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1、MultibodySystDynDOI10.1007/s11044-007-9097-8Leastactionprinciplesandtheirapplicationtoconstrainedandtask-levelproblemsinroboticsandbiomechanicsVincentDeSapio·OussamaKhatib·ScottDelpReceived:30November2006/Accepted:3October2007©SpringerScience+BusinessMediaB.V.2007AbstractLeastactionprin
2、ciplesprovideaninsightfulstartingpointfromwhichproblemsinvolvingconstraintsandtask-levelobjectivescanbeaddressed.Inthispaper,theprincipleofleastactionisfirsttreatedwithregardtoholonomicconstraintsinmultibodysystems.Avariantofthis,theprincipleofleastcurvatureorstraightestpath,istheninvest
3、igatedinthecontextofgeodesicpathsonconstrainedmotionmanifolds.Subsequently,taskspacedescriptionsareaddressedandtheoperationalspaceapproachisinterpretedintermsofleastaction.Task-levelcontrolisthenappliedtotheproblemofcostminimization.Finally,task-leveloptimizationisformulatedwithrespectt
4、oextremizinganobjectivecriterion,wherethecriterionisinterpretedastheactionofthesystem.Examplesarepresentedwhichillustratetheseapproaches.KeywordsLeastaction·Constraints·Task-levelcontrol·Musculoskeletalsystem·Optimization1IntroductionVariationalprincipleshavesharedarichhistoryinmathemat
5、icsandphysics.Theirefficacyhasbeenparticularlyapparentwithregardtoproblemsinmechanics.Ofspecialimportanceamongvariationalprinciplesareso-calledleastactionprinciples[6,14,20].Thefundamen-talthemeassociatedwiththeseprinciplesisthattheevolutionofadynamicalsystemcanberevealedbyexaminingthest
6、ationaryconditionforanappropriatelydefinedactionintegral.V.DeSapio()·O.KhatibArtificialIntelligenceLaboratory,StanfordUniversity,Stanford,CA94305,USAe-mail:vdesap@robotics.stanford.eduO.Khatibe-mail:khatib@robotics.stanford.eduS.DelpNeuromuscularBiomechanicsLaboratory,StanfordUniversity,
7、Stanford,CA94305,USAe-mail:delp@stanford.eduV.DeSapio,O.Khatib,S.DelpInthefieldofrobotics,therehasbeenmoreinterestinthemultibodyequationsofmo-tionthatresultfromsuchprinciplesthanintheprinciplesthemselves.However,significantinsightcanbederivedbyusingaleastactionprincipleasapointof