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IEEETRANSACTIONSONROBOTICS,VOL.24,NO.5,OCTOBER20081199RealTimeAdaptiveMotionPlanningRAMPofMobileManipulatorsinDynamicEnvironmentsWithUnforeseenChangesJohnVannoyandJingXiao,SeniorMember,IEEEAbstractThispaperintroducesanovelandgeneralrealtimeadaptivemotionplanningRAMPapproachsuitableforplanningtrajectoriesofhighDOForredundantrobots,suchasmobilemanipulators,indynamicenvironmentswithmovingobstaclesofunknowntrajectories.TheRAMPapproachenablessimultaneouspathandtrajectoryplanningandsimultaneousplanningandexecutionofmotioninrealtime.Itfacilitatesrealtimeoptimizationoftrajectoriesundervariousoptimizationcriteria,suchasminimizingenergyandtimeandmaximizingmanipulability.Italsoaccommodatespartiallyspecifiedtaskgoalsofrobotseasily.Theapproachexploitsredundancyinredundantrobotssuchaslocomotionversusmanipulationinamobilemanipulatorthroughloosecouplingofrobotconfigurationvariablestobestachieveobstacleavoidanceandoptimizationobjectives.TheRAMPapproachhasbeenimplementedandtestedinsimulationoveradiversesetoftaskenvironments,includingenvironmentswithmultiplemobilemanipulators.TheresultsandalsotheaccompanyingvideoshowthattheRAMPplanner,withitshighefficiencyandflexibility,notonlyhandlesasinglemobilemanipulatorwellindynamicenvironmentswithvariousobstaclesofunknownmotionsinadditiontostaticobstacles,butcanalsoreadilyandeffectivelyplanmotionsforeachmobilemanipulatorinanenvironmentsharedbymultiplemobilemanipulatorsandothermovingobstacles.IndexTermsAdaptive,dynamicobstaclesofunknownmotion,loosecoupling,mobilemanipulators,partiallyspecifiedgoal,realtime,redundantrobots,trajectoryoptimization.I.INTRODUCTIONMOTIONPLANNINGisafundamentalprobleminrobotics1,2concernedwithdevisingadesirablemotionforarobottoreachagoal.MotionplanningforhighDOFarticulatedmanipulatorsormobilemanipulatorsismorechallengingthanformobilerobotsbecausethehighdimensionalconfigurationspaceofarobothaslittleornoresemblancetothephysicalspacethattherobotworksin,andhowtoconstructManuscriptreceivedMay16,2007revisedDecember13,2007andMarch5,2008.FirstpublishedOctober10,2008currentversionpublishedOctober31,2008.ThispaperwasrecommendedforpublicationbyAssociateEditorK.YamaneandEditorL.Parkeruponevaluationofthereviewerscomments.ApreliminarypartofthispaperwaspresentedattheIEEEInternationalConferenceonIntelligentRobotsandSystems,Sendai,Japan,2004.TheauthorsarewiththeIntelligent,MultimediaandInteractiveSystemsIMILaboratory,DepartmentofComputerScience,UniversityofNorthCarolinaatCharlotte,Charlotte,NC28223USAemailjmvannoygmail.comxiaouncc.edu.Thispaperhassupplementarydownloadablematerialavailableathttp//ieeexplore.ieee.org,providedbytheauthorsavideoshowingtherealtimeplanningandexecutionofmobilemanipulatormotionbyourRAMPalgorithm.Thisvideois14MBinsize.Colorversionsofoneormoreofthefiguresinthispaperareavailableonlineathttp//ieeexplore.ieee.org.DigitalObjectIdentifier10.1109/TRO.2008.2003277aconfigurationspacehigherthanthreedimensionsefficientlyremainsalargelyunsolvedproblem.A.RelatedResearchonMotionPlanningRandomizedalgorithms,suchasthepopularprobabilisticroadmapPRMmethod3andrapidlyexploringrandomtreeRRTmethod4,arefoundtobeveryeffectiveinfindingacollisionfreepathforarobotwithhighDOFsofflinebecausesuchalgorithmsavoidbuildingtherobotsconfigurationspaceexplicitlybysamplingtheconfigurationspace.ThePRMmethodhasinspiredconsiderableworkonimprovingsamplingandroadmapconstruction2,includingarecentpaper5onproducingcompactroadmapstobettercapturethedifferenthomotopicpathgroups.Bybuildingatreeratherthanagraph,theRRTmethodismoresuitableforgeneratingapathinoneshotorgeneratingatrajectorydirectlyandthusmoresuitableforonlineoperation6.Bothmethodshaveseenmanyvariants2.TherearealsomethodsforpathplanningbasedongeneticalgorithmsGAs,ormorebroadly,evolutionarycomputation7,8,whicharegeneralframeworksofrandomizedsearchsubjecttouserdefinedoptimizationcriteria.Suchoptimizationtechniqueshavebeenusedwidelyandsuccessfullyinmanyapplicationdomains8,9totackleNPhardoptimizationproblems.Therearetwomajorwaysofapplications.Onestraightforwardwayistomapaproblemintotheformsuitableforastandard,offtheshelfGA,solveitbyrunningtheGA,andthen,maptheresultsbacktotheapplicationdomain.ThisonesizefitallapproachisoftennoteffectivebecauseitforcesartificialtransformationofaproblemintosomethingelsethatisconfinedintheformatofastandardGAbutmaylosecertainimportantnatureoftheoriginalproblem.SomeGAbasedpathplanningmethods10,11adoptsuchanapproach,whereCspaceisdiscretizedintoagrid,andapathisintermsofafixedlengthsequenceofgridpoints.AsthestandardGAoperatesonfixedlengthbitstrings,searchisoftenveryslow.Amoreeffectiveapproachistoadoptthegeneralideaofevolutionarycomputationtosolveaprobleminamorenaturalandsuitablerepresentation.Thepathplanningmethodsreportedin12–14belongtosuchacustomizedapproach.Arealtimepathplanningmethodisreportedin12for2DOFpointmobilerobots,whichisextendedin13for3DOFpointflyingrobotswithspecificconstraints.Amultiresolutionpathrepresentationisproposedin14forpathplanning.However,allevolutionaryalgorithmshaveanumberofparametersthatmustbesetappropriately,whichisoftennotatrivialtask.15523098/25.00©2008IEEE1200IEEETRANSACTIONSONROBOTICS,VOL.24,NO.5,OCTOBER2008Unlikepathplanning,motionplanninghastoproduceanexecutabletrajectoryforarobotinconfigurationtimespace,orCTspace,andnotmerelyageometricalpath.Acommonapproachistoconducttrajectoryplanningonthebasisofapathgeneratedbyapathplanner.Anotableframeworkistheelasticstripmethod15,whichcandeformatrajectoryforarobotlocallytoavoidmovingobstaclesinsideacollisionfreetunnelthatconnectstheinitialandgoallocationsoftherobotina3Dworkspace.Suchatunnelisgeneratedfromadecompositionbasedpathplanningstrategy16.Theotherapproachistoconductpathandtrajectoryplanningsimultaneously.However,mosteffortinthiscategoryisfocusedonofflinealgorithmsassumingthattheenvironmentiscompletelyknownbeforehand,i.e.,staticobjectsareknown,andmovingobjectsareknownwithknowntrajectories17–20.Asfordealingwithunknownmovingobstacles,onlyrecentlysomemethodswereintroducedformobilerobots21,22.Thecombinationofmobilityandmanipulationcapabilitymakesamobilemanipulatorapplicabletoamuchwiderrangeoftasksthanafixedbasemanipulatororamobilerobot.Foramobilemanipulator,ataskgoalstateisoftenpartiallyspecifiedaseitheraconfigurationoftheendeffector,whichwecallaplacetoplacetask,oradesiredpathortrajectoryoftheendeffector,whichwecallacontourfollowingtask,andthetargetlocation/pathofthebaseisoftenunspecified.Here,amajorissueofmotionplanningisthecoordinationofthemobilebaseandthemanipulator.Thisissue,asitinvolvesredundancyresolution,presentsbothchallengesandopportunities.Thereexistsarichliteratureaddressingthisissuefrommanyaspects.Someresearcherstreatthemanipulatorandthemobilebasetogetherasaredundantrobotinplanningitspathforplacetoplacetasks23–25.Somefocusedonplanningasequenceofcommutationconfigurationsforthemobilebasewhentherobotwastoperformasequenceoftasks26,27subjecttovariousconstraintsandoptimizationcriteria.Othersfocusedoncoordinatingthecontrolofthemobilebaseandthemanipulatorinacontourfollowingtask28,29bytryingtopositionthemobilebasetomaximizemanipulability.Manyconsiderednonholonomicconstraints.Whilemostoftheexistingworkassumesknownenvironmentswithknownobstaclesforamobilemanipulator,afewresearchersconsideredlocalcollisionavoidanceofunknown,movingobstaclesonline.Onemethod30usedRRTasalocalplannertoupdatearoadmaporiginallygeneratedbyPRMtodealwithmovingobstacles.Forcontourfollowingtasks,anefficientmethod31allowsthebasetoadjustitspathtoavoidamovingobstacleifpossiblewhilekeepingtheendeffectorfollowingacontour,suchasastraightline.Anothermethod29allowedthebasetopauseinordertoletanunexpectedobstaclepasswhilethearmcontinueditscontourfollowingmotionunderaneventbasedcontrolscheme.Othermethodsincludeonebasedonpotentialfield32toavoidunknownobstaclesandonebasedonaneurofuzzycontroller33tomodifythebasemotionlocallytoavoidamovingobstaclestably.Thereisalsoanonlineplannerforthespecialpurposeofplanningthemotionsoftworobotarmsgettingpartsfromaconveyerbelt34.However,wearenotawareofanyexistingworkthatcanplanmotionsofhighDOFrobotsgloballyamongmanyunknowndynamicobstacles.B.OurProblemandApproachPlanninghighDOFrobotmotioninsuchanenvironmentofmanyunknowndynamicobstaclesposesspecialchallenges.First,planninghastobedoneinrealtime,cannotbedoneoffline,andcannotbebasedonacertainprebuiltmapbecausetheenvironmentisconstantlychanginginunforeseenways,i.e.,theconfigurationspaceobstaclesareunknownandchanging.Examplesofsuchenvironmentsincludealargepublicsquarefullofpeoplemovingindifferentways,awarehousefullofbusymovingrobotsandhumanworkers,andsoon.Suchanenvironmentisverydifferentfromstaticorlargelystaticenvironmentsorknowndynamicenvironmentsi.e.,withotherobjecttrajectoriesknown,wheremotionplanningcanreasonablyrelyonexploringCspaceforknownstaticenvironmentsorCTspaceforknowndynamicenvironmentsofflinesuchasbyPRM.Theelasticstripmethodprovidestheflexibilitytomakesmalladjustmentsofarobotmotiontoavoidunknownmotionsofobstacles,iftheunderlyingtopologyoftheCspacedoesnotchange.ForanenvironmentwithchangingCspacetopologyinunknownways,aplannedpath/trajectorycanbeinvalidatedcompletelyatanytime,andthus,realtimeadaptiveglobalplanningcapabilityisrequiredformakingdrasticchangesofrobotmotion.Planningandexecutionofmotionshouldbesimultaneousandbasedonsensingsothatplanninghastobeveryfastandalwaysabletoadapttochangesoftheenvironment.Bynature,totacklemotionplanninginanunknowndynamicenvironmentcannotresultinacompleteplanningalgorithm.Thatis,noalgorithmcanguaranteesuccessinsuchanunknownenvironment.WecanonlystriveforarationalalgorithmthatservesasthebestdriverofahighDOFrobot,buteventhebestdrivercannotguaranteetobeaccidentfreeifotherthingsintheenvironmentarenotunderhis/hercontrol.ThispaperaddressestheproblemofrealtimesimultaneouspathandtrajectoryplanningofhighDOFrobots,suchasmobilemanipulators,performinggeneralplacetoplacetasksinadynamicenvironmentwithobstaclemotionsunknown.Theobstaclemotionscanobstructeitherthebaseorthearmorbothofamobilemanipulator.WeintroduceauniqueandgeneralrealtimeadaptivemotionplanningRAMPapproach.OurRAMPapproachisbuiltuponboththeideaofrandomizedplanningandthatoftheanytime,parallel,andoptimizedplanningofevolutionarycomputation,whileavoidingthedrawbacks.Theresultisauniqueandoriginalapproacheffectivefortheconcernedproblem.TheRAMPapproachhasthefollowingcharacteristics.1WholetrajectoriesarerepresentedatonceinCTspaceandconstantlyimprovedduringsimultaneousplanningandexecution,unlikealgorithmsthatbuildapath/trajectorysequentiallyorincrementallysothatawholepath/trajectorycanbecomeavailableonlyattheendoftheplanningprocess.OuranytimeplannercanprovideavalidtrajectoryquicklyandcontinuetoproducebetterVANNOYANDXIAOREALTIMEADAPTIVEMOTIONPLANNINGRAMPOFMOBILEMANIPULATORSINDYNAMICENVIRONMENTS1201trajectoriesatanylatertimetosuittheneedofrealtimeglobalplanning.2Differentoptimizationcriteriasuchasminimizingenergyandtimeandoptimizingmanipulabilitycanbeaccommodatedflexiblyandeasilyinaseamlessfashion.Optimizationisdonedirectlyintheoriginal,continuousCTspaceratherthanbeingconfinedtoacertainlimitedgraphorroadmap.Trajectoriesareplannedandoptimizeddirectlyratherthanconditionaltotheresultsofpathplanning.3Ourplannerisintrinsicallyparallelwithmultiplediversetrajectoriespresentallthetimetoallowinstant,andifnecessary,drasticadjustmentofrobotmotiontoadapttonewlysensedchangesintheenvironment.Thisisdifferentfromplannerscapableofonlylocaltrajectoryadjustmentbasedonaknownsetofhomotopicpaths.Itisalsodifferentfromsequentialplanners,suchasanytimeAsearch35,whichalsorequiresbuildingadiscretestate–spaceforsearchalimitationthatourplannerdoesnothave.4Trajectorysearchandevaluationofitsoptimalityareconstantlyadaptivetochangesbutbuiltupontheresultsofprevioussearchi.e.,knowledgeaccumulatedtobeefficientforrealtimeprocessing.5Asplanningandexecutioni.e.,robotmotionfollowingtheplannedresultsofararesimultaneous,partiallyfeasibletrajectoriesareallowed,andtherobotmayfollowthefeasiblepartofsuchatrajectoryifitisthecurrentbestandswitchtoabettertrajectorytoavoidtheinfeasiblepart.6Withmultipletrajectoriesfromourplanner,eachtrajectorycanendatadifferentgoallocationinagoalregion,i.e.,partiallyspecifiedgoals,ratherthanasinglegoalconfiguration.7Ourplannerrepresentsatrajectoryforaredundantrobot,suchasamobilemanipulator,aslooselycoupledtrajectoriesofredundantvariablestotakeadvantageoftheredundancyinordertobestachieveobstacleavoidanceandvariousoptimizationobjectives.Therestofthepaperisorganizedasfollows.SectionIIprovidesanoverviewofourRAMPapproachSectionsIIIandIVdescribeproblemrepresentationandinitializationSectionVoutlinesouroptimizationcriteriafortrajectoryevaluationanddescribesthestrategiesforevaluation.SectionsVIandVIIdescribethestrategiestoaltertrajectoriestoproducebetterones.SectionVIIIdescribeshowtheRAMPplannercancreateandpreserveadiversesetoftrajectories.SectionIXprovidesimplementationandexperimentationresultsanddiscussesperformanceoftheplanner.SectionXconcludesthepaper.II.OVERVIEWOFTHERAMPAPPROACHOnebasicpremiseofourapproachisthattheplanningprocessandtheexecutionofmotionareinterweavingtoenablesimultaneousrobotmotionplanningandexecution.ThisisachievedthroughouranytimeplanningalgorithmthatalwaysmaintainsasetofcompletetrajectoriesintheCTspaceoftherobotcalledapopulation.Thefeasibilityandoptimalityofeachtrajectory,calledfitness,isevaluatedthroughanevaluationfunctioncodingtheoptimizationcriteria.Feasibilityreferstocollisionfreeandsingularityfree.Bothinfeasibleandfeasibletrajectoriesareallowedinapopulation.Feasibletrajectoriesareconsideredfitterthaninfeasibletrajectories.Withineachtype,trajectoriesarecomparedforoptimalityinfitness.Theinitialpopulationisacombinationofrandomlygeneratedanddeliberatelyseededtrajectories.Deliberatelyseededtrajectoriesincludeonesconstructedtorepresentdistinctsubpopulationsinordertoachievecertaindiversityinthepopulation.Iftheenvironmentcontainsknownstaticobstacles,trajectoriesbasedonpreplannedfeasiblepathswithrespecttotheknownstaticobstaclescanalsobeincluded.SeeSectionIVformoredetails.Oncetheinitialpopulationisformed,itisthenimprovedtoafitterpopulationthroughiterationsofimprovements,calledgenerations.Ineachgeneration,atrajectoryisrandomlyselectedandalteredbyarandomlyselectedmodificationoperatoramonganumberofdifferentmodificationoperators,andtheresultingtrajectorymaybeusedtoreplaceatrajectorythatisnotthefittesttoformanewgeneration.Thefittesttrajectoryisalwayskeptinthepopulationandcanonlyimprovefromgenerationtogeneration.Eachgenerationisalsocalledaplanningcycle.Toimprovethefitnessoftheinitialpopulation,anumberofinitialplanningcyclesmayberunbasedontheinitialsensinginformationoftheenvironmentbeforetherobotbeginsexecutingthefittesttrajectory.Therobotneednotwaitforafeasibletrajectorytoemergeifnofeasibletrajectoryisavailable,therobotwillbeginmovingalongthefittestinfeasibletrajectorywhilecontinuingthesearchforafitter,andhopefullywilllocateafeasibletrajectorybeforeitcomeswithinadistancethresholdDofthefirstpredictedcollisionorsingularityoftheexecutedtrajectory.Thisstrategymakessensebecause1thepresentlypredictedinfeasibletrajectorymaybecomefeasiblelaterandviceversa2astobedescribedlater,ourplannermakestherobotswitchtoabettertrajectoryifoneisavailable,andthus,beforetheinfeasiblepartofthecurrentlyfollowedtrajectoryisencountered,therobotmayalreadyswitchtoabettertrajectory3thestrategyallowslimitedsensing,inwhichtherobotmaynotsenseanobstacleuntilgettingcloserand4itprovidesameasureofsafetyintrajectoryevaluationseeSectionV.Astherobotmoves,planningcontinuestoimprovethepopulationoftrajectoriesuntilthenextcontrolcycle,whentherobotcanswitchtoafittertrajectorysothatitalwaysfollowsthebesttrajectory.Forthatpurpose,eachtrajectoryisalwaysupdatedtostartfromthecurrentrobotconfigurationwiththecurrentvelocitywhenanewcontrolcyclebegins.Forthetrajectorythatisbeingfollowed,thismeansthattheexecutedportionofthetrajectoryisdroppedfromthetrajectory,whileforeveryothertrajectory,itmeansthatonlythestartingconfigurationandvelocityarechangedtherestoftheknotpointsonthetrajectoryseeSectionIIIremainintact.Notethateachcontrolcycleheredoesnotnecessarilyhavetobeaservocycleofthelowlevelcontroller.Ourcontrolcycle,whichishighlevelforcontrollingtherateofadaptation,canbelongerthanaservocycletoensurethatwithinacontrolcycle,therecanbemorethanoneplanningcycle.Thisisbecauseadaptationisguidedbyplanning.1202IEEETRANSACTIONSONROBOTICS,VOL.24,NO.5,OCTOBER2008Fig.1.Relationshipamongplanning,control,andsensingcycles.Changesinadynamicenvironmentaresensedandfedtotheplannerineachsensingcycle,whichleadtoupdatedfitnessvaluesoftrajectoriesinthesubsequentplanningcycles,andunknownmotionsofmovingobstaclesarepredictedinfitnessevaluationofrobottrajectories.Thepresenceofadiversepopulationofeverimprovingtrajectoriesenablestherobottoquicklyadapttochangesintheenvironment.Itdoessobyfollowingthefittesttrajectoryundereachcircumstancewhenthecurrenttrajectorythattherobotfollowsbecomesworseorcannolongerbefollowedduetoimminentcollisioni.e.,thethresholdDisreached,therobotmaynotneedtostopitsmotionandreplanfromscratchrathertheplanneroftenmerelyneedstoswitchtherobottoafeasibleorbettertrajectoryinthepopulationswiftlyinaseamlessfashion.Thechosentrajectorycanbeofaverydifferenthomotopicgroupfromthepreviousonetodealwithdrasticandlargechanges.InthecasewhentherobotreachesDofthecurrenttrajectorybutfindsnobettertrajectorytoswitchto,itwillstopitsmotionatD,whichiscalledaforcedstop.However,theRAMPplanneri.e.,therobotsthinkingprocessneverstops,anditcontinuestoplanandsearchforabettertrajectoryfortherobot.Therobotresumesitsmotiononceabettertrajectoryisfound.Suchplanning/control/sensingcyclescontinuetointeractandmovetherobottowardagoalconfigurationinthebestpossiblewayinrealtimeimprovingthetrajectoriesitfollowsifthereisnochangeintheenvironment,orbothadaptingandimprovingthetrajectoriesifthereisasensedchange.Fig.1illustratesapossiblerelationshipamongplanning,control,andsensingcyclesnotethattheplanningcyclesactuallyvaryinlength.TheRAMPalgorithmisoutlinedasAlgorithm1.Unlikeanevolutionaryalgorithm,weuserandomselectionandrandommodificationoperatorsthatcannotbecalledmutationoperatorsbecausetheyintroducedrasticratherthansmallchangestocreateadiversepopulationoftrajectoriesreadytoadapttochangingenvironments.OurRAMPalgorithmfurthermaintainsdiversityandpreventshomogeneityinapopulationoftrajectoriesbycreatingandpreservingdistinctsubpopulationsoftrajectoriesasexplainedindetailinSectionVIII.Moreover,theRAMPalgorithmdoesnotneedtuningprobabilitiesaswellasmostotherparametersthatmanyevolutionaryalgorithmsdo.Astheresult,itiseasytoimplementandisrobusttodifferenttaskenvironments.Infact,ouralgorithmonlyneedstodecidetheparameterpopulationsize,butthevaluecanbeinvariantorratherinsensitivetomanydifferentenvironments,aswillbedescribedlaterinSectionVIII.ThefitnessevaluationprocedureofRAMPisalsooriginal,incorporatingmultiplecriteriathatareoftennotconsideredinmanyothermotionplanningalgorithms,andnotonlyfeasiblebutalsoinfeasibletrajectoriesareevaluated.OurRAMPapproachalsosupportsthepartialspecificationofagoalonlytheendeffectorpositionandorientationwithrespecttotheworldcoordinatesystemareneeded.Differenttrajectoriesmayholddifferentgoalbaseconfigurationsandarmconfigurationsthatachievethesameendeffectorgoalinthecaseofmobilemanipulatorssothatredundancyisexploitedtoachieveflexibilityamidenvironmentswithdynamicchanges.ThedetailsoftheRAMPalgorithmarepresentedinthesectionsnext.III.TRAJECTORYREPRESENTATIONWerepresentatrajectoryofamobilemanipulatoruniquelyasapairoflooselycoupledmanipulatorandbasesubtrajectorieswiththefollowingcharacteristics.1Forthemanipulatorsubsystem,apathofknotconfigurationsisspecifiedinthejointspace,basedonwhichacubicsplinedtrajectoryisused.2Forthebasesubsystem,apathofknotconfigurationsisspecifiedintheCartesianspaceoftheworldcoordinate
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