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RoboticsTOOLBOXforMATLAB(Release7)−1−0.500.51−1−0.8−0.6−0.4−0.200.20.40.60.81−1−0.8−0.6−0.4−0.200.20.40.60.81Puma560xyz−4−2024−4−202422.533.544.555.5q2q3I11PeterI.CorkePeter.Corke@csiro.auApril2002://finallyincludesmanyofthefeaturesI’vebeenplanningtoaddforsometime,particularlyMEXfiles,SimulinksupportandmodifiedDenavit-Hartenbergsupport.Thepreviousreleasehashadthousandsofdownloadsandthemailinglisthashundredsofsubscribers.TheToolboxprovidesmanyfunctionsthatareusefulinroboticsincludingsuchthingsaskinematics,dynamics,andtrajectorygeneration.TheToolboxisusefulforsimulationaswellasanalyzingresultsfromexperimentswithrealrobots.TheToolboxisbasedonaverygeneralmethodofrepresentingthekinematicsanddynam-icsofserial-linkmanipulators.TheseparametersareencapsulatedinMatlabobjects.Robotobjectscanbecreatedbytheuserforanyserial-linkmanipulatorandanumberofexamplesareprovidedforwellknowrobotssuchasthePuma560andtheStanfordarm.TheToolboxalsoprovidesfunctionsformanipulatingandconvertingbetweendatatypessuchasvec-tors,homogeneoustransformationsandunit-quaternionswhicharenecessarytorepresent3-dimensionalpositionandorientation.Theroutinesarewritteninastraightforwardmannerwhichallowsforeasyunderstanding,perhapsattheexpenseofcomputationalefficiency.MyguideinallofthisworkhasbeenthebookofPaul[1],nowoutofprint,butwhichIgrewupwith.Ifyoufeelstronglyaboutcomputationalefficiencythenyoucanalwaysrewritethefunctiontobemoreefficient,compiletheM-fileusingtheMatlabcompiler,orcreateaMEXversion.1.1What’snewThisreleasehassomesignificantnewfunctionalityaswellassomebugfixes.Fullsupportformodified(Craig’s)Denavit-Hartenbergnotation,forwardandinversekinematics,Jacobiansandforwardandinversedynamics.Simulinkblocksetlibraryanddemonstrationsincluded,seeSection2MEXimplementationofrecursiveNewton-EuleralgorithmwritteninportableC.Speedimprovementsofatleast1000.TestedonSolaris,LinuxandWindows.SeeSection1.9.Fixedstillmorebugsandmissingfilesinquaternioncode.Remove‘@’notationfromfdyntoallowoperationunderMatlab5and6.Fairlymajorupdateofdocumentationtoensureconsistencybetweencode,onlinehelpandthismanual.1INTRODUCTION4AllcodeisnowunderCVScontrolwhichshouldeliminatemanyoftheversioningproblemsIhadpreviouslyduetodevelopingthecodeacrossmultiplecomputers.1.2ContactTheToolboxhomepageisatfixesandnewcodeinbetweenmajorreleases.AMailingListisalsoavailable,subscriptionsdetailsareavailableoffthatwebpage.1.3HowtoobtaintheToolboxTheRoboticsToolboxisfreelyavailablefromtheToolboxhomepageatfilesareavailableineithergzippedtarformat(.gz)orzipformat(.zip).Thewebpagerequestssomeinformationfromyouregardingsuchasyourcountry,typeoforganizationandapplication.Thisisjustameansformetogaugeinterestandtohelpconvincemybosses(andmyself)thatthisisaworthwhileactivity.Thefilerobot.pdfisacomprehensivemanualwithatutorialintroductionanddetailsofeachToolboxfunction.Amenu-drivendemonstrationcanbeinvokedbythefunctionrtdemo.1.4MATLABversionissuesTheToolboxworkswithMATLABversion6andgreaterandhasbeentestedonaSunwithversion6.TheToolboxdoesnotfunctionunderMATLABv3.xorv4.xsincethoseversionsdonotsupportobjects.AnolderversionoftheToolbox,availablefromtheMatlab4ftpsiteisworkablebutlackssomefeaturesofthiscurrentToolboxrelease.1.5AcknowledgementsIamgratefulforthesupportofmyemployer,CSIRO,forsupportingmeinthisactivityandprovidingmewiththeMatlabtoolsandwebserver.IhavecorrespondedwithagreatmanypeopleviaemailsincethefirstreleaseofthisTool-box.Somehaveidentifiedbugsandshortcomingsinthedocumentation,andevenbetter,somehaveprovidedbugfixesandevennewmodules,thankyou.1INTRODUCTION51.6Support,useinteaching,bugfixes,etc.I’malwayshappytocorrespondwithpeoplewhohavefoundgenuinebugsordeficienciesintheToolbox,orwhohavesuggestionsaboutwaystoimproveitsfunctionality.HoweverIdrawthelineatprovidinghelpforpeoplewiththeirassignmentsandhomework!ManypeopleareusingtheToolboxforteachingandthisissomethingthatIwouldencour-age.Ifyouplantoduplicatethedocumentationforclassusetheneverycopymustincludethefrontpage.IfyouwanttocitetheToolboxpleaseuse@ARTICLE{Corke96b,AUTHOR={P.I.Corke},JOURNAL={IEEERoboticsandAutomationMagazine},MONTH=mar,NUMBER={1},PAGES={24-32},TITLE={ARoboticsToolboxfor{MATLAB}},VOLUME={3},YEAR={1996}}whichisalsogiveninelectronicformintheREADMEfile.1.7AnoteonkinematicconventionsManypeoplearenotawarethattherearetwoquitedifferentformsofDenavit-Hartenbergrepresentationforserial-linkmanipulatorkinematics:1.Classicalaspertheoriginal1955paperofDenavitandHartenberg,andusedintext-bookssuchasbyPaul[1],Fuetal[2],orSpongandVidyasagar[3].2.ModifiedformasintroducedbyCraig[4]inhistextbook.Bothnotationsrepresentajoint