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1、700IEEETRANSACTIONSONAUTOMATICCONTROL,VOL.38,NO.5,MAY1993NonholonomicMotionPlanning:SteeringUsingSinusoidsRichardM.Murray,Member,IEEE,andS.ShankarSastry,SeniorMember,IEEEAbstract--Inthispaper,weinvestigatemethodsforsteeringtary:theyinvolvemotionplanning
2、inthepresenceofsystemswithnonholonomicconstraintsbetweenarbitrarycon-nonholonomicornonintegrableconstraints.Thatis,wefigurations.EarlyworkbyBrockettderivestheoptimalcontrolsconsidersystemsinwhichthereareconstraintsontheforasetofcanonicalsystemsinwhichth
3、etangentspacetotheconfigurationmanifoldisspannedbytheinputvectorfieldsandvelocitiesoftherobotswhichcannotbeintegratedtogivetheirfirstorderLiebrackets.UsingBrockett’sresultasmotiva-constraintswhichareexclusivelyafunctionoftheconfig-tion,wederivesuboptima
4、ltrajectoriesforsystemswhicharenoturationvariables.Thesesituationsariseinanumberofincanonicalformandconsidersystemsinwhichittakesmoredifferentwaysandwedescribeafewofthesourcesofthanonelevelofbracketingtoachievecontrollability.Thesetheirorigin:trajectori
5、esusesinusoidsatintegrallyrelatedfrequenciestoachievemotionatagivenbracketinglevel.Wedefineaclassof1)MobileRobotsNavigatinginaClutteredEnvironment:systemswhichcanbesteeredusingsinusoids(chainedsystems)Thekinematicsofthedrivemechanismsofrobotcartsandgive
6、conditionsunderwhichaclassoftwo-inputsystemsresultsinconstraintsontheinstantaneousvelocitiesthatcanbeconvertedintothisform.canbeachieved.Forinstance,acartwithtwoforwarddrivewheelsandtwobackwheelscannotmovesideways.ThiswasfirstpointedoutbyLaumondinthecon
7、textofI.INTRODUCTIONmotionplanningfortheHilaremobilerobot1291,[301.MOTIONplanningforrobotshasarichhistory.The2)MultifngeredHandsManipulatingaGraspedObject:traditionaldifficultyinplanningrobottrajectoriesIfanobjectistwirledthroughacyclicmotionthatreturns
8、istheavoidanceofobstacles,oftenreferredtoasthetheobjecttoitsinitialpositionandorientation,andthepianomover’sproblem,inwhichweattempttomoveanfingersrollwithoutslippingonthesurfaceoftheobject,object(thepiano)throughaclutteredenviro
