基于状态空间的机械臂轨迹规划

241Vol.24No.1ControlandDecision20091Jan.2009:2007210225;:2008205204.:(60428303);(60675041).:(1977),,,,;(1969),,,,,.:100120920(2009)0120049206,(,200240):,,,.,.,,,.,.:;;;:TP24:ATrajectoryplanningforrobotmanipulatorsbasedonstatespaceXIEWen2long,SUJian2bo(DepartmentofAutomation,ShanghaiJiaotongUniversity,Shanghai200240,China.Correspondent:XIEWen2long,E2mail:[e-mail])Abstract:Thispaperproposesatrajectoryplanningapproachforrobotmanipulatorsbasedonstatespace.Thestatespaceofmanipulatorsystemisdefinedandconstructed,bywhichthereachablescopeofthesystemstateistracedoutaccordingtotheinternalphysicalconstraintsandexternalenvironmentconstraints.Conditionsofperformingthetasksuccessfullyaregiven.Forrealizabletask,theoptimalstrategyfortaskexecutionisobtainedbysearchinginstatespace.Ifthetaskisunrealizable,itcouldbetransformedtobeachievableviaadjustingsystemsconfigurationorconstraint,andthetransformationconditionfortaskrealizationisdeterminedinreconstructedstatespace.Thiscontributestothedesignandplanoftherobotictasks.Point2to2pointtasksfor22linkmanipulatorareinvestigatedandexperimentresultsshowthevalidityoftheproposedmethod.Keywords:Trajectoryplanning;Configurationspace;Statespace;Statetransition1,,.Paul[1],;..Lin[2]3,,n,,.Dissanayake[3],.Saramago[4]B,,.,,.()[5,6],,.:1),,,;2),;3),,.()[7,8],,,,,.,24.,,.,,:1),,;2),,,,..,,,.,.,,.2,,.,,.3:.,,,.,,.,,.,,,(PTP),,.,,,,.,.:1);2).2.1,,,,,.,,.m,mRm,=(1,,m)Rm,iminiimax,i=1,,m.(1)0=(01,,0m),g=(g1,,gm).(2)S,A,A=Ap+Ao+At=iApi+jAoj+kAtk,(3)Ap,AoAt.A,S=AA.A0g.:1).2)Ii(i=1,,m),1m,m-1,[mmin,mmax]Imm,A.,;.3)Im-1m-1,m,m-1.,m-2,.,,,.,,=(x,y,z,,,).(4):x,y,z;,,...,,.1,3,=(x,y,).(5)051::x,y2;2.12.2,,1,.(5),.,,.,Bx=1,By=1,L1=L2=0.5.q1q2x=Bx+L1cosq1+L2cos(q1+q2),y=By+L1sinq1+L2sin(q1+q2),=q1+q2.(6)0qi2(i=1,2),I1=1,I2=2.2(a).2(b)=0,/2,,3/2,4,c,(6)x=C1+L1cosq1,y=C2+L1sinq1.(7):C1,C2,C1=Bx+L2cos(q1+q2)=Bx+L2cosc,C2=By+L2sin(q1+q2)=By+L2sinc.(8)(C1,C2),L1.2,.(CP),,.1,/2SG,S=(1.36,1.86,/2),G=(0.8,1.86,/2),SG=/2.2,S,G,.2.3,,,.3(a),,,3(b).33:1q10,1,q2,,3(b)(1,,1);2q1=/2,q2=0,2,=(1,2,/2),Goal1();,3q1=3/4,q2=0,2,=(0.29,1.71,3/4),Goal1.,.32.4,,0g,.,.,,,A3,D3,Best2First.,,,1524,A3[9].A3^f(n)=^g(n)+^h(n).(9):^g(n)n,^h(n)n,^f(n)n.^g(n)=C(0,n)=ni=1C(i-1,i),(10)^h(n)=(n1-g1)2++(nm-gm)2,(11)C(i-1,i)i-1i.Goal1,0=(1.68,1.68,1.05),g1=(0.66,1.92,2.09),3(a).(),C(i-1,i)=(xi-xi-1)2+(yi-yi-1)2.(12),,(,,).2,,,,3(b).4(a),4(b).4(b).,,,.,.,q1,q2,1(1.43,1.25),r=L2=0.5;,q1,q2,,=q1+q2=3/4,(0.65,1.35),r=40.5,3/4;,q1(q1/2),q2,q2,.3,.,,,,.3.13(a),Goal2,g2=(0.38,1.94,2.44),Goal2,.,.,,,2q3,5(a),=(x,y,,q3).(13)q3[q3min,q3max].q3min=0,q3max=1(q3max,),,0=(1.68,1.68,1.05,0),g2=(0.38,1.94,2.44,0.2).,,.5Qq3max,Q=argmin(q3max),(14)q3maxQ.Q,C(i-1,i)=(xi-xi-1)2+(yi-yi-1)2+[10(qi3-qi-13)]2.(15)251:6q3,q3Q,Q=0.2.,q3q3max0.2,.,.i,ii()=(1,,i-1,i+1,,m);(16)i[ai,bi](),aiibii[ai,bi]()={i()|Sandi[ai,bi]}.(17)5(b)q34[0,0.2]().,,,Goal2,,.3.2,.6(a),0=(1.68,1.68,1.05),g3=(0.36,0.24,3.84).6(b),,,.,.,,.,Bx,=(x,y,,Bx).(18)Bx[Bxmin,Bxmax].Bxmin=0.7,Bxmax=1.3(,Bxmin,Bxmax),0=(1.68,1.68,1.05,1),g3=(0.36,0.24,3.84,1),.QminQmaxBxminBxmax,Qmin=argmax(Bxmin),Qmax=argmin(Bxmax).(19)BxminQminBxmaxQmax.QminQmax,C(i-1,i)=(xi-xi-1)2+(yi-yi-1)2+[10(Bix-Bi-1x)]2.(20)BxQminQmax,Qmin=0.86,Qmax=1.,Bx[0.86,1],.6(c)Bx4[0.86,1]().,,x,,.4,[10].AdeptAdeptOne,4(,).,.3(b),,,(6),.3[11],.7,73524,,.5,,.:1);2).,;,,.,,.(References)[1]PaulRP.Manipulatorcartesianpathcontrol[J].IEEETransonSystem,ManandCybernetics,1979,9(1):7022711.[2]LinCS,ChangPR,LuhJYS.Formulationandoptimizationofcubicpolynomialjointtrajectoriesforindustrialrobots[J].IEEETransonAutomaticControl,1983,28(1):106621073.[3]DissanayakeMWM,GohCJ,PhenthienN.Timeoptimaltrajectoriesforroboticmanipulators[J].Robotica,1991,9(2):1312138.[4]SaramagoSFP,JuniorVS.Optimaltrajectoryplanningofrobotmanipulatorsinthepresenceofmovingobstacles[J].MechanismandMachineTheory,2000,35(8):107921094.[5]PerezTL.Asimplemotion2planningalgorithmforgeneralrobotmanipulators[J].IEEEJofRoboticsandAutomation,1987,3(3):2242238.[6]SunK,LumelskyVJ.Motionplanningforthree2linkrobotarmmanipulatorsoperatinginanunknownthree2dimensionalenvironment[C].Procofthe30thConfonDecisionandControl.Brighton,1991:101921026.[7]AntonelliG,ChiaveriniS,PalladinoM,etal.Cartesianspacemotionplanningforrobots:Anindustrialimplementation[C].The4thIntWorkshoponRobotMotionandControl.Puszczykowo,2004:2792284.[8]XuXR,ChenYB.Amethodfortrajectoryplanningofrobotmanipulatorsincartesianspace[C].Procofthe3rdWorldConfonIntelligentControlandAutomation.Hefei,2000:122021225.[9]NilssonNJ.Artificialintelligence:Anewsynthesis[M].SanFrancisco:MorganKauffmann,1998.[10]ZhangKJ,SuJB.RTOS2basedsoftwarearchitectureformultisensorfusionsystem[C].The5thAsianControlConf.Melbourne,2004:9062913.[11]LinCS,ChangPR,LuhJYS.Formulationandoptimizationofcubicpolynomialjointtrajectoriesforlndustrialrobots[J].IEEETranonAutomaticControl,1983,28(12):106621073.(48)[10],.[J].A,2000,15(3):3052310.(DingYM,FanWT.Discretetimesystemswithrandomlyappliedstochasticperturbations[J].ApplicationMathematicsJofChineseUn