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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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