... 3$\vee$$\dot{\cdot}$Inthisnetwork,nonlineartransformationwasmadeonlyofcascadeoflinearweightedsummation and sigmoidnonlinearity.Thatis,wedidnotuseanyaprioriknowledgeaboutthedynamicalstructureofthecontrolledobject.Thelearningwentwell and thenetworkhassomeextentofgeneralizationcapability.Inthelearning,westillusedthefeedbacktorquecommandastheerrorsignal.SummaryInordertocontrolvoluntarymovements,thecentralnervoussystemmustsolvethefol-lowingthreecomputationalproblemsatdifferentlevels:(1)determinationofadesiredtrajectoryinthevisualcoordinates,(2)transformationoftrajectoryfromvisualcoordi-natestobodycoordinates and (3)generationofmotorcommand.Basedonphysiologicalinformation and previous models, computationaltheoriesareproposed for thefirsttwoproblems, and ahierarchicalneuralnetworkmodelisintroducedtodealwithmotorcom-mand.Combinationofthesecond and thethirdapproachwasfoundtobeveryefficient for learningtrajectorycontrolofanindustrialroboticmanipulator[14].References[1]Allen,G.I. and Tsukahara,N.(1974).Physiol.Rev.54,957-1006.[2]Atkeson,C.G. and Hollerbach,J.M.(1985).JNeurosci.5,2318-2330.[3]Flash,T. and Hogan,N.(1985).J.Neurosci.5,1688-1703.[4]Fujita,M.(1982).Biol.Cybern.45,195-206.[5]Ito,M.(1970).Intern.J.Neurol.7,162-176.[6]Jordan,M.I. and Rosenbaum,D.A.(1988).COINSTechnicalReport$8\delta- ... k$Trajectoriesderivedfromtheminimumtorque-changemodelarequitedifferentfrom$\backslashi$thoseoftheminimumjerkmodelunderthefollowingbehavioralsituations.(i)Bighor-todeterminetheuniquetrajectorywhichminimizes$C_{T}$.Unoetal.[18]overcamethisdifficultybydevelopinganiterativescheme,sotheuniquetrajectory and theassociatedmotorcommand(torque)canbedeterminedsimultaneously.Thatis,thethreeproblems oftrajectoryformation,coordinatestransformation and generationofmotorcommandare.solvedsimultaneouslybythisalgorithm.Mathematically,theiterativelearningschemecanberegardedasaNewton-like ... J$$\circ,\Omega$$\vee l/7-$$\eta$26NeuralNetwork Models for Formation and ControlofMulti-jointArmTrajectory川人光男MitsuoKawatoATRAuditory and VisualPerceptionResearchLaboratories,Twin21Bldg.MIDTower,Shiromi$2-...