南昌航空大學科技學院（論文）-附錄AFifthMotionandVibrationConference,MOVIC2000,Sydney,Australia,4.-8.December2000byUniversityofTechnology,SydneySPEED-ADAPTEDTRAJECTORIESINTHECASEOFINSUFFICIENTYDRAULICRESSUREFORTHEFOUR-LEGGEDLARGE-SCALEWALKINGVEHICLEALDURODanielGermann,JorgMullerandManfredHillerGerhard-Mercator-UniversitatGHDuisburgFachgebietMechatronik,Lotharstrae1,47057Duisburg,GermanyEmail:fgermann,mueller,hillergmechatronik.uni-duisburg.deABSTRACTWhenoperatingwalkingmachines,onlyacoordinatedmovementofallcylindersand/ormotorscanleadtosafe,stablewalking.ThelargehydraulicallydrivenwalkingmachineALDURO,whichisinvestigatedinthispaper,hasnoexternalpowersupply,andthereforethesizeoftheon-boardhydraulicpowerpackanditsdieselengineislimitedbyitsweight.Whenmovingseveralcylinderswithhighspeed,thehydraulicsupplycanbecomeinsufficientandtheresultingtrajectoriesoffeetandplatformcanbecomeunpredictable.WhentheALDUROisnearitsstabilitylimitsuchbehaviourcanleadtoinstabilityandtopplingofthesystem.Theproposedsolutionunderdiscussionhereistoobservethepositionerrorsandtimederivativesforthecylindersandbasedonthisreducethespeedwhennecessary.1.INTRODUCTIONThesysteminvestigatedinthispaperistheAnthropomorphicallyLeggedandWheeledDuisburgRobot(ALDURO).Itconsistsofaplatformof2.0mby2.2mwithacabinfortheoperatorandfourlegs,each1.8mlong.Theestimatedweightis1200kg.Itcanbeusedasaquadrupedwalkingmachine(Fig.2),andbyreplacingthetwohindfeetwithwheels,itcanalsobeusedasacombinedleggedandwheeledvehicle(Fig.1).Thelattercombinestheadvantagesofawalkingmachine-highmobility-withthestabilityandspeedofwheeledvehicles2.Whenoperatinginsteepanddangerousterrain,safetyplaysanimportantrole.Itmustbeguaranteedthatthecylindersfollowthecalculatedtrajectoriesexactlysinceawrongmovementmightcausetherobotto南昌航空大學科技學院（論文）-becomeinstable.ALDUROslegsarehydraulicallydriven,withanopenhydraulicsystem.Normally,whenplanninghydraulicsystems,lowweighthasnohighpriority1.ForthewalkingmachineALDUROtheratiopowerperweightwasoptimized.Fig.1:CombinedLeggedFig.2:WalkingMachineandWheeledVehicleWhileactuatingseveralcylinderssimultaneouslyormovingveryfast,thevolumeflowofthehydraulicsupplybecomesinsufficientandtheresultingmovementsuncontrollable.Theproposedsolutionunderdiscussionhereisadecreaseinspeedofallcalculatedtrajectories.Thisisadmissibleaslongastherobotisstaticallystableatanymoment.Byobservingthepositionerrorsofthecylindersandtheirtimederivatives,adecisionistakenonwhethertodecreaseorincreasethespeedalongthetrajectories.Toensurethatallmovementsareinfluencedsimultaneously,themodel-time,uponwhichallcalculationsdepend,issloweddown.Thuswecanguaranteethatlegsandplatformcananddofollowtheprescribedtrajectories.ThisstrategyisbeingtestedonavirtualmodeloftheALDUROandisbeingtestedonavirtualmodeloftheALDUROandateststandinthelaboratory,consistingofasingleleginscale1:1,givingverygoodresults.Fig.3:Experimentalsetup2.EXPERIMENTALSETUP南昌航空大學科技學院（論文）-ThelegoftheALDUROisanthropomorphic,i.e.itisbasedonthegeometryandfunctionofthehumanleg.Thehipjointisasphericalballjointwiththreedegreesoffreedom(d.o.f.)andthekneearevolutejointwithoned.o.f.Thesejointsareactuatedwithhydrauliccylinders(Fig.4),whereasthetwoadditionald.o.f.ofthefootarepassive.Tomakesolutionoftheexplicitinversekinematicspossiblewelockoneofthehipcylinders.Theexplicitsolutionofthedirectandinversekinematicsisshownindetailin4.Toexaminethedynamicbehaviouroftheleg,andtotestdifferentcontrolschemes,anexperimentalsetupforafullysizedlegwasdevelopedandbuilt(seeFig.3).ItincludesallthehydrauliccomponentsthatwillbeusedonthefirstprototypeALDUROandisdrivenbyastationaryhydraulicpowerpackinthelaboratory.Theexperimentalset-upisequippedwithanopenhydraulicsystemwitha15kWelectricalmotorandanaxialpistonpumpproducingavolumeflowof40l/minat200bar.Thisissmallerthanwhatwillbeusedontherealsystem,whichwillbepowerdbya27kWdieselengine.Fortestswithaninsufficienthydraulicflow,asecondsetoffourhydrauliccylinders(asusedtomoveoneleg)ismountedonthefloornexttotheteststand.Anopticalfieldbusforthetransferofthesensorandactuatordatabetweentheteststandandthecontrolcomputer(withreal-timeoperatingsystem)isalsoinstalled.Thehydrauliccylindersincludepositionandpressuresensorsthatareusedascontrollerinputs.Thusdynamictestscanbecarriedouttoexaminetheco-operationbetweenthemechanicalandhydrauliccomponentsandtheelectroniccontrolsystem.Thehipplateoftheexperimentalset-upismountedonapairoflinearbearings,andthusismobileinverticaldirection.Whencombinedwiththefoot,asshowninFig.3,orthepassivewheelusedonthehindlegofthecombinedleggedandwheeledsystem,thisallowsloadingtestsonthelegwhileperformingwalkingmotions.Mechanicalstopsbelowthehipplateallowthefoottobeliftedintheswingphaseofthewalkingmotion.Thefirst(unloaded)testshaveshownthemobilityoftheanthropomorphiclegmechanismtobeverygood,andtheopticalfieldbussystemhasalsoproventobereliable.南昌航空大學科技學院（論文）-3.SPEEDADAPTATION3.1InsufficientHydraulicFlowAsalreadymentioned,theweightandsizeoftheonboardpowerpackislimitedandhastobekeptlow.Whenmovingseveralcylinderssimultaneouslyorwithahighspeedthehydraulicsupplycanbecomeinsufficientandthepressurewillcollapse.Inthiscasetheresultingmovementdependsmainlyonthesizesoftheproportionalvalvesandexternalloadsonthecylinders.Thetrajectoriesofthefeetandplatformbecomeerratic.WhenALDUROisnearlimitofitsstabilitysuchbehaviorscanleadtoinstabilityandtopplingofthesystem.Asthesafetyissueisaveryimportantone(peoplecouldbeharmed)thispressurecollapsehastobeprevented.Toinvestigatethisbehavior,acircularmovement(radius0.2m,velocity0.5m/s)ofthefootinthehorizontalplane1mbelowthehipwaschosenasareference.Thistrajectoryhastheadvan