstheperformancesoftheproposed controllerfor��=1,��=3and��=10.TheUAVstarting pointis (��0,��0,��0) equalto(100m,60m,0rad/s) anditsparametersaregiveninTable 1, �� is ixedto 10m.Theresultsofthismethodareverysimilarto theresultsofthe irstmethodconceivedintherotating frame.However,calculatingthetrackingalgorithmin therotatingframeiseasier.

5.SimulationResultsandComparison

Thissectioncomparesthesimulationresultsofthe fourpreviouslypresentedcontrolmethods.The irst

Figure7. Minimumtimemethodinthexyreference frame

Figure8. ThepathfollowedbytheUAVfor ��=1, ��=3 and ��=10 usingsecondtrackingalgorithm

Figure10. ThepathfollowedbytheUAVusingthethree proposedalgorithmsstartingfrom (��0,��0,��0) equalto ��2 =(50��,−120��,0������/��)

controlmethod(������ℎ����1)subjecttocomparisonis theLyapunov‐basedmethodpresentedinSection3.1, thesecondone(������ℎ����2)isthe irstshortersta‐bilizationmethodpresentedinsection 4.1,thethird one(������ℎ����3)isthesecondsimplercomputation stabilizationmethodpresentedinsection4.2andthe fourthmethod(������ℎ����4)isthetime‐optimalmethod presentedinsection3.2.

Multipleinitialconditionsareconsideredinorder toshowtheperformancesofeachmethod.Itshould bementionedthatthecontrolparametersofthe irst methodare ��=0.2������/�� and ��=10��.The parametersofthesecondalgorithmare ��=�������� and ��=10��.Finally,thethirdalgorithmparam‐etersare ��=10 and ��=10��.TheUAVparam‐etersaregivenintable 1,andtheinitialconditions (��0,��0,��0) are ��1 =(−200��,−50��,0������/��) and ��2 =(50��,−120��,0������/��)respectively.

Figure 9 and 10,showthepathfollowedby theUAVstartingfrom(−200��,−50��,0������/��)and (50��,−120��,0������/��)respectively,usingthepro‐posedtrackingcontrolalgorithms.Thethreepro‐posedmethodsareconvergingtowardthehovering pattern.Inthe irstalgorithm(������ℎ����1)thetrajec‐toryusedtogettothe inalpatternistwisting.The secondandthirdalgorithms(������ℎ����2 and������ℎ����3) showtrajectoriesinwhichtheUAVfollowsthetan‐genttowardthehoveringpattern.Thesethreecon‐trolmethodsarecomparedtothetime‐optimaltra‐jectory(������ℎ����4).Table 2 showsthetimeneeded bytheUAVtoreachitscircularhoveringpattern.

������ℎ����1 isshowingverypoorperformancescom‐paredto������ℎ����2,������ℎ����3 and������ℎ����4.Moreover, theoptimalmethodisshowingthebestpossibleper‐formances.������ℎ����2 and������ℎ����3 showverysimilar performances,despitebeingcalculatedindifferent ways,andtheirresultsareverycloseto ������ℎ����4. Finally,itispossibletoassumethatbycarefullychoos‐ingparameter ��(��,��) itispossibletoobtainnearly time‐optimalperformancesusinglesscomputational time.

Insummary,the irstmethodemployedacom‐putationallyef icientalgorithmtoconvergetowards thehoveringpattern.However,itsconvergencetime wasnotablyslow,makingittheleastexpedientamong thefourmethodspresented.Thesecondandthird methodshavecomparableperformance,converging towardsthecircularhoveringpatterninnearlyopti‐maltime.Bothmethodswerecomputationallyef i‐cient,withthesecondmethodbeinglessdemanding thanthethird.Thefourthand inalalgorithmalso successfullyconvergedtowardsthehoveringpattern usinganoptimaltrajectorybutprovedtobecomputa‐tionallydemanding.

6.Conclusion

Thispaperstudiestrackingcontrolalgorithms appliedto ixedwingUAVs lyingatconstantspeedand constantaltitude.Threecontrolalgorithmsarepre‐sentedforthetrackingofa ixedtarget.Theproposed methodensurestheconvergenceoftheUAVstoward acircularhoveringpattern.

Inthe irstmethod,thetrajectoryobtaineddid notallowtheUAVtoreachthepatternquickly.Inthe secondandthirdmethodpresentedabove,thetrajec‐toriescomputedfollowthedirectionofthetangentto thepattern,whichmakesitpossibletoapproachthe time‐optimalmethodresults.

Figure9. ThepathfollowedbytheUAVusingthethree proposedalgorithmsstartingfrom (��0,��0,��0) equalto ��1 =(−200��,−50��,0������/��)

Table2. Thetime(inseconds)neededbyeachcontrol algorithmtoreachthehoveringpatternstartingfrom

AUTHORS

JeanSawma∗ –FacultyofEngineering,Saint JosephUniversityofBeirut,Beirut,Lebanon,e‐mail: jean.sawma@usj.edu.lb.

AlainAjami –FacultyofEngineering,SaintJoseph UniversityofBeirut,Beirut,Lebanon,e‐mail: alain.ajami@usj.edu.lb.

ThibaultMaillot –Agrosup,Dijon,France,e‐mail: thibault.maillot@agrosupdijon.fr.

JosephelMaalouf –CollegeofEngineeringandTech‐nology,AmericanUniversityoftheMiddle,Kuwait, e‐mail:joseph.el‐maalouf@aum.edu.kw.

∗Correspondingauthor

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Abstract:

NEWROBUSTMODELFORSTABILITYANDH∞ ANALYSISFORINTERCONNECTED

DOI:10.14313/JAMRIS/4‐2023/30

NEWROBUSTMODELFORSTABILITYANDH∞ ANALYSISFORINTERCONNECTED

EMBEDDEDSYSTEMS

EMBEDDEDSYSTEMS ∞ ANALYSISFORINTERCONNECTED EMBEDDEDSYSTEMS

Submitted:22nd June2022;accepted:6th March2023

AmalZouhri

Thispaperpresentsanovelapproachtoanalyzingthe robuststabilityofinterconnectedembeddedsystems.The paperstartsbydiscussingthechallengesassociatedwith designingstableandrobustembeddedsystems,particu‐larlyinthecontextofinterconnectedsystems.Thepro‐posedapproachcombinestheH∞ controltheorywitha newmodelforinterconnectedembeddedsystems,which takesintoaccounttheeffectsofcommunicationdelays anddatalosses.Thepaperprovidesadetailedmathe‐maticalanalysisofthenewmodelandpresentsseveral theoremsandproofsrelatedtoitsstability.Theeffective‐nessoftheproposedapproachisdemonstratedthrough severalpracticalexamples,includinganetworkedcon‐trolsystemandadistributedsensornetwork.Thepaper alsodiscussesthelimitationsoftheproposedapproach andsuggestsseveraldirectionsforfutureresearch.The proposedfilterdesignmethodestablishesasufficient conditionfortheasymptoticstabilityoftheerrorsystem andthesatisfactionofapredefinedH∞ performance indexfortime‐invariantboundeduncertainparameters. Thisisachievedthroughtheuseofthestrictlinearmatrix inequalities(LMI)approachandprojectionlemma.The designisformulatedintermsoflinearmatrixinequalities (LMI).Numericalexamplesareprovidedtodemonstrate theeffectivenessoftheproposedfilterdesignmethods.

Keywords: Interconnectedembeddedsystems,Stability, H∞ analysis,Linearmatrixinequalities

1.Introduction

Interconnectedembeddedsystemsarewidely usedinmanyapplicationdomains,suchasaerospace, automotive,andindustrialautomation.Thesesys‐temsarecharacterizedbytheircomplex,distributed nature,andtheiroperationisoftensubjecttovari‐ousuncertainties,suchascommunicationdelaysand datalosses.Thedesignandanalysisofsuchsystems presentseveralchallenges,particularlyinensuring theirstabilityandrobustness.

Toaddressthesechallenges,researchershavepro‐posedvariousapproachesforanalyzingthestabil‐ityandrobustnessofinterconnectedembeddedsys‐tems.Oneofthemostwidelyusedapproachesisthe H∞ controltheory,whichprovidesaframeworkfor designingrobustcontrollersthatcanhandleuncer‐taintiesanddisturbances.

Severalrecentstudieshavefocusedondevelop‐ingnewmodelsandapproachesforapplyingtheH∞ controltheorytointerconnectedembeddedsystems. Forexample,inthepaper“RobustStabilityandH∞ AnalysisforInterconnectedUncertainSystems”byX. Zhangetal.(2019)[1],thispaperpresentsanovel approachforanalyzingtherobuststabilityandperfor‐manceofinterconnecteduncertainsystemsusingH∞ controltheory.Theauthorsproposeanewmathemat‐icalframeworkformodelinginterconnectedsystems withuncertaintiesandderiveconditionsforrobust stabilityandH∞ performanceusinglinearmatrix inequality(LMI)techniques.Theproposedapproach isappliedtotheanalysisofatwo‐areapowersystem, demonstratingitseffectivenessinhandlinguncertain‐tiesanddisturbancesininterconnectedsystems.The paperalsodiscussesthepotentialapplicationsofthe proposedapproachinother ields,suchastransporta‐tionandcommunicationsystems.Theauthorspresent acomprehensiveanalysisoftheH∞ controltheory forinterconnecteduncertainsystems.Thepaperpro‐videsadetailedmathematicalanalysisofthetheory andpresentsseveralpracticalexamplestoillustrate itseffectiveness.

H∞ controltheoryisarobustcontrolmethodol‐ogythathasbeenusedinvarious ields,including aerospace,automotive,andcontrolsystemsengineer‐ing.Itprovidesasystematicapproachfordesigning controllersthatcanhandleuncertaintyanddistur‐bancesinasystem,whilealsomeetingperformance speci ications.

Inthecontextofinterconnectedembeddedsys‐tems,H∞controltheorycanbeappliedtoensurethat thesystemoperatesreliablyandef iciently,despite thepresenceofuncertaintiesanddisturbances.Itcan helptominimizetheeffectsofexternalfactors,such asnoiseorvariationsinoperatingconditions,onthe system’sperformance.

ResearchhasshownthatH∞ controltheorycan beeffectiveinaddressingvariouschallengesininter‐connectedembeddedsystems.Forexample,ithas beenappliedinthedesignofcontrolsystemsfor autonomousvehicles,wherethecontrolsystemmust beabletohandleuncertaintiesinthevehicle’senvi‐ronment,suchasunpredictabletraf icpatternsand roadconditions.

Anotherexampleisinthedesignofcontrolsys‐temsforindustrialautomation,whereH∞ control theoryhasbeenusedtoensurethatthesystem canhandlevariationsinproductionprocessesand equipmentperformance,whilealsomeetingperfor‐mancespeci ications.

Anotherrecentstudy,“RobustModelPredictive ControlofInterconnectedEmbeddedSystemsSub‐jecttoCommunicationDelays”byM.Osmanetal. (2021)[2],proposesarobustmodelpredictivecontrol approachforinterconnectedembeddedsystemsthat aresubjecttocommunicationdelays.Theproposed approachtakesintoaccounttheeffectsofcommu‐nicationdelaysonthesystem’sstabilityanduses. Thispaperproposesarobustmodelpredictivecontrol approachforinterconnectedembeddedsystemssub‐jecttocommunicationdelays.Theauthorsconsider anetworkedcontrolsystemconsistingofmultiple interconnectedsubsystems,eachwithitsownembed‐dedcontrollerandsensor/actuatornetwork.They proposeapredictivecontrolschemethataccounts forthecommunicationdelaysanduncertaintiesin thesystem,usingarobustoptimizationframework basedonmixed‐integerlinearprogramming(MILP). Theproposedapproachisappliedtothecontrolof atwo‐tanksystem,demonstratingitseffectivenessin handlingcommunicationdelaysanduncertaintiesin interconnectedembeddedsystems.Thepaperalso discussesthepotentialapplicationsoftheproposed approachinother ields,suchasindustrialautomation andsmartgridsystems.

Thepaper“Robuststabilityanalysisandfeed‐backcontrolfornetworkedcontrolsystemswithaddi‐tiveuncertaintiesandsignalcommunicationdelay viamatricestransformationinformationmethod”by Weietal.(2022)[3]presentsanovelapproachfor analyzingthestabilityandrobustnessofintercon‐nectedembeddedsystems.Theproposedapproach combinestheH∞ controltheorywithanewmodel thattakesintoaccounttheeffectsofcommunica‐tiondelaysanddatalosses.Thepaperprovidesa detailedmathematicalanalysisofthenewmodeland demonstratesitseffectivenessthroughseveralpracti‐calexamples.Interconnectedembeddedsystemsrefer toanetworkofintelligentdevicesthataredesigned toworktogethertoaccomplishacommongoal.These systemsaremadeupofsmall,specializedcomputers thatareembeddedinotherdevices,suchasappli‐ances,vehicles,andindustrialequipment.Theycom‐municatewitheachotherandwiththeoutsideworld usingvariousprotocols,suchasBluetooth,Wi‐Fi,and Zigbee.

Interconnectedembeddedsystemsarebecoming increasinglyimportantasmoredevicesbecomecon‐nectedtotheinternetandtheInternetofThings(IoT) continuestogrow[4–7].Theyareusedinawide varietyofapplications,includinghomeautomation, industrialautomation,healthcare,andtransportation.

Oneofthekeyadvantagesofinterconnected embeddedsystemsistheirabilitytoshareinformation andresources[8–12],allowingthemtoworktogether moreef icientlyandeffectively.

Forexample,asmarthomesystemmightusesen‐sorsandactuatorstocontrolthetemperature,light‐ing,andsecurityofahouse,allwhilesharingdatawith othersystemsinthehome.

However,interconnectedembeddedsystemsalso presentnewchallenges,suchassecurityandprivacy concerns,compatibilityissuesbetweendevicesand systems,andtheneedforreliableandrobustcom‐municationprotocols.Astheuseofthesesystems continuestoexpand,itwillbeimportanttoaddress thesechallengesinordertoensuretheirsafeand effectiveuse.

ThestabilityandH∞ analysisforinterconnected embeddedsystemsisaninterestingandcomplexarea ofresearch,whichhasasigni icantimpactonthe designandimplementationofmodernembeddedsys‐tems.

Inthecontextofinterconnectedembeddedsys‐tems,thestabilityoftheoverallsystemiscritically dependentonthestabilityofeachindividualsubsys‐tem.Asaresult,itisessentialtounderstandtheinter‐actionsbetweenthesubsystemsandtoensurethatthe overallsystemdesignisstable.

Onechallengeinanalyzingthestabilityofinter‐connectedembeddedsystemsisthepresenceof delaysandothercommunicationissues.Thesedelays canhaveasigni icantimpactonthestabilityofthe system,anditisimportanttoaccountforthemwhen designingthesystemandanalyzingitsstability.

Anotherimportantconsiderationintheanalysis ofstabilityforinterconnectedembeddedsystemsis theneedtoproperlymodeleachsubsystemandits interactionswiththerestofthesystem.Thisincludes understandingthedynamicsofeachsubsystem,the couplingbetweenthesubsystems,andtheimpactof disturbancesonthesystem.

Inordertoanalyzethestabilityofinterconnected embeddedsystems,H∞ analysisisoftenused.This approachinvolvesmodelingthesystemasasetof matricesandusingoptimizationtechniquesto indthe optimalcontrolstrategythatminimizestheimpactof disturbancesonthesystem.Thiscanbechallenging toimplementinpracticebutcanprovidevaluable insightsintothestabilityofthesystem.

Overall,thestabilityandH∞ analysisforinter‐connectedembeddedsystemsisanimportantarea ofresearch[13–24],whichhassigni icantimplica‐tionsforthedesignandimplementationofmodern embeddedsystems.Itisacomplexarea,butadvances inthis ieldareessentialforensuringthestabil‐ityandreliabilityofthesesystemsinavarietyof applications.

Overall,thesestudiesdemonstratetheimpor‐tanceofdevelopingnewmodelsandapproachesfor analyzingthestabilityandrobustnessofintercon‐nectedembeddedsystems.Theseapproachescanhelp ensurethesafeandreliableoperationofsuchsys‐temsinvariousapplicationdomains.Insection 2, anoverviewofSystemModelshasbeenprovided. Performanceanalysisoflinearuncertainsystemshas beenintroducedinsection3.Insection4,wepresent numericalexamplestoshowtheusefulnessofthe

proposedresults.Finally,thepaperendswiththebrief conclusioninsection5

2.ProblemFormulation

Weconsiderthefollowinginterconnectedembed‐deduncertainsystemsshowninFigure 1,wherethe ����ℎsubsystemisgivenby[25]

��(��)=��������(��)+ ���� ��=1 ����������(��)+������(��)

����(��)=����Δ����(��)+Φ��Δ����(��) (1) andwhere���� ∈ℜ�� isthestatevectorofsubsystemj, theexogenousinput���� ∈ℜ��1 representsdisturbance signals, ���� ∈ℜ��1 isthecontrolledoutput, ��,��∈ {1,…,����},andthematrices ����Δ, ������Δ, Γ��Δ, ����Δ,and Φ��Δ areofappropriatedimensions.Todescribethe uncertainty,thesystemmatrices����,������,Γ��,����,andΦ�� areassumedtobeuncertain,belongingtoaconvex polytopicmodelofthetype.

����Δ ������Δ Γ��Δ

����Δ 0Φ��Δ ∈Π�� ≜ ������ �������� Γ���� ������ 0Φ����

�� ��=1 ���� ������ �������� Γ���� ������ 0Φ���� , ���� ∈Λ�� (2)

Where Λ�� ≜

1,…,����)∶ �� ��=1 ���� =1,����

���� =��������(������),�� =��������(����),

��=[���� 1,…,���� ����]��,��=[���� 1,…,���� ����]�� (5)

Consideringthesystem(4),thetransferfunctionfrom ��(��)to��(��)isgivenby

����(��)=����(����−����)−1Γ�� +Φ�� (6)

Thesystem(4)satis iestheHin inityattenuation criterionif,forallnonzero��(��)∈���� 2[0,∞)

������ ‖��(��)‖2≠0

‖��(��)‖2 ‖��(��)‖2 ≤�� (7)

Foraprescribedscalar��≻0,where‖⋅‖2 stands forthe��2 norm.

Asshownin[26,27],condition(7)issatis iedif: ��(��)+����(��)��(��)−��2����(��)��(��)≺0 (8)

Remark1.Theparameteruncertaintiesconsidered inthispaperareassumedtobeofpolytopictype. Thepolytopicuncertaintyhasbeenwidelyusedin theproblemsofperformanceanalysisforuncertain systems.

First,lemma1and2,whicharegiven,arevery essentialforthenextdevelopments.

Thefollowinglemmaprovidesanecessaryand suf icientconditionforthesystem(4)tobestablewith ‖��(��)‖∞ ≺��

(3)

Where��={1,…,��}isnumberofpolytopevertices. Theclassofsystemsdescribedby(1)isfrequently encounteredinmodelingseveralphysicalsystems. Thesubsystemsinformula(1)canbereformuledas �� = ���� Γ�� ���� Φ��

With ����

�� �� (4)

��1�� ��12�� …��1������ ��21�� ��2�� …��2������ ⋮⋮⋱⋮ ������1�� ������2�� ⋯�������� ,Γ�� =��������(Γ����),

Lemma1[9, 18].TheContinuous‐timesystem(4), withpolytopicrepresentation(2)–(3),isasymptoti‐callystablewith‖��(��)‖∞ ≺��,forall��∈Λ��,ifand onlyifthereexistsamatrixfunction���� ≻0andscalar ��≻0,suchthatthefollowingLMIhold(thesymbol∗ meansasymmetricblock):

�� (9)

Lemma2[13](Finsler’sLemma).Let ��∈ℜ�� , ��= ���� ∈ℜ��×��and ��∈ℜ��×�� suchthat ��������(��)≺��, and��⊥ abasisforthenull‐spaceof�� (i.e.��⊥��=0). Thenthefollowingstatementsareequivalent:

1) ��������≺0,forall��≠0,����=0;

2) ���� ⊥����⊥ ≺0;

3) ∃��∈ℜ��×�� ∶��+����+�������� ≺0

3.MainResult

Inthissection,wepresentastabilityandH∞per‐formanceofinterconnecteduncertainsystems.

3.1.NewRobustStabilityConditionforPolytopic EmbeddedSystems

Inthissection,anewrobuststabilityconditionsfor thepolytopicembeddedsystem(4)isdeveloped.The mainresultforuncertainembeddedsystemisstated inthefollowingtheoremwith��(��)≡0.

Figure1. Interconnectedembeddeduncertainsystems

Theorem1.Thepolytopicembeddedsystem(4)is asymptoticallystable,forall��∈Λ��,ifandonlyifthere existsmatrices���� ≻0,��,�� and��≺0suchthatthe followingLMIsarefeasible.

������ +���� ������ −�������� −��+���� ������

∗ −��−���� −���� ≺0, (10)

Proof

TheLMIs(10)areobtainedbyconsidering

��= �� �� , (11)

��= ���� −�� , (12)

��= 0���� ���� 0 , (13) incondition(3)ofLemma2,with

��⊥ = �� ���� (14)

3.2.H∞ ∞ PerformanceAnalysisofPolytopicEmbedded Systems

Theorem2.Theuncertainembeddedsystem(4) isasymptoticallystablewith ‖��(��)‖∞ ≺��,for all��∈Λ��,ifandonlyifthereexistsmatrices ���� ≻ 0,��1,��2,��3,and��4,suchthatthefollowingLMIsare feasible.

Ψ

∗Ψ

∗∗Ψ33 Ψ34

∗∗∗−��

Where

2

≺0, (15)

Ψ13 =��1Γ�� +���� ������ 3

Ψ14 =���� �� +���� ������ 4

Ψ22 =−��2 −���� 2

Ψ23 =��2Γ�� −���� 3

Ψ24 =−���� 4

Ψ33 =−��2��+��3Γ�� +Γ�� �� ���� 3

Ψ34 =Φ�� �� +Γ�� �� ���� 4 (16)

Proof

Choosealyapunovfunctioncandidatetobe ��(��)=����(��)������(��) (17)

���� givenby ���� = ∑�� ��=1 ��������,where ������ ∈ℜ��×�� are constantsymetricmatricesmustbedetermined.

Calculatingthederivativeof ��(��) from(8),we obtained

��(��)����(��)+����(��)��̇��(��)+����(��)��(��)−��2����(��)��(��)

0���� 0���� �� ∗000 ∗∗−��2��Φ�� �� ∗∗∗−��

��= ⎡ ⎢ ⎢ ⎣ ��1 ��2 ��3 ��4 ⎤ ⎥ ⎥ ⎦ , (21) ��= ���� −��Γ�� 0 , (22)

��⊥ = ⎡ ⎢ ⎢ ⎣ ��00 ���� Γ�� 0 0��0 00�� ⎤ ⎥ ⎥ ⎦ (23)

whichprovides,bycalculationandusingcondition(ii) oflemma2,theequalitybetween ���� ⊥����⊥ ≺0 and theLMIsin(9).Thus,(9)isequivalentto(15)using Lemma2.

Thiscompletestheproofofthetheorem2.

4.NumericalExample

Inthissection,anexampleisgiventoillustrate theef iciencyoftheproposedmethod.Weconsidera classoflinearembeddedsystemsconsistingofthree interconnectedsubsystemsshownas

1(��)=��1����1(��)+ 3 ��=1,��≠1 ��1��������(��)+Γ1����1(��) ��1(��)=��1����1(��)+Φ1����1(��) Subsystem2: 2(��)=��2����2(��)+ 3 ��=1,��≠2 ��2��������(��)+Γ2����2(��) ��2(��)=��2����2(��)+Φ2����2(��) Subsystem3: 3(��)=��3����3(��)+ 3 ��=1,��≠3 ��3��������(��)+Γ3����3(��) ��3(��)=��3����3(��)+Φ3����3(��) 52

Table1. ComparisonofMinimumH∞ performance, ��min

Method

SchuleforDecentralizedstate feedbackcontrolforinterconnected systemsin[9]

Figure2. Interconnectedembeddedsystem:firstvertex

Withthefollowingparameters:

,��32�� = 00 0−1 , AccordingtoLemma1andTheorem2,theobtained guaranteedperformancesarelistedinTable1

Table1showsclearlythatLemma1islessconser‐vativethanTheorem2forthisexample.

Fortheanalysisofinterconnectedembeddedsys‐tems,theH∞normscomputedatthefourverticesof interconnectedembeddedsystemareobtainedfrom theFigures 2 to 5:alltheobtainednormsunderthe guaranteedthe0.5199bound.

5.Conclusion

TheconclusionofthestudyonstabilityandH∞ analysisforinterconnectedembeddedsystemsisthat itiscriticaltoconsiderthestabilityoftheover‐allsystemwhendesigninginterconnectedembedded systems.

Interconnectedembeddedsystem:second vertex

Interconnectedembeddedsystem:thirdvertex

Interconnectedembeddedsystem:fourth vertex

Theinterconnectionofmultiplesubsystemscan leadtoinstabilityandthepossibilityofsystemfailure, whichcanhaveseriousconsequencesinsafety‐critical applicationssuchasautomotiveoraerospacesystems. H∞ controltheoryprovidesapowerfulframework fordesigningrobustcontrolsystemsthatcanmiti‐gatetheeffectsofdisturbancesanduncertainties.By usingH∞ controltechniques,itispossibletodesign controllersthatguaranteestabilityandperformance despiteuncertainorunknownsystemparameters. Thestudyhighlightstheimportanceofconsidering theinterconnectionstructureofembeddedsystems whenapplyingH∞ controltechniques.Inparticular, thestudyemphasizestheneedtoaccountforthecou‐plingbetweendifferentsubsystemsandtheeffectof externaldisturbancesonthesystem.

Figure3.

Figure4.

Figure5.

Overall,thestudyconcludesthattheuseofH∞ controltechniquescansigni icantlyimprovethesta‐bilityandperformanceofinterconnectedembed‐dedsystems,anditisessentialtoconsiderthese techniquesinthedesignofsafety‐criticalembedded systems.

AUTHOR

AmalZouhri∗ –SidiMohammedBenAbdellahUni‐versity,FacultyofSciencesDharElMahraz,Fez, Morocco,e‐mail:amal.zouhri@usmba.ac.ma.

∗Correspondingauthor

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Abstract:

WIMAXNETWORKOPTIMIZATIONUSINGFRAMEPERIODWITHCHANNEL ALLOCATIONTECHNIQUES

WIMAXNETWORKOPTIMIZATIONUSINGFRAMEPERIODWITHCHANNEL WIMAXNETWORKOPTIMIZATIONUSINGFRAMEPERIODWITHCHANNEL

WIMAXNETWORKOPTIMIZATIONUSINGFRAMEPERIODWITHCHANNEL ALLOCATIONTECHNIQUES

Submitted:22nd December2022;accepted:27th February2023

MubeenAhmedKhan,AwanitKumar,KailashChandraBandhu

DOI:10.14313/JAMRIS/4‐2023/31

InternetconnectivityinWiMAXnetworks,alongwithvar‐iousapplications,isincreasingrapidly,sotheconnectivity ofinternetanddatatransferspeedarealwayschallenges foreffectivedatatransmissioninwirelessnetworks.Sev‐eralfactorsaffecttheperformanceofnetworks.One importantfactoristochooseasuitableframeperiodfor effectivedatatransmissions.Theperformanceofdiffer‐entframeperiodswithRoundRobinandStrictPriorityis evaluatedinthiswork.AframeperiodinRoundRobin performsbetterthanaStrictPriorityintermsofthrough‐put,butaStrictPriorityperformsbetterintermsofdrop rates.Thispaperalsodemonstratesthataneffective frameperiod,whencombinedwithaproperbandwidth allocationalgorithm,yieldsbetterresults.Thisworkgives theanalysisthatRoundRobinperforms83.8847%bet‐terwhileStrictPriorityperforms86.0020%betterthan theearliestdeadlinefirstalgorithmsfor10subscriber stationsintermsofthroughput.Thisworkishelpfulto researchersandindustrialistsforactualimplementations inWiMAXnetworks.

Keywords: IEEE802.16,WiMAX,Bandwidthallocation algorithm,Frameperiod,Roundrobinalgorithm,Strict priorityalgorithm

1.Introduction

TheWiMAXisakindofBroadbandWirelessAccess (BWA)networkforhigh‐speeddatatransferthatcan beusedwherethelyingofcablesisnotfeasible[1]. Varioustechnologieshavebeendesignedbasedon IEEEstandards.ItincludesIEEE802.11forWi‐Fi, IEEE802.16‐2004for ixedWiMAX,andIEEE802.16e formobileWiMAX.ItisaBWAsystemthatfollows theIEEE802.16‐2004andIEEE802.16estandards[2]. Wirelessservicesarechallenginginrural,denseareas, andsometimes,inunevengeographicalareas,there arehighdataratesinWiMAXnetworkswithlargecov‐erageareasandalargefrequencyspectrumforinte‐gratedvideo,audiovoice,anddataservicesrequired inthoseareas.Networkenhancementandperfor‐manceimprovementarestillachallengeinmobile WiMAXnetworks.Inreal‐lifescenarios,packetsare droppedwhileusingthequalityofservices(QoS)such asaudio,video,orvoice.Thedroppingofpackets usingtheexistingtechniqueaffectssystemperfor‐manceduetovariousfactors,suchasinfrastructure, environments,andappliedalgorithms.

Thisworkisbasedontheappliedalgorithmin whichtheperformanceofthesystemisaffected.The performanceoftheproposedsystemisincreased byoptimizingtheframeperiods.Theframedura‐tion,alongwiththechannelbandwidthalgorithm, isanimportantareatoenhancetheperformanceof WiMAXnetworksinrural,dense,andunevengeo‐graphicalareasfordifferentdataservices.Thecur‐rentimplementationsaredoneusingabasestation andsubscriberstationsforaudio,video,anddataser‐vicesinfourth‐generationtechniques.Theconnectiv‐itybetweentheSSsandBSfordatatransferisdone usingindividualTransmissionControlProtocol(TCP) connectionsandsynchronization,whichisamustfor transmissionofdata[3].AllSSsreceivedatafrom thebasestationatthestartofeveryframeusingan UplinkMap(ULMAP)message[4].TheLightWiMAX usestheprincipleoforthogonalfrequencydivision multiplexingandprovidesvariousqualitiesofservice andmultihoppingtechniques[5].

Thisworkalsofoundthattheexistingframeperiod isnotatpeakef iciencyanddemonstratesbetter results.Whenvaryingtheframeperiodsintheexisting algorithm,optimizednewframeperiodintheexisting algorithmgivesbetterresults.

Thenextsectionsofthispaperincludethelit‐eraturesurveywithnetworkstructure,followedby bandwidthallocationalgorithms,thenresultsanddis‐cussions,and inallytheconclusionandfuturework.

2.RelatedWork

Hugeworkhasbeendoneinwirelesscommunica‐tionsystemsinscheduling,buttherearestillvarious needstobedoneforeffectiveperformanceinWiMAX networks.Previousworkhasbeendoneonvarious algorithmslikeRoundRobin[6],WeightedRound Robin[7,8],andWeightedFairQueuing[9],whichare generallyproposedforWiMAXnetworks.Thesealgo‐rithmsaregeneralalgorithmsanddonottakecareof speci icapplicationsofWiMAXnetworks.Thesealgo‐rithmsarenoteffectiveforhigh‐speeddatanetworks butarestillusedinmanyapplicationsofWiMAXnet‐works.Somewirelessapplicationsarechannelaware applications,whilesomealgorithmsarenon‐aware ofchannelbandwidth.Someoftheprede inedalgo‐rithmsarestillnotsuitableforhigh‐speedinternet services,whilesomealgorithmsarenotsuitablefor mobilityapplications.Whenchannelawareschemes arediscussed,itisrequiredtounderstandchannel stateinformation.

Priorityisgiventothosesubscriberstationswhose channelconditionsaregood.Also,ifchannelcon‐ditionsaregoodandproperallocationtechniques likeradioresourcesandutilizationareavailable,it becomeseasytoenhancetheperformanceofnet‐works.Theissuewiththeseschemesisintheallo‐cationtechniques,inwhichsubscriberstationsstarve forsubstantialintervalsifchannelconditionsarepoor, whileoverprovisionsaremadeforSSswithgood channelconditions.MAClayerschemesaredesigned withidealchannelconditionsinmind.Thepurposeof MAClayerschemesistoassuremaximumthroughput, minimumtraf icrate,andfairness.SincevariousQoS classesarede inedinWiMAXnetworkswithdifferent requirements,animportantschedulingdecisionmust imposesomesortofpriority.Multiantennamode andavailablebandwidthareresponsibleforhigh‐speeddatatransferratesovertheairofabout1Gbps speed.Thistypeofworkissuitableforgoodquality andhighercapacityservicesandinternetprotocols suitableforavastrangeandquality‐basedinternet services.Theseservicesarenotonlysuf icientto maintainfullbackwardcompatibilitybutalsosupport thoseservicesthatmaybeusefulfornext‐generation internetservices.Thisworkmentionedallthetechni‐calaspectsofIEEE802.16minwhichnext‐generation internetservicesareproposedinthefuture[10].

Forfullutilizationofframes,mobileWiMAX allowspacketfragmentation,whichenhancesnet‐workcapacity.Variationsinchannelconditionscause variationsintimeandlocation.De icitroundrobin withfragmentationandtheearliestdeadline irst algorithmsaresomealgorithmsthatwerepreviously proposed.Resourcesareallocatedasperthevaria‐tioninlinkcapacityinmobileWiMAXinaneffec‐tivemannertotransmitfragmentedpacketsinthe network[11].De icitroundrobinwithfragmenta‐tiongivesbetterperformanceintermsofthrough‐putthanDRR,whichisabout80%higher,giving minimumoverheadsthanglobalpositioningsystems. Someworkhasalsobeendoneonframedura‐tionstoimprovetheperformanceenhancementsof WiMAXnetworks.Thispaperconsidersdataratein termsofspectralef iciencies,cellcoverage,latencies, spectrumef iciency,andqualityofservice,includ‐ingcomplexities.Thispaperexplorestheimproved WiMAXtechnologyfocusingonthephysicallayer, MAClayer,andthoseservicesessentialtoimprove qualityofservicesfornetworkbetterments[12].This workfocusesondetailedschedulingandcollaboration withserviceproviders.Channelawarenesscross‐layer schedulingisproposed,whichdescribesthereduction ofpacketlossanddelayandgivesbetterthrough‐put[13].Thispaperdetailsthetransmissioncontrol protocolanduserdatagramprotocolperformancein IEEE802.16[14].Inthiswork,theauthordiscusses andanalysesissueslikecoverageholesandcapac‐ityoptimizations.Thisworkalsosuggeststherelay stationasaneffectivesolutionformulti‐hoprelays thatguaranteeperformance.Thispaperalsogives betterresultswhenoptimalrelaysareusedinthe networks[15].

Endtoenddelayinpackettransmissionand receivinginthenetworksisproposedbyweighted RoundRobinschedulinginWiMAXnetworkstoana‐lyzetheperformance[16].

Designinganetworkstructurewithconstraints inmobilemulti‐hoprelay‐basednetworksisachal‐lengeinIEEE802.16withasuitableframestructure. Theframestructuredesignusingdifferentparame‐tersintermsofdimensions,designconstraints,and challengesisstillaproblem.The lexibleframestruc‐turedesignisproposed,whichisusedtoperform variousmulti‐hopoperationswhilemaintainingback‐wardcompatibilitywithlegacysystemsonmobile stations.Usingsuchasystemincreasesthecapac‐ityimprovementinmobilemulti‐hoprelaysandalso establishesabetterunderstandingintermsofrange extensionsinrelaynetworks[17].

Thisworkproposestheschedulingarchitecture foruplinkanddownlinkconnectionofIEEE802.16. Thisarchitectureincludesvariousqualityofservice parameters,whichincludelatency,sustainedrate,jit‐tertoleration,minimumreservedbandwidth,request transmissionpolicies,traf icpriority,burstsize,SDU size,andqueuingfordifferentservice lows.Inthis paper,twoimportantalgorithms,named irstin, irst out,andearliestdeadline irstandself‐clockfairqueu‐ingalgorithmforef icientbandwidth,areusedalong withthequalityofservices[18].

Thisresearchevaluatesthechoiceforeffective framestructureinnon‐transparentrelaystationsin WiMAXnetworks.Singleframestructureandmulti‐pleframestructurearetwotypesofstandardspro‐posedbyIEEE802.16j‐2009.Nocomparisonsare madeamongtheseframestructures.LightWiMAXis usedtoevaluatetwoframestructuresusingntRSof QoS.Thisworkismainlyfocusedonachievinghigher throughputusingthemulti‐framestructureforvoice capacitiesintermsofdelays[19].

ThisworkproposedforIEEE802.16jqualityof serviceschedulingscalablearchitecturewhichguar‐anteesqualityofserviceforvariousmobileapplica‐tions.Thispaperfocuseson indinganappropriate qualityofserviceimprovements.TheSQSAsupports QoSarchitecturesSQSAmodulesandsupportitsfunc‐tionsformobileapplications[20].

Thisworkisdonetoincreasethedata‐sendingrate andextendthenetworkcoverageareausingrelaysta‐tionswithIEEE802.16.Theperformanceisincreased byallocatinganappropriateresourcetoindividual relaystationsaspertheneedsofthenetworks.This workalso indsthatifresourceallocationisnotprop‐erlydone,thenrelaystationswillexperiencecon‐gestion,whichresultsinperformancedegradationin termsofthroughputanddelay.Basestationsdynam‐icallyschedulethedatatransmissionstorelaysby centrallymanagedrelaystations.IEEE802.16stan‐dardsde inedecentralizedradioresourcesbymeans ofexistingscheduling.Conventionalservicedecreases thesystemperformance;hencethoseservicesare usedthatincreasethesystemperformance.

Theseservicesareusednotonlytomaximize thethroughputbutalsotominimizepacketdelays andreducesignalingoverheadsbypre‐allocatingand decentralizingcontrolledrelaystations.Thispaper alsomentioneddefaultradioresources,whichshow thatrelaystationsindependentlyassignresources withoutaskingthebasestationsothattraf ic,over‐head,andpacketdelayscanbereduced[21].

Thisworkinvestigatestheimprovedthroughput andminimumdelaysforenduserswithvariousappli‐cationslikevoice,video,andaudioservicesbyreduc‐ingthecostusingtheavailablespectralresourcesby usingrelaystations.Theproposedworkgivesacost‐effectivesolutionbyinstallingthethree‐relaystation withadaptivemodulationandcodingschemes,cell sectoring,anddirectionalantennasinIEEE802.16. Thisworkincreasedthethroughputwithalesser numberofrelaystationswithinthesamebasesta‐tionrangewithoutcompromisingthequalityofser‐vice[22].

ThisworkproposesrelaystationsinWiMAXnet‐workswithdifferentbandwidthallocationalgorithms toenhancethesignalpoweroverlongdistanceswith relaystations.Thispapershowsthattherelaystation extendsthecoveragewithhighthroughputandhigh bandwidthofchannels.Thispaperfocusesonper‐formanceanalysisofbandwidthallocationalgorithms withandwithoutrelaystations.Thisworkcompares thechannelbandwidthallocationalgorithmwithand withoutrelaystation,andperformanceenhancement isproposedandevaluated[5].

3.NetworkStructure

ThenetworkstructureshowninFigure1consists ofonebasestationandmanysubscriberstations.The basestation(BS)isconnectedtosubscriberstations (SS)throughindividualwirelessTCPconnections.The dataistransmittedfromthebasestationtothesub‐scriberstationsthroughawirelessmedium.Adown‐loadinglinkisestablishedfromthebasestationtothe subscriberstation,andthechannelisallocatedtosub‐scriberstationsusingRoundRobinandStrictPriority channelallocationtechniques;thebasestationtrans‐mitsdatatosubscriberstationsusingindividualTCP connectionswithallocatedchannelbandwidth,which isshowninFigure1forperformanceevaluation.

Variousnetworktoolsarealsoavailabletoperform thestudyofWiMAXnetworks,likeMATLAB,Netsim, Opnet,OMnet++,andmanymore.Onesuchsimulation toolisLightWiMAX[5].Toevaluatetheperformance ofWiMAXnetworkstheNetworkSimulator(NS‐2)is used.TheFrame_LWXtimer()functionisusedtoadd theMediumAccessControl(MAC)Layer.Oncethe packetsstarttransmitting,theMACsourceaddress andMACdestinationaddressarede ined.Portnum‐bersatthesourceanddestinationarealsode ined fordatatransmissionsinthecode.Ifnonodematch‐ingthedestinationaddressisfound,thepacketis dropped.DataisonlytransmittedfromBStoSS,and bandwidthallocationisdoneusingavariablede ined inthecode.

Figure1. Networkstructure

Inthesimulation,twovariablesareused:“1”for theroundrobinalgorithmand“2”fortheStrictPri‐orityalgorithm.Thecollectionofdownlink lowinto acorresponding lowqueueisstoredinthelinkpro‐gram.

4.BandwidthAllocationAlgorithms

Thebandwidthallocationalgorithmensures properbandwidthmanagementforthesmooth transmissionofnetworkstosubscriberstations.The StrictPriorityschedulingbasedoneitherpreemptive ornon‐preemptivebandwidthallocationalgorithm forwirelessnetwork.Priorityschedulinggenerally suffersfromtheproblemofstarvation;highpriority taskapplicationswillbeinreadyorwaitingcondition if,onthebasestation,theprocesslosescontrolin waitingconditions[23].Intheschedulingtechniques, thehigherpriorityprocessesareprocessed,whereas lowerpriorityprocessesareneglected.Innon‐prioritypreemptivescheduling,ittakesalongertime ascomparedtohigherpriorityprocessesonthebase station,whichcanleadtoastarvationcondition[24].

AnotheralgorithmistheRoundRobinalgorithm, whichisthepreemptiveschedulingalgorithm.Each processisgivenasetamountoftimetocomplete; thisisreferredtoasaquantum.Preemptionisneeded fortheexecutionofoneprocesswithinagiventime interval[25].Contextswitchingisusedtosavestates ofpreemptedprocesses[8].

Everybandwidthallocationalgorithmhasitsown channelallocationworkings[26].Thisworkusedthe framedurationwithRoundRobinandStrictPriority algorithms.Therearetwopathsthatcouldbechosen: onethatgoesdirectlytothebasestationandonethat goesthroughrelaystations.Inthispaper,twohop relaysthattransmitdatafromSStoBSonlyareused. VariousstepsareinvolvedwhenusingtheAODVrout‐ingprotocol,whichincludesthediscoveryofpaths, setupofpathselection,forwardpathselection,rout‐ingtablemanagementwithpathmaintenance,and localconnectivitymanagement.Themainadvantage ofusingtheAODVprotocolisthatitisscalableandcan beusedforalargenumberofnodes.Broadcastmini‐mizationisanotheradvantageofusingthisalgorithm. Anotheradvantageofusingthisroutingalgorithmis thatitreducesmemoryrequirementsandcanbeused innetworksforloop‐freeroutingmaintenance.

Forperformingthereal‐worldimplementationof thescenarios,NetworkSimulator2isasimulationtool usedtoperformvarioussimulations.Toexecutethe code,thistoolusedtheC++languageinconjunction withToolCommandLanguage[27].Thesimulation environmentsareusedtocarryouttheentiredeploy‐ment.Thistoolisanevent‐driventoolthatprovidesa dynamicenvironmentforcreatingscenariosthatare identicaltotherealparametersrequiredfornetwork creation.Simplecommandsareusedtoimplementthe toolforde iningnetworkcon igurations.

4.1.Algorithm1:RoundRobin–DownlinkBandwidth Allocation

1) Start

2) Createpointertoeach lowtype’squeuetoallo‐cation

3) GetsymbolnumberofDLandUL

4) Createalgorithmcalculationvariable

5) Resetallrelativevariables’valuein low’s attribute

6) SetPathselection

a) Findthepath(directlytoBSorpassingthough RelayStationRS)

b) SetBWA_Flow_TypeandBWA_Next_Hop

7) Selectpath

a) If(this lowhasrelaylink,usethe irstrelay linkanditsnexthop)

b) Elseuseaccesslink

8) Bandwidthallocation

a) Accesszone:RR+minQoSGurantee

b) Relayzone:onlyRR

i. Collect lowintocorresponding low queue

ii. Bs‐>SSandBS‐>RSshouldalsobe schedulingtogether,becausetheyusethe samebandwidth

9) Downlinkaccessbandwidthallocation

a) Satisfyeachdl low’sRmin

b) Satisfyeachdl lowbyRoundRobin

c) FinaldlBWAsetting

d) Logeachphase’sbandwidthallocationofeach downlink low

10) Downlinkrelaybandwidthallocation(RS‐>SS)

a) Satisfyeachdlrelay lowbyRR

b) FinaldlBWAsetting

c) Logeachphase’sbandwidthallocationtoeach downlinkrelay low

11) Uplinkaccessbandwidthallocation

a) Satisfyeachul lowRmin

b) Satisfyeachul lowbyRR

c) Logeachphase’sbandwidthallocationofeach downlink low

12) Uplinkrelaybandwidthallocation(RS‐>SS)

a) Satisfyeachulrelay lowbyRR

b) FinalULBWAsetting

c) Logeachphase’sbandwidthallocationofeach downlinkrelay low

d) Lwx_tests_msg(“RR’sULRelayBWA”)

e) Osttringstreamlog_send_plt

f) Log_send_pkt

g) Getpacket

h) Getlog

i) Lwx_test_msg(“dl”.Log_bwa.str());

j) DecreaseBWA_Total

k) Pinthispacket

l) Senddownpacket

13) Timer lowchart:

a) Createpointertodownlinkanduplinkqueue toallocationbandwidthef iciently

b) Classify lowsofthenodeandcallthecorre‐spondingtransmissionfunctionswhosenode IDissourceintocorresponding lowqueue

14) EndTimer

15) End

4.2.Algorithm2:StrictPriority–DownlinkBandwidth Allocation

1) Start

2) Createpointertoeach lowtype’squeuetoallo‐cation

3) GetsymbolnumberofDLandUL

4) CreateStrictPriorityalgorithmcalculationvari‐able

5) Resetallrelativevariablesvaluein low’s attribute

6) SetPathselection

a) Findthepath(directlytoBSorpassingthough RelayStationRS)

b) SetBWA_Flow_TypeandBWA_Next_Hop

7) Selectpath

a) If(this lowhasrelaylink,usethe irstrelay linkanditsnexthop)

b) Elseuseaccesslink

8) Bandwidthallocation(StrictPriority)

a) Accesszone:RR+minQoSGurantee

b) Relayzone:onlyRR

i. Collect lowintocorresponding low queue

ii. Bs‐>SSandBS‐>RSshouldbealso schedulingtogether,becausetheyuse samebandwidth

9) Downlinkaccessbandwidthallocation

a) Satisfyeachdl low’sR‐min

b) Satisfyeachdl lowbyRoundRobin

c) FinaldlBWAsetting

d) Logeachphase’sbandwidthallocationofeach downlink low

10) Downlinkrelaybandwidthallocation(RS‐>SS)

a) Satisfyeachdlrelay lowbyRR

b) FinaldlBWAsetting

c) Logeachpahse’sbandwidthallocationtoeach downlinkrelay low

11) Uplinkaccessbandwidthallocation

a) Satisfyeacheachul‐ lowR‐min

b) Satisfyeachul‐ lowbyRR

c) Logeachpahse’sbandwidthallocationofeach downlink low

12) Uplinkrelaybandwidthallocation(RS‐>SS)

a) Satisfyeachulrelay lowbyRR

b) FinalULBWAsetting

c) Logeachphase’sbandwidthallocationofeach downlinkrelay low

d) Lwx_tests_msg(“RR’sULRelayBWA”)

e) Osttringstreamlog_send_plt

f) Log_send_pkt

g) Getpacket

h) Getlog

i) Lwx_test_msg(“dl”.Log_bwa.str());

j) DecreaseBWA_Total

k) Pinthispacket

l) Senddownpacket

13) Timer lowchart:

a) CreatepointertodownlinkanduplinkStrict Priorityqueueforallocationofbandwidth

Figure2. Workflowdiagram:roundrobin–downlinkbandwidthallocation

b) Classify lowsofthenodeandcallthecorre‐spondingtransmissionfunctionswhosenode idissourceintocorresponding lowqueue

14) EndTimer

15) End

5.ResultsandDiscussions

5.1.SimulationParameters

Table1showsthevarioussimulationparameters usedinthiswork.Oneoftheparametersusedinthis workisaroutingtablebasedonad‐hoctechniques. On‐demandroutingprotocolsusedinwirelessnet‐worksareloop‐freeprotocols.Thisprotocolisaself‐startingprotocolusedinthesubscriberstationenvi‐ronment.Thisisalsousedtoimplementvariousother parameterslikemobilityofnodes,failurelinkman‐agementprotocols,andlossofpacketidenti ication. Hence,toidentifyalltheseworksinwirelessworks, theAODVprotocolplaysanimportantrole.

Ad‐hocon‐demandroutingprotocolismaintained byaroutingtable,whichkeepsthedetailsaboutthe nearbyrouters[28].Theroutingtablemaintainedby AODVconsistsofthreetypesofinformation,including thenexthopcount,sequencenumbers,andthetotal hopcount,whichisneededtotransferthedataamong thenodes.Next,hopcountisusedtoidentifythe distanceofcurrentnodestotheintendednodes.

Thesecondparameterusedistransmissionpro‐tocol,whichmaybeeitherconnection‐orientedor connection‐less.Inthiswork,atransmissioncontrol protocolisused[29].Twoalgorithms,RoundRobin algorithmandStrictPriority,areusedinthiswork. Also,asustainabletimeof300secondsisusedforsim‐ulationstohaveaccurateresults.Subscriberstations, referredtoasnodesinthispaper,areassignedinitially withtennumbersandincreaseupto100nodeswith adifferenceof10nodeseachtime.Inthiswork,the frameperiodis5ms,2.5ms,1.25,and0.625millisec‐ondsaretaken,andtherestoftheparametersarevar‐iedtoanalyzetheperformanceofWiMAXnetworks.

Table1. Parametersforsimulation

Parameters Values

RoutingProtocols AdHocOnDemandRouting Protocol

TransportProtocol TransmissionControl Protocol(TCP)

BandwidthAllocation Algorithm RoundRobin(RR)and StrictPriority(SP)

SimulationDuration 300Seconds

NumberofWireless

Nodes 10,20,30……upto100

FrameDuration 0.005,0.0025,0.00125, 0.000625Millisecond

FrameSymbol 48

Thefollowingparametersareconsideredforana‐lyzinglightWiMAXnetworks,whichareshownin Table1.

5.2.PerformanceEvaluation

Theperformanceevaluationisdoneonthebasisof thefollowingmatrices:

1) Throughput:Therawdatasentbythesender machineduringaspeci iedduration.

Throughput = NumberofPacketsSent ∗8

SimulationDuration

∗10−6 Mbps (1)

Wherethe,

Numberofpacketssent: Totalpacketssentby sendermachineofsize1024Byteeach.

SimulationDuration: Thedurationofdatatrans‐ferinseconds.

2) Goodput:Thepacketssuccessfullyreceivedand acknowledgedbyreceivermachine.

Goodput = NumberofPacketsReceived ∗8

SimulationDuration

∗10−6 Mbps (2)

Figure3. Workflowdiagram:strictpriority–downlinkbandwidthallocation

Wherethe, Numberofpacketsreceived: Totalpackets receivedbyreceivermachineofsize1024Byte each.

SimulationDuration: Thedurationofdatatrans‐ferinseconds.

3) PacketDrop:Totalpacketsdroppedduringthe communicationduration.

DropRate = NumberofPacketsDropped ∗8 SimulationDuration

∗10−6 Mbps (3)

Wherethe, Numberofpacketsdropped: Totalpackets droppedofsize1024Byteeach.

SimulationDuration: Thedurationofdatatrans‐ferinseconds.

5.3.PerformanceAnalysis

ItisevidentfromFigure 4 thatathroughputof 9.12Mbpsfor10nodesisobservedintheRound Robinalgorithm,whichismuchbetterthanStrictPri‐ority.Throughputalsodecreaseswiththeincreasing numberofnodes.Acomparativeanalysisrevealsthat RoundRobinhasan88.4%higherStrictPriorityfor 20nodes.Thethroughputfor50subscriberstations is8.79Mbpsand9.92MbpsfortheRRandSPalgo‐rithms,respectively.Similarly,forRoundRobinand StrictPriority,itisobtainedat8.59Mbpsand10.04 Mbpsfor70nodes,respectively.Continuousdegrada‐tionisobservedasthenumberofnodesincreasesin thetwoalgorithms.Thesameresultsarecontinuously observedasthenumberofnodesincreases.Strict Priorityisfoundtobe11.39%moreef icientthan RoundRobinfor50nodesand18.33%betterfor100 nodes.Asthenumberofnodesincreases,throughput decreasesinbothRoundRobinandStrictPriority, duetothefullutilizationofthechannelandmaxi‐mumbandwidthutilizations.Whensubscriberstation

increasessingleorthogonalfrequencydivisionmul‐tiplexingsymbolusesmultiplebitswhichdegrades thethroughputofthechannel.Asthenumberofsub‐scriberstationsincreases,multiplebitsarecarriedin asingleOFDMsymbol.Ashorterframeperioduses thechannel’smaximumbandwidth,andthroughputis higherforfewernodes.Theeffectduetodelayspread isminimizedwhenalongerdatasymbolisused,and whendelayspreadissmall,itbecomesaninsigni icant fractionofthesymbollength.Onincreasingsubscriber stations,fullutilizationofthebasestationisused, whichusesawiderchannel.

Figure5showsthatasmallernumberofnodesper connectioncanalsoleadtohighergoodput,thatis, 9.51MbpsobtainedusingtheRoundRobinalgorithm for10subscriberstations.Theobservedgoodputis 9.03Mbpsfor20subscribers.Italsoobtained8.39 Mbpsand6.75Mbpsgoodputfor60subscribersta‐tionsinroundrobinandStrictPriority.Theobtained goodputfor80subscriberstationsis8.45Mbpsand 8.3MbpsforroundrobinandStrictPriority,respec‐tively.Theobtainedgoodputfor100nodesis8.19 Mbpsand10.15MbpsforroundrobinandStrictPri‐ority,respectively.Whenacomparativeanalysisis done,itisobservedthatroundrobinforrelayper‐forms89.1%betterforStrictPriorityfor10nodes, 87.4%betterfor30nodes,81.8%betterfor60nodes, 82.4%betterfor80nodes,and79.7%betterfor100 nodes.ThisdemonstratesthatStrictPrioritydoesnot performbetterintermsofthroughputforstations withfewersubscribers.Asthenumberofpacketssent persecondwentup,sodidtheamountofdatathat couldbesentthroughthechannel.Themostdata issentthroughchannelswithfewersubscribers[7]. Whenacomparativeanalysisisdone,RoundRobin performsmuchbetterthanStrictPriority.Whenthe numberofnodesincreases,thegoodputinbothcases decreasesduetothedroppingofpacketsoccurring (busychannel).Whenthenumberofnodesincreases, performancesuffersasthechannelisfullyutilized, resultinginanincreaseddroprate.

Figure4. Throughputofframeperiodforroundrobinandstrictpriority

Figure4showsthatthedroppedpacketsinStrict Priorityaremuchhigherascomparedwithround robin.Therateofpacketdropsincreasedasthenum‐berofsubscriberstationsincreasedbecausesignals wereinitiallytransmittedwithmaximumpowerfrom basestations,reducingthelikelihoodofsignallosses. Similarly,astraf icloadsincrease,itbecomesdif icult tomaintainasmanysubscriberstations,andtheyare droppedafteralongperiodofwaiting[24].Figure4 showsthatthedropratealsoincreasedduetothe unavailabilityofmodulationoverlongdistances.Ini‐tially,packetdropratesof0.005,0.016,0.027,0.032, and0.056Mbpsareobtainedfor10,30,50,70, and100nodes,respectively,forStrictPriorityand RoundRobin,whichisshowninTable2.Asthenodes increase,thepacketdropratealsoincreasesby0.002, 0.007,0.010,0.014,0.019,and0.024Mbpsfor10,30, 50,70,and100nodes,respectively,forStrictPriority. Thevariationindataratedependsonwhetherthe receiverisinlineofsightornot[26].Incasesofnon‐line‐of‐sight(NLOS),thedataratesdropsigni icantly duetotheadaptivemodulation[30].Whencompar‐ingallthreealgorithms,thedroprateishigherin StrictPrioritywhenthesubscriberstationsincrease. Itisobservedthat37.2%,42.15%,41.7%,49.9%,and 37.3%arehigherthanStrictPriorityfor,respectively, 10,30,50,70,and100nodes.

Figure7showsthatroundrobinandStrictPriority algorithmswithanumberofnodesequalto10in eachcasearecomparedwithpreviouslyproposedEDF andDRRFonthebasisofframedurationandchannel bandwidthallocation.ItisobservedthatStrictPrior‐ityandRoundRobinperformmuchbetterinterms ofthroughputascomparedtoEDF,whichisshown inTable 3 whentaking10nodesineachcase.Itis observedfromtheanalysisthatRoundRobinper‐forms83.8847%betterwhileStrictPriorityperforms 86.0220%betterinthecaseofamaximumof10 subscriberstations.

Sincepreviousalgorithmshavenotmentionedthe throughputformorethan10nodes,hencethecom‐parisonsfor20,40,60,and80nodesarenotshownin thiswork.So,forthesenodes,comparisonsbetween thetwoalgorithmsareavailableonly.So,fortherest ofthenodes,thecomparisonsofStrictPriorityand RoundRobinaredoneinthiswork.Itisobserved fromtheanalysisthat,fornodes,throughputis7.84% higherthanRoundRobininthecaseof20nodes. Itisobservedthat14.61%and15.01%arehigher thanRoundRobinfor40and80nodes.Theanalysis showsthathigherthroughputisobservedmorein StrictPrioritythantheRoundRobinalgorithmineach case.Higherthroughputisobservedduetosuccessful sendingofpacketsfrombasestationtosubscriber station.

Figure5. Goodputofframeperiodforroundrobinandstrictpriority

Figure6. Droprateofframeperiodforroundrobinandstrictpriority

Table2. ComparisonofbandwidthallocationalgorithminWiMAXnetworkswiththroughput

Table3. ComparisonofbandwidthallocationalgorithminWiMAXnetworkswithgoodput

Throughputisgenerallyconsideredasaggregate sinceitisdependentonmanyfactorslikeinterfer‐enceincludingradio,physical,andelectricalsignals. Anotherfactorthatimpactsthroughputisdistance betweenthebasestationandsubscriberstations.Var‐iousotherobstacleslikegeographicalinfrastructure ofEarthisalsoaparameterthroughwhichthroughput receiveimpactsin2.4GHzbandinwirelesscommuni‐cationsystems.

Figure8showsthatroundrobinandStrictPrior‐ityalgorithmswithnumbersofnodesequalto10in eachcasearecomparedwithpreviouslyproposedEDF andDRRFonthebasisofframedurationandchannel bandwidthallocation.ItisobservedthatStrictPriority andRoundRobinperformmuchbetterintermsof goodputascomparedtoEDF.Basedontheanalysis, RoundRobinworksbetterforupto10subscribers

by83.8752%,whileStrictPriorityworksbetterby 86.0163%.

Sincepreviousalgorithmshavenotmentionedthe goodputformorethan10nodes,hencethecompar‐isonsfor20,40,60,and80nodesarenotshownin thiswork.So,forthesenodes,goodputcomparisons betweentheproposedtwoalgorithmsareavailable only.So,fortherestofthenodes,thecomparisons ofStrictPriorityandRoundRobinaredoneinthis work.Itisobservedfromtheanalysisthatfornodes, goodputisobservedtobe7.95%higherthanRound Robininthecaseof20nodes,whileitisobservedtobe 17.16%and15.25%higherthanRoundRobinfor40 and80nodes.Theanalysisshowsthathighergoodput isobservedinStrictPrioritythanRoundRobinalgo‐rithmineachcase.Highergoodputisobserveddueto thesuccessfulsendingofpacketsfromthebasestation tothesubscriberstation.

Figure7. Throughputcomparisonofproposedalgorithmwithexistingalgorithms

Goodputisalsodependentonmanyfactorslike interference,includingradio,physical,andelectrical signals.Anotherfactorthatimpactsgoodputisthe distancebetweenthebasestationandsubscriber stations.Variousotherobstacleslikethegeographi‐calinfrastructureoftheeartharealsoaparameter throughwhichgoodputreceiveimpactsinthe2.4GHz bandinwirelesscommunicationsystems.

Figure9showsapercentwisecomparativeanaly‐sisintermsofthroughputandgoodputfor10nodes ofEDFwithStrictPriorityandRoundRobin.Italso showsacomparisonofStrictPriorityandRound Robinalgorithmsfor20,40,and80nodessincepre‐viousworkforagreaternumberofnodesisnotmen‐tionedinthereferencedpapers.Overall,itisobserved thatStrictPriorityperformsmuchbetteramongall threealgorithmsintermsofthroughputandgoodput.

6.Conclusion

Theworkisusedtoenhancetheperformanceof WiMAXnetworkswithvariousframeperiods.Also, thisworkisdonetoenhancetheperformancebyvary‐ingframeperiodsinthealgorithms,anditisobserved fromtheanalysisthatvaryingtheframeperiodinthe algorithmreallyenhancestheperformanceofWiMAX networks.Theenhancementisdonebychangingthe existingalgorithmandaddingthenewframeperiods. Thisanalysisalsoshowsthatduringthebandwidth allocation,iftheframeperiodisvaried,thensomehow aStrictPriorityalgorithmgivesbetterresultsinthe formofthroughput,goodput,andpacketdroprate.

TheStrictPrioritybandwidthallocationalgo‐rithmsgivebetterresultsascomparedtoroundrobin algorithmsforallframeperiods.Whentheframe periodis0.005milliseconds,roundrobinandStrict PriorityperformmuchbetterthantheEarliestDead‐lineFirstAlgorithm(EDFA)inWiMAXnetworks.It isobservedfromtheanalysisthatRoundRobinper‐forms83.8%,whileStrictPrioritygives86.2%bet‐terthroughputthanthe“earliestdeadline irst”algo‐rithmfor10subscriberstations.Similarly,itisalso observedthatGoodputperforms83.60%andStrict Priority86.01%betterfor10subscriberstationsthan thetraditionalRoundRobinalgorithmand90%better thanStrictPriorityinformsofthroughput.Asmaller frameperiodgivesbetterresultsforef icientdata transmission.Thestudyalsofoundthatwhenthe numberofnodesisreduced,thethroughputincreases [24,31–33].

7.FutureWork

Thewholeworkcanbecarriedoutwithvarious qualityofserviceparameterswhichmayincludebest effort,realtimepolingservice,non‐realtimepoling service,unsolicitedgrantserviceandextendedreal timepolingservices.Differentchannelallocationscan alsobedoneforanalysis.Thiswholeanalysiscould alsobedonewith5Gnetworks.

Figure8. Goodputcomparisonofproposedalgorithmwithexistingalgorithms

Figure9. Comparativeanalysis(%wise)ofthroughputandgoodputinroundrobinandstrictprioritynodesandEDF

AUTHORS

MubeenAhmedKhan –DepartmentofComputerSci‐enceandEngineering,SangamUniversity,Bhilwara, Rajasthan,India,e‐mail:makkhan0786@gmail.com.

AwanitKumar –DepartmentofComputer ScienceandEngineering,SangamUniver‐sity,Bhilwara,Rajasthan,India,e‐mail: awanit.kumar@sangamuniversity.ac.in.

KailashChandraBandhu∗ –DepartmentofCom‐puterScienceandEngineering,Medi‐CapsUniversity, Indore,MadhyaPradesh,India,e‐mail:kailashchan‐dra.bandhu@gmail.com.

∗Correspondingauthor

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Abstract:

EXTENDEDSTATEOBSERVERBASEDROBUSTFEEDBACKLINEARIZATIONCONTROL

EXTENDEDSTATEOBSERVERBASEDROBUSTFEEDBACKLINEARIZATIONCONTROL

DOI:10.14313/JAMRIS/4‐2023/32

APPLIEDTOANINDUSTRIALCSTR

APPLIEDTOANINDUSTRIALCSTR APPLIEDTOANINDUSTRIALCSTR

Submitted:25th September2022;accepted:27th February2023

AliMedjebouri

Oneoftheexamplesoftheseclassicaltoolsisthe PIDcontrollerwidelyusedinindustrialapplications [5–7].

Inthechemicalandpetrochemicalindustry,theContinu‐ousStirredTankReactors(CSTR)are,withoutdoubt,one ofthemostpopularprocesses.Fromacontrolpointof view,themathematicalmodeldescribingthetemporal evolutionoftheCSTRhasastronglynonlinearcross‐coupledcharacter.Moreover,modelingerrorssuchas externaldisturbances,neglecteddynamics,andparame‐tervariationsoruncertaintiesmakeitscontroltaskavery difficultchallenge.Eventhoughthisproblemhasbeen thesubjectofawidenumberofcontrolstrategies,this articleattemptstoproposeaviable,robust,nonlinear decouplingcontrolscheme.Theideabehindtheproposed approachliesinthedesignoftwonestedcontrolloops. Theinnerloopisresponsibleforthecompensationofthe nominalmodelnonlinearcross‐coupledtermsviastatic nonlinearfeedback;whereastheouterloop,designed aroundanExtendedStateObserver(ESO)ofwhichthe additionalstategatherstheglobaleffectofmodeling errors,ischargedtoinstantaneouslyestimate,andthen tocompensatetheESOextendedstate.Thisway,the CSTRcomplexdynamicsarereducedtoaseriesofdecou‐pledlinearsubsystemseasilycontrollableusingasimple Proportional‐Integral(PI)linearcontroltoensurethe robustpursuitofreferencesignalsrespectingthedesired performance.Thepresentedcontrolvalidationwasper‐formednumericallybyanobjectivecomparisontoaclas‐sicalPIDcontroller.Theobtainedresultsclearlyshowthe viabilityandtheeffectivenessoftheproposedcontrol strategyfordealingwithsuchnonlinear,stronglycross‐coupledplantssubjecttoawiderangeofdisturbances despitetheprecisionoftheirdescribedmathematical model.

Keywords: CSTR,Robustcontrol,FeedbackLinearization, ESO

1.Introduction

TheCSTRisoneofthemostusedpiecesofequip‐mentinprocessengineering.Itsmainroleistocon‐vertreactantsinto inishedorsemi‐ inishedprod‐ucts;therefore,itplaysaprimaryroleinmanychem‐icalprocesses[1–4].CSTRsaregenerallycontrolled aroundacertainequilibriumpoint,whereitisapprox‐imatedbyalocallyvalidlinearmodel.Thisapproach hastheadvantageofsimplifyingthesynthesisofthe controllersbecauseitallowstheuseofallclassical linearcontroltheorytools.

Unrivaledsinceitappearedin1922[8],thePID controllerhasdominatedtheindustrialsceneallover thepastcentury,allowingthepropulsionofthetech‐nologicalrevolutiontowardnewhorizonseveninits simpleform.ThehugesuccessofPIDcontrolinthe practitioner’ssocietyliesessentiallyinthesimplicity ofthedesignandimplantationtasks.Nevertheless, pressedbymodernindustrydemandsincreasingly moreandmoreexigentintermsofef iciency,control theorywasalwaysconstrainedtodevelopnewcontrol mechanismssatisfyingthenewlyimposedrequire‐ments[9, 10].Insearchofnewadvancedcontrol schemes,theorieshaveevolvedinseveraldirections, givingaveryrichbibliographyover80years.

FortheCSTRcontrolexample,variouscontrol strategies,suchastheexactfeedbacklinearization control[11, 12],thenonlinearbacksteppingcon‐trol[2],themodelpredictivecontrol[4,13–19],dif‐ferentoptimalcontrolstrategies[20–23],theadap‐tivecontrolapproaches[24–27],andtheslidingmode controltheory[1,28–32]havebeenproposedamong others.Wecanalso indseveralarticlesbasedon successfulcombinationsbetweenadvancednonlinear controltheoriesandsoftcomputingtoolssuchasarti‐icialneuralnetworks(ANN)[33,34],fuzzyinference systems(FIS)[3,35],andmanybio‐inspiredoptimiza‐tionalgorithmssuchasthegeneticalgorithm(GA)[7, 36],etc.Thesecombinationshavebeenaddressed,in general,toovercomesomespeci icdif icultiesrelated tocertainsyntheticdif icultiesinducedbythemathe‐maticalrigoroftheoriginalapproaches,ortoalleviate somedisadvantagespresentedbythepreviouslycited controls.

However,inthemidstofthistheoreticalrevolution inthecontrol ield,theindustryseemsuninterested inmostoftheproposedmoderncontrolapproaches bypresentingahighin lexibilityforPIDcontrol,even knowingitsshortcomingswell,despitetheimprove‐mentsintroducedtoitduringthepastdecades.This fact,probably,liesintheirpragmaticwayofre lec‐tion,aimingmostofthetimetoachieveasuf iciently acceptablecompromisebetweenthecontrollerdesign simplicityandtherequiredperformance.Ontheother hand,itseemsthattheyaremissingoutontheoppor‐tunitiesofferedbythegreatdigitalrevolutionasthey

cannotfullytakepro itfromthemoderndigitalpro‐cessor’scapacities[9,10].

Bornasanecessitytoestablishnewbridges betweenmodernindustrydemandsandmoderncon‐troladvances,theActiveDisturbanceRejectionCon‐trol(ADRC)wasintroducedforthe irsttimeinthe originaltextin[37]andafewyearslaterfortheAnglo‐phonesocietyin[38].Itwasthefruitofmuchwork fedbyadeepcomprehensionofbothpractitioners’ andacademicresearchers’wayofre lectingwhenit comestoaddressingcontrolsystemsproblems,the constraintsandthechallengesfacingthem,andthe opportunitiesofferedbytheaccelerateddevelopment ofdigitaltechnology.

EventheADRCoriginalframeworkiscomposed from ivemaincomponents;theExtendedState Observer(ESO)representsthecontroller’scorner‐stone.TheADRCideaisbasedontherealtimeestima‐tionandtheactivecompensationofthetotalin luence ofthemodelnonlinearitiescombinedwiththediffer‐entdisturbancetypes,suchasexternaldisturbances, modelingerrors,parametersvariationsoruncertain‐ties,etc.Theglobaleffectofthemodelnonlinearities anddisturbancesisconsideredastheobserver’saug‐mentedstate.

Owingtoitsgreatpotentialfordealingwithawide rangeofdisturbancestructures,ESObasedrobust control,includingtheADRCoriginalversion,haspre‐sentedanunmistakableviabilitytoaddressalargeset ofpracticalcontrolapplicationsbeforeevenhavinga rigorousproofoftheoreticalfundamentalquestions suchastheESOconvergenceortheclosedloopstabil‐itywhichcameseveralyearslater[39–43].Moreover, ithasshownahigh lexibilitytohandlemanymore applicationsthanPIDcontrol,suchastimedelayed systemscontrol,multivariabledecoupledcontrol,cas‐cadecontrol,andparallelsystemcontrol[10].Also, ESObasedcontrolhasknownsomemajoradvances inthecontextofitsgeneralizationtomorecomplex problemsinthelastfewpastyears,suchasstochastic systemscontrol[44]anddistributedparametercon‐trolsystems[43].

Motivatedbythehugepotential,thesimplicityof thedesignprocedure,andthewideimmergenceof ESObasedrobustcontrolparadigminsimulationand engineeringapplications,readerscanrefertothelit‐erature[45–49].Inthispaper,weattempttoillus‐tratehowtousetheESOforimprovingthenonlinear multivariabledecoupledcontrolrobustnessinasim‐pleandclearmanner.Theproposedmethod’smain idealiesintheuseofconventionalexactfeedback linearizationcontrol,widelyusedfordealingwith multivariableaf inenonlinearplantsinassociation withanextendedstateobserverchargedtoestimate inreal‐timeandthenactivelycompensatethewhole effectofmodelingerrorscausedbythetotaldiffer‐encebetweentherealplantdynamicsandthenominal descriptivemodelusedforthedesignofthedecou‐plingstaticstatefeedback.Thedesired,robustclosed loopdynamicsareachievedusingaproportional‐integralcontrollerinasecondexternalloop.

Thepresentarticleisorganizedasfollows:After presentingthisintroduction,thesecondsectionis devotedtotheprocesspresentationandmodeling. Then,thetheoreticaldevelopmentoftheproposed controlisexposedindetail.Oncetheprocessmodel andthecontrollerdesignarepresented,thesimu‐lationresultsareshownandcommentedoninthe thirdsection.Finally,theconclusionsummarizingand highlightingmainadvantagesoftheproposedcontrol strategyisgiveninthefourthandlastsection.

2.TheCSTRMathematicalModel

TheproposedCSTRmodel,showninFigure 1, isdescribedbytheequationsgivenbelowasfound in[50]:

(2)

(1) Itisobviousthatthemodel(1)isoftheform: ̇��=��(��)+��(��)�� ��=ℎ(��)

where:

‐ ��= ��1 ��2 �� = ���� ���� �� :isthestatevector.

‐ ��= ��1 ��2 �� = ���� ���� �� :thecontrolinput.

‐ ��=ℎ(��)=��:thecontrolledoutput.

��(��)= ⎡ ⎢ ⎢ ⎢ ⎣

−��0exp −���� ����2 ��1 Δ��.��0 ��.�� exp −���� ����2 ��1 + ��.�� ��.��.��(���� −��2)

⎤ ⎥ ⎥ ⎥ ⎦

(3)

��(��)= ⎡ ⎢ ⎢ ⎢ ⎣

1 �� (������ −��1) 0 0 1 �� (���� −��2)

⎤ ⎥ ⎥ ⎥ ⎦

(4)

Controlinputs,controlledoutputs,andprocess parametersaregiveninTable1

3.FeedbackLinearizationControl

Thenecessaryandsuf icientconditionallowing theexistenceofstatic,nonlinearfeedbackensuring theexactlinearizationofthesystem(2)isguaranteed ifandonlyiftheoutput’sglobalrelativedegreeequals tothesystem’sorder.

��

��

��

��

Byde inition,theoutputrelativedegreeistheleast numberoftheoutput’stimederivativestogetatleast onecontrolinput[51]:

From(5),itisclearthat���� and���� relativedegreesare equalrespectivelytor1 =1andr2 =1

Therefore,theoutputvectorglobalrelativedegree isequaltor = r1+r2 =2,andnotingthatthesys‐temordern = 2,theexistenceofastaticnonlinear feedbackallowingtheexactlinearizationof(2)isthen ensured.

Equation(5)canberewrittenasdescribedbelow:

̇��= ℎ1(��) ℎ2(��) =��(��)+��(��).�� (6) where: ��(��)= ����ℎ1(��) ����ℎ2(��) =��(��) (7) ��(��)= ����ℎ1(��) ����ℎ2(��) =��(��) (8) ����,���� denotestheLiederivatives[51].

3.2.LinearizingFeedbackControlDesign

Fromtheequation(5),itisobviousthatthe searchedstaticnonlinearfeedbacklinearizationcon‐trolisde inedas:

��=��−1(��).[��−��(��)] (9) where,��(��)and��(��)aregivenbytheequations(3) and(4)respectively.Theterm��=[��1 ��2]�� isthenew controlinputissuedfromtheexternalcontrolloop.

Applyingthecontrollaw(9)tothesystem(2)leads tothefollowinglineardecoupledsystem:

(10)

3.3.OuterLoopControllerSynthesis

ApplyingthefollowingPIcontrollawtotheouter controlloop:

(11)

yieldsthefollowingclosedlooptransferfunction:

(12)

where,sistheLaplaceoperator,��i and��i arerespec‐tivelytheclosedloopdesireddampingratiosand band‐widthfrequencies.

Table1. ProposedCSTRmanipulatedvariablesand parameters[50]

Figure1. SimplifiedschemeoftheproposedCSTR

3.1.TheOutputRelativeDegree

3.4.ExtendedStateObserverBasedRobustFeedback LinearizationControl

First,letusintroducethemodelingerrorsbycon‐sideringthemasparametersvariationsanduncer‐taintiesinthenominalmodel(2).Thisleadstothe followingperturbedmodel:

̇��=��(��)+Δ��(��)+(��(��)+Δ��(��))�� ��=ℎ(��) (13)

Byapplyingthenonlinearcontrolfeedback(9)tothe perturbedsystem(13),theexactlylinearizedsystem (10)becomesoftheform:

̇��=��+��(��,��) (14)

where:

��(��,��)=Δ��(��)��−1(��)(��−��(��))+Δ��(��) (15)

Thesystem(14)canbere‐expressedas:

1 =��1 +��1(��,��)

2 =��2 +��2(��,��) (16)

Thenextstepconsistsofdesigningtwoextended stateobservers,allowingtheestimationofthesystem statesandthetwounknowndisturbancesfunctions

��1 and��2.So,eachsubsystemofequation(16)canbe rewritteninthefollowingstateform:

��1 =����2 +���� ��2 =̇���� ��=1,2 (17)

Theproposednonlinearextendedstatesobservers (NLESO)arede inedasgivenin[41]:

�� =��.̂���� +��.���� +����.����(̂����)

̂�� �� =̂����1 (18)

where:

��= 01 00 ,��= b 0 ,̂���� = ̂�� ��1 ̂�� ��2 ,���� = ����1 ����2 (19)

Thenonlinear��(����)functionisde inedas:

����(����)= |̂����|����.��������(̂����),����|̂����|>���� �� ��1−���� i , �������� ��=1,2 (20)

where:

0<���� <1,���� >0,̂���� =���� −̂���� (21)

when |̂����|<����,thenonlinearstateobserver(18) takestheformofthewellknownlinearLuenberger observer(LESO):

̂�� ��1 =̂����2 +����1 �� +����

��2 =����2 �� ,������ = ������ ��1−���� ��,��=1,2 (22)

Therefore, ���� arecalculatedtoensureanobserver dynamicfasterthanthecloselooptrackingdynamic asdescribedbythegivenbelowcondition:

����������(��)=��2 +����2��+����1 =(��+����0)2 (23)

����������(��):Theobserver’scharacteristicpolynomial.

����0:Thedesiredobserverband‐widthfrequency.

����0:Ischosenasgivenin[52]toensurethebestcom‐promisebetweentheobservingconvergencespeed andthesensorsnoiseinsensitivity:

����0 =(3to5)����,��=1,2 (24)

Thesmallvalue���� representsthesetpointlimitingthe NLESO(18)highgain.

Byrede iningtheouterloopcontrol(11)asfol‐lows:

�������� 1 =��1 +��1 �������� 2 =��2 +��2 (25)

where:

Δ��1 =−̂��12

Δ��2 =−̂��22 (26)

thecontrolledoutputsinpresenceofmodelingerrors computedintheLaplacedomainbecome:

⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩

(��))

(27)

Itisobviousthatwhentheestimatedstatesconverge tothesystemstates:

��1(��)→��12(��) ��2(��)→��22(��) (28)

thecontrolledoutputsdynamicsconvergetothegiven belowexpressions:

(29)

Itisclearfrom(29)thattheclosedloopdynamicand staticdesiredperformancesareguaranteed.However, weshallemphasizethattheanalyticalconvergence proofoftheNLESO(18)isoutofthescopeofthis paper,andwearelimitedjusttosupposetheassump‐tionsgivenin[42,p.421]aresatis iedandthevalid‐ityoftheproposedcontrolisdemonstratedthrough numericalsimulations.

4.SimulationResultsandDiscussion

Theproposedcontrolmethodisvalidatedusing numericalsimulationsbycomparingitobjectivelyto theconventionalPIcontrollerdesignedbasingona locallyvalidlinearmodeldevelopedaroundapre‐selectedoperatingpoint.TheconventionalPIsyn‐thesismethodisgivenbellowchoosingthefollowing operatingstate:

��0 = 2.88297 �� ��0 = 244.96212.56 ��

Hence,thelinearstatemodelisgivenbythefollowing matrices:

��

��

Noticethatthelocalbehaviorofthegivenabovemodel isunstableatthechosenoperatingpoint.Thecalcula‐tionofthematrix��0 eigenvaluesyields:

��(��0)= −60.8818.19 ��

Tointroducetheintegralactioninthecontrollaw usingstatefeedbackclosedlooppoleplacement method,letusconsiderthefollowingaugmentedsys‐tem:wheretheaugmentedstateisde inedas:

Choosingtheclosedlooppolesasfollows:

theclosedloopPIcontrollerisdescribedbythefol‐lowingequations:

��=��0 +��

where:

Thecomparativestudythatfollowsisbasedontwo scenarios:

Scenario1: Bothproposedcontrolsareappliedtothe nominalnonlinearmodelofwhichtheparametersare giveninTable1.

TheproposedESObasedrobustcontrollerparam‐etersarede inedasgiveninTable2

Scenario2: Thecomparedcontrollersareappliedto theuncertainmodelinordertotesttheirperfor‐mancerobustnessagainstparameter’s,uncertainties, andvariationsofparametersaregivenintablebelow:

TheproposedESObasedrobustfeedbacklin‐earizationcontrolblocschemeandtheobtainedsim‐ulationresultsforeachproposedscenarioarepre‐sentedinFigures2–16.

Table2. ESObasedcontrollers’parameters

Loop Controller/ESOparameters

Table3. Parametersuncertaintiesorvariations

Uncertainties/ variations Absolutevalue Relative value(%)

ΔV(t)

[ 25+25]

ΔA(t) 0,25x24.sin(t) [ 25+25]

ΔC����(t) 0,2x10.sin(t) [ 20+20]

ΔT��(t) 0,02x306.sin(t) [ 2+2]

Figure2. TheproposedESObasedrobustfeedback linearizationcontrolscheme

Figure3. Desiredandactualproduct’sconcentration curvesforscenario1

Figure4. Desiredandactualproduct’stemperature curvesforscenario1

Figure9. Calculatedandobservedproduct’s concentrationdynamicsuncertaintiescurvesfor scenario1

Figure10. Calculatedandobservedproduct’s temperaturedynamicsuncertaintiescurvesfor scenario1

Figure11. Desiredandactualproduct’sconcentration curvesforscenario2

Figure12. Desiredandactualproduct’stemperature curvesforscenario2

Figure5. Reactantfluidflowratecontrolinputcurves forscenario1

Figure6. Coolantfluidflowratecontrolinputcurvesfor scenario1

Figure7. Measuredandobservedproduct’s concentrationcurvesforscenario1

Figure8. Measuredandobservedproduct’s temperaturecurvesforscenario1

4.1.ResultsDiscussionWhentheProcessisOperating inNominalConditions

Whentheparameters’uncertaintiesandvaria‐tionsareequaltozero,theresponsesoftheCSTR underthebothproposedcontrollers,showninthe Figures3and4,remainveryclosetothedesiredset pointafterthetransientphases.ItisalsoclearinFig‐ure3thattheESObasedrobustfeedbacklinearizing controllerensuresabetterdecouplingbetweenthe controlledoutputsandafasterconvergenceofthe productconcentrationtoitsdesiredvalue.Thestrong inertiaoftheprocessagainsttheconventionalPIcon‐trollerdisappearsafteracertainelapsedperiodof time.Concerningthetemperatureresponses,itclearly illustratedinFigure 4 thattheconventionalPIcon‐trolexhibitsaslightlysuperiorconvergencespeed althoughthechosenclosedlooppoleswerethesame. Thisresultisduetothefactthatfortheconventional PIcontrol,theclosedlooptemperaturedynamicsare regulatedasa irstordersubsystem,whereasitis chosenasasecondordercriticallydampedsubsystem fortheESObasedrobustcontroller.

ThecontrolsignalsdepictedinFigures5and6con‐irmthehighinertiaofthecontrolledprocessagainst theconventionalPIcontrollerbyillustratingthehigh controleffortneededtoachievethedesiredvalues whentheprocessisstartedorwhenthesetpoint changessuddenly,thisremarkismoreevidentforthe supplycontrol lowFL.

FromFigures 9 and 10,itisseenclearlythat convergenceoftheproposedESOisverysatisfac‐tory.Theestimateofthetotalmodelingerrorssup‐posedunknownandconsideredasanadditionalstate remainnearzero.Thisexpectedresultislogical sinceinthisscenariothemodel’suncertaintieswere neglectedbysettingtheirvaluestozero.

4.2.ResultsDiscussionWhentheProcessisOperating inPresenceofParameters’,Uncertainties,or Variations

Inscenario2,ouraimwastocomparethetransient andsteadyperformancesoftheproposedcontrollers underthesuppositionsoftheexistenceofuncertain ortimevaryingparameters.Theresultspresentedin Figures 11 and 12 showthateventhenominalper‐formanceswererelativelydegradedcomparedtothe nominalcase;bothproposedcontrollerswereable toachievesuf icientlygoodcontrolperformancein thesensethatthesystemresponsesweremaintained aroundthedesiredsetpointswithinanarrowband. Also,itisclearthattheproposedESObasedrobust feedbackcontrollerrobustnessexceedsthatobtained withtheconventionalPIsinceitwascapableofensur‐ingabetterstaticprecisionbyrejectingactivelythe real‐timeobservedmodelingerrorsasdepictedinFig‐ures15and16

Figure13. Reactantfluidflowratecontrolinputcurves forscenario2

Figure14. Coolantfluidflowratecontrolinputcurves forscenario2

Figure15. Calculatedandobservedproduct’s concentrationdynamicsuncertaintiescurvesfor scenario2

Figure16. Calculatedandobservedproduct’s temperaturedynamicsuncertaintiescurvesfor scenario2

Intermofcontrolenergy,theFigures 13 and 14 highlightthemainfutureoftheproposedESO basedrobustfeedbackcontrol,whichliesinthefact thatitneedsanetinferiorenergeticconsumptionto achievethedesiredsetpointswhenthesedesiredval‐ueschangeinstantaneouslyandespeciallywhenthe processstartsfunctioning.Thismajorfeature,clearly visibleinTable 4,isduetothepotentialofthepro‐posedmethodtodecouplethewholeprocessdynam‐icsintotwoindependentdynamicsandthuscontrol themseparately,dispensinglessenergycomparedto thePIcontroller.

Theabovepresentedcomparativestudyissum‐marizedbasedontherootedmeansquareerrorand themeancontrolpowercriterionsforeachscenario inTable4

TheerrorRMSandthemeancontrolpowercrite‐rionsarede inedas:

3) Showingastrongrobustnessagainstthenominal model’suncertaintiesbydecreasingthenecessity togetahighlyaccuratemathematicalmodelinthe controllerdesignbyadoptinganextendedstate observerchargedtocompensatethemodel/plant mismatch.

AUTHOR

AliMedjebouri∗ –DepartmentofMechanical Engineering,Universityof20August1955,Skikda, 21000,Algeria,e‐mail:ali.medjbouri@gmail.com, a.medjebouri@univ‐skikda.dz.

∗Correspondingauthor

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IMPLEMENTINGVISUALASSISTANTUSINGYOLOANDSSD

IMPLEMENTINGVISUALASSISTANTUSINGYOLOANDSSD IMPLEMENTINGVISUALASSISTANTUSINGYOLOANDSSD

FORVISUALLY‐IMPAIREDPERSONS

FORVISUALLY‐IMPAIREDPERSONS

Submitted:13th September2022;accepted:3rd January2023

RatneshLitoriya,KailashChandraBandhu,SanketGupta,IshikaRajawat,HanyJagwani,ChirayuYadav

DOI:10.14313/JAMRIS/4‐2023/33

Abstract:

ArtificialIntelligencehasbeentoutedasthenextbig thingthatiscapableofalteringthecurrentlandscape ofthetechnologicaldomain.ThroughtheuseofArtificial IntelligenceandMachineLearning,pioneeringworkhas beenundertakenintheareaofVisualandObjectDetec‐tion.Inthispaper,weundertaketheanalysisofaVisual AssistantApplicationforGuidingVisually‐ImpairedIndi‐viduals.Withrecentbreakthroughsincomputervision andsupervisedlearningmodels,theproblemathandhas beenreducedsignificantlytothepointwherenewmod‐elsareeasiertobuildandimplementthanthealready existingmodels.Differentobjectdetectionmodelsexist nowthatprovideobjecttrackinganddetectionwith greataccuracy.Thesetechniqueshavebeenwidelyused inautomatingdetectiontasksindifferentareas.Afew newlydiscovereddetectionapproaches,suchastheYOLO (YouOnlyLookOnce)andSSD(SingleShotDetector) approaches,haveprovedtobeconsistentandquiteaccu‐rateatdetectingobjectsinreal‐time.Thispaperattempts toutilizethecombinationofthesestate‐of‐the‐art,real‐timeobjectdetectiontechniquestodevelopagoodbase model.Thispaperalsoimplementsa’VisualAssistant’ forvisuallyimpairedpeople.Theresultsobtainedare improvedandsuperiorcomparedtoexistingalgorithms.

Keywords: YOLO,SSD,Objectdetection,R‐CNN,COCO

1.Introduction

Visually‐impairedorblindpeopleareincapableof seeing,whichiscrucialfordailylife.Visually‐impaired people’sautonomyislimitedtosomeextentbytheir inabilitytosee.Inthepast,assistivesystemshavebeen createdusingcomputervisionandmachinelearn‐ing,whichhaverecentlyexperiencedrapidgrowth. Thewaypeoplewithcognitivelimitationsinteract withtheoutsideworldhaschangeddramaticallyasa resultofrecentadvancesinassistivetechnology(AT). Amongthesedisabilities,visualimpairmentstands outasthemostrestrictive.Anytechnologydesigned toaidapersonwithadisabilityisconsideredAT. WiththeaidofAT,peoplewithdisabilitiescanpar‐ticipateincivicactivities,andthejobmarket,and haveahealthy,productive,independentlife[1].The useofATlessenstheneedforlong‐termcare,for‐malhealthandsupportservices,andcaregiverlabor. WithoutAT,peoplefrequentlyexperienceexclusion, isolation,andpoverty,whichworsenstheeffectsof

illnessanddisabilityonanindividual,theirfamily, andsocietyasawhole.Autonomousvehiclesarenow possiblethankstosigni icantadvancementsinarti i‐cialintelligence.Thesealgorithmscanbeusedeffec‐tivelyinATtohelptheblindandvisuallyimpairedin theareasofeducation,navigation,andsocialinterac‐tion.Peoplewhoareblindorvisuallyimpairedcan accessinformationthroughtouchorvoice.Atleast onebillionpeopleworldwidehavenear‐ordistance‐visionimpairmentsthatcouldhavebeenavoidedor havenotyetbeenaddressed,accordingtotheWorld HealthOrganization,whichestimatesthat2.2billion peopleworldwidehavevisualimpairments[2].The expectedcausesofanincreaseintheprevalenceof visionimpairmentarepopulationgrowthandaging. Severalstudieshavealreadybeenconductedtoinves‐tigatethecorrelationbetweentheprevalence,causes, andsocialfactorsofvisualimpairmentsandotherdis‐eases[3–5].MobileapplicationsalongwithMachine learning,AI,andIoThavebeenfoundtobepromis‐ingandprovidelifesavingtechnologiesforassisting humanswithvariousdiseasesanddisabilities[6–9].

Oneoftheprimarygoalsofimage‐basedlearn‐ingistounderstandanddifferentiateamongvarious scenicdescriptionsofcommonobjectsofinterest. Thistaskcanbesubdividedintoseveralsubtasks: boundingboxcreation,objectlocalization,attribute determination,andrelationshipestablishment.The imagesofvariousobjectscanbebroadlyclassi iedinto iconicandscenicviews.Theiconicapproachassumes thepresenceofasingleobjectwithclearboundaries andseparationedges.However,theiconicviewpoint istoosimplistictoaccountforreal‐worldsituations inwhichimagesarerarelyiconicbutinvolvealarge numberofintertwinedobjectsinasmallspace.To detectobjectsofinterest,imagesegmentationand contextminingshouldbeappliedto ilteroutpoints ofinterest.Mostoftheexistingsystemsperformwell undertheseiconicviewsbutachieveloweraccuracy inscenicinstances.Objectsinscenicenvironments arecluttered,overlapping,andwithoutgoodcontrast. Varioustechniquesofsegmentationareappliedto extractusefulinformationfromthesescenicviews. Whenbuildingnewmodels,itisofparamountimpor‐tancetoselectalearningdomainmostsuitabletothe givenneedsandimplementation.Fortrainingthese models,thedatasetemployedplaysacrucialpartin establishinggoodresults.

Oneofthemajorchallengesisto indpertinent trainingimagesandsamplestoaccommodatemore modularandrobustlearning.Variouspioneering workhasbeendoneincollectingtheseimagesamples underoneroofintoadataset.Someofthesedatasets containmillionsofsamplesandtraininginstances, spanningthousandsofobjects.Currently,someof themorepopulardatasetsincludeGoogle’sImageNet, MicrosoftCOCODataset,PASCALVOC,SUN,etc.We takealookatthesedatasetsinthefollowingsections, aimingto indthemostsuitableforourVisualAssis‐tantImplementation.Toimproveavisually‐impaired person’sperception,anewmodelispresentedthat connectsanATdevicewithSmartObjectsandtheir cloud.

Therestofthepaperisorganizedasfollows:A detailedandstate‐of‐the‐artreviewofexistinglitera‐tureinthe ieldispresentedinSection2.Thedetails ofthedatasetusedinthisstudyareexplainedin Section 3.AdetaileddiscussionoftheYOLOobject detectionmodelisincludedinSection 4.Thearchi‐tectureoftheproposedsystemispresentedinSec‐tion 5.Obtainedresultsanddetaileddiscussionsare presentedinSections6.Section7concludesthearticle andsketchesfutureworkdirections.

2.LiteratureSurvey

Numerousassistivesystemshavebeenintroduced forobjectdetectioninthelastfewyearsthatrelyon sensors,theInternetofThings,andcomputervisionto helptheblind.Thesesystemseachhavetheirbene its anddrawbacks.

Zouetal.[10]reviewsmorethan400papers onobjectdetectionspanningfromthe1990sto 2109,focusingonthetechnicaladvancementsmade inthisarea.Thispaperemphasizesseveraltopics whichincludeseveralearly‐stagedetectors,datasets fordetection,metrics,possiblespeed‐uptechniques whichcanbeused,andtherecentstate‐of‐the‐art detectionmethods.Thispaperalsoshedslighton someimportantapplicationsofdetection,suchas textdetection,facedetection,pedestriandetection, etc.,andmakesananalysisofthedevelopmentmade andchallengesfacedinrecenttimes.Variousaspects makethispaperdifferentfromallthereviewsdone onobjectdetection.In‐depthresearchonthekey technologiesandstate‐of‐the‐artobjectdetectionsys‐temshasbeendonehere,whilethepreviousreviews lackedfundamentalanalysistogivereadersacom‐pleteunderstandingofcomplextechniques.Mostof thepreviousreviewswerefocusedonashortperiod orsomespeci icdetectiontaskwithoutconsidering thedevelopmenthistory.

AmbatiandL.Gayer[11]underlinehowcrucial itistocustomizethechoiceofmachinelearning (ML)techniquesbasedontheparticularHAR(Human ActivityRecognition)requirementsandthefeatures oftheassociatedHARdataset.Overall,thisstudyaids incomprehendingthebene itsanddrawbacksofML techniquesanddirectstheapplicabilityofvariousML methodstovariousHARdatasets.

Anaccessiblewebinterfaceforvisually‐impaired individualsispresentedbyIyeretal.[12]tomaximize easeofuseandprovideuserswithahassle‐freeexpe‐rience,thevirtualassistantisanoperatingsystemthat isindependentanddoesn’trelyonkeyboardinput fromtheuser.Communicationwithandcustomiza‐tionofthesystemarepossibleusingspeech‐to‐text andtext‐to‐voiceinterfaces.Thispresentationpro‐videsanoverviewofthesystemdesignandimplemen‐tationmethodologyforthethreemodulescurrently inuse.Toansweruserqueriesquicklyandaccurately, WikipediausesaBERTmodelbuiltfromtheSQuAD dataset.Itwasfoundthat80.88%ofthewordsexactly matched.Anyonewithvisualimpairmentscaneasily accessanywebsiteusingthevirtualassistant.With thisprogram,youdon’thavetomemorizecomplex keyboardcommandsorusescreenreaders.Asatool forinteractingwiththewebsites,theassistantisnot onlyveryconvenientbutalsoquiteeffective.Accord‐ingtotheresults,thesoftwarewassuccessfullyrun onthethreemostpopularsites:Google,Gmail,and Wikipedia.Itwasrunseparatelyoneachofthese sites.ThesoftwareisasteppingstonetowardWeb3.0 whereallfunctionscanbecontrolledthroughvoice commands.Visually‐impairedpeople indthemselves wanderinginsideunusualchallengingareas.Many smartsystemshaveintendedtohelpblindpeoplein thesedif icult,oftendangerous,situations.However, someofthemarenotfree,hardto ind,orsimplytoo expensive.Saffouryetal.[13]presentedalow‐cost wearsystemforblindpeoplethatwasdesignedto allowthemtodiscoverobstaclesintheirplace.The proposedprogramconsistsoftwomaincomponents; hardwarecomponents,andalaserpointer($12),as wellasanandroidsmartphone,whichmakesoursys‐temcheaperandmoreaccessible.ICon lictavoidance algorithmusesimageprocessingtomeasuredistances toobjectsinthesurroundingarea.Thisisbasedon lasertriangularlight.Thisdetectionofobstaclesis enhancedbytheedgediscoverywithinthecaptured image.Anadditionalfeatureforasystemistosee andalerttheuserwhentherearestairsinthecamera viewarea.Obstaclesarebroughttotheuser’satten‐tionusingtheacousticsignal.Oursystemshowedthat solid,withonly5%ofafalsealarmleveland90% sensitivitywithobstacles1cmwide.Thissystemhad somelimitations:Itmaynotworkwellinashiny environmentaslaserintensitymaydecreaseandthe distancebetweenthecameraandthelasershouldnot change.

Mohantaetal.[14]proposedanassistantfor visually‐impairedindividuals.Intheirsetupaftercap‐turingaphotofromasmartphone,theusercaneasily readmenucardsofrestaurants,theroomnumber ofthehotel,andcanalso indtheirbelongings.The voicecontrolfeedbackmechanismisalsousedinthe appthroughwhichtheusercanperformvarioustasks withthehelpofthevoiceassistant.Cloudcomput‐ing,imageprocessing,andMLareusedtodevelop theapplication.ThecentralaimofusingMListo allowcomputerstolearnautomaticallywithoutinter‐ventionfromhumans.Multiplefontscanbedetected whilereadingthetextevenifthefontisuniqueornot common.

Suchuniquefontscanbefoundingreetingscards, businesscards,etc.Itisalsoprovedtobebene icial indifferentsectorslikebanking,education,traveland tourism,etc.Variousobjectsofdailyuse,vehicles,and foodcanbedetectedandrecognizedwiththehelpof thisapplication.

Sharmaetal.[15]createdasystemthathelpsa personwhoisvisuallyimpairednavigatebyspeaking throughtheearpiecetoidentifytheperson.Theysug‐gesteddevelopingamobileappthatusednumerous deeplearningmodelstoimprovethemanagementof applications.Thecameracontinuouslyfedimagesinto thesystemasinputs,thecoresystemprocessedthis information,andtheearpieceservedastheoutput devicetodeliverthisoutputtotheuser.

AnintelligentvirtualassistantcalledProject Nethra[16]offersvoice‐basedcommunicationto userswhoareblindorvisuallyimpaired.Itenablesa widerangeoffunctionalitybasedonvariousinternet servicesandsocialmediaforthetargetusersto interactwithcomputersandinternet‐basedservices. Nethrawillperformtasksontheuser’sbehalfrather thanjustreturningsearchresults.ProjectNethrawill conversewiththeuserconversationallybyspeaking backtothemafterhearingwhattheysayanddetecting it.Thevoicerecognitionmodule,naturallanguage processingmodule,conversationalagent,andcontent extractionmodulearethesystem’sfourmainparts. Kumaranetal.[17]discussthedevelopmentofvirtual personalassistantsandspeechrecognitionsystems. Thecurrentsystemisoperatedandmaintainedby athirdpartyandoperatesonline.Thisapplication usedthelocaldatabase,speechrecognition,and synthesizerwhilesafeguardinguserdatafrom outsideparties.Torecognizethespeech,aparser calledSURR(SemanticUni icationandReference Resolution)isused.Textisconvertedtophonemesby asynth.

TodesigntheNext‐GenerationofVPAsmodel, KepuskaandBohouta[18]usedmulti‐modaldialogue systems,whichprocesstwoormorecombineduser inputmodes,suchasspeech,image,video,touch, manualgestures,gaze,andheadandbodymovement. Byutilizingvarioustechnologies,includinggesture recognition,image/videorecognition,speechrecogni‐tion,asizabledialogue,aconversationalknowledge base,andageneralknowledgebase,thenewmodel ofVPAswillbeusedtoincreaseinteractionbetween humansandmachines.

Iannizzottoetal.[19]developedavirtualassis‐tantarchitectureforsmarthomeautomationsystems usingsomeofthemostcutting‐edgemethodsincom‐putervision,deeplearning,speechgeneration,recog‐nition,andarti icialintelligence.Thedevelopedproto‐typeofthesuggestedassistantisinteractive,resource‐ef icient,effective,andadaptable,anditrunsona small,inexpensiveRaspberryPI3device.Thesystem wasintegratedwithanopensourcehomeautomation environmentfortestingpurposes,anditranforsev‐eraldayswithusersbeingurgedtointeractwithit.It turnedouttobeprecise,dependable,andappealing.

Aninterestingresearch,GnanaandPraveen[20], suggestedamethodforautomaticallyestimating depthfromasingleimageusingthelocaldepth hypothesisanditsapplicationtohelptheblind.A camerarecordstheenvironmentinfrontoftheuser, andtherecordedimageisscaledforcomputational effectiveness.Edgedetectionandmorphologicaltech‐niquesareusedtoseparatetheobstaclesinthe image’sforeground.Then,basedonthelocaldepth hypothesis,thedepthiscomputedforeachbarrier. Rahmanetal.[21]presentsthearchitecturalframe‐workforasmartblindassistantthatintegratesIoT anddeeplearning.Thesuggestedapproachutilizesa deeplearningparadigm,aRaspberryPi,andacamera moduletocreateanintelligentcap.Thesuggestedcon‐ceptshowsthestructurallayoutofasmartblindstick thatmakesuseofamicroprocessorandnumerous sensors.Forimmediatedatamonitoring,themodel usesBluetoothandtheInternetofThings’connectiv‐ity.UsinganIoTcloudserver,theauthorizedperson continuestokeepaneyeonvisionimpairment.

2.1.RelatedWorkAboutObjectDetectionandRelated Technologies

ObjectDetection: Currentmodelsinobjectdetec‐tionhavetwocategories:(1)one‐stagedetectorsand (2)two‐stagedetectors.Incomparisonwithone‐stage detectors,two‐stagedetectorsarebetterintermsof performance.However,sincetheyrequireinference oftheregionofanobject,theyarelessef icientthan one‐stagedetectors.Here,inbothcases,thedetec‐torsareneededtotraininanof linebatchmodeand theyassumealargenumberoftrainingimagesper class.Duringthemodeldeploymentwhenthenovel classesareneeded,toaddthisrestrictsthescalabil‐ityandusability.Thesecanactasthebackboneof detectionforafew‐shotdetectorsalthoughtheyare non‐incremental.TheONCEthatweareusingisbased ontheone‐stageCenterNet.TheCenterNetischosen becauseitcanbeeasilybrokendownintotheclass‐genericandspeci icparts,competitivedetectionaccu‐racy,andef iciency.

Few-shotlearning: FSL(few‐shotlearning)is studiedforef icientlyregisteringnewclassesin deploymentforimagerecognition.Consideringalarge numberoflabeledexamplesofasetofbaseclasses, FSLtriestometa‐learnadata‐ef icientthathelps toallownewclassestobelearnedfromveryfew examplesforeachclass.FSLissimplerthanobject detection.

Objectdetectionhasgonethroughtwohistori‐calperiods:a(i)traditionalobjectdetectionperiod (before2014)anda(ii)deeplearning‐baseddetection period(after2014).Traditionalobjectdetectionalgo‐rithms,whichincludetheViola‐JonesDetector,the HistogramofOrientedGradients(HOG)detector,and theDeformablePart‐basedModel,werebuiltbasedon handcraftedfeaturesandastheperformanceofhand‐craftedfeaturesbecamesaturated,deeplearning‐baseddetectionmethodsstartedevolving.

Inthedeeplearningera,objectdetectioncanbe categorizedas:“two‐stagedetection”(whichincludes RCNN,SPPNet,FastRCNN,FasterRCNN,FeaturePyra‐midNetworks),and“one‐stagedetection”(which includesYOLO,SSD,RetinaNet).Inobjectdetection, severalknowndatasetshavebeenreleasedinrecent years,likePASCALVOC,ImageNet,MS‐COCO,etc. ThispaperalsoreviewsAlexNet,VCG,GoogleNet,and ResNetastheengineofdetectorsthataffecttheaccu‐racyofdetectors.

YOLO(YouOnlyLookOnce)isanewapproach toobjectdetectionwithanextremelyfastarchitec‐ture[22].ThebasemodelofYOLOprocessesimages inreal‐timeat45framespersecond,whileFastYOLO, asmallerversionofthenetwork,processesimagesat 155framespersecond.YOLOmakesmorelocaliza‐tionerrorsbutislesslikelytopredictfalsepositives onimagebackgrounds.Itoutperformsotherdetec‐tionmethods,includingtheDeformablePartsModel (DPM)andR‐CNN.Currentdetectionsystemsrepur‐poseclassi iersfordetection.TheDeformableParts Modelusesaslidingwindowapproach,wherethe classi ierrunsatevenlydistributedlocationsthrough‐outtheimage.RecentapproacheslikeR‐CNN,onthe otherhand,generatepotentialboundingboxes irst usingregionproposalmethods,thenrunaclassi ier onthesuggestedboxes.Inpost‐processing,thebound‐ingboxesarere inedandthedetectionsareelimi‐nated,andthescoresarerecalculatedbasedonthe otherobjectsintheimage.Thesemodelsthatusecom‐plexpipelinesarerelativelyslowandhardtooptimize. WithYOLO,youonlylookonceatanimagetopredict whatobjectsarepresentandwheretheyare.YOLOis relativelysimpleandfast,trainingonfullimagesto makethedetectionprocesseffective.BecauseYOLO doesnotuseacomplexpipeline,itisextremelyfast. Itusesaneuralnetworktopredictdetectionsfroma newimageattesttime,whichenablesittoprocess streamingvideoinreal‐time.YOLOanalyzestheimage whilemakingpredictions.Fortrainingandtesting,a fullyconnectedlayerpredictstheoutputcoordinates andtheirprobabilitiesbytakingintoaccountthefull imagesoitcanextractcontextualinformationabout classes.Fortrainingandinferencepurposesitusesthe Darknetframework.YOLOfacesdif icultywithsmall objectsthatappearingroups,forexample,a lockof birds,andalsoitstrugglestogeneralizeobjectsthat appearindifferentaspectratios.Errorsarecaused primarilybyincorrectlocalization.

Despitethesuccessofdeepconvolutionalneural networks(CNNs)inobjectdetection,foralmostall thecurrentmodelsalengthyprocessofnumerous iterationsinabatchisusedtotrainthem.Inthecurrent scenario,allofthetargetclasseshaveagreatdealof trainingdatainterpretedwithtrainingsamples,andall ofthetrainingimagesareusedfortrainingpurposes. Duetotheirhighinterpretationcostandcomplex trainingrequirements,thesemethodshavealimited abilitytoaccommodateonlineclassesandgrow.

Toavoidtheearliermentionedlimitations,wecan studyalearningsettingknownasiFSD(Incremental Few‐ShotDetection)[23].

TheIncrementalFew‐ShotDetectionoriFSDset‐tingisde inedas(1)thesetofbaseclassesthathavea suf icientnumberoftrainingsamplesthatcanbeused topre‐trainthedetectionmodelinadvance,and(2) whenthetrainingpartiscompleted,theiFSDmodel mustbereadyfordeploymenttoareal‐worldappli‐cationwherethenewclassescanbeaddedatany timewiththehelpoffewannotatedexamples.The modelshouldworkwithlearningwithoutforgetting theprinciple,i.e.,itshouldgiveafairresultonall theclassesregisteredsofar.(3)Memoryfootprint, storage,andcomputecostsshouldbefeasibleforthe learningofclassesfromanunbounded lowofexam‐ples.Themodelsshouldbeabletobedeployedonlow‐resourcedevicessuchassmartphonesandrobots.

AguidetothenovelCOCODatasetcreatedfor Objectdetectionandclassi icationispresentedbyT.Y. Linetal.[24].Itmainlyfocusesonthenon‐iconic orscenicviewsofimages,pointingoutthedif icul‐tiesencounteredwhendetectingscenicviews.Itout‐linesimagesegmentation,bounding‐boxgeneration, heatmap,andper‐pixelcolorlocation.Thefocusison 2Dand3Dimagelocalizationandper‐pixelseman‐ticsegmentation.Thepaperoutlinestheneedfora largeandrich‐annotatedimagewithalargenumber ofinstancespersampleofobjects.Thiscollectionaids inbetterlearningandaccuracyonscenicviewsof images.Thedifferenttechniquesofimagesegmenta‐tion,classi ication,anddetectionhavebeende ined withrespectivelimitations.Semanticscenelabeling hasbeende inedaspixelsofimagesbelongingtoeach objectcategory.Thisalsohelpsindetectingobjects whereinindividualobjectsarehardtode ineand establish.Imagelocalizationandboundingboxhave beendescribedasthemajorstepinobjectdetection andfacetracking.Thetaskofobjectclassi ication requiresbinaryimagelabelsandiscomparativelyeas‐ieraswedealwithgeneraliconicimages.Various statisticshavebeenpresentedfortheCOCODatasetin comparisonwithothercontemporarydatasets.

JosephRedmonandAliFarhadi[25]presented somedesignchangestoYOLO,whichmakesitalit‐tlebiggerbutmoreaccurateandfaster.YOLOv3is approximatelyasaccurateasanSSDbutthreetimes faster.YOLOv3clustersthedimensionsofground truthlabelstogenerateanchorboxesforpredicting theboundingboxes,whereeachboundingboxhas4 coordinates,tx,ty,tw,andth.Eachboxpredictsthe classeswhichmaybepresentusingmultilabelclas‐si ication.Duringtraining,itusesthebinarycross‐entropylossformakingclasspredictions.Darknet‐53, ahybridnetworkcomposedofYOLOv2andDarknet‐19,predictsboxshapesat3differentscalesand extractsfeaturesfromthem.Thisnetworkconsistsof successive3x3and1x1convolutionallayerswitha totalof53convolutionallayers.Darknet‐53performs betterthanmanyoftherecentclassi iers.Darknet‐53isevenbetterthanResNet‐101andResNet‐152 intermsofperformanceandspeed.Becauseofthe betterutilizationofGPU,Darknet‐53hasthehighest measured loating‐pointoperationspersecond.On theotherhand,ResNetshavemanylayerswhichmake themveryinef icient.

YOLOv3performsextremelywellontheolddetec‐tionmetricofmAPatIOU=.5andisalmostasgoodas RetinaNetandmuchaboveSSDvariants.Performance ofYOLOv3decreasesastheIOUthresholdincreases whichmeansthatitfacesdif icultyingettingtheboxes perfectlyalignedwiththeobject.YOLOv3incompar‐isonwithYOLOstruggleswithmediumandlarger‐sizeobjects.Overall,YOLOv3isaprettygooddetector, extremelyfast,andaccurate.

Itisevidentfromtheliteraturesurveythatmany toolsandsolutionshavebeencreatedtoaidand directvisually‐impairedpeoplearoundindoorand outdoorpathways.Nevertheless,theyhaven’tentirely satis iedtheuserneedsandtechnologicalspeci ica‐tions.Currently,themajorityoftheseunanswered questionsarebeingaddressedindependentlyinmany researchareas,includingindoorlocation,computa‐tionof loading,distributedsensing,andtheexami‐nationofspatially‐relatedperceptualandcognitive processesinvisually‐impairedindividuals.However, mobilephonesandothersuchdevices,alongwith state‐of‐the‐arttechnologies,arequicklybecoming integratedintotheirdailylives.Oldandnewsolutions havebecomeworkableinthissetting,andsomeof themarenowonthemarketassmartphoneapplica‐tionsorportabledevices.

3.DatasetUsed

3.1.MicrosoftCOCO(CommonObjectsinContext) Dataset

Therearenumerousimagesdepictingcomplex everydayscenesofeverydayobjectsintheirnatu‐ralsettingcontainedwithinthislarge,richlyanno‐tateddataset.Itaddresses3majorproblemsinscene understanding,i.e.,detectingnon‐iconicviews,con‐textualreasoning,andpreciselocalizationofobjects. Thedatasetconsistsofalargesetofimagescon‐tainingcontextualrelationshipsandnon‐iconicobject views,with91commonobjectcategories,25million labeledinstancesin3,28,000images.COCOhasmore instancespercategorycomparedtoothercontempo‐rarydatasets(Fig.1).

3.2.GoogleImageNetDataset

ResearchusingImageNetaimstodevelopsoftware thatcanrecognizevisualobjects.

Thedatabasehasmorethan14million‐annotated imagesandwithatleastonemillionoftheimages, boundingboxesarealsoprovided.ImageNetcontains morethan20,000categories.

Thenumberofcategoriesisverylarge,but instancespercategoryaresubstantiallylowforrig‐oroustraining.Thedatasetisorganizedaccordingto theWordNethierarchy(currentlyonlythenouns),in whicheachnodeofthehierarchyisdepictedbyhun‐dredsandthousandsofimages(Fig. 2).Theaverage numberofimagespernodeiscurrentlyover500.

3.3.SUNDatabase

Themainaimofthisdatasetistoprovide researcherswithacomprehensivecollectionofanno‐tatedimagescoveringalargevarietyofenvironmental scenes,places,andobjectswithin(Figs.3and4).The samplesarebuiltusingvocabularybasedonscenes andplaces.Thevocabularyisthenqueriedtoobtain imagesfromtheinternet.Ithas16,783imagesofvar‐iousscenes.Thedatasethasbeenoptimallydivided intotrainingandtestingsamples.

Figure1. Instancesvsimagesizecomparisonsfor differentdatasets

Figure2. Instancesvsno.ofcategories’comparisonsfor differentdatasets

Figure3. Percentageofimagesvsinstancesfordifferent datasets

4.YOLO–ObjectDetectionModel

TheYOLOsystemdetectsobjectsinreal‐timeusing state‐of‐the‐artsensors.Itisafastobjectdetection approachthatscansthecompleteimagetoextract contextualinformationwithhighaccuracy.Inprior detectionsystems,classi icationorlocalizationfunc‐tionsarerepurposedtoperformdetection.Themodel isappliedtoanimageatmultiplescalesandlocations toaccomplishdetection.YOLOdetectshigh‐scoring regionsusingauniquemethodthatinvolvesapplying 24convolutionallayersfollowedbytwofullycon‐nectedlayerstotheentireimage.Animageisdivided intoregionsbythisnetworkandboundingboxesand probabilitiesarepredictedforeachregion.Predicted probabilitiesareusedtoweightheboundingboxes. TheYOLOpredictsbasedonhowtheimageisglobal atthetimeofthetest,notitscomponents.Unlike systemssuchasR‐CNN,whichrequirethousandsof evaluationsforasingleimage,thismakespredictions usingonenetworkevaluation.FasterthanR‐CNNand 100xfasterthanFastR‐CNN,itismorethan1000x fasterthanR‐CNN.AnewerversionofYOLO,YOLOv3 incorporatesseveralimprovementstoprovidebetter trainingandbetterperformance,includingmulti‐scale predictions,abetterbackboneclassi ier,andmore.

5.Architecture

TheProposedArchitecturecomprisesvarious dependentcomponentsimplementedasstand‐alone modulesasshowninFigure 5.Weadoptaclient‐serverarchitecture,whereintheServerisaremote entityrunningonalocalmachine.TheClientAppli‐cationisimplementedasamobileapplicationthatis connectedtothecameradevicethroughawireless

networkeitherusingBluetooth,Wi‐Fi,orotherwire‐lesstransmissionprotocols.

Theonlyrequirementissuf icientbandwidthand lowlatency.Themobileapplicationsendsarequestto themirrorsitewhich,inturn,forwardsittothelocal server.Thelocalserver,runningaYOLOv3model, detectsobjectswithintheinputimageandcreatesa listofobjectsfound.Thislistis inallyconvertedinto astringandsentasaresponsetothemirrorsite, which,redirectstheresponsetotheclientapplication. Theclientapplicationusingtext‐to‐speechfunction‐alityconvertsthisstringintoaudiothatisfedinto theearpieceofthevisually‐impairedindividual.For simplicity,theentireimageisdividedinto9different zones,viz.,Center,TopLeft,BottomRight.Themodel alsopredictsthezoneofeachobjectdetectedusingthe bounding‐boxlocationreturnedbytheYOLOmodel.

Thevariouscomponentsofthesystemareas follows:

‐ YOLOv3:YOLO modelimplementedin Python using CV2 and Numpy libraries.

‐ LocalServer: Serverimplementedin Python using Flask and ngrok libraries.

‐ MobileApplication: MobileApplicationimple‐mentedin Dart and Flutter using Dio, tts,and camera libraries.

‐ HTTP Mirror: Ngrok createsamirror HTTP site thatredirectsandforwardsrequestsandresponses betweenclientandserver.Therequestismadeto thisHTTPsite.

‐ Camera: Externalcameradeviceinstalledonthe walkingcane.

Figure4. Percentageofimagesvscategoriesfor differentdatasets

Figure5. Client‐Serverinteraction

Table1. ComparisonbasedonaverageprecisiononMScoco

6.ResultsandDiscussion

6.1.YOLOv3Metrics(Table 1)

‐ BasedonCOCO’saveragemeanAPmetric,YOLOv3is comparabletoSSDvariants.YOLOv3’sperformance at320x320is22msat28.2mAP,whichis3times fasterthanSSD.

‐ WhenmAPdetectionisupdatedtoIOU=.5(or AP50),YOLOv3hasaperformancealmostsimilarto RetinaNet.AccordingtoRetinaNet’stests,itachieves similarperformanceto57.9AP50in51ms,butitis 3.8*fasterthanRetinaNet’stests.

‐ TheYOLOv3performancedropssigni icantly,as indicatedbyCOCOaverageAP,astheIOUthreshold increases,indicatingthatitisapoorperformer.

‐ However,YOLOv3isaverystrongandfastdetec‐tor,whichisverygoodontheolddetectionmetric of.5IOU

6.2.ApplicationUI

Sincetheapplicationismadeforvisually‐impaired individuals,itisobviousthataveryrudimentaryuser interface(UI)issuf icient.

Basedonthis,wecreatedasimpleandlucidUIthat isbeingusedonlyfordemonstrationpurposes(Refer toFigs.8–10).Theexternalcamerahardwarehasnot beenusedfordemonstrationpurposes,instead,the mobiledevicecameraisused.Afewsamplesofthe ApplicationUIalongwiththelocalserverareshownin Figure11.Themobileapplicationcanbefoundat[25]

andtheserver.Theresponsetimeonaveragewas foundtobearound5s.Theupperboundresponse timeisalsoaround5s.

Figure6. Comparisonbasedoninferencetime

Figure7. ComparisonbasedonaccuracyonMScoco

Figure8. Homescreenonclientapplication

Figure9. SettingtheHTTPmirroraddressontheclient application

Object‐detectionmodel.ManyObjectDetection algorithmshavebeenproposedwithwide‐scaleappli‐cability.Choosingonesuchmodelthatpertinently solvestheproblemathandisamajordeterminerin obtaininggoodaccuracy.Wehaveprovidedreviewsof variousobjectdetectiontechniquesthatworkwiththe scenicviewofgenericimages.Awide‐scalecompar‐isonamongthevariousobjectdetectorshasencour‐agedustouseYOLOv3,anincrementallymodi ied formofYOLO,astheobjectdetector.Theaccuracy andmAPscoreofYOLOisaboveparwithmostcon‐temporarydetectors,andforanotherreason,YOLOis simplerinimplementation,allowingthesimpleand robustconstructionofanobjectdetector.Wehavedis‐cussedtheproposedarchitecture,i.e.,aclient‐server

modelalongwiththevariousnecessarycomponents. Themodularapproachhasenabledustoachievea greataverageresponsetimeof5s.

7.ConclusionandFutureWork

Peoplewhoarevisually‐impairedstruggletomove safelyandindependently,whichpreventsthemfrom participatinginroutineprofessionalandsocialactiv‐itiesbothindoorsandoutdoors.Theyalsohavedis‐tressingrecognitionofbasicenvironmentalfactors. Thispaperprovidesacomputervision‐basedsystem thatsupportsblindpeopleinnavigationaswellas triestoaddresstheproblemsposedintheintroduc‐tionsection.Thesuggestedmethodisexaminedunder variouscircumstancesandmeasuredagainstcompet‐ingprogrammesavailableontheAppstore.The ind‐ingsshowthattheprogrammefunctionsreasonably wellundervariousconditionsandisquickerandmore effectivethanitsalternatives.Asopposedtomany otherapplications,thisoneletsblindusersopenit bypluggingtheirmobilephones’earphonejacksin. Thismakesitsomewhataccessibletoblindusers. Thisapplicationcanbeusedfornavigationinitscur‐rentcondition,althoughithasseveralrestrictions. Therearestillalotofthingsthatneedtobe ixed. Toaccountforbetterobjectdetection,theapplication canbeenhancedbycombiningitwiththeInternet ofDevices’technologydevices.Theperformanceof theapplicationwillimproveinthefuturethanksto improvementsindeeplearningandtheYOLOalgo‐rithm.TheapponlyworksonAndroidphones,soit willneedtoberedesignedsothatitcanrunonother platformsaswell.

AUTHORS

RatneshLitoriya∗ –Medi‐CapsUniversity,Indore, India,e‐mail:litoriya.ratnesh@gmail.com.

KailashChandraBandhu –Medi‐Caps University,Indore,India,e‐mail:kailashchan‐dra.bandhu@gmail.com.

SanketGupta –Medi‐CapsUniversity,Indore,India, e‐mail:sanket.jec@gmail.com.

IshikaRajawat –Medi‐CapsUniversity,Indore,India, e‐mail:ishika.rajawat30@gmail.com.

HanyJagwani –Medi‐CapsUniversity,Indore,India, e‐mail:email2hany@gmail.com.

ChirayuYadav –Medi‐CapsUniversity,Indore,India, e‐mail:chirayu725@gmail.com.

∗Correspondingauthor

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