基于李群李代数的统一开闭环机械多体系统递推动力学研究

南京航空航天大学博士学位论文基于李群李代数的统一开闭环机械多体系统递推动力学研究姓名：邵兵申请学位级别：博士专业：机械电子工程指导教师：吴洪涛2010-04IO(N)SimMechanicsO(N3)O(N)IIBennettMathematicaVB.NET.NETLINKMathematicaMatlabCS-FunctionMathematicaMatlabStanfordPIDIIIAbstractWiththedevelopmentofmodernscienceandtechnologyengineeringobjectswhichcomposedalargenumberofobjectshaveemerged.Newmethodsareneededtostudyvariouscomplexmechanicalsystems,suchasvehicles,serialandparallelmechanisms,robots,aviationandspaceflights.TheaimofMulti-bodysystemdynamicsistoresearchtheforward,reverse,andhybridproblemsoflarge-scalesystems.Itcontainsthedynamicalproblemsofrigidbodymechanics,analyticalmechanics,computa-tionalmechanics,materialmechanicsandbio-mechanics.Multi-bodysystemdynamicsisorientedtotheareasofaerospaceengineering,mechanicalengineeringandautomobile,bionicartificiallimbs.Itisahigh-technologydisciplineaftermanyyearsofpracticalapplication.Aunifiedrecursivemulti-bodydynamicstheory,algorithmsandapplicationsofopenandclosedloopmechanicalsystemsarestudiedinthispaper.Itaimsatfastandefficientrecursivemodeling,optimization-baseddesignandsimulationofdynamiccontrolproblemsofmulti-bodysystems.Itcontainstheproblemsofcomparingandselectingofmodelingmethod,serialsystemsexpandingtotreetopologysystems,freeflyingsystemsandthesystemswithactiveandpassivejoints,therecur-siveclosed-loopsystemdynamicsandtheefficientflexiblemulti-bodydynamics.Thesoftwaresys-temsandcontrolsimulationofsuchproblemsaredescribed.First,adetailedcomparisonbetweenthreeclassicO(N)recursivedynamicsmethodsofspatialop-eratoralgebramethod,articulatedbodyinertiamethodandLieGroupsandLiealgebraicmethodisinvestigated.Fromthecorealgorithmofthebasictheoryandrecursiveprocessofinverseandforwarddynamics,itcanbeconcludedthatthesemethodsusedifferentprinciplesreachingtheformationsofefficientrecursivedynamicsalgorithms.Screwtheoryisthefundamentaltoformahighlyefficientrecursivedynamics.ComparingwiththeresultsofdynamicalsoftwareSimMechanics,itcanbeveri-fiedthecorrectnessofthealgorithm.Thetheoreticalcalculationisstudiedfromtheadditionandmul-tiplicationtimesrequiredfortherecursivealgorithm.Theactualcomputationtimearecomparedbe-tweentheO(N3)methodsandO(N)method.Thenonthebasisofchainsystems,recursivedynamicsdescribedofLiegroupsandLiealgebrasareextendedtotreetopologysystems,freeflyingsystemsandthesystemswithactiveandpassivejoints.Basedonnaturalorthogonalcomplementanddecouplingofnaturalorthogonalcomplement,therecursivedynamicsfortheclosedloopsystemsarediscussed.Gaussianeliminationmethodisusedtosolvetheinverseandforwarddynamicalproblems.Dynamicsmethodbasedonsix-barpresseswereoptimized.IVThefinitesegmentandthefiniteelementmodelareinvestigatedtosolvetheflexiblemulti-bodysystem.Combinedwithrecursivedynamicsalgorithmpresentedearlier,arecursivefinitesegmentmethodforflexiblemulti-bodysystemdynamicsisstudied.Twotypesofspacedeployablemecha-nisms–thehingeddeployablemechanismandthree-dimensionaldeployablemechanismareanalyzed.Thedeployingprocessofonesatelliteantennamodelisgiven.Thethree-dimensionaldeployablemechanismsbasedonBennettarediscussed.Dynamicalsimulationresultsofplanefour-barlinkageandspatialfour-barlinkagearegiven.Atlast,threepartsisproposedtosolvemulti-bodysystemdynamicssimulationprogramdesignandcontrolproblems.Mathematicasymbolicanalysissoftwareisusedtoestablishthesystemofsym-bolicalmodel.ByNETLINKofVB.NET,theuserinterfaceachievesaseamlessconnectionwithMathematica.WithMatlab,theprogramtoachievenumericalcalculation,simulationandcontrolisdeveloped.ByautomaticallyprogrammingCcodeandS-Function,MathematicaandMatlabarecon-nectedtogether.Discussesaremadetothedynamics-basedcontrolalgorithm.ThesimulationresultsaregivencomparingthePIDcontrolmethodandforce/displacementhybridcontrollawforaspace-floatingStanfordrobot.Keywords:MechanicalMulti-bodySystems,Dynamics,Recursive,LieGroupsandLieAlgebras,ClosedLoop,ForceControlVIII1.1.......................................................................................................................21.2...............................................................................................................................21.3....................................................................................................................21.4...........................................................................................................................32.1..............................................................................................................................182.2..............................................................................................................................212.3..............................................................................................................................252.4......................................................................................................................272.5SIMMECHANICS......................................................312.6O(N3)O(N)............................................................................3