两篇外文翻译

外文翻译毕业设计题目： 多轴转向系统的设计 原文1：AgriculturalRoboticPlatformwithFourWheelsSteeringforWeedDetection译文1： 原文2：Turningcharacteristicsofmulti-axlevehiclesAgriculturalRoboticPlatformwithFourWteheereinlsgSforeWedDetectionThomasBak;HansJakobsenDepartmentofAgriculturalEngineering,DanishInstituteofAgriculturalSciences,Schoottesvej.17,DK-8700Horsens,Denmark;e-mailofcorrespondingauthor:tb@control.auc.dk(Received10January2003;acceptedinrevisedform14October2003;Publishedonline23December2003)Aroboticplatformformappingofweedpopulationsinfieldswasusedtodemonstrateintelligentconceptsforautonomousvehiclesinagriculturewhichmayeventuallyresultinanewsustainablemodelfordevelopedagriculture.Thesoftwareimplementsahybriddeliberatesoftwarearchitecturethatallowsahierarchicaldecompositionoftheoperation.Thelowestlevelimplementsareactivefeedbackcontrolmechanismbasedonanextensionofsimplecontrolforcar-likevehiclestothefourwheelcase.Thecontrollerdesignforcesthefrontandrearofthevehicletofollowapredeterminedpathandallowsthevehicletomaintainafixedorientationrelativetothepath.Thecontrollerrationaleisoutlinedandresultsfromexperimentsinthefieldarepresented.1.IntroductionAdvancesinmechanicaldesigncapabilities,sensingtechnologies,electronics,andalgorithmsforplanningandcontrolhaveledtoapossibilityofrealizingfieldoperationsbasedonautonomousroboticplatformsTheneedforsuchsystemsisdrivenbyincreasingfinancialpressureonfarmerscombinedwithpublicconcernabouttheenvironmentandworkingconditions.Efficientdeploymentofautonomousroboticplatformsinthefieldwillallowcareandmanagementofcropsinaverydifferentwayfromwhatisknowntoday(Belascoetal.,2002;Choetal,2002).Roboticplatformsandimplementsmaysenseandmanipulatethecropanditsenvironmentinaprecisemannerwithminimalamountofmaterialsandenergymakingthempotentiallymoreefficientthantraditionalmachinery.Thisislikelytoreducetheenvironmentalimpactwhileincreasingprecisionandefficiency(Kondo&Ting,1998;DeBaerdemaekretal,2001).Theresultisanewsustainablemodelfordevelopedagriculture.Thispaperpresentsanoverviewofthesystemandapproach.Section2providesasystemdescription.ThisincludesadescriptionofmodularmechanicalconceptswellastheTechtronicimplementationofthesystem.Everythingistiedtogetherinhierarchicalhybridsoftwarearchitecture.InSection3,thefocusisonaspecificmobilitycontrolstrategythatextendssimplecontrollersto4WS.Theresultisasystemthatallowsthevehicletotrackagivenpath,whilemaintainingthefrontandrearimplementbarsonthepath.ResultsfromexperimentsinthefieldaresummarizedinSection4anddemonstratetheeffectivenessoftheproposed4WSsolution.Finally,conclusionsaredrawnanddiscussfurtherresearch.Thispaperconcentratesontheengineeringaspectsoftheresearchandevaluationoftheexperimentalsystem.SystemdescriptionTheroboticplatformdescribedhereismeanttodemonstratenovelsensingcapabilities(Sgaard&Olsen,2000)andsemi-autonomousoperationofaroboticplatformforagriculture.Theimmediateagronomicaimoftheprojectistodemonstrateefficientmeasurementofspatialandtemporalcropandweedmeasurements.Giventhatthevariabilityinweedsismeasuredandmapped,inputscanbevariedaccordingtoadefinedstrategyprovidingenvironmentalandeconomicbenefits.Studiesshowthat50-0%ofthecostsforherbicidescanbesavedwhentreatingonlypatcheswhereweedsactuallygrow(Greenetal.,1997;Nordmeyeretal.,1997).Fundamentalforthesuccessofsuchasystemistheintegrationintofarmmanagementsystems,e.g.jobcreationandpathplanning(Srensenetal.,2002).RoboticplatformThebasisfortheroboticplatformisthemobilitycapabilityprovidedbythewheelmodulemechanismshowninFig.1.Eachofthefouridenticalwheelmodulesincludeabrushlesselectricmotorforpropulsionthatprovidedirectdrivewithoutgearing.Motor,amplifierandmicrocontrollerareallmountedinthewheelhub.Steeringcapabilityisachievedbyaseparatesteeringmotormountedontopofthewheelmoduleshafttocreateatwo-degree-of-freedommechanism.Thesteeringmotoramplifierandthecontrolelectronicsaremountednexttothesteeringmotor.Thecontrolelectronics(wheelnode)arebasedonacommercialagriculturaljobcomputerandhandlethelocalpositionservocontrolforthesteeringandprovidetorquecontrolofthedrivemotors.Thedrivermotorelectronicsallowspeedandcurrent(torque)feedbackwhilethesteeringservosystemprovideasteeringanglefeedbackderivedfrommotorshaftencoders.PlatformelectronicsThisallowsprogramstobebuiltautomaticallyandsubsequentlyexecuteinnearreal-timeontheplatformcomputer.Thesolutionsupportstransmissioncontrolprotocol/internetprotocol(TCP/IP)socketsforremotecommunicationwiththerunningcodewhichallowmonitoringandmodificationofparametersduringdevelopment.2.3.SystemarchitectureThesystemarchitectureadoptedissimilartothehybriddeliberateapproach(Arkin,1990)thatisnowcommoninmobileroboticssystems(Orebaack.&Christensen2003).Thethree-layerarchitectureconsistsof:(1)areactivefeedbackcontrolmechanismthathandlesstabilizationandtracking,(2)aplan-executionmechanismthatdealswithe.g.trajectorygenerationandtaskdecomposition,and(3)amechanismforperformingtime-consumingdeliberativecomputationsandinteractionwithhumanoperators,i.e.jobcreation.ThehierarchicalstructureisshowninFig.4.3MobilitycontrolThemotionoftherobotcanalwaysbeviewedasaninstantaneousrotationaroundatimevaryingpointcalledtheinstantaneouscentreofrotation(ICR).Hence,ateachinstant,thevelocityvectorofanypoint.OftheframeisorthogonaltothestraightlinejoiningthispointandtheICR.Controllingthevehiclepositioninthefieldimpliescontrollingthetwo-dimensionallocationoftheICR,whichmaybeachievedbyspecifyingthedirectionoftraveloftwopointsofthevehicle.Togetexperimentalresultswiththe4WSsystem,asimplecontrollerthatcontrolstwosteeringpointswasimplemented,oneatthefrontendandoneattherearofthevehicle.The4WSisthenutilizedtominimizethedistancetothedesiredpathforbothsteeringpointsindependentlyasindicatedinFig.5.Thisapproachwithtwoindependentcontrollersallowsustoswitchbetween2WSand4WSwithouthavingtochangethecontrollerstructure.Asfrontandrearcontrollersareidenticalsowithoutlossofgenerality,thedescriptionhereisfocusedonthefrontsteeringcontroller.Itscontrolobjectiveistominimizetheperpendiculardistancetothepathdf.Thesignofdfindicatesthesideofthepathonwhichthesteeringpointislocated.Fromdfitcalculatesacommandeddirectionofthefrontsteeringpoint(FSP)relativetothevehiclef,using:Pulli?2Fig.6. centreofrotarum(Pulli?2Fig.6. centreofrotarum(fCR)exclusionzfme^i：lh.eZfme^i lo 裁哄侶治wheelconjiifi^a!mrZMenforceIbmtxrmlhexteaimjt^glex;lheuehicleFolulesiiboiitlheICR;5gvehiclefhffue;i'/..&referencefrarue;x,y7po^itirminrefa^icefhmewhere:hisapositivescalarconvertingthecontrolsignaltomotorvoltage.G=石依曲备嗣-K珂门■/i=I……4 (6)Thissimpledistributionactuallyworksverywellinpracticeandinadditionitalsohasananti-spineffect.Ifawheelslips,itwillofcourserotatealittlefasterastheEMFwillgrowtocompensateforthemissingtorque,butthetorquedistributionamongthewheelsisnotchanged.Aslippingwheelhasaminorinfluenceonthemeasuredvehiclespeedasitisbasedontherotationspeedofallwheels,butthiscanbesolvedbyomittingawheelifaslipdetectionindicatesthatitisslipping.作者：ThomasBak;HansJakobsen国籍：Danish出处：DepartmentofAgriculturalEngineering,DanishInstituteofAgriculturalSciences,Schoottesvej.17,DK-8700Horsens,Denmark;除草的四轮农业机器车机器人平台测绘杂草种群的领域是用来展示智能概念车辆，这最终将为高度发达的农业引进一种可持续的模式，现有的车辆适用于0.25米和0.5米行距的作物，这种车辆装备了适用于行间向导和搜寻杂草的相机。携带有四个特备的轮子的组合方法，允许转向装置和推进力。这种结果被改进了，允许机器在转向时平行移动，是通过去耦合装置来调节方向的。机器的控制是通过工具系统和基于控制的系统，这种软件工具混合了成熟的建构软件，这种农业软件混合有机的操作。最低水准是运用反馈系统，这种反馈系统基于汽车简单控制的延伸，这种控制设计使得前后轮服从以设计的路径，允许机器维持复杂的相关路径，这种控制方法正在试验中。1.引言在控制方面的机械设计能力，传感技术，电子学和运算学的进步已经使得自动化的机器人操作的可能性。这种系统的需要正被逐渐增加的财政压力，公众对环境和工作条件的关注而驱动着。机器平台和工具或许能精确的感觉到和控制到农作物和他所处的环境从而使其比传统的机器更有效。这能够在提高精度和效率的同时降低对环境的反作用，这种结果对于高度发达的农业是一种新的可持续模式，农业机器向导已经成为一种积极地研究领域好多年了，最初的商业导向系统已经普及，拖拉机被提前预设的路径控制，这种路径是基于GPS系统。这些自动向导机器解决了以上许多问题，但是在土壤，压实，能源使用、排放物和精密等方面不是最好的解决方案。把重心集中到能不断操作和最小误差的机器，能让我们想到一系列的更小更特殊更精确更有效的机器。这种机器能够以更低的频率来工作更长的时间，同时比以往机器提供同样甚至是更多的输出。机器在无人的情况下更长时间的操作时一项重大挑战。最近在机械手工程的区域农业者有很大的贡献。给在田里的杂草数量进行草绘的机器人平台在农业里被用来示范自动车辆的智能观念，这最终将为高度发达的农业引进一种可持续的模式，现有的车辆适用于0.25米和0.5米行距的作物，指导与农作物相关的车辆线使用指导照相机提高工作率，减到最少的同时提供有价值的局限输入对农作物的伤害。四轮转向（4WS）的引进为这次研究提供了一种更灵活的平台，但改善的变动性也提供了一个数量更多的实际利益。四轮转向系统允许车辆在转向中平行的位移，从而调整位移取向。鉴于有车辆的四个非线性性质的独立控制车轮的控制问题不是小事情，然而，那样的控制系统在一种低速的情况下也能给出很好的结果。一种已经成功被使用的方法就是在车辆的前头安上比例控制器，这些结果解决了传统的轿车般的车辆在两个转向车轮的问题，当时四轮转向的模糊控制被讨论中。这里采用的方法建立在两轮转向成功的试验的基础上的，同时引进了一种简单的4WS案例。2.系统描述这里描述的机器人平台。旨在展示新型传感功能和一种农业机器人半自动化操作。农业经济项目的目的是控制有效的测量时间和控制的作物和杂草测量，考虑到杂草的测量方法和映射，输入的不同，参照一个提供环境和经济效益的明确方法。研究表明50%-80%的除草剂费用可以节省。机器人平台机器人平台的基础是车轮模块提供的流动性能力如图1，每个特定功能的车轮模块包括无刷电机提供无齿轮直接驱动推进，电机，放大器和微控制器都安装在轮毂上。通过在车轮模块安装具有独立转向电机轴轮模块来创建两个自由度的机制。转向电机放大器和控制电子器安装在方向盘马达上，控制电子系统是基于商业农业工作电脑和处理具体情况的控制系统。车轮模块有一个简单的机械接口允许它可以安装在几乎任何车辆上，电器接口包括一个电源接口和一个控制器区域网络（CAN）的总线接口控制模板如图二。该平台是专门为农业0.5米间隙作物的使用，具有良好的离地间隙，较小的车轮和0.25米行的驾驶区间。实现由被动稳定三点悬挂系统，确保所有车轮与地面接触。该平台为车辆提供细密的前面车厢电子系统，车厢后部的电池和可能的用户界面。平台电子系统通过提供控制平台机电一体化系统，包括刚才所描述的机械概念和汽车电子控制系统来正确驱动机械子系统。电子架构是围绕平台计算机（pc/104系统），如图3所示。该平台计算机软件实现Linux操作系统，该发展是由MathWorks公司的支持实行车间。允许带定制C代码直接来源于仿真模型，这使得程序将自动建立和随后在近实时的平台上执行。本地化是实现冗余的传感器集是连接到计算机使用平台RS232系列动力通信协议以及一个CAN2.0b协议。主导航传感器是旧拓普康双频载波相位差GPS接收能够优于2厘米的标准偏差的绝对精度，一个KVH的E-CORE2000光纤陀螺仪精确测量的标题率，包括测量控制陀螺漂移从磁轮和转向编码器。相结合，与绝对位置编码器，磁强计和陀螺仪的可靠性，标题绝对的唯一参考磁铁烁效应，但该计划包括该行的指导在融合过程中，以抵消这些问题的相机磁测量的灵敏度。系统构架系统架构采用的是类似混合蓄意的做法（阿金，1990年），现在是常见的移动机器人系统。三层建筑是由以下部分组成：（1）无反馈控制机制处理稳定和跟踪，（2）计划执行如轨迹生成和处理机制任务分解和（3）执行费时审议计算和机制与人类的运营商的互动，即创造就业机会。层次结构如图4.作者：汤姆斯贝克；汉克斯杰克森国籍：丹麦出处：农业工程学部，农业科学丹麦学会（2003年1月10日收到，2003年十月14日以修正的形式接受，2003年十月23日网上发表）Turningcharacteristicsofmulti-axlevehiclesAbstract：Thispaperpresentsamathematicalmodelformulti-axlevehiclesoperatingonlevelground.Consideringpossiblefactorsrelatedtoturningmotionsuchasvehicleconfigurationandtireslipvelocities,equationsofmotionwereconstructedtopredictsteerabilityanddrivingdecencyofsuchvehicles.Turningradius,slipangleatthemasscenter,andeachwheelvelocitywereobtainedbynumericallysolvingtheequationswithsteeringanglesandaveragewheelvelocityasnumericalinputs.Toelucidatetheturningcharacteristicsfaulty-axlevehicles,theejectoffundamentalparameterssuchasvehiclespeed,steeringanglesandtypeofdrivingsystemwereexaminedforasampleofmulti-axlevehicles.Additionally,fieldtestsusingfull-scalevehicleswerecarriedouttoevaluatethebasicturningchar-ataracticsonlevelground.Keywords:Multi-axlevehicles;Turningmaneuverability;Mathematicalmodel1.IntroductionTracklayingrunninggearhasbeenmainlyusedinthefieldsofmilitaryandconstructionforheavyvehicleapplications.Recently,runninggearwithpneumatictireshasbeenexpandingtoheavyvehiclesinsuchfields,sincetireequippedvehiclesexcelinspeed,silenceandenergye?-cogency.Severalpapershavebeenpublishedonthesubjectoftractabilityandmaneuverabilityofmulti-axlevehicles[1,2].AtheoreticalstudytoevaluatetheturningmotionofskidsteeringvehicleswasalsodevelopedbyRenoirandCravat[3].Morerecentarmyvehicles,suchastheMODIX,aredesignedtobeequippedwithindependentwheeldriveandsteering,andloadcontrolsuspensions[4].TheMODIXcanturnbynormalsteering,skidsteering,oramixtureofboth.Additionally,theconversionfrommechanicaldrivetoanelectricdriveunitcontrolledbyeachin-hubmotorhasbeenexamined[5-].Ahybridwheelsteersystemisbeingdevelopedtocomplementtheindependentdrivecapabilityofthein-hubwheelmotors.However,therehasnotbeenapaperortechnicalpublicationdealingwiththesubjectcomprehensivelyandinalogicalsequencebecausethephenomenonofdynamicmotionsofthemulti-axlevehicleiscomplex.Thispaperdescribesacomputersimulationmodeltopredictturningcharacteristicsofmulti-axlevehicles.Theequationsofmotionforthevehiclesareconstructedforlevelground.Tractateandsideforcesactingunderpneumatictiresduetointeractionwiththegroundareoffundamentalimportancetopredictthemotionofvehicles.Inthenumericalsimulation,thebrushmodelbasedonaphysicalapproachwasadoptedforthetiremodel[8].Thebrushmodelisanidealizedrepresentationoftiresintheregionofcontact.Inordertodeterminetheturningmotionofmulti-axlevehicles,theejectsoffundamentalparameterssuchasvehiclespeed,steeringanglesandtypeofdrivingsystemareexaminedbyusingspecificationofanexamplevehicle.Fieldtestsonmulti-axlevehicleswerealsoconductedandcomparedtothepredictedresultswiththedatanumericallyobtainedbythemodel.Theresultsdemonstratedthattheproposedmathematicalmodelcouldaccuratelyassesstheturningcharacteristicsofmulti-axlevehicles.2.Mathematicalmodelofmulti-axlevehiclesCoordinatesystemandkinematicsofthevehicleFig.1showscoordinatesystemsusedtodescribeamulti-axlevehiclewithvelocityvectorVandyawangularvelocityhatthemasscenter.Thecoordinatesystem(X1,X2)isfixedonthelevelgroundwithunitbasevectors{E1,E2}.Amovingcoordinatesystem(x1,x2)isattachedtothevehicle,whoseoriginislocatedatthemasscenter,withunitbasevectors{e1,e2}.EquationsofmotionNewton'ssecondlawappliedtothevehicleyields:・・亠2/tM= (1)J=l2jt/张=y、g1}(e3=fix (2)i=\wheremandIarethemassandthemomentofinertiaforthevehicle,respectively.ThefrictionalforceQisdefinedundertheitchwheel,andxidenotesthepositionvectoroftheitchwheel.Inasteadystateturn,theequilibriumequationsforthevehicleareobtainedbysettingVandzero.TireslipandfrictionalforcesModelingofshearforcegenerationforpneumatictireshasbeenreviewedbyPacificaandSharp[8]whocoversphysicalandempiricalmodels.Thebrushmodel,ananalyticalmodelphysicallyderived,hasbeenwidelyusedforvehicledynamicsstudies.Therelationbetweendeformationsoftiretreadsandshearforces,i.e.,sideforceandtractateforce,issimplifiedandthemodelidealizestherepresentationoftiresintheregionofcontact.Thehorizontalshearforcesactingunderthetireduetointeractionwiththegroundareassumedtobelinearlydependentonthetreaddisplacementfromthetreadbase.Fie;.!.Amulti.-ax.LevehLcleunderturningmoLionEndthecoordinates\rsterns.Inthispaper,thebrushmodelhasbeenadoptedtothevehiclemodel.AschematicslipmotionofatirewithslipangleisshowninFig.2.TheslipvelocityvectorViSisdefinedbytheSrelativevelocityoftreadsurfaceandthegroundasfollows:叫=心一X ⑴WhereViandVidenotethetravelingvelocityvectorandtheperipheralspeedvector,Rrespectively,oftheitchwheel.Anon-dimensionalslipratioSisdefinedbytheratioofthenormofslipvelocitywiththemagnitudeoftheperipheralvelocity:亍=|叫|/|叫|一 ⑷Frictionalforceyieldsatthelimitoftheadhesionandthecoincidentofyieldingfrictionisexpressedasafunctionofslipratioasfollows:卩十3(K•巧-3(K•5;)2+(K•左丫｝if©<Sar.(5)卩=用if亍事S加 ⑹whereKisapositiveconstantdependentonthestaidnessofthetire,andl0isthemaximumcoincidentoffriction.ThelimitofslipratioSmrepresentsthefullslidingstateofthetirethroughoutthetread,expressedbySm=1/K.Fig.4showsthelateralforceversusthelongitudinalforce(brakingortractionforce)plottedatgivenvaluesofslipangles(rod)foratirewiththepropertyofK=5.0.Asthedrivingpowerfromtheengineistransmittedtothewheelthroughthedeferential,thedrivingforceandtherotationalspeedofeachwheelareinfluencedbypowertraintypes.ThegeneraltypeofdrivingsystemformultivalvevehiclesisillustratedinFig.5.Deferentialaremountedineachaxletodistributeequaltractateforcetobothsidewheelsandtherotationalspeedsofthewheelsdependonthepathlengthofthetires.Thepropertyofdifferentialismathematicallyexpressedasconstraintequations:©=外- (^)叫亠F翼=2F翎. (fib)whereQiisthetractateforceorthelongitudinalshearforceontheithtire,andV isthelR0averageperipheralvelocityofthetires.ExperimentalevaluationFieldtestswereconductedbyusingtwofull-scalevehicles.Thelowspeedturningperformanceofthevehicleswasevaluatedonaconcretetestgroundandonsandyground.Onevehiclewasaneight-wheel-vehiclewithfront-four-wheel-steering,whichisidentifiedbyvehicleA.TheotherwasaTADANOALLTERRAINVEHICLEorvehicleB,whichisaneight-wheel-vehiclewithall-wheel-steeringshowninFig.6.Themaximumcoincidentoffrictionl0dependsonthegroundcondition.Thecoercionsweremeasuredinthefieldandl0=0.6wasobtainedwithvehicleBontheconcretegroundandl0=0.8withvehicleAonthesandyground.Inthefieldtests,twosteeringtypeswereexamined.Onewassteeringbythefrontfourwheels,andtheotherbyallthewheels.Fig.7showstheexperimentalandpredictedresultsoftheturningradiusversussteeringangles.Theparameterindicatestheaveragesteeringangleofthefrontwheelsand,forall-wheelsteering;theanglesoftherearfourwheelsarefixedatamaximuminitssteeringcapability.ItisclearthattheturningradiiofthevehiclesAandBdecreaseasthesteeringanglesincrease.ThelowerlineforvehicleBindicatestheresultsofall-wheelsteeringwithrearsteeringangles,=13.7°, 54=23.0°,57=14.3°,58=25.0°.FromFig.7itcanbeseenthattheturningradiushasbeensubstantiallydecreasedbymakinguseofallthewheelsforsteering.NumericalsimulationandresultsVehicleresponseinfourwheelsteeringInordertoevaluatetheturningcharacteristicsofmultivalvevehicles,thenumericalsimulationwascarriedoutusingthespecificationsofafull-scalevehicle.Themassism=24,500kgandthemasscenterislocatedatthegeometriccenter.ThedeterminationofsteeringangleofeachwheelisshowninFig.8forthecaseofthefirstandsecondaxlewheelsbeingsteered(4WS:four-wheelsteering).EachwheelsteeringangledcanbeobtainedgeometricallysuchthatallwheelshaveasteeringcenterConthemiddlelinebetweenthethirdandthefourthaxles,inasimilarwaytotheAckermanangledetermination.Inthissimulation,itisassumedthatthereisanimaginarywheelinthemiddleofthetwowheelsonthefirstaxleandtheangleoftheimaginarywheeldisusedtorepresenttheaverageangleofthefrontwheels.Fig.9showsthesteeringanglesversustimeusedinthesimulations.ThevehiclemodelstartsattheoriginandacceleratesintwosecondsuptowheelvelocityVR0=1.4m/s,(inFigs.9and10thetimeaxisbeginsatthispoint)thenafter0.5sofstraightmotion,thevehiclebeginssteeringuptothemaximumsteeringangle5=10.Fig.11.Frictionforcesactingonwheelsattowspeed.Additionally,thelateralforceonthethirdaxleismuchlargerthantheforcesonthefirstandsecondaxles.Itwasfoundfromthenumericalresultsthatthesideslipangleofthethirdaxletiresislargeandoppositeindirectioncomparedtotheothertires.EffectofrearwheelsteeringonturningcharacteristicsTheturningradiusofvehiclesatlowspeedisexpectedtodecreaseiftherearwheelsaresteeredwithoppositeanglestothefrontwheels.Fig.13showsthesteeringradiuswhenthetiresonthethirdandfourthaxlesareinverselysteeredtothefrontwheels.Theaveragesteeringangleoftherearwheels8isdefinedastheangleofanimaginarywheelinthemiddleofthewheelsronthefourthaxleasshowninFig.13.V5Fig.13.Detenninationofrearsteeringangles.Thechangeinturningradiusversusrearsteeringangles8atl=1.0misillustratedinFig.r14forthefrontsteeringangles,d=10,20and30.Itisclearthattheturningradiusdecreasesconsiderablyastherearsteeringangleincreases.Inthedesignofmulti-axlevehiclesthesteercentersofthefrontwheelsdonotgenerallycoincidewiththecenteroftherearwheels,asseenpreviously.作者：K.Watanabe,J.Yamakawa,M.Tanaka,T.Sasaki国籍：American出处：TheNationalDefenseAcademy,1-10-20Hashirimizu,Yokosuka