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ID:40057631
大小:412.07 KB
页数:6页
时间:2019-07-18
《Conditions for symmetric running in single- and d...》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、ConditionsforSymmetricRunninginSingle-andDouble-SupportKennethY.GoldbergandMarcH.RaibertDepartmentofComputerScienceandtheRoboticsInstituteCarnegie-MellonUniversity,Pittsburgh,PA.15213ABSTRACT2.ReviewofSymmetryEvenandoddfunctionsoftime-symmetricfunctions-Motivationforsymmetryinrunning
2、comesfromcon-havebeenusedtosimpliiythecontrolofrunningrobotssideringtherequirementsforsteady-state.Insteady-andhavebeenobservedinthebodyandlegmotionofstate,thenetaccelerationofthesystemoveranentirerunninganimals.Thispaperexplorestherelationshipbe-strideiszero.Thereisnoforwardaccelera
3、tionduringtweensymmetricmotionofthebodyandsymmetricusetheflightphaseifweassumenegligibleairresistance,soofthelegsinthreeplanarmodels.Thealgebraofsym-theaccelerationduringstancemustintegratetozerometricfunctionsisappliedtotheequationsofmotiontoshowthatsymmetriclegactuationisrequiredfo
4、rsym-fxdt=0.(1)metricbodymotioninthesingle-supportcase,butnotinJthedouble-supportcaseunlessadditionalconstraintsarestrideimposed.wherefxistheforwardforceactingonthebody.Ifthetimeoriginisdefinedsothatt=0midwaythroughthestancephaseandiffxisanoddfunctionoftime,fx(t)=-fz(-t),then(1)issat
5、isfied-theintegralofan1.Introductionoddfunctionoversymmetriclimitsiszero.Therearemanypatternsofmotionaleggedsystemcanusetopropelitselfforwardinsteady-statetravel.Oneinterestingclassofsuchpatternsisthesymmetricmotions.Whenmotionofthebodythroughspaceisde-scribedbyappropriateevenandoddf
6、unctionsoftime,thebodyexperienceszeroaverageaccelerationinthefor-ward,vertical,andangulardirections.Thesekindsofsymmetricmotionshavebeenusedtocontrolthebehav-iorofleggedrobots(Raibert1986a),anddatafroman-imalssuggestthattheysometimesrunwithsymmetricmotion(Hildebrand1966,1976;Raibert1
7、986b,1986~).Inthispaperweexplorethenecessityofsymmet-ricmotionforsimpleleggedmodels.Themodelsassumemasslesslegs,mechanicallysymmetricbodies,andmotionFigure1:Symnletricrunning.Theleft-mostdrawingshowsrestrictedtothesagittalplane.Themainfindingisthatthesystematthepointoftouchdown;thece
8、nterdrawingi
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