AutonRobot(2006)21:227242DOI10.1007/s10514-005-9717-9AkinematicallycompatibleframeworkforcooperativepayloadtransportbynonholonomicmobilemanipulatorsM.Abou-SamahC.P.TangR.M.BhattV.KroviReceived:5August2005/Revised:25May2006/Accepted:30May2006/Publishedonline:5September2006CSpringerScience+BusinessMedia,LLC2006AbstractInthispaper,weexaminethedevelopmentofakinematicallycompatiblecontrolframeworkforamod-ularsystemofwheeledmobilemanipulatorsthatcanteamuptocooperativelytransportacommonpayload.Eachin-dividuallyautonomousmobilemanipulatorconsistsofadifferentially-drivenWheeledMobileRobot(WMR)withamountedtwodegree-of-freedom(d.o.f)revolute-jointed,planarandpassivemanipulatorarm.Thecompositewheeledvehicle,formedbyplacingapayloadattheend-effectorsoftwo(ormore)suchmobilemanipulators,hasthecapabilitytoaccommodate,detectandcorrectbothinstantaneousandfiniterelativeconfigurationerrors.Thekinematically-compatiblemotion-planning/controlframeworkdevelopedhereisintendedtofacilitatemain-tenanceofallkinematic(holonomicandnonholonomic)constraintswithinsuchsystems.Givenanarbitraryend-effectortrajectory,eachindividualmobile-manipulatorsbi-levelhierarchicalcontrollerfirstgeneratesakinematically-feasibledesiredtrajectoryfortheWMRbase,whichisthentrackedbyasuitablelower-levelposturestabilizingcontroller.Twovariantsofsystem-levelcooperativecon-trolschemesleader-followeranddecentralizedcontrolM.Abou-SamahMSCSoftwareCorporation,AnnArbor,MI48105,USAe-mail:C.P.TangR.M.BhattV.Krovi(envelopeback)MechanicalandAerospaceEngineering,StateUniversityofNewYorkatBuffalo,Buffalo,NY14260,USAe-mail:C.P.Tange-mail:R.M.Bhatte-mail:arethencreatedbasedontheindividualmobile-manipulatorcontrolscheme.Bothmethodsareevaluatedwithinanimple-mentationframeworkthatemphasizesbothvirtualprototyp-ing(VP)andhardware-in-the-loop(HIL)experimentation.Simulationandexperimentalresultsofanexampleofatwo-modulesystemareusedtohighlightthecapabilitiesofareal-timelocalsensor-basedcontrollerforaccommodation,detectionandcorectionofrelativeformationerrors.KeywordsCompositesystem.Hardware-in-the-loop.Mobilemanipulator.Physicalcooperation.Redundancyresolution.Virtualprototyping1IntroductionCooperationhasbeenthekeytosuccessofmosthumanendeavorsandthesimilarincorporationofcooperationinroboticsystemsiscriticaltorealizethenextgenerationofsystemsandapplications.Interestincooperatingsystemsariseswhenthetasksareinherentlytoocomplexforasinglesystemtoaccomplish；orwhenbuildingandusingseveralsimplesystemscanbemoreflexible,fault-tolerantorcheaperthanusingasinglelargesystem.Ourguidingvisionistocreateandevaluateanoverallframeworkforcooperativepayloadtransportusingafleetofsemi-autonomouswheeledmobilemanipulatormodules.Withinthisframeworkweexaminecouplingofvariousmod-ulestocreatealargervariable-topologycomposite-wheeledsystem,withinherentinternalreconfigurabilitytoaccommo-datedisturbancesandenhancepayloadmanipulationcapa-bilities.Theproposedapplicationarenarangesfromindus-trialapplications,wheresuitablenumbersofsuchmodulescanbetaskedtomanipulatevariable-sizedpayloads,toextra-terrestrialapplications,whereindividualrovermodulessentonseparatemissionscancooperatetosupportplanetarySpringer228AutonRobot(2006)21:227242colonizationefforts(Adamsetal.,1996；Juberts,2001；Schenkeretal.,2000).Inoursystem,eachbasicmoduleconsistsofapassive,planar,twodegree-of-freedom(d.o.f.)revolute-jointedma-nipulatormountedonadifferentially-drivenWheeledMo-bileRobot(WMR),asshowninFig.1(a)and(c).Anef-fectivearticulatedcompliantlinkagebetweenthewheeledbasesiscreatedwhenacommonpayloadisplacedontheend-effectorsofmultipleadjacentmodules,asshowninFig.1(b)and(d).Theresultingcompositevehiclenowpos-sesses:(a)theabilitytoaccommodatechangesintherela-tiveconfiguration(byvirtueofthecompliantlinkage)；(b)amechanismfordetectingsuchchanges(usingsensedarticu-lations)；and(c)meanstocompensateforsuchdisturbances(usingtheredundantactuationofthebases),whileperform-ingthepayloadtransporttask.1.1BackgroundOverthemillennia,wheeledplatformdesigns(withmultiplesetsofdiscwheelsattachedtoacommonchassis)havere-mainedpopularinpayloadtransportapplicationssincetheypermittheloadandtractionforcestobedistributedbetweenthemultiplewheels.However,themobility,steerability,andcontrollabilityoftheoverallwheeledsystemdependlargelyuponthetype,natureandlocationsoftheattachedwheels.Theprocessofselectingandattachingthesetofwheelsinamultiple-wheeledsystemcreatesvariouskinematic(holo-nomic/nonholonomic)compatibilityconstraints.Arbitrarilyactuatingsuchwheelscanprecipitateviolationofthecon-straintsandresultindegradationinoverallsystemperfor-mance(Campionetal.,1996).Hence,thedesignandcontrolofsuchvehiclesneedtofirstexplicitlytakeintoaccountthemaintenanceofthekinematiccompatibilityconditions(beforedynamicand/orcontactconditionscanevenbecon-sidered).Mostdesignapproachesconsidertheadditionofactiveorpassivearticulationsbetweenthewheelsandchassistoensurekinematiccompatibility.ThisispertinentsinceweconsiderformationoflargercompositewheeledsystemsbycouplingtogethermultipleindividualWMRswithanar-ticulatedcompliantlinkage.Thisallowssuchsystemstoaccommodatemomentarycontrollererrorswithouttransfer-ringanyinteractionforcesbetweentheWMRs.ExamplesincludetheCLAPPERandtheOMNIMATE(Borensteinetal.,1996),whichfeaturecompliantlinkageswithtwopassiverevolutejointsandonepassiveprismaticjoint.How-ever,thebiggestlimitationoftheCLAPPER/OMNIMATEdesignscomesfromthefactthatthetwoWMRshavetostayassembledtogetherbecauseofthecompliantlinkage.Fig.1CADmodelsofthe(a)individualmodule(b)compositewheeledsystemwiththeircorrespondingphysicalprototypesbelowin(c)and(d)respectivelySpringerAutonRobot(2006)21:227242229Hence,weproposethealternatedevelopmentofacom-positewheeledsystemwithamodularformationoftheartic-ulatedcompliantlinkagebetweenthewheeledbases.Whilewewillfocusthediscussionarounda2-module/payloadcompositesystemfortherestofthepaper,wewouldliketomakesomegeneralobservations.First,ourselectionofthetopologyoftheindividualmobilemanipulatormodulesisguidedbytherequirementformodularity(intermsofeasyattachment/detachmentofmultiplesuchmodulestoacom-monpayloadwhilemaintainingatleastthreed.o.f.withineachsub-chain).Inthislight,wenotethatapassiveplanarfour-barmechanismisformedwhentwosuchmodulesat-tachtoapayloadandthisarticulatedlinkageintroducesmorethantheminimum(three)requiredd.o.f.betweenthebases.However,suchexcessmobilitywithinthearticulatedsuperstructureiseliminatedwhenthemoregeneralcaseofthreeormoremodulesisconsidered.Second,weassumethatthesecondlink(shownasa“flatsupport”inFig.1(a)isrigidlyattachedtothepayload.Itisworthnotingthatavarietyofotherjointsmaybeformedbyrelaxingthisrigidattachmentrequirement；adiscussionofthesealternatives,however,isbeyondthescopeofthispaper.1.2ResearchissuesWeseethatwhilethearticulatedcompliantlinkageresolvestheissueofmaintenanceofcompatibilityconditions,itintro-ducesavarietyofotherchallenges.First,itcreatesholonomic(loopclosure)constraintsthatlimitthed.o.f.Hence,carefulselectionofthetypeandnumberofjointswithinthelinkageaswellastheconfigurationparameters(linklengthsandini-tialpose)iscriticalandtheseaspectsareexaminedelsewhere(Abou-SamahandKrovi,2002；Tang,2004).Further,there-strictionind.o.f.duetotheholonomicconstraintstranslatesintothefactthatnotalljointsneedtobeactuated.These-lectionofthelocationofactiveandpassivejointswithinthecompliantlinkageisyetanotherdesignchoicethatplaysanimportantroleindeterminingthepayloadtransportperfor-mance(TangandKrovi,2004).Theuniquecontributionsofthispapercomefromthedevelopmentandevaluationofcontrolschemesforthecom-positewheeledvehiclethatfacilitatemaintenanceofallkinematic(holonomicandnonholonomic)constraintswithinsuchsystems.Givenanarbitraryend-effectortrajectory,eachindividualmobile-manipulatorsbi-levelhierarchicalcontrollerfirstgeneratesakinematically-feasibledesiredtrajectoryfortheWMRbase,whichisthentrackedbyasuitablelower-levelposturestabilizingcontroller.Whilethemechanicalarticulatedstructurefacilitatesaccommoda-tionofdisturbanceswithinthemobilemanipulators,suchacontrollerensuresthemaintenanceofrelativeconfigura-tionwhiletrackingthedesiredend-effectortrajectory.Thecompositewheeledvehiclecontrollers,builtupfromtheseindividualmobile-manipulatorcontrollers,nowallowforac-commodation,detectionandcorrectionofrelativeformationerrorsandhelpmaintaindesiredformations.Thesesystem-levelcontrollersarealsowell-suitedforonlineimplemen-tationfromtheviewpointofbotheaseofincorporationoflocalsensordataandcomputationalefficiency.Therestofthepaperisorganizedasfollows:Sec-tion2providesabriefsummaryofthepertinentlit-erature.InSection3,wepresentthedevelopmentofthekinematically-compatiblecontrollersfortheindividualmobile-manipulatorsthatcanhelpmaintainadesiredconfig-urationwhiletrackingagivenend-effectormotiontrajectory.InSection4,wederivetwovariantsofsystem-levelcooper-ativecontrolschemesleader-followeranddecentralizedbasedonthecontrollersdevelopedfortheindividualmobilemanipulator.Section5describesthehardwareandsoftwareimplementationframeworkofoursystemwithexperimentalresultspresentedinSection6.Section7concludesthepaperwithadiscussion.2LiteraturesurveyMobilemanipulatorsystemsaretypicallycomposedofaWMRplatformwithone(ormore)mountedmanipulators(Honzik,2000；Seraji,1998；Yamamoto,1994；YamamotoandYun,1994).Whiletrack-,gantry-ormanipulator-basesmaybemodeledandanalyzedeasily,WMRbasesofferspecialchallenges.WMRscannotbestabilizedtoasingleequilibriumpointbyacontinuous(smooth)time-invariantpurestatefeedbacklaw,duetotheviolationofBrockettscondition(Brockett,1981).Hence,themotionplanningandcontrolofsuchWMRsrequiresspecialtreatment(CanudasdeWittetal.,1996；Latombe,1991；LiandCanny,1993；MurrayandSastry,1993).Concomitantlytheclassofnon-holonomicmobilemanipulatorwithsuchbasesrequirescarefulhanding.Further,combiningthemobilityofthebaseplatformandthemountedmanipulatorcreatesredundancy(Seraji,1998；YamamotoandYun,1994).Thedeterminationoftheactu-atorratesforagivenend-effectormotionofaredundantmanipulatoristypicallyanunder-constrainedproblembutessentialformotionplanning/controlofsuchsystems.Mostoftheredundancyresolutionmethodsavailableinthelit-eraturehaveaprincipalunderlyingthemeofoptimizingameasureofperformancebasedonkinematics(orinsomecasesthedynamics)ofthesystem.SeeNakamura(1991)forareviewofthesemethods.Severaloftheseresultshavebeenextendedandap-pliedtomobilemanipulators.Serajis(1998)extensionofWhitneys(1969)approachtokinematicredundancyreso-lutionofmobilemanipulatorshingesonafullyactuatedmanipulatorconfiguration.ThismakesitdifficulttoadaptSpringer230AutonRobot(2006)21:227242thisapproachtoourcase,sinceourmobilemanipulatorpos-sessesamixtureofactiveandpassivejoints.Alternatively,YamamotoandYun(1994)decomposethemotionofthemo-bilemanipulatorintodecoupledWMR-baseandmanipulatorsubsystems.TheWMRisthencontrolledsoastobringthemanipulatortoapreferredconfiguration(usingcriteriasuchasthemanipulabilitymeasure)astheend-effectorperformsavarietyofunknownmanipulationtasks.Thisapproachlendsitselfbettertodecentralizedplanningandcontrol,andwede-velopourcontrollersinthispaperbuildingonthisapproach.Oursituationisonewheretheagentsphysicallyinteractwitheachotherlesserliteratureexistsbutwithconsider-ablevarietyintheirproposedapproaches.Someapproachesemphasizecooperativephysicalmanipulationbyteamsofrelativelysimplepushingmobilerobots(Donaldetal.,1997；KubeandZhang,1997；Spletzeretal.,2001；StilwellandBay,1993；Wangetal.,1994).Khatibetal.(1996)usedadecentralizedcontrolstructureforcooperativetaskswithmobilemanipulationsystems,butwithholonomicbasesandfullyactuatedmanipulators.Othershaveconsidereddevel-opmentofoptimalmotion-planning/controlschemes(DesaiandKumar,1999)andcontrolschemesfornonholonomiccooperatingmobilemanipulatorsgraspingandtransportingpayload(Adamsetal.,1996),includingtheeffectsofflexi-bility(Tanneretal.,1998)butonlyfromacentralizedper-spective.Furthermore,inalmostallcases,thefocusisonafullyactuatedmanipulator,withoutanypassiveorsemi-passivejoints,whichisadominantfeatureinoursystem.Relativelylimitedliteraturediscussesdesign/controlmodi-ficationsintendedtoaidthedecentralizationofcooperationtask,includingapproachesofselectivelocking/unlockingofjoints(Kosugeetal.,1998)and/orspecialmechanicalde-signsofthecouplingsbetweenthemultiplemanipulators(HumberstoneandSmith,2000).3KinematiccontrolInthissection,wepresentthedevelopmentofabi-levelhier-archicalcontrolimplementationthatenforcesthekinematiccompatibilityconditionfortheindividualmobilemanipu-lator.Theimplementationcombinesanupper-leveldesignofthekinematically-compatibledesiredtrajectoriesfortheWMRswhicharethentrackedusingalower-levelposturestabilizationcontroller.3.1ModelingoftheindividualmobilemanipulatorsFigure2depictsadifferentially-drivenWMRwiththebaseofanRRR-manipulator1mountedatthemidpointofthe1Rindicatesrevolutejoint.RRRindicatesseriallink