机器人学基础-第4章-机器人动力学-蔡自兴培训讲学.ppt

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1、机器人学基础-第4章-机器人动力学-蔡自兴2Ch.4ManipulatorDynamicsIntroductionCh.4ManipulatorDynamicsManipulatorDynamicsconsiderstheforcesrequiredtocausedesiredmotion.Consideringtheequationsofmotionarisesfromtorquesappliedbytheactuators,orfromexternalforcesappliedtothemanipulator.2Ch.4ManipulatorD

2、ynamicsTwomethodsforformulatingdynamicsmodel：Newton-EulerdynamicformulationNewton'sequationalongwithitsrotationalanalog,Euler'sequation,describehowforces,inertias,andaccelerationsrelateforrigidbodies,isa"forcebalance"approachtodynamics.LagrangiandynamicformulationLagrangianfor

3、mulationisan"energy-based"approachtodynamics.Ch.4ManipulatorDynamics3Ch.4ManipulatorDynamicsTherearetwoproblemsrelatedtothedynamicsofamanipulatorthatwewishtosolve.ForwardDynamics:givenatorquevector,Τ,calculatetheresultingmotionofthemanipulator,.Thisisusefulforsimulatingthemani

4、pulator.InverseDynamics:givenatrajectorypoint,,findtherequiredvectorofjointtorques,Τ.Thisformulationofdynamicsisusefulfortheproblemofcontrollingthemanipulator.Ch.4ManipulatorDynamics4ContentsIntroductiontoDynamicsRigidBodyDynamicsLagrangianFormulationNewton-EulerFormulatio

5、nArticulatedMulti-BodyDynamics5Ch.4ManipulatorDynamics564.1DynamicsofaRigidBody刚体动力学LangrangianFunctionLisdefinedas:DynamicEquationofthesystem(LangrangianEquation):whereqiisthegeneralizedcoordinates,representcorrespondingvelocity,Fistandforcorrespondingtorqueorforceontheithc

6、oordinate.4.1DynamicsofaRigidBodyKineticEnergyPotentialEnergy64.1.1KineticandPotentialEnergyofaRigidBody7图4.1一般物体的动能与位能4.1DynamicsofaRigidBody4.1DynamicsofaRigidBody78isageneralizedcoordinate①KineticEnergydueto(angular)velocity②KineticEnergyduetoposition(orangle)③DissipationEn

7、ergydueto(angular)velocity④PotentialEnergyduetoposition⑤ExternalForceorTorque4.1.1KineticandPotentialEnergyofaRigidBody4.1DynamicsofaRigidBody①②③④⑤89x0andx1arebothgeneralizedcoordinates4.1.1KineticandPotentialEnergyofaRigidBody4.1DynamicsofaRigidBodyWritteninMatricesform:910Ki

8、neticandPotentialEnergyofa2-linksmanipulatorKineticEnergyK1an