Robot_Motion_Planning.pdf

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1、RobotMotionPlanningGaneshSwaminathanSchoolofEngineeringScienceSimonFraserUniversity,Canadagswamina@sfu.caFebruary27,20061IntroductionMotionplanningisafundamentalprobleminrobotics.Theclassicpathplanningproblemisdescribedasthefollowing:givenathreedimensionalrigidbodyandaknownsetofobstacle

2、s,thetaskisto¯ndacollision-freepathfromastartcon¯gurationtoagoalcon¯guration.Additionally,thistaskistobecompletedinareasonableamountoftime.Thisisknownasthepianomover'sproblem[1].Amoregeneralscenario,knownasthegeneralizedmover'sproblemwouldhavetherobotas°exiblepolyhedrawithmovingpolyhedr

3、alobstacles.Thisreportwillreviewclassicalmotionplanningparadigms-potential¯eldmethods,roadmapmethodssuchasvisibilitygraphmethodsandprobabilisticroadmaps.Moreemphasiswillbeplacedonroadmapsasthistechniquehasshownpromisingresultsforcomplicatedrobotplanningproblems.Actionsinthephysicalworld

4、aresubjecttophysicallaws,uncertainityandgeometricconstraints.Thedesignandanalysisofmotionplanningalgorithmsraisesquestionsinanumberof¯elds-mechanics,controltheory,computationalanddi®erentialgeometry,andcomputerscience.Thisreportwillonlyconsiderthesimpli¯edgeometricproblemandassuchignore

5、issuessuchasincompleteinformation,nonholonomicconstraints.movinganddeformableobjects,multiplerobotsandcontrolrelatedissues.1.1Mathematicalde¯nitionsBeforewecangoonwiththereviewonmotionplanning,itisinstructionaltoestablishauniformmathematicnotation.Thenotationfollowedinthisreportisthesam

6、easin[2].Thecon¯gurationspaceQisde¯nedasthesetofallcon¯gurationsarobotcanachieve.Thisspaceisgenerallynon-Euclidean.Thedimensionofthisspaceisequaltothenumberofdegreesoffreedomintherobot.Forexample,arigidbodyinthreedimensionshassixdegreesoffreedom-threefortheposition(x,y,z)andthreefortheo

7、rientation(roll-yaw-pitch).Qfreeisde¯nedasthesetofrobotcon¯gurationsthatdonotinteresectanobstacle.Aparticularcon¯gurationfromthisspaceisde¯nedasq.2PotentialFieldMethodPotential¯eldmethodswere¯rstdescribedbyKhatib[3]foron-linecollisionavoidanceforarobotwithproximitysensors.Thisa