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AutonRobot200621227–242DOI10.1007/s1051400597179AkinematicallycompatibleframeworkforcooperativepayloadtransportbynonholonomicmobilemanipulatorsM.AbouSamahC.P.TangR.M.BhattV.KroviReceived5August2005/Revised25May2006/Accepted30May2006/Publishedonline5September2006C©SpringerScienceBusinessMedia,LLC2006AbstractInthispaper,weexaminethedevelopmentofakinematicallycompatiblecontrolframeworkforamodularsystemofwheeledmobilemanipulatorsthatcanteamuptocooperativelytransportacommonpayload.EachindividuallyautonomousmobilemanipulatorconsistsofadifferentiallydrivenWheeledMobileRobotWMRwithamountedtwodegreeoffreedomd.o.frevolutejointed,planarandpassivemanipulatorarm.Thecompositewheeledvehicle,formedbyplacingapayloadattheendeffectorsoftwoormoresuchmobilemanipulators,hasthecapabilitytoaccommodate,detectandcorrectbothinstantaneousandfiniterelativeconfigurationerrors.Thekinematicallycompatiblemotionplanning/controlframeworkdevelopedhereisintendedtofacilitatemaintenanceofallkinematicholonomicandnonholonomicconstraintswithinsuchsystems.Givenanarbitraryendeffectortrajectory,eachindividualmobilemanipulatorsbilevelhierarchicalcontrollerfirstgeneratesakinematicallyfeasibledesiredtrajectoryfortheWMRbase,whichisthentrackedbyasuitablelowerlevelposturestabilizingcontroller.TwovariantsofsystemlevelcooperativecontrolschemesleaderfolloweranddecentralizedcontrolM.AbouSamahMSCSoftwareCorporation,AnnArbor,MI48105,USAemailgishmhotmail.comC.P.TangR.M.BhattV.KrovienvelopebackMechanicalandAerospaceEngineering,StateUniversityofNewYorkatBuffalo,Buffalo,NY14260,USAemailvkrovieng.buffalo.eduC.P.Tangemailchintangeng.buffalo.eduR.M.Bhattemailrmbhatteng.buffalo.eduarethencreatedbasedontheindividualmobilemanipulatorcontrolscheme.BothmethodsareevaluatedwithinanimplementationframeworkthatemphasizesbothvirtualprototypingVPandhardwareintheloopHILexperimentation.Simulationandexperimentalresultsofanexampleofatwomodulesystemareusedtohighlightthecapabilitiesofarealtimelocalsensorbasedcontrollerforaccommodation,detectionandcorectionofrelativeformationerrors.KeywordsCompositesystem.Hardwareintheloop.Mobilemanipulator.Physicalcooperation.Redundancyresolution.Virtualprototyping1IntroductionCooperationhasbeenthekeytosuccessofmosthumanendeavorsandthesimilarincorporationofcooperationinroboticsystemsiscriticaltorealizethenextgenerationofsystemsandapplications.Interestincooperatingsystemsariseswhenthetasksareinherentlytoocomplexforasinglesystemtoaccomplishorwhenbuildingandusingseveralsimplesystemscanbemoreflexible,faulttolerantorcheaperthanusingasinglelargesystem.Ourguidingvisionistocreateandevaluateanoverallframeworkforcooperativepayloadtransportusingafleetofsemiautonomouswheeledmobilemanipulatormodules.Withinthisframeworkweexaminecouplingofvariousmodulestocreatealargervariabletopologycompositewheeledsystem,withinherentinternalreconfigurabilitytoaccommodatedisturbancesandenhancepayloadmanipulationcapabilities.Theproposedapplicationarenarangesfromindustrialapplications,wheresuitablenumbersofsuchmodulescanbetaskedtomanipulatevariablesizedpayloads,toextraterrestrialapplications,whereindividualrovermodulessentonseparatemissionscancooperatetosupportplanetarySpringer228AutonRobot200621227–242colonizationeffortsAdamsetal.,1996Juberts,2001Schenkeretal.,2000.Inoursystem,eachbasicmoduleconsistsofapassive,planar,twodegreeoffreedomd.o.f.revolutejointedmanipulatormountedonadifferentiallydrivenWheeledMobileRobotWMR,asshowninFig.1aandc.Aneffectivearticulatedcompliantlinkagebetweenthewheeledbasesiscreatedwhenacommonpayloadisplacedontheendeffectorsofmultipleadjacentmodules,asshowninFig.1bandd.Theresultingcompositevehiclenowpossessesatheabilitytoaccommodatechangesintherelativeconfigurationbyvirtueofthecompliantlinkagebamechanismfordetectingsuchchangesusingsensedarticulationsandcmeanstocompensateforsuchdisturbancesusingtheredundantactuationofthebases,whileperformingthepayloadtransporttask.1.1BackgroundOverthemillennia,wheeledplatformdesignswithmultiplesetsofdiscwheelsattachedtoacommonchassishaveremainedpopularinpayloadtransportapplicationssincetheypermittheloadandtractionforcestobedistributedbetweenthemultiplewheels.However,themobility,steerability,andcontrollabilityoftheoverallwheeledsystemdependlargelyuponthetype,natureandlocationsoftheattachedwheels.Theprocessofselectingandattachingthesetofwheelsinamultiplewheeledsystemcreatesvariouskinematicholonomic/nonholonomiccompatibilityconstraints.ArbitrarilyactuatingsuchwheelscanprecipitateviolationoftheconstraintsandresultindegradationinoverallsystemperformanceCampionetal.,1996.Hence,thedesignandcontrolofsuchvehiclesneedtofirstexplicitlytakeintoaccountthemaintenanceofthekinematiccompatibilityconditionsbeforedynamicand/orcontactconditionscanevenbeconsidered.Mostdesignapproachesconsidertheadditionofactiveorpassivearticulationsbetweenthewheelsandchassistoensurekinematiccompatibility.ThisispertinentsinceweconsiderformationoflargercompositewheeledsystemsbycouplingtogethermultipleindividualWMRswithanarticulatedcompliantlinkage.ThisallowssuchsystemstoaccommodatemomentarycontrollererrorswithouttransferringanyinteractionforcesbetweentheWMRs.ExamplesincludetheCLAPPERandtheOMNIMATEBorensteinetal.,1996,whichfeaturecompliantlinkageswithtwopassiverevolutejointsandonepassiveprismaticjoint.However,thebiggestlimitationoftheCLAPPER/OMNIMATEdesignscomesfromthefactthatthetwoWMRshavetostayassembledtogetherbecauseofthecompliantlinkage.Fig.1CADmodelsoftheaindividualmodulebcompositewheeledsystemwiththeircorrespondingphysicalprototypesbelowincanddrespectivelySpringerAutonRobot200621227–242229Hence,weproposethealternatedevelopmentofacompositewheeledsystemwithamodularformationofthearticulatedcompliantlinkagebetweenthewheeledbases.Whilewewillfocusthediscussionarounda2module/payloadcompositesystemfortherestofthepaper,wewouldliketomakesomegeneralobservations.First,ourselectionofthetopologyoftheindividualmobilemanipulatormodulesisguidedbytherequirementformodularityintermsofeasyattachment/detachmentofmultiplesuchmodulestoacommonpayloadwhilemaintainingatleastthreed.o.f.withineachsubchain.Inthislight,wenotethatapassiveplanarfourbarmechanismisformedwhentwosuchmodulesattachtoapayloadandthisarticulatedlinkageintroducesmorethantheminimumthreerequiredd.o.f.betweenthebases.However,suchexcessmobilitywithinthearticulatedsuperstructureiseliminatedwhenthemoregeneralcaseofthreeormoremodulesisconsidered.Second,weassumethatthesecondlinkshownasaflatsupportinFig.1aisrigidlyattachedtothepayload.Itisworthnotingthatavarietyofotherjointsmaybeformedbyrelaxingthisrigidattachmentrequirementadiscussionofthesealternatives,however,isbeyondthescopeofthispaper.1.2ResearchissuesWeseethatwhilethearticulatedcompliantlinkageresolvestheissueofmaintenanceofcompatibilityconditions,itintroducesavarietyofotherchallenges.First,itcreatesholonomicloopclosureconstraintsthatlimitthed.o.f.Hence,carefulselectionofthetypeandnumberofjointswithinthelinkageaswellastheconfigurationparameterslinklengthsandinitialposeiscriticalandtheseaspectsareexaminedelsewhereAbouSamahandKrovi,2002Tang,2004.Further,therestrictionind.o.f.duetotheholonomicconstraintstranslatesintothefactthatnotalljointsneedtobeactuated.TheselectionofthelocationofactiveandpassivejointswithinthecompliantlinkageisyetanotherdesignchoicethatplaysanimportantroleindeterminingthepayloadtransportperformanceTangandKrovi,2004.Theuniquecontributionsofthispapercomefromthedevelopmentandevaluationofcontrolschemesforthecompositewheeledvehiclethatfacilitatemaintenanceofallkinematicholonomicandnonholonomicconstraintswithinsuchsystems.Givenanarbitraryendeffectortrajectory,eachindividualmobilemanipulatorsbilevelhierarchicalcontrollerfirstgeneratesakinematicallyfeasibledesiredtrajectoryfortheWMRbase,whichisthentrackedbyasuitablelowerlevelposturestabilizingcontroller.Whilethemechanicalarticulatedstructurefacilitatesaccommodationofdisturbanceswithinthemobilemanipulators,suchacontrollerensuresthemaintenanceofrelativeconfigurationwhiletrackingthedesiredendeffectortrajectory.Thecompositewheeledvehiclecontrollers,builtupfromtheseindividualmobilemanipulatorcontrollers,nowallowforaccommodation,detectionandcorrectionofrelativeformationerrorsandhelpmaintaindesiredformations.Thesesystemlevelcontrollersarealsowellsuitedforonlineimplementationfromtheviewpointofbotheaseofincorporationoflocalsensordataandcomputationalefficiency.TherestofthepaperisorganizedasfollowsSection2providesabriefsummaryofthepertinentliterature.InSection3,wepresentthedevelopmentofthekinematicallycompatiblecontrollersfortheindividualmobilemanipulatorsthatcanhelpmaintainadesiredconfigurationwhiletrackingagivenendeffectormotiontrajectory.InSection4,wederivetwovariantsofsystemlevelcooperativecontrolschemesleaderfolloweranddecentralized–basedonthecontrollersdevelopedfortheindividualmobilemanipulator.Section5describesthehardwareandsoftwareimplementationframeworkofoursystemwithexperimentalresultspresentedinSection6.Section7concludesthepaperwithadiscussion.2LiteraturesurveyMobilemanipulatorsystemsaretypicallycomposedofaWMRplatformwithoneormoremountedmanipulatorsHonzik,2000Seraji,1998Yamamoto,1994YamamotoandYun,1994.Whiletrack,gantryormanipulatorbasesmaybemodeledandanalyzedeasily,WMRbasesofferspecialchallenges.WMRscannotbestabilizedtoasingleequilibriumpointbyacontinuoussmoothtimeinvariantpurestatefeedbacklaw,duetotheviolationofBrockettsconditionBrockett,1981.Hence,themotionplanningandcontrolofsuchWMRsrequiresspecialtreatmentCanudasdeWittetal.,1996Latombe,1991LiandCanny,1993MurrayandSastry,1993.Concomitantlytheclassofnonholonomicmobilemanipulatorwithsuchbasesrequirescarefulhanding.Further,combiningthemobilityofthebaseplatformandthemountedmanipulatorcreatesredundancySeraji,1998YamamotoandYun,1994.Thedeterminationoftheactuatorratesforagivenendeffectormotionofaredundantmanipulatoristypicallyanunderconstrainedproblembutessentialformotionplanning/controlofsuchsystems.Mostoftheredundancyresolutionmethodsavailableintheliteraturehaveaprincipalunderlyingthemeofoptimizingameasureofperformancebasedonkinematicsorinsomecasesthedynamicsofthesystem.SeeNakamura1991forareviewofthesemethods.Severaloftheseresultshavebeenextendedandappliedtomobilemanipulators.Serajis1998extensionofWhitneys1969approachtokinematicredundancyresolutionofmobilemanipulatorshingesonafullyactuatedmanipulatorconfiguration.ThismakesitdifficulttoadaptSpringer230AutonRobot200621227–242thisapproachtoourcase,sinceourmobilemanipulatorpossessesamixtureofactiveandpassivejoints.Alternatively,YamamotoandYun1994decomposethemotionofthemobilemanipulatorintodecoupledWMRbaseandmanipulatorsubsystems.TheWMRisthencontrolledsoastobringthemanipulatortoapreferredconfigurationusingcriteriasuchasthemanipulabilitymeasureastheendeffectorperformsavarietyofunknownmanipulationtasks.Thisapproachlendsitselfbettertodecentralizedplanningandcontrol,andwedevelopourcontrollersinthispaperbuildingonthisapproach.Oursituationisonewheretheagentsphysicallyinteractwitheachotherlesserliteratureexistsbutwithconsiderablevarietyintheirproposedapproaches.SomeapproachesemphasizecooperativephysicalmanipulationbyteamsofrelativelysimplepushingmobilerobotsDonaldetal.,1997KubeandZhang,1997Spletzeretal.,2001StilwellandBay,1993Wangetal.,1994.Khatibetal.1996usedadecentralizedcontrolstructureforcooperativetaskswithmobilemanipulationsystems,butwithholonomicbasesandfullyactuatedmanipulators.Othershaveconsidereddevelopmentofoptimalmotionplanning/controlschemesDesaiandKumar,1999andcontrolschemesfornonholonomiccooperatingmobilemanipulatorsgraspingandtransportingpayloadAdamsetal.,1996,includingtheeffectsofflexibilityTanneretal.,1998butonlyfromacentralizedperspective.Furthermore,inalmostallcases,thefocusisonafullyactuatedmanipulator,withoutanypassiveorsemipassivejoints,whichisadominantfeatureinoursystem.Relativelylimitedliteraturediscussesdesign/controlmodificationsintendedtoaidthedecentralizationofcooperationtask,includingapproachesofselectivelocking/unlockingofjointsKosugeetal.,1998and/orspecialmechanicaldesignsofthecouplingsbetweenthemultiplemanipulatorsHumberstoneandSmith,2000.3KinematiccontrolInthissection,wepresentthedevelopmentofabilevelhierarchicalcontrolimplementationthatenforcesthekinematiccompatibilityconditionfortheindividualmobilemanipulator.TheimplementationcombinesanupperleveldesignofthekinematicallycompatibledesiredtrajectoriesfortheWMRswhicharethentrackedusingalowerlevelposturestabilizationcontroller.3.1ModelingoftheindividualmobilemanipulatorsFigure2depictsadifferentiallydrivenWMRwiththebaseofanRRRmanipulator1mountedatthemidpointofthe1Rindicatesrevolutejoint.RRRindicatesseriallinkagesconnectedbythreerevolutejoints.Fig.2Schematicdiagramofa3linkmobilemanipulatorwheelaxle.Theframe{M}isrigidlyattachedtotheWMRwiththeXaxisorientedinthedirectionoftheforwardtravel.Frames{1},{2}and{3}arerigidlyattachedattheproximalendsofthefirst,secondandthirdlink,respectively.Frame{E}isattachedattheendeffectoroftheplanarmanipulator.Theconfigurationofthemanipulatorcanbeparameterizedbythreerelativeanglesofθ1,θ2andθ3.ThelengthsofthemanipulatorlinksareL1,L2andL3,respectively,orderedfromthebase.TheconfigurationoftheWMRcanbedescribedbythepositionXM,YMandtheorientationφMofframe{M}withrespecttotheglobalframe{F}.Theforwardkinematicsofthelocationofframe{E}withrespecttoframe{F}canbewrittenasbracketleftbiggXEYEbracketrightbiggbracketleftbiggXMYMbracketrightbiggbracketleftbiggcosφM−sinφMsinφMcosφMbracketrightbiggbracketleftBiggL1cosθ1L2cosθ12L3cosθ123L1sinθ1L2sinθ12L3sinθ123bracketrightBiggTheta1EφMθ1231whereθ12...nθ1θ2θn.3.2UpperleveldesiredtrajectorycreationforkinematiccompatibilityInthisapproach,anarbitrarydesiredtrajectoryisspecifiedfortheendeffectorofeachmobilemanipulator{E}.Foragivendesiredmanipulatorconfiguration,thisallowscomputationofthecorrespondingdesiredtrajectoryforthereferenceframe{1},fixedrigidlytothefirstmanipulatorlink.Ingeneral,thecomputeddesiredtrajectoriesfor{1}tendtobeunsuitablefortheframe{M}whichiscollocatedbutWMRfixedsincetheymaynotsatisfythenonholonomicconstraintsoftheWMR.However,wetakeadvantageoftheSpringer
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