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IEEETRANSACTIONSONROBOTICS,VOL24,NO5,OCTOBER20081199REALTIMEADAPTIVEMOTIONPLANNINGRAMPOFMOBILEMANIPULATORSINDYNAMICENVIRONMENTSWITHUNFORESEENCHANGESJOHNVANNOYANDJINGXIAO,SENIORMEMBER,IEEEABSTRACTTHISPAPERINTRODUCESANOVELANDGENERALREALTIMEADAPTIVEMOTIONPLANNINGRAMPAPPROACHSUITABLEFORPLANNINGTRAJECTORIESOFHIGHDOFORREDUNDANTROBOTS,SUCHASMOBILEMANIPULATORS,INDYNAMICENVIRONMENTSWITHMOVINGOBSTACLESOFUNKNOWNTRAJECTORIESTHERAMPAPPROACHENABLESSIMULTANEOUSPATHANDTRAJECTORYPLANNINGANDSIMULTANEOUSPLANNINGANDEXECUTIONOFMOTIONINREALTIMEITFACILITATESREALTIMEOPTIMIZATIONOFTRAJECTORIESUNDERVARIOUSOPTIMIZATIONCRITERIA,SUCHASMINIMIZINGENERGYANDTIMEANDMAXIMIZINGMANIPULABILITYITALSOACCOMMODATESPARTIALLYSPECIFIEDTASKGOALSOFROBOTSEASILYTHEAPPROACHEXPLOITSREDUNDANCYINREDUNDANTROBOTSSUCHASLOCOMOTIONVERSUSMANIPULATIONINAMOBILEMANIPULATORTHROUGHLOOSECOUPLINGOFROBOTCONFIGURATIONVARIABLESTOBESTACHIEVEOBSTACLEAVOIDANCEANDOPTIMIZATIONOBJECTIVESTHERAMPAPPROACHHASBEENIMPLEMENTEDANDTESTEDINSIMULATIONOVERADIVERSESETOFTASKENVIRONMENTS,INCLUDINGENVIRONMENTSWITHMULTIPLEMOBILEMANIPULATORSTHERESULTSANDALSOTHEACCOMPANYINGVIDEOSHOWTHATTHERAMPPLANNER,WITHITSHIGHEFFICIENCYANDFLEXIBILITY,NOTONLYHANDLESASINGLEMOBILEMANIPULATORWELLINDYNAMICENVIRONMENTSWITHVARIOUSOBSTACLESOFUNKNOWNMOTIONSINADDITIONTOSTATICOBSTACLES,BUTCANALSOREADILYANDEFFECTIVELYPLANMOTIONSFOREACHMOBILEMANIPULATORINANENVIRONMENTSHAREDBYMULTIPLEMOBILEMANIPULATORSANDOTHERMOVINGOBSTACLESINDEXTERMSADAPTIVE,DYNAMICOBSTACLESOFUNKNOWNMOTION,LOOSECOUPLING,MOBILEMANIPULATORS,PARTIALLYSPECIFIEDGOAL,REALTIME,REDUNDANTROBOTS,TRAJECTORYOPTIMIZATIONIINTRODUCTIONMOTIONPLANNINGISAFUNDAMENTALPROBLEMINROBOTICS1,2CONCERNEDWITHDEVISINGADESIRABLEMOTIONFORAROBOTTOREACHAGOALMOTIONPLANNINGFORHIGHDOFARTICULATEDMANIPULATORSORMOBILEMANIPULATORSISMORECHALLENGINGTHANFORMOBILEROBOTSBECAUSETHEHIGHDIMENSIONALCONFIGURATIONSPACEOFAROBOTHASLITTLEORNORESEMBLANCETOTHEPHYSICALSPACETHATTHEROBOTWORKSIN,ANDHOWTOCONSTRUCTMANUSCRIPTRECEIVEDMAY16,2007;REVISEDDECEMBER13,2007ANDMARCH5,2008FIRSTPUBLISHEDOCTOBER10,2008;CURRENTVERSIONPUBLISHEDOCTOBER31,2008THISPAPERWASRECOMMENDEDFORPUBLICATIONBYASSOCIATEEDITORKYAMANEANDEDITORLPARKERUPONEVALUATIONOFTHEREVIEWERS’COMMENTSAPRELIMINARYPARTOFTHISPAPERWASPRESENTEDATTHEIEEEINTERNATIONALCONFERENCEONINTELLIGENTROBOTSANDSYSTEMS,SENDAI,JAPAN,2004THEAUTHORSAREWITHTHEINTELLIGENT,MULTIMEDIAANDINTERACTIVESYSTEMSIMILABORATORY,DEPARTMENTOFCOMPUTERSCIENCE,UNIVERSITYOFNORTHCAROLINAATCHARLOTTE,CHARLOTTE,NC28223USAEMAILJMVANNOYGMAILCOM;XIAOUNCCEDUTHISPAPERHASSUPPLEMENTARYDOWNLOADABLEMATERIALAVAILABLEATHTTP//IEEEXPLOREIEEEORG,PROVIDEDBYTHEAUTHORSAVIDEOSHOWINGTHEREALTIMEPLANNINGANDEXECUTIONOFMOBILEMANIPULATORMOTIONBYOURRAMPALGORITHMTHISVIDEOIS14MBINSIZECOLORVERSIONSOFONEORMOREOFTHEFIGURESINTHISPAPERAREAVAILABLEONLINEATHTTP//IEEEXPLOREIEEEORGDIGITALOBJECTIDENTIFIER101109/TRO20082003277ACONFIGURATIONSPACEHIGHERTHANTHREEDIMENSIONSEFFICIENTLYREMAINSALARGELYUNSOLVEDPROBLEMARELATEDRESEARCHONMOTIONPLANNINGRANDOMIZEDALGORITHMS,SUCHASTHEPOPULARPROBABILISTICROADMAPPRMMETHOD3ANDRAPIDLYEXPLORINGRANDOMTREERRTMETHOD4,AREFOUNDTOBEVERYEFFECTIVEINFINDINGACOLLISIONFREEPATHFORAROBOTWITHHIGHDOFSOFFLINEBECAUSESUCHALGORITHMSAVOIDBUILDINGTHEROBOT’SCONFIGURATIONSPACEEXPLICITLYBYSAMPLINGTHECONFIGURATIONSPACETHEPRMMETHODHASINSPIREDCONSIDERABLEWORKONIMPROVINGSAMPLINGANDROADMAPCONSTRUCTION2,INCLUDINGARECENTPAPER5ONPRODUCINGCOMPACTROADMAPSTOBETTERCAPTURETHEDIFFERENTHOMOTOPICPATHGROUPSBYBUILDINGATREERATHERTHANAGRAPH,THERRTMETHODISMORESUITABLEFORGENERATINGAPATHINONESHOTORGENERATINGATRAJECTORYDIRECTLYANDTHUSMORESUITABLEFORONLINEOPERATION6BOTHMETHODSHAVESEENMANYVARIANTS2THEREAREALSOMETHODSFORPATHPLANNINGBASEDONGENETICALGORITHMSGAS,ORMOREBROADLY,EVOLUTIONARYCOMPUTATION7,8,WHICHAREGENERALFRAMEWORKSOFRANDOMIZEDSEARCHSUBJECTTOUSERDEFINEDOPTIMIZATIONCRITERIASUCHOPTIMIZATIONTECHNIQUESHAVEBEENUSEDWIDELYANDSUCCESSFULLYINMANYAPPLICATIONDOMAINS8,9TOTACKLENPHARDOPTIMIZATIONPROBLEMSTHEREARETWOMAJORWAYSOFAPPLICATIONSONESTRAIGHTFORWARDWAYISTOMAPAPROBLEMINTOTHEFORMSUITABLEFORASTANDARD,OFFTHESHELFGA,SOLVEITBYRUNNINGTHEGA,ANDTHEN,MAPTHERESULTSBACKTOTHEAPPLICATIONDOMAINTHISONESIZEFITALLAPPROACHISOFTENNOTEFFECTIVEBECAUSEITFORCESARTIFICIALTRANSFORMATIONOFAPROBLEMINTOSOMETHINGELSETHATISCONFINEDINTHEFORMATOFASTANDARDGABUTMAYLOSECERTAINIMPORTANTNATUREOFTHEORIGINALPROBLEMSOMEGABASEDPATHPLANNINGMETHODS10,11ADOPTSUCHANAPPROACH,WHERECSPACEISDISCRETIZEDINTOAGRID,ANDAPATHISINTERMSOFAFIXEDLENGTHSEQUENCEOFGRIDPOINTSASTHESTANDARDGAOPERATESONFIXEDLENGTHBITSTRINGS,SEARCHISOFTENVERYSLOWAMOREEFFECTIVEAPPROACHISTOADOPTTHEGENERALIDEAOFEVOLUTIONARYCOMPUTATIONTOSOLVEAPROBLEMINAMORENATURALANDSUITABLEREPRESENTATIONTHEPATHPLANNINGMETHODSREPORTEDIN12–14BELONGTOSUCHACUSTOMIZEDAPPROACHAREALTIMEPATHPLANNINGMETHODISREPORTEDIN12FOR2DOFPOINTMOBILEROBOTS,WHICHISEXTENDEDIN13FOR3DOFPOINTFLYINGROBOTSWITHSPECIFICCONSTRAINTSAMULTIRESOLUTIONPATHREPRESENTATIONISPROPOSEDIN14FORPATHPLANNINGHOWEVER,ALLEVOLUTIONARYALGORITHMSHAVEANUMBEROFPARAMETERSTHATMUSTBESETAPPROPRIATELY,WHICHISOFTENNOTATRIVIALTASK15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