基于阿克曼原理的车式移动机器人运动学建模

46Vo.l4.6200912CAAITransactionsonIntelligentSystemsDec.2009do:i10.3969/.jissn.16734785.2009.06.011任孝平,蔡自兴(中南大学信息科学与工程学院,湖南长沙410083):.,.,.,,.:;;;:TP242.6:A:16734785(2009)06053404UsingtheAckermanprincipleforkinematicmodelingofwheeledmobilerobotsRENXiaoping,CAIZixing(SchoolofInformationScience&Engineering,CentralSouthUniversity,Changsha410083,China)Abstract:ApplyingtheAckermanprincipletokinematicmodelingofwheeledmobilerobotsisofvitalimportanceforimprovingtheperformanceofunmannedautonomousvehicles.Thekinematiccharacteristicsofwheeledmobilerobotswereanalyzedinthispaper,andakinematicmodelwassetupthatdidnotconsiderslidingorbraking.TheAckermanprinciplewasthenintroducedtothiskinematicmode.lMathematicalformulaswereproposedforturningangle,steeringangleandturningradius.Theseaccuratelyreflectthemovementstatusofthemobilerobo,tprovidingatheoreticalbasisforanalysisoffutureintelligentvehicles.Theconclusionswerevalidatedthroughasimulation.Keywords:wheeledmobilerobo;tkinematicsmode;lAckermanprinciple;turningcharacteristics:20091002.:(90820302,60805027);(200805330005);(2009FJ4030).:.Emai:[e-mail].,[1],[2].,[1,34].,.,.[5],[6]:.,,[2].(),,.Ackerman(),,.[7],.1四轮车式机器人的运动学建模.,,,,,,[8].,[9],.,,[10].1Fig.1Localandglobalcoordinatesystemofcarlikerobot,XIOYIXRMYR,Mr.,Mr(xr,yr),Mf(xf,yf).XIOYIMrMfxf=xr+lcos,yf=yr+lsin.(1)(),I=[x,y,]T.R()XIOYIXRMYR,R=R()I,I=R()-1R.:R()=cossin0-sincos0001,R()-1=cos-sin0sincos0001.2,l,,d,ICR(instantaneouscenterofrotation)[11].MrMfrf.2Fig.2Localcoordinatesystemoftherobotvr,XR;vf,,vrvfvf=vr/cos.(2)t,XRvtdt,YR;XRvfcosdt,YRvfsindt.,,s,ds=d,3.:d=vdt.(3)3Fig.3Thecircumferentialmovementsystemtrackoftherobot=l/tan,f=l/sin,d=vrdtr=vrtanldt,ddt=tanlvr,ddt=sinlvf.Rr=[vr0tanlvr]T,Rf=[vfcosvfsinsinlvf]T.MrXIOYIIr=R()-1Rr=cos-sin0sincos0001[vr0vrltan]T,(4)Ir=[vrcosvrsinvrltan]T.(5)MfIf=R()-1Rf=cos-sin0sincos0001[vfcosvfsinsinlvf]T.(6)If=[vfcos(+)vfsin(+)vflsin]T.(7)5356,:(2)(7)If=[vrcos(+)cosvrsin(+)cosvrltan]T.(8),MrMf(5)(8),vr.2阿克曼约束的机器人运动模型,2,4.,,[11].2,1.,,4ICR,(9)[10]:cot1-cot2=r+d/2l-r-d/2l=dl.(9)cot1=cot+d/2l,cot2=cot-d/2l.(10)4Fig.4KinematicsmodelingofcarlikemoblierobotbasedonAckermanprinciplelfrf,lf=l/sin1,rf=l/sin2.lr=l/tan+d/2,rr=l/tan-d/2.=lf-lr(=rf-rr)[11].3仿真实验Matlab7.0.:l=2.7m,d=1.5m,vr=10m/s.Ir=[00/4]T,(1)If=[1.91.9/4]T.,.,t(t).5,.5Fig.5Movementtrackoftherobot612.12,(9)cot1-cot20.5556,0.5505,.612Fig.6Turningangles1,2and7,4,ABC.,,A.AB,;BC,..7Fig.7Truningangleanddirection53648.,,.,12,.8Fig.8Directionandinnertyreminus4结束语,.,.12.,.:[1]RENXiaodong,FENGZuren,CHANGHong,MURuofeng.Kinematicsmodelingandanalysisforthreewheelomnidirectionalmobilerobot[C]//Proceedingsofthe7thWorldCongressonIntelligentControlandAutomation.Chongqing,China,2008:26082613.[2]SIEGWARTR,NOUBAKHSHIR.Introductiontoautonomousmobilerobots[M].MA,USA:MITPress,2004:202205.[3]CHENLe,iMAJie,GAOHaibo.Kinematicsmodelingofeightwheellunarrover[C]//Proceedingsofthe27thChineseControlConference.Kunming,China,2008:346350.[4],,,.[J].,2008,44(6):148154.SONGXiaokang,TANDalong,WUZhenwe,iWANGYuechao.Kinematicsmodelingandanalysesofallterrainwheeledmobilerobots[J].ChineseJournalofMechanicalEngineering,2008,44(6):148154.[5]TLALEN,DeVILLIERSM.Kinematicsanddynamicsmodellingofamecanumwheeledmobileplatform[C]//15thInternationalConferenceonMechatronicsandMachineVisioninPractice(M2VIP08).Auckland,NewZealand,2008:657662.[6]MUIRPF,NEUMANCP.KinematicmodelingofwheeledmobilerobotsCMURITR8612[R].RoboticsInstitute,CarnegieMellonUniversity,1986.[7],.4[C]//2002.,2002:168171.ZHOUWenqin,JIAYingmin.Improvementadaptivecontrolof4WScar[C]//2002ProceedingsofChineseControlandDecisionConference.Shenyang,2002:168171.[8],.[J].,2007(1):2326.DENGZhaowen,ZHANGFuxing.Theanalysisofsteadystatesteeringcharacteristicturningradiusbasedinvehicle[J].AgriculturalEquipment&VehicleEngineering,2007(1):2326.[9]MORETTEN,NOVALESC,VIEYRESP.InverseversusdirectkinematicsmodelbasedonflatnessandescapelanestocontrolCyCabmobilerobot[C]//2008IEEEInternationalConferenceonRoboticsandAutomation.Pasadena,CA,USA,2008:22402245.[10]RATNERD,MCKERROWP.DynamicsoftheTitanfourwheeldrivemobilerobotwithfloatingAckermansteering[C]//Brisbane,1999:144149.[11].[J].,2007,20(4):3638.MENGGang.AnalysisofturningcharacteristicandtheprincipleofAckermanturningforvehicle[J].MechanicalResearch&Application,2007,20(4):3638.:,,1984,,,10.,,1938,,.,500.5376,: