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MODERN SPACECRAFT

GUIDANCE, NAVIGATION,AND CONTROL

Thispageintentionallyleftblank

MODERN SPACECRAFT

GUIDANCE, NAVIGATION,AND CONTROL

FROMSYSTEMMODELINGTOAIAND INNOVATIVEAPPLICATIONS

Editedby

VINCENZOPESCE

AirbusD&S,AdvancedStudiesDepartment,Toulouse,France

ANDREACOLAGROSSI

PolitecnicodiMilano,AerospaceScienceandTechnology Department,Milan,Italy

STEFANOSILVESTRINI

PolitecnicodiMilano,AerospaceScienceandTechnology Department,Milan,Italy

Elsevier

Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates

Copyright 2023ElsevierInc.Allrightsreserved.

Nopartofthispublicationmaybereproducedortransmittedinanyformorbyany means,electronicormechanical,includingphotocopying,recording,oranyinformation storageandretrievalsystem,withoutpermissioninwritingfromthepublisher.Detailson howtoseekpermission,furtherinformationaboutthePublisher’spermissionspolicies andourarrangementswithorganizationssuchastheCopyrightClearanceCenterandthe CopyrightLicensingAgency,canbefoundatourwebsite: www.elsevier.com/permissions . Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyright bythePublisher(otherthanasmaybenotedherein).

Notices

Knowledgeandbestpracticeinthis fieldareconstantlychanging.Asnewresearchand experiencebroadenourunderstanding,changesinresearchmethods,professional practices,ormedicaltreatmentmaybecomenecessary.

Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgein evaluatingandusinganyinformation,methods,compounds,orexperimentsdescribed herein.Inusingsuchinformationormethodstheyshouldbemindfuloftheirownsafety andthesafetyofothers,includingpartiesforwhomtheyhaveaprofessional responsibility.

Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,or editors,assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasa matterofproductsliability,negligenceorotherwise,orfromanyuseoroperationofany methods,products,instructions,orideascontainedinthematerialherein.

ISBN:978-0-323-90916-7

ForinformationonallElsevierpublicationsvisitourwebsite at https://www.elsevier.com/books-and-journals

Publisher: MatthewDeans

AcquisitionsEditor: ChiaraGiglio

EditorialProjectManager: SaraGreco

ProductionProjectManager: SuryaNarayananJayachandran

CoverDesigner: ChristianJ.Bilbow

TypesetbyTNQTechnologies

VincenzoPesce,AndreaColagrossiandStefanoSilvestrini

ModernspacecraftGNC:what,why,how,forwhom?3

AbriefhistoricalreviewofclassicalspacecraftGNC10

GNCterminology13

GNCarchitecture:fromrequirementstopreliminarydesign15 Notationrules38 References42

PART1FundamentalGNCtools

2.Referencesystemsandplanetarymodels 45

AndreaColagrossi,StefanoSilvestriniandVincenzoPesce

Earthandplanetarymodels46

Coordinatereferencesystems53 Coordinatetransformations63 Time69

WhatisrelevantforGNC?73 References75

3.Thespaceenvironment 77

AndreaCapannolo,EmanuelePaolini,AndreaColagrossi,VincenzoPesce andStefanoSilvestrini

Perturbationsources78

Externalperturbations79

Externalperturbationsmodelingguidelines97

Internalperturbations100

Internalperturbationsmodelingguidelines123

WhatisrelevantforGNC?124 References126

4.Orbitaldynamics

AndreaCapannolo,StefanoSilvestrini,AndreaColagrossiand VincenzoPesce

Two-bodyproblem132

Three-bodyproblem161

Irregularsolarsystembodies170

Relativeorbitaldynamics174 References204

5.Attitudedynamics

AurelianoRivolta,AndreaColagrossi,VincenzoPesceand StefanoSilvestrini

Attitudekinematics208

Attitudedynamics227

Three-bodyproblemattitudedynamics248

Relativeattitudedynamics249

Multibodyspacecraftdynamics250 References252

6.Sensors

AndreaColagrossi,VincenzoPesce,StefanoSilvestrini, DavidGonzalez-Arjona,PabloHermosinandMatteoBattilana

SensormodelingforGNC254 Sensorfaults275 Orbitsensors276 Attitudesensors286

Inertialsensors306

Electro-opticalsensors322 Altimeters330 References334

7.Actuators

AndreaColagrossi,LisaWhittle,VincenzoPesce,StefanoSilvestriniand MatteoBattilana

ActuatormodelingforGNC338 Thrusters344 Reactionwheels354

Controlmomentgyros366 Magnetorquers369 References375

PART2SpacecraftGNC

8.Guidance 381

ThomasPeters,StefanoSilvestrini,AndreaColagrossiandVincenzoPesce

Whatisguidance?381

On-boardversusground-basedguidance382 Guidanceapplications385 Guidanceimplementationbestpractices438 References438

9.Navigation

VincenzoPesce,PabloHermosin,AurelianoRivolta,ShyamBhaskaran, StefanoSilvestriniandAndreaColagrossi

441

Whatisnavigation?441 On-boardversusground-basednavigation443

10.Control

FrancescoCavenago,AurelianoRivolta,EmanuelePaolini, FrancescoSanfedino,AndreaColagrossi,StefanoSilvestriniand VincenzoPesce

543

Whatiscontrol?543

Controldesign545

Reviewofcontrolmethods592

Controlbudgets618

Controlimplementationbestpractices626 References629

11.FDIRdevelopmentapproachesinspacesystems 631

MassimoTipaldi,StefanoSilvestrini,VincenzoPesceandAndreaColagrossi

FDIRinspacemissions,terms,anddefinitions633

CurrentFDIRsystemdevelopmentprocessandindustrialpractices637

FDIRsystemhierarchicalarchitectureandoperationalconcepts639

FDIRsystemimplementationinEuropeanSpacemissions641

FDIRsystemverificationandvalidationapproach642

FDIRconceptandfunctionalarchitectureinGNCapplications:ashortoverview642 References645

12.GNCverificationandvalidation 647

FrancescoPace,EmanuelePaolini,FrancescoSanfedino,DanielAlazard, AndreaColagrossi,VincenzoPesceandStefanoSilvestrini

Whyitisimportant?648

13.On-boardimplementation 685

DavidGonzalez-Arjona,VincenzoPesce,AndreaColagrossiand StefanoSilvestrini

Spacecraftavionics686 On-boardprocessingavionics694

On-boardimplementationalternatives700 On-boardimplementationandverification705 References711

PART3AIandmodernapplications

14.ApplicativeGNCcasesandexamples

StefanoSilvestrini,AndreaColagrossi,EmanuelePaolini, AurelianoRivolta,AndreaCapannolo,VincenzoPesce,ShyamBhaskaran, FrancescoSanfedinoandDanielAlazard

AOCSdesign717

Orbitalcontrolsystem730

Attitudecontrolsystem742

RelativeGNC775

On-boardsensorprocessing791

Irregularsolarsystembodies flyaround803

GNCforplanetarylanding806 References814

15.ModernSpacecraftGNC 819

StefanoSilvestrini,LorenzoPasqualettoCassinis,RobertHinz, DavidGonzalez-Arjona,MassimoTipaldi,PierluigiVisconti,FilippoCorradino, VincenzoPesceandAndreaColagrossi

AIinspace Introduction821

Artificialintelligenceandnavigation867

ValidationofAI-basedsystems883

Reinforcementlearning890

AIusecases906

AIon-boardprocessors923

InnovativetechniquesforhighlyautonomousFDIRinGNCapplications925

Smallsatellites/CubeSats938 References971

Furtherreading981

16.Mathematicalandgeometricalrules

AndreaCapannolo,AurelianoRivolta,AndreaColagrossi, VincenzoPesceandStefanoSilvestrini

983

Matrixalgebra983

Vectoridentities991

Quaternionalgebra994

Basicsofstatistics1000

ECI-ECEFtransformation1002 References1006

17.Dynamicalsystemstheory 1007

FrancescoCavenago,AndreaColagrossi,StefanoSilvestriniand VincenzoPesce

State-spacemodels1007

Discrete-timesystems1009

Transferfunctions1011 References1015

Contents

18.Autocodingbestpractices

FrancescoPace,VincenzoPesce,AndreaColagrossiand StefanoSilvestrini

Listofmainarchitecturalandimplementationrules1017 Reference1026 Index1027

Listofcontributors

DanielAlazard

ISAE-SUPAERO,Toulouse,France

MatteoBattilana

OHBItaliaS.p.A.,Milan,Italy

ShyamBhaskaran

NASAJetPropulsionLaboratory,Pasadena,CA,UnitedStates

AndreaCapannolo

PolitecnicodiMilano,Milan,Italy

LorenzoPasqualettoCassinis

TUDelft,Delft,theNetherlands

FrancescoCavenago Leonardo,Milan,Italy

AndreaColagrossi

PolitecnicodiMilano,Milan,Italy;AirbusD&SAdvancedStudies,Toulouse,France

FilippoCorradino

TyvakInternational,Turin,Italy

DavidGonzalez-Arjona

GMVAerospace&Defence,Madrid,Spain

PabloHermosin

DeimosSpace,Madrid,Spain

RobertHinz

DeimosSpace,Madrid,Spain

FrancescoPace

GMVAerospace&Defence,Madrid,Spain

EmanuelePaolini

D-Orbit,FinoMornasco,Italy

VincenzoPesce

AirbusD&SAdvancedStudies,Toulouse,France

ThomasPeters

GMVAerospace&Defence,Madrid,Spain

AurelianoRivolta

D-Orbit,FinoMornasco,Italy

FrancescoSanfedino

ISAE-SUPAERO,Toulouse,France

StefanoSilvestrini

PolitecnicodiMilano,Milan,Italy

MassimoTipaldi

UniversityofSannio,Benevento,Italy

PierluigiVisconti

TyvakInternational,Turin,Italy

LisaWhittle

AsteroidExploration,Leiden,theNetherlands

Biography

Dr.VincenzoPesce isaguidance,navigation,andcontrol(GNC) engineeratAirbusD&SAdvancedStudiesDepartmentinToulouse Prior tojoiningAirbus,heworkedforGMV,Spain.HeholdsaPhDinAerospace EngineeringfromPolitecnicodiMilanowithathesistitled “Autonomous NavigationforCloseProximityOperationsaroundUncooperativeSpace Objects.” Duringhisstudies,hespentaresearchperiodatNASA Jet PropulsionLaboratory(2017)andattheUniversityofFlorida(2015).He isauthororcoauthorofabout30scientificpublicationsonGNC,autonomousnavigation,small-bodyexploration,andmicrogravityexperimentsin internationaljournalsandconferenceproceedings.Hereceivedthe prestigiousLeonardoCommitteeGraduationAwardandtheGuidoHorn D’ArturoAwardforhisresearchonvision-basedautonomousnavigation. Hehasbeeninvolvedinseveralinternationalprojectsincollaboration withEuropeancompaniesandagencies.Recently,hehasbeenworking onthedevelopmentofGNCalgorithmsfortheMarsSampleReturn missionandfortheESA’sEuropeanLargeLogisticsLanderproject.HiscurrentresearchinterestsincludeautonomousGNCforproximityoperations, rendezvousandlanding,vision-basednavigation,andGNCinnovative methods.

Dr.AndreaColagrossi isanassistantprofessorof flightmechanicsat theAerospaceScienceandTechnologyDepartmentofPolitecnicodi Milano.HeholdsaPhDinAerospaceEngineeringwithathesison “AbsoluteandRelative6DOFDynamics,GuidanceandControlforLargeSpace StructuresinCislunarEnvironment.” HeearnedhisMScdegreeinSpace Engineeringin2015fromPolitecnicodiMilano,withadoubledegree fromPolitecnicodiTorino.In2012,heobtainedhisBScdegreeinAerospaceEngineeringatPolitecnicodiTorino.Hewasavisitingresearcherat DeimosSpace(Spain)andPurdueUniversity(Indiana,USA).Hehas beeninvolvedinseveralnationalandinternational-fundedprojects,collaboratingwithItalianandEuropeancompanies,institutions,andagencies, workingondevelopmentstudiesaboutGNCformodernapplications, suchasnanosatconstellationsforastrophysicalobservations,rendezvousin cislunarenvironment,andproximityoperationsforactivedebrisremoval. Heisauthorandcoauthorofabout30scientificpublicationsininternational journalsandconferenceproceedingsonGNC,smallspacesystems,and non-Kepleriandynamics.HismainresearchinterestsarespacecraftGNC

andsystemengineeringforadvancedsmallsatelliteapplications,withafocus oneffectiveGNCimplementationwithlimitedhardwareresources,innovativeGNCtechniques,andautonomousfailureandcontingencymodes management.

Dr.StefanoSilvestrini isapostdoctoralresearcherattheAerospace ScienceandTechnologyDepartmentofPolitecnicodiMilano.Heobtained hisPhDcumlaudewithathesistitled “AI-augmentedGuidance,NavigationandControlforProximityOperationsofDistributedSystems.” He earnedhisMScdegreeinAerospaceEngineeringin2017fromTUDelft. In2016,heworkedasatraineeforAirbusD&SinMunich.In2015,he earnedhisBScdegreeinAerospaceEngineeringattheUniversitadegliStudi diPadova.DuringhisBSc,hespentasix-monthresearchperiodattheCollegeofAerospaceEngineeringofBostonUniversityunderawardedscholarship.HehasbeeninvolvedinnationalandEU/ESA-fundedprojectsfor developingnanosatconstellationforscienceobservation,missionanalysis, andsystemdesignforfractionatedspacearchitectureandartificialintelligence(AI)forspacecraftGNC.Hehasworkedasateachingassistantfor severalcoursesthroughouthisMScandPhDcareer.Hisresearchinterests includethedevelopmentofAIalgorithmsforautonomousGNCindistributedspacesystemsandproximityoperations,particularlytailoredfor embeddedapplicationsinsmallplatforms.

Introduction

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VincenzoPesce1,AndreaColagrossi2,StefanoSilvestrini2

1AirbusD&SAdvancedStudies,Toulouse,France

2PolitecnicodiMilano,Milan,Italy

ModernspacecraftGNC:what,why,how,forwhom?

Eversincethebeginningofhumanexistence,humanshadtorelyon basictools,orsimplyontheirintuition,to “guide” themselvesthroughout theirhabitat,developinginstrumentto “determinetheirlocation” andto “act” accordingly.TheconceptofGuidance,Navigation,andControl (GNC),evenifinadifferentfashion,wasfamiliartothe firstnomadictribes andtothefollowingpioneersofhumanexploration.Still,itistruethat everyoneapproachedtheGNCprobleminhisownlife,bysimplygoing outsidehomeandwalking.

Spaceflighthasbeenoneofthemostrevolutionaryshadesofhuman exploration,allowingmenandautomatedvehiclestoescapeEarth’sgravity, turningimaginationandwonderintoreality.Thetechnologyofsatellites andspacevehicleshasrapidlyevolvedsincethe firstsignalreceivedfrom theSputnik1(Спутник 1)orthe firstawe-inspiringimagesfromthe Moonsurface,becomingnowcapabletolandman-madeobjectsonplanets, comets,andasteroids,ortodeployconstellationsoforbitingbodies,orto maketwospacecraftencounterwhiletravelingthousandsofkilometers persecond.

Inperformingalltheseactivities,oneoftheoriginalproblemsofhumanitycamebackunderanewperspective:spacecraftGNC.Eveninspace,one needstoknowthepath,thecurrentlocation,andthestepstostayonthe righttrack.Intheseregards,spacecraftGNChasfollowedaquicktechnologicalevolution,drawinginspirationfromthe firstEarth-basedmethods, suchassextants,chronometers,andlandmarks,torapidlyevolveacquiring thepeculiaritiesofthespaceenvironment.Then,withthearisingofpowerfulcomputersandadvancedtechniques,thisbranchofspacecrafttechnology madegiantleapstowardautonomyandhighperformances.Nowadays,itis atthedawnofanewera,withartificiallyintelligentmachinesstartingto helpspaceexplorerstotravelacrossthesolarsystem.

ModernSpacecraftGuidance,Navigation,andControl

ISBN:978-0-323-90916-7

https://doi.org/10.1016/B978-0-323-90916-7.00001-9

ThisbookaimsatpresentinganupdatedandcomprehensivesetoftheoryandapplicationsaboutspacecraftGNC,fromfundamentalstoadvanced concepts,includingmodernartificialintelligence(AI)-basedarchitectures, withfocusonsoftwareandhardwarepracticalapplications.Infact,oneof themainpurposesofthisbookistodiscussupdatedGNCdesignandvalidationprocesses,fromrequirementsto finalsystemimplementation.This bookisfocusedondeliveringacoherentpathtodesignaspacecraftGNC system,startingfromtheoryanddiggingthecriticalstepstowardimplementation.Inotherwords,thebookisintendedtoprovidethenecessarytheory, omittingredundantderivations,alreadypresentinliterature,fromthespecificperspectiveofspacecraftsystems.

Thetopicsdiscussedinthebookaretypicallyfoundscatteredinavast poolofliterature;ortheyarelimitedtoacademictheoreticalmanuals,which havebeenpublishedquitefewyearsago;ortheyareavailablefromdocumentationandtechnicalnotes,retrievedfrominternationalstandards,which arenoteasytobeunderstoodmaintainingageneraloverlookonthewhole problem.Moreover,GNCistypicallyregardedastheconvergenceofthe threeindividualentities:Guidance,Navigation,andControl.Thisis partiallyvalid;nevertheless,aholisticapproachinthedesignofthesystem islackinginbook-typeliterature.

Thebookstartsfromarevisionofthebasictoolsandtheoreticalbackgroundrequiredtounderstandhowaspacecraftmovesinspaceandwhat aretheelementsaGNCsystemrequirestobeoperative.Then,themain GNCblocksareintroduced,describingtheirrolewithintheoverall ensemble,andexplainingsometheoreticalfoundationstounderstandthe methodsandtechnologiesofspacecraftGNC.Thediscussionbeginsfrom thebasicknowledgeneededtounderstandtheGNCsystemdesignprocess, anditisintegratedwiththestepsdrivingfromtherequirementstothesystemimplementationandverification.Finally,spacecraftGNCapplications andexamplesarediscussed,togetherwithabroadsurveyonmoderntechniques,methods,andscenario,includinganextensivechapterontheroleof AIinmodernspacecraftGNC.

Thisbookdoesnotwanttoprovideanin-depththeoreticaldescription ofGNCfoundations,butitoffersauniqueperspectiveondesignandverificationprocesses,practicalapplications,andnovel,cutting-edge, techniques.

Auniquetexttounderstandthefundamentalsofmodernspacecraft GNCdesign,fromtheorytoapplications,whichcanguidebothstudents, youngprofessionals,andexperts,iscurrentlymissing.Thepracticaland

applicativefocusofthebookmakesisappealingtojuniorandgraduateaerospaceengineers.Moreover,thediscussiononmodernandadvancetechniquesshouldmakeitareferenceupdatedhandbook.Infact,spacecraft systemengineersandattitudeandorbitcontrolsystem(AOCS)/GNCspecialistsmaywanttouseittobeupdatedonthelatestpromising advancements.

Insummary,thebookmayaddressdifferentcategoriesofreaders:developers,researchers,youngprofessionals,Ph.D.students,designersinthe field ofspacecraftGNC;AOCSandsystemengineers;AssemblyIntegrationand Verification/AssemblyIntegrationandTest(AIV/AIT)technicians;professionalsinthe fieldofestimationandcontrolscienceswhowanttoapproach thespacesector;expertswhoarelookingforanupdateddiscussiononmodernproblemsandapplications.

Bookcontent

Followingthisintroductorypart,thebookhasthreemainpartsplusanappendixsection.

The firstPart1 BasicTools offersanoverviewofthemaintheoretical andfundamentalconceptssupportingspacecraftGNC.Inparticular,the usedreferencesystemsandplanetarymodelsaredetailedalongwiththe mostimportantelementsofthespaceenvironment.Anoverviewofthe mainorbitalandattitudedynamicalmodelsisprovided.Subsequently, sensorsandactuatorsaredescribed,withparticularfocusoncommon GNC-relatedissuesandonthemostrelevantmodelingprinciples.With moredetails:

ReferenceSystemsandPlanetaryModels containsthemodelstodescribe planetarygeometry,withabriefintroductiontopositionrepresentation methods;themaincoordinatereferencesystems;themethodstotransform thecoordinatesfromonereferencesystemtoanotherone;theprimarytime conventionsandscales,includingtheconceptofJuliandates;a finalsection summarizingthemostrelevantaspectsfortheGNCsystem.

The SpaceEnvironment chapterdescribesthemainperturbationsources influencingthespacecraftdynamics,dividingbetweenexternalperturbations(i.e.,nonsphericalgravitational,magnetic field,atmosphericdrag,solar radiationpressure,andthird-body)andinternalones(i.e., flexibilityand sloshing,electromagneticdisturbances,internalvibrations,thermalsnap, parasiticforcesandtorquesduetothruster firingandplumeimpingement); themainguidelinestomodeltheperturbationcontributions;theconcepts relatingexternalandinternalperturbationswiththeGNCdesign.

Thechapteron OrbitalDynamics introducesthetwo-bodyproblemand thethree-bodyproblem,withthemostusefulelementsforaGNCengineer;thegravitationalenvironmentaroundirregularsolarsystembodies; therelativeorbitaldynamics.

The AttitudeDynamics chapterpresentsthefundamentalrulesand methodstodealwithattitudekinematics;attitudedynamics,includingadiscussionontheinertiapropertiesofthespacecraftandonthemainequations todealwithsignificantattitudemotions;relativeattitudedynamics;multibodyspacecraftdynamics.

Thechapterabout Sensors discussesthemainsensormodelingconcepts forspacecraftGNC,includingsomeelementsofmetrology,andthebasic principlesaboutstatisticsandrandomvariables;orbitsensors;attitudesensors,inertialsensors;electro-opticalsensors;altimeters.

Thechapterabout Actuators discussesthemainactuatormodelingprinciplesforspacecraftGNC;thrusters;reactionwheels;controlmomentgyros; magnetorquers.

Part2 SpacecraftGNC representsthecoreofthebook,inwhichthe maintechniquesandmethodsforspacecraftGNCarepresentedanddeeply analyzed.Faultdetectionisolationandrecoverymethods,GNCverification andvalidationtools,andon-boardpracticalimplementationaredetailed withparticularemphasis.Specifically:

The Guidance chaptercontainsthedifferentimplementationphilosophiesofon-boardandground-basedguidance,theformaldiscriminantbetweenAOCSandGNCsystems;theguidancesystemdesignprocess, includingtwoapplicativecasesofrendezvousguidanceandattitudeguidance;themostrelevantguidanceimplementationbestpractices.

The Navigation chapterdescribesthemainnavigation filteringtechniques,includingsequentialandbatch filters;absoluteorbitnavigation, includingthebasicsofGNSS,pulsars,ground-basedorbitdetermination techniques;absoluteattitudenavigation;relativenavigation;imageprocessingtechniques;theinfluenceofnavigationbudgetsontheoverallGNC chain;themostrelevantnavigationimplementationbestpractices.

The Control chapterdiscussesthecontroldesignprocess,includingboth thedesigninthestatespaceandinthefrequencydomain;anintroductionto nonlinearcontroldesign;Proportional-Integral-Derivativecontrol methods;LinearQuadraticRegulatormethods;robustcontrolfundamentals,includingModelPredictiveControlandSlidingModeControl;the controlbudgets;themostrelevantcontrolimplementationbestpractices.

Thechapterabout FDIRDevelopmentApproachesinSpaceSystems presents technicalsolutionsandindustrialprocessesusedbythespaceengineersto design,develop,test,andoperatehealthmanagementsystems,alsoknown asFailureDetection,Isolation,andRecovery(FDIR)systems.

The GNCVerificationandValidation chapterintroducesthemainindustrialprocesstoverifyandvalidateaGNCsystem,includingModel-in-theLoop,Software-in-the-Loop,Processor-in-the-Loop,Hardware-in-theLoop,In-Orbittestingactivities.

The On-boardImplementation chapterpresentsabriefoverviewonthe finalimplementationoftheGNCalgorithmsandfunctionsintheonboardavionics’ modules,withtheassociateddatainterfaces;themaintechnologiesformodernprocessingdevices,suchasgeneral-purposeProcessors/ Microcontrollers,DigitalSignalProcessors,GraphicalProcessingUnits, FieldProgrammableGateArray,orspecificad-hocelectroniccircuits.

ThelastmainPart3 AIandModernApplications introducesthemost advancedsolutionsforspacecraftGNC.ThefundamentalsofAItheory andsomecutting-edgespacecraftGNCapplicationsaredescribedinthis part.Astrongfocustothespaceenvironmentisimposed,andthemainalgorithmsthatcanbenefitfromAIorothermoderncomputingtechniques areconsidered,withoutanextensive,generaltreatmentasaclassicalAIor computersciencetextbook.ThispartisdifferentfromagenericAIorcomputersciencebooktostressonlythepeculiaralgorithmsandaspectsofmodernspacecraftGNCthatareapplicableinthespacecontext.Inparticular:

The ApplicativeGNCCasesandExamples chapterpresentsasetofapplicativeGNCexamplesandusecasescoveringthetopicsofGNCthatareof relevanceforpracticalandmodernapplications.Itcontainsexampleson AOCSdesign;orbitalcontrolsystems;attitudecontrolsystems;relative GNC;on-boardsensorprocessing;irregularsolarsystembodies flyaround; planetarylanding.

The ModernSpacecraftGNC chaptergivesanoverviewonmodernGNC techniquesandmethods,includinganoverviewonAItechniquesforspacecraft,ontheinnovativemethodsforGNCFDIR,andontheemerging topicofCubeSatsandnanosatellites.ItcontainsanintroductiontoAIin space;AItechniquesforspacecraftnavigation;validationofAI-basedsystems;reinforcementlearning;AIusecases;AIon-boardprocessors;innovativetechniquesforhighlyautonomousFDIRsystems;smallsatellitesand CubeSatsGNC.

Finally,anappendixsectionprovidesasummaryofthefundamentalsof mathematicalandgeometricalrules;dynamicalsystemstheory;Automated CodeGeneration(ACG)orautocoding.

Howtousethebook?

ThisbookisintendedtocovertheentirespacecraftGNCdomain,withthe mostupdateddevelopments,tryingnottoleaveanyconceptorapplication unexplored.However,thetopicscannotbetreatedwiththe finestdetailsof aspecializedbook.Thus,thebookpresentsthemaintoolsandmethodsto dealwiththecoveredcontentsandsupportthediscussionwithseveralliteraturereferencestofurtherexplorethetopics.Thereadershouldeitherhave asufficienttheoreticalbackgroundonthematter,oritshoulddeepenand reviewthoseconceptsthatarenotcompletelyclearaftera firstreadingof thebookcontent.

Thebookisdesignedandstructuredtosupportthepracticalworkand thedailylifeofmodernspacecraftGNC/AOCSengineers,aerospaceengineers,avionicdevelopers,andAIV/AITtechnicians.Thus,itcanbeusedas ahandbook,withouttheneedofreadingitfromthebeginningtotheend. TheapplicativeexamplesandthemodernGNCpresentedinPart3aresupportedbythefundamentalsofspacecraftGNCdiscussedinPart2,whichare developedstartingfromthebasictoolsintroducedinPart1.Hence,reading itbottom-upcanbeusefulforanexperiencedGNCengineerwhowantto updatehisknowledge,whileastudentorayoungprofessionalissuggested toreaditfollowingthenormal flow.

MostofthechaptersinPart1andPart2areenrichedwithsectionsdedicatedinsummarizingthechapter’saspectsrelevantforGNCapplicationsor tolisttipsandbestpracticestodesignandpracticallyimplementtheGNC functionsintothespacecraftsystem.Similarly,somemodelingguidelinesare clearlyoutlinedtobettersupporttheGNCdesignprocess.Thechapters aboutFDIRsystems,verificationandvalidationprocesses,andon-board implementationareself-contained,andtheyshouldbeusedtohaveaclear preliminaryoverviewontheseimportantconcepts,oftenoverlookedin classicaltextbooksaboutspacecraftGNC.

Part3containsdiverseandvariousapplicativeandmodernconcepts, spanningtheentireapplicativespectrumofspacecraftGNC.Thus,itisnot uncommonthatthedifferentsectionsofthispartbelongtodifferentdomains andhaveabroadvarietyofterminologyandtheoreticalconcepts.Thus,Part 3couldbereadconsideringeachsectionasanautonomousblock,performing thenecessarylinkstothepreviouspartsandtotheappendicesofthebook.

Whatisnotcontainedinthisbook?

Thebookisintendedtobeapracticalandusefulsupporttotheworkandto theknowledgeofspacecraftGNC/AOCSengineers,aerospaceengineers, avionicdevelopers,andAIV/AITtechnicians.Thus,itisnotdesignedto provideallthebasicandtheoreticalconceptsbehindeachofthecovered contents.Moreover,thereaderisexpectedtohaveasolidknowledgeon mathematics,physics,dynamics,andbasicsofspacesystems.

Thedescriptionoforbitalandattitudedynamicsisconstrainedtothe mostrelevantaspectsusefulfortheGNCdesign.Consequently,fewtopics aboutorbitandattitudedynamicshavebeenomitted,mainlybecauseof lengthrestrictions.AllthelandmarksandmilestonesoftheGNCdesign andverificationareincluded,butthedetailsaresometimesjusthintedinordertoavoidalengthyandcumbersomediscussionthatwouldnot fitwith thehandbookpurposesofthisbook.Inallthesecases,invitationforthe readertodeepenthoseaspectsonexistingliteraturereferencesisincluded.

Thebookdoesnotcontainextensivediscussionontheoreticalaspectsof spacecraftdynamicsandenvironmentmodeling.Furthermore,itoverlooks thetheoreticaldetailsonsensorsandactuators,focusingmoreonthepracticalaspectsabouttheirintegrationintheGNCdesign(e.g.,calibration, testing,andnumericalmodeling).Inotherwords,inthisbook,environmentalterms,dynamicalequations,sensorsandactuatorsaremoreintended asmathematicalmodels,ratherthanasthephysicalprinciplestheyrepresent.

TheGNCdescriptiondirectlyappliesthemethodstothespacecraft design;hence,noextensivediscussionaboutgeneralGNCmethodsis included.Moreover,mathematicalderivationsandproofsarelimitedto thosecaseswheretheyaredirectlyapplicableinthedesignandverification processes.

Theexampleandapplicativecasesarelimitedtothosewithinterestin presentandfuturemissionscenario.Moreover,thefocusisdedicatedto modernapplicationsthataresomehowlesscommoninclassicliterature aboutspacecraftGNC.Eveninthiscase,properreferencestoclassicliteratureexamplesareincluded.TheAIsectiononlyconsiderstechniquesand methodologiesthataremoreconsolidatedinspacecraftGNCdesign.As alreadysaid,AIisspecificallylimitedtospacecraftGNC;thus,anextensive, generaltreatmentasaclassicalAItextbookisnotcontainedinthisbook. Furthermore,giventhecloserelationtoresearchaspects,somedetailson themostinnovativeapplicationsaregiven,highlightingtheircurrentdevelopmentstatusandtheirapplicativelimitations.

Thelistofcoveredapplicationsisobviouslynotexhaustive,butcontains thoseexamplesthataredeemedtobemorerelevantforthemodernchallengesfaced,onaday-by-daybasis,bythespacecraftGNCengineers. Theeditorsapologizefromnowforanymissingcontentthereaderwould havedesiredto findinthisbook;theinterestedreaderisinvitedtocontact themtodirectlyaskforspecificsuggestionsonhowto findanddeepenits knowledgeaboutthemissingtopics.

AbriefhistoricalreviewofclassicalspacecraftGNC

DespitetheconceptsofGNCareintrinsicwiththehumanmovementsacrosstheglobe,thetrueancestorofspacecraftGNCistheancient mariner,whohadtoexploretheworldbyguiding,navigating,andcontrollingthemotionofanartificialobjectthroughavastenvironment,stillunexplored,withoutreferencesandlandmarks.Indeed,tomastertheartof drivingashipacrossthesea,humansoutlinedfundamentalconcepts, inventedmethodsandtoolsthatarenowadaysstillapplicabletothewhole fieldofGNC.Threethousandyearsago,PolynesiansandPhoeniciansmarinerswerecapabletosailonthehighseas,andeversincethehumanshave beendevelopingcelestialnavigation,compassbearing,landmarkranging, routetracing,andsoon.Theyalsoinventedavarietyofinstrumentsand methodstoaccomplishthesetasks.The firstmagneticcompassusedinnavigationapplicationsisdatedbacktothe11thcentury,themariner’sastrolabe tothe14thcentury,themarinechronometerandthesextanttothe17thand 18thcentury.Similarly,therhumblineorloxodromenavigationmethod wasformulatedandappliedinthe16thcentury.Moreover,alsotheetymologyoftheword “navigation” belongstotheseaandtothemariners:itwas firstusedinthe1530s,fromLatin “navigationem,” whichderivesfrom “navigatus” meaning “tosail,sailover,gobysea,steeraship,” from “navis” (i.e.,ship)andtherootof “ agere ” (i.e.,todrive).Notehowatthattime,and sometimesalsoinpresentdays,thewordnavigationwasencompassingthe entireGNCdefinition.

Thedirectevolutionofmaritimenavigation(i.e.,maritimeGNC)was theaircraftGNC,whichsharedseveralcommonelementswithhisprogenitor.Indeed,airplanesmoveinvastregionsfollowingroutesbymeansof navigationinstrumentsandcontrolsystems,suchasthepilotortheautopilot.Infact,asfortheships,the firstaircraftswerecontrolledbymen, whoreadtheinformationofon-boardinstruments(e.g.,altimeter,compass, attitudeindicator,etc.)tofollowthepaththeycomputedbeforethetake-

off.Namely,the firstaircraftGNCwashumanintheloop.Averysimilar evolutionhappenedinspaceforspacecraftGNC.

Asobvious,spacecraftmovinginspacesharemostofthefundamental characteristicswiththeshipsandairplanestravelingacrosstheseasandin theskies,eventhoughtheorbitalconditionsareevenmoreharshanddifficult.The firstspacecraftwereindeedonlypassivelycontrolled:launched intoballistictrajectories(i.e.,thenaturalorbits)andwithpassiverotational stabilization.The firstman-madeobjectorbitingaroundtheEarthwas theSputnik1,launchedbytheSovietUniononthefourthofOctober 1957.Itwasasimplepolishedmetalspherewithadiameterof58cm,but ithadnoorbitalandattitudecontrolcapabilities.The firstAmericansatellite wastheExplorer1,launchedonthe firstofFebruary1958.Ithadnotorbital control,anditsrotationalstatewasdesignedtospinthespacecraftaroundits elongatedaxistoachieveapassiveattitudestabilization.However,soonafter therelease,thespacecraftenteredina flatspindynamics,anundesirablerotationaboutanaxisperpendiculartothepreferredaxis.Lateritwasdiscovered thatthiswasduetoenergydissipationfrom flexiblestructuralelements,and thissmallaccidentmotivatedfurtherdevelopmentsofthetheoryofrigid bodydynamicsafternearly200yearsfromthe firstEulerianformulation. Thespacecraftdynamicswasnotcompletelyunderstoodyettocorrectly developaGNCsystem.

TheunmannedLuna-3sovietspaceprobe,whichtookpicturesofthefar sideoftheMoonin1959,wasthe firstguidedspacecraft,havingaverybasic attitudecontrolsystem.Itwasspin-stabilizedformostofits flight,butits three-axisattitudecontrolsystemwasactivatedwhiletakingphotos.However,theneedtocontrolthespacecraftmotionincreasedwiththeadventof mannedspacecraftandmorecomplexorbitaloperations.

The firsthumaninspacewastheSovietcosmonautYuriGagarin, launchedwithaVostok1ontheApril12,1961.Despitehewasatrained airforcepilot,carefullyselectedtoaccomplishhistask,themissionwas designedtobeautomaticallycontrolledorcontrolledfromground.In fact,themedicaldoctorswerenotsurehowahumanmightreacttospace environment,andthereforeitwasdecidedtolockthepilot’smanualcontrols.Thisprimitivespacecraftcontrolsystemwasonlypartiallytrustedby thespacecraftengineersthemselves,andthusacodetounlockthecontrols wasplacedinanon-boardenvelopetobeusedincaseofemergency.The codewas “1-2-5,” andGagarinwasanywaytoldaboutitbeforelaunch. Anyhow,thissun-seekingattitudecontrolsystem,inheritedfromthe Luna-3mission,wascorrectlyactivatedat06:51UTCtoorienttheVostok

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