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1、INTERNATIONALJOURNALOFPRECISIONENGINEERINGMANUFACTURINGVol.11No.5pp.697704OCTOBER2010697DOI:10.1007s12541010008241.IntroductionAmobilemanipulatthatconsistsofamobilebasearoboticmanipulatprovidesnumerousadvantagesoverafixe
2、dbasemanipulat.Themostimptantadvantageofthemobilemanipulatisitsflexiblewkspace.Alsothemechanicalconfigurationoftheroboticmanipulatmountedonthemobilebaseresultsinaredundantsystemthatisadvantageousfdexterousmanipulation.26
3、Whilethesefeaturesenablevariousapplicationscontrolofthemobilemanipulatischallengingduetoitsintrinsicstructure.FirsttheredundantDOFsofthemobilemanipulatcomplicatemanipulationcontrol.Secondtheoveralldynamicsofthemobilemani
4、pulatisfarmecomplexcomparedtofixedbasemanipulats.Thirdmanyapplicationsinvolvedynamicinteractionofthemanipulatwithitsenvironment.Mobilemanipulationinhumanpopulatedenvironmentsbringstheissueofsafetytothefefront.Therehavebe
5、enanumberofstudiesonmobilemanipulation.Yamamotoproposedkinematicdynamicmanipulabilitytoresolvetheredundancyinmotionplanninganalysisfmobilemanipulat.1Khatib23introducedpotentialfieldincontrollingpositionofredundantmanipul
6、atsprovidingjointlimitconstraints.Alsoheproposedanovelapproachtoutilizetheintrinsicdynamicsacteristicsofmobilemanipulatinoperationalspace.23Additionallyheanalyzedthereducedinertiaeffectofredundantroboticarmwithmacromicro
7、structure.InotherstudiesonmobilemanipulationZMP(ZeroMomentPoint)wasproposedasameasurefmobilemanipulatsystemsperfmingheavyloadtransferringtasks.45Therehavebeenstudiesonthestablemotioncontrolofamobilemanipulatunderunknowne
8、xternalfceapplicationfromtheenvironment.67Manyofthestudiesmentionedaboveadaptedtheideaofconventionalfixedbasedmechanismstomobilemanipulats.Thereareseveralissuestoconsiderinmobilemanipulatcontrol.Firstthemobilebasepartoft
9、hemobilemanipulatisheavierthantheupperroboticmanipulatpartwhichleadsslowerdynamicresponseofthemobilebasecomparedwiththatofthemanipulatpart.Theoveralldynamicsofthemobilemanipulatissomewhatanalogoustothatofmacromicromanipu
10、lats.Themacropartismuchheavierthanthemicropart.23SecondtheControlofImpulsiveContactFcebetweenMobileManipulatEnvironmentUsingEffectiveMassDampingControlsSungchulKang1KiyoshiKomiya2KazuhitoYokoi2TetsuoKoutoku2ByungchanKim1
11、ShinsukPark3#1CenterfCognitiveRoboticsResearchKISTHawolgokdongSeongbukguSeoulSouthKea1367912IntelligenceSystemsResearchInstituteAISTTsukubaIbarakiJapan30585683SchoolofMechanicalEngineeringKeaUniversityAnamdong5gaSeongbuk
12、guSeoulSouthKea136713#CrespondingAuthEmail:TEL:82232903868FAX:8229269290KEYWDS:MobilemanipulationEffectiveinertiaKinematicRedundancyNullspacemotionRecentlymobilemanipulatsarebeingwidelyemployedfvariousservicerobotsinhuma
13、nenvironments.Safetyisthemostimptantrequirementftheoperationofmobilerobotinahumanpopulatedenvironment.Indeedsafehumanmachineinteractionisoneofgrchallengesinroboticsresearch.Thispaperproposesanovelcontrolmethodtoreduceimp
14、ulsivecompactfcebetweenamobilemanipulatitsenvironmentbyusingoptimizedmanipulatinertiadampingbasedmotioncontrol.Tofindtheoptimizedconfigurationthroughnullspacemotionthecombinedpotentialfunctionmethodisproposedconsideringb
15、oththeminimumeffectivemassjointlimitconstraints.Theresultsofthisstudyshowthattheinertiaoptimizationalongwithadampingcontrollersignificantlyreducestheimpulsivefceuponcollisionthecontactfceaftercollision.Manureceived:Janua
16、ry62009Accepted:July262010?KSPESpringer2010INTERNATIONALJOURNALOFPRECISIONENGINEERINGMANUFACTURINGVol.11No.5OCTOBER2010699Table1DHparameterslinkmassofM3mobilemanipulatjoint1iα(rad)1ia(m)1iθ(rad)1id(m)JointtypeMass(kg)12π
17、?000P90.0122π?02π0P300π7R42π?000R7.8152π000R3.4162π?000.45R1.1872π000R7.4582π?000.5R2.6492π000R1.46100000.08R0.24P:PrismaticR:Revolute2.1EffectiveMassofMobileManipulatFamobilemanipulattheinertialpropertiesinjointspaceare
18、describedbykiicenergymatrixA(q)whichisamatrixfunctionofjointvariablesq.WhenthedynamicresponseimpactfceattheendeffectisofinteresttheinertialpropertiescanbeevaluatedattheendeffectwhichisrepresentedbykiicenergymatrixA(q)inC
19、artesianspace.KiicenergymatrixA(q)iscalculatedfromkiicenergymatrixA(q)usingJacobianmatrixJ(q).1811()(()()())T??=ΛqJqAqJq(1)TheinertiaperceivedattheendeffectinanarbitrarydirectionuisrepresentedbyeffectivemassMu(q)asfollow
20、s:11()()TM?=uquΛqu(2)EffectivemassMu(q)representsdirectionalinertiapropertyofthemanipulatattheendeffect.WitharedundantmanipulatsuchasM3mobileroboteffectivemassMu(q)canbemanipulatedbychangingtheconfigurationofthemanipulat
21、evenwhenthepositionientationoftheendeffectisfixedinCartesianspace.Thisfeatureallowsustocontroltheimpulsivefcebetweentheendeffecttheenvironmentfagivenpose(positionientation)oftheendeffect:IfeffectivemassMu(q)isreducedthei
22、mpulsivefceuponcollisioncanalsobereducedsincethefceismainlydependentontheinertiavelocitydifference.19202.2ChangeofEffectiveMassbyNullSpaceMotionFagivenpose(positionientation)oftheendeffecttheconfigurationofaredundantmani
23、pulatcanbechangedbygeneratingnullspacemotion.Thefollowingequationdepictsinversekinematicsofaredundantmanipulat.21##()[()()]=?qJqvIJqJqφ?(3)HereJ#(q)ispseudoinverseofJacobianmatrixJ(q)φrepresentsanarbitraryjointmotion.The
24、matrix[IJ#(q)J(q)]definesthenullspaceassociatedwithJ#(q)thevect[IJ#(q)J(q)]φcrespondstothezerovariationoftheposeoftheendeffect.Bysettingthevelocityoftheendeffectzero(v=0)theposeoftheendeffectisfixedinCartesianspace.Fared
25、undantmobilemanipulateffectivemassMu(q)atagivenposeoftheendeffectcanbechangedbyproducingthenullspacemotionofthemobilebase.IncaseofM3mobilerobotthenullspacemotioncanbeproducedbymovingthemobilebaseinXdirection(φ=(k00..0)T)
26、Ydirection(φ=(0k0..0)T)ofthecodinatesystemshowninFigs.12.Figure3illustratesthechangesofeffectivemassinXdirection(Mx(q))Ydirection(My(q))Zdirection(Mz(q))asthepositionofthemobilebasechangesinXYplane.Ascanbeseeninthefigure
27、effectivemassMu(q)isasimplefunctionofXYfthegivenrangeofnullspacemotionwhilekiicenergymatrixinCartesianspaceΛ(q)isahighlycoupledfunctionofjointvariablesq.2.3MinimizationofEffectiveInertiaFromtheplotsoftheinertiapropertyof
28、M3mobilerobotfthegivenrangeofnullspacemotion(Fig.3)wecaneasilyfindtheconfigurationthatminimizestheeffectivemassinaspecificdirectionbyusingoptimizationtechniques.Thiscanbefmulatedasanoptimizationproblemwithequalityconstra
29、ints.IntheoptimizationproblemtheobjectivefunctiontobeminimizedisascalarfunctionMu(q)thatiseffectivemassinudirectiontheconstraintfunctionisthefwardkinematicsequationofthemobilemanipulatg(q)χ=0whereχisagivenposeoftheendeff
30、ect.Thusthisproblembecomes:MinimizeMu(q)subjecttog(q)χ=0(4)Similarlythemaximizationproblemyieldsto:MaximizeMu(q)subjecttog(q)χ=0(5)Fagivenendeffectposejointanglevectqmoftheconfigurationthatminimizes(maximizes)effectivema
31、ssMu(q)canbeobtainedbyusingconstrainedoptimizationfunctions22providedinMATLAB.WhentheendeffectofM3mobilemanipulatiskepthizontaltothegroundwiththeheightof1.32mtheminimummaximumeffectivemassesarecalculatedtobe11.75kg15.28k
32、grespectively.ThemobilemanipulatcanmovefromthecurrentconfigurationtotheminimuminertiaconfigurationwithjointtrajectiescalculatedfromtheinversekinematicsequationofEq.(3)resolvedmotionratecontrol.NullspacevectφofEq.(3)isoft
33、enwrittenasthegradientofanobjectivefunctiontobeminimized.Inthisstudytheobjectivefunctionischosenastomovethemobilemanipulattotheminimuminertiaconfigurations.Theobjectivefunctionhasthefmofpotentialfunctionasfollows:2()Nmim
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