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1、RobotMotionPlanningGaneshSwaminathanSchoolofEngineeringScienceSimonFraserUniversity,Canadagswamina@sfu.caFebruary27,20061IntroductionMotionplanningisafundamentalprobleminrobotics.Theclassicpathplanningproblemisdescribedasthefollowing:givenathreedimensionalrigidbodyandaknownsetofobstacle
2、s,thetaskistoˉndacollision-freepathfromastartconˉgurationtoagoalconˉguration.Additionally,thistaskistobecompletedinareasonableamountoftime.Thisisknownasthepianomover'sproblem[1].Amoregeneralscenario,knownasthegeneralizedmover'sproblemwouldhavetherobotas°exiblepolyhedrawithmovingpolyhedr
3、alobstacles.Thisreportwillreviewclassicalmotionplanningparadigms-potentialˉeldmethods,roadmapmethodssuchasvisibilitygraphmethodsandprobabilisticroadmaps.Moreemphasiswillbeplacedonroadmapsasthistechniquehasshownpromisingresultsforcomplicatedrobotplanningproblems.Actionsinthephysicalworld
4、aresubjecttophysicallaws,uncertainityandgeometricconstraints.Thedesignandanalysisofmotionplanningalgorithmsraisesquestionsinanumberofˉelds-mechanics,controltheory,computationalanddi?erentialgeometry,andcomputerscience.Thisreportwillonlyconsiderthesimpliˉedgeometricproblemandassuchignore
5、issuessuchasincompleteinformation,nonholonomicconstraints.movinganddeformableobjects,multiplerobotsandcontrolrelatedissues.1.1MathematicaldeˉnitionsBeforewecangoonwiththereviewonmotionplanning,itisinstructionaltoestablishauniformmathematicnotation.Thenotationfollowedinthisreportisthesam
6、easin[2].TheconˉgurationspaceQisdeˉnedasthesetofallconˉgurationsarobotcanachieve.Thisspaceisgenerallynon-Euclidean.Thedimensionofthisspaceisequaltothenumberofdegreesoffreedomintherobot.Forexample,arigidbodyinthreedimensionshassixdegreesoffreedom-threefortheposition(x,y,z)andthreefortheo
7、rientation(roll-yaw-pitch).Qfreeisdeˉnedasthesetofrobotconˉgurationsthatdonotinteresectanobstacle.Aparticularconˉgurationfromthisspaceisdeˉnedasq.2PotentialFieldMethodPotentialˉeldmethodswereˉrstdescribedbyKhatib[3]foron-linecollisionavoidanceforarobotwithproximitysensors.Thisa
