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Robot Dynamics: Equations and Algorithms

Robot Dynamics: Equationsand AlgorithmsRoy FeatherstoneDepartment of ComputerScienceUniversity of Wales,AberystwythPenglais,AberystwythSY2 33DB,Wales,UKDavid OrinDepartment of ElectricalEngineeringOhioStateUniversity Columbus,OH 43210-1272,USAA bstractThispaper reviewssomeof theaccomplishments inthe eldof Robot dynamicsresearch, fromthedevel-opment of therecursive Newton-Euleralgorithmtothepresent day. Equationsandalgorithmsaregivenforthemost important dynamicscomputations,ex-pressedin a commonnotationto IntroductionMany contributionshave beenmadein theareaofrobot eldof thedynamicsof mecha-nisms,theroboticscommunity hasespeciallyfocusedontheproblemof computationale ciency. Infact,many of themoste cient algorithmsindynamics,thatareapplicableto a wideclassof mechanisms,weredeveloped by roboticsresearchers[23, 33, 10].Whilecomputationale ciencycontinuesto be im-portant forthesimulationandcontrolof increasinglycomplexmechanismsoperatingat higherspeeds,otheraspectsof formulatedwitha compactsetof equationsforeaseof development ,thereshouldbe a clearrelationshipbetweentheseequationsan dtherecur-sive setfromwhich thegreatestcomputationale -ciencyis spatialnotationandspatialoperatoralgebra [11, 29] hasbeenverye ec-tive in ,it is important to developalgorithmswhich have applicability to roboticmech-anismswithgeneralgeometriesa ndjoint [23,33, 10] wereapplica-0c thismaterialis ,permissionto reprint/republishthismaterialforad-verti singor promotionalpurposesor forcreatingnew

static equilibrium and a composite rigid body in mo-tion at the outer end of the chain. Because of the need to solve a linear system of equations whose size grows with N, the algorithm was O(N3). For small N, the rst-order terms dominated the computation so that the result was quite e cient. The earliest known O(N) algorithm for forward dy-

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