外文翻译 空间机器人防碰路径规划.docx

外文翻译 空间机器人防碰路径规划.docx

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外文翻译空间机器人防碰路径规划

课程名称：

计算机集成制造系统

作业名称：

ROBOT

学生班级：

K数控

学生学号：

学生姓名：

成绩评定：

教师签字：

SpaceRobotPathPlanning

forCollisionAvoidance

YuyaYanoshitaandShinichiTsuda

Abstract—Thispaperdealswithapathplanningofspacerobotwhichincludesacollisionavoidancealgorithm.Forthefuturespacerobotoperation,autonomousandself-containedpathplanningismandatorytocaptureatargetwithouttheaidofgroundstation.Especiallythecollisionavoidancewithtargetitselfmustbealwaysconsidered.Oncethelocation,shapeandgrasppointofthetargetareidentified,thosewillbeexpressedintheconfigurationspace.Andinthispaperapotentialmethod,Laplacepotentialfunction,isappliedtoobtainthepathintheconfigurationspaceinordertoavoidso-calleddeadlockphenomenon.Someimprovementonthegenerationofthepathhasbeenobservedbyapplyingpathsmoothingmethod,whichutilizesthesplinefunctioninterpolation.Thisreducesthecomputationalloadandgeneratesthesmoothpathofthespacerobot.Thevalidityofthisapproachisshownbyafewnumericalsimulations.

KeyWords—SpaceRobot,PathPlanning,CollisionAvoidance,PotentialFunction,SplineInterpolation

I.INTRODUCTION

Inthefuturespacedevelopment,thespacerobotanditsautonomywillbekeyfeaturesofthespacetechnology.Thespacerobotwillplayrolestoconstructspacestructuresandperforminspectionsandmaintenanceofspacecrafts.Theseoperationsareexpectedtobeperformedinanautonomousmannerinplaceofextravehicularactivitiesbyastronauts.

Intheabovespacerobotoperations,abasicandimportanttaskistocapturefreeflyingtargetsonorbitbytheroboticarm.Forthesafecapturingoperation,itwillberequiredtomovethearmfrominitialposturetofinalposturewithoutcollisionswiththetarget.

Theconfigurationspaceandartificialpotentialmethodsareoftenappliedtotheoperationplanningoftheusualrobot.Thisenablestherobotarmtoevadetheobstacleandtomovetowardthetarget.Khatibproposedamotionplanningmethod,inwhichbetweeneachlinkoftherobotandtheobstacletherepulsivepotentialisdefinedandbetweentheend-effecteroftherobotandthegoaltheattractivepotentialisdefinedandbysummingbothofthepotentialsandusingthegradientofthispotentialfieldthepathisgenerated.Thismethodisadvantageousbyitssimplicityandapplicabilityforreal-timeoperation.Howevertheremightbepointsatwhichtherepulsiveforceandtheattractiveforceareequalandthiswillleadtotheso-calleddeadlock.

Inordertoresolvetheaboveissue,afewmethodsareproposedwherethesolutionofLaplaceequationisutilized.Thismethodassuresthepotentialfieldswithoutthelocalminimum,i.e.,nodeadlock.InthismethodbynumericalcomputationLaplaceequationwillbesolvedandgeneratespotentialfield.Thepotentialfieldisdividedintosmallcellsandoneachnodethediscretevalueofthepotentialwillbespecified.

Inthispaperfortheeliminationoftheabovedefects,splineinterpolationtechniqueisproposed.Thenodalpointwhichisgivenasapointofpathwillbedefinedtobeapartofsmoothedsplinefunction.Andnumericalsimulationsareconductedforthepathplanningofthespacerobottocapturethetarget,inwhichthepotentialbysolvingtheLaplaceequationisappliedandgeneratesthesmoothandcontinuouspathbythesplineinterpolationfromtheinitialtothefinalposture.

II.ROBOTMODEL

ThemodelofspacerobotisillustratedinFig.1.

Therobotismountedonaspacecraftandhastworotaryjointswhichallowthein-planemotionoftheend-effecter.Inthiscasewehaveanadditionalfreedomofthespacecraftattitudeangleandthiswillbeconsideredtheadditionalrotaryjoint.Thismeansthatthespacerobotisthreelinkedwith3DOF（DegreeOfFreedom）.Thelengthofeachlinkandtheangleofeachrotaryjointaregivenby

and

（i=1,2,3）,respectively.Inordertosimplifythediscussionsafewassumptionsaremadeinthispaper:

-themotionofthespacerobotisin-plane,i.e.,twodimensionalone.

-effectofrobotarmmotiontothespacecraftattitudeisnegligible.

-robotmotionisgivenbytherelationofstaticgeometryandnotexplicitlydependingontime.

-thetargetsatelliteisinertiallystabilized.

Ingeneralin-planemotionandout-of-planemotionwillbeseparatelyperformed.Soweareabletoassumetheabovefirstonewithoutlossofgenerality.Thesecondassumptionderivesfromthecomparisonoftheratioofmassbetweentherobotarmandthespacecraftbody.Withrespecttothethirdassumptionwefocusongeneratingthepathplanningoftherobotandthisisbasicallygivenbythestaticnatureofgeometryrelationshipandisthereforenotdependingonthetimeexplicitly.Thelastonemeansthesatelliteiscooperative.

Fig.1ModelofTwo-linkSpaceRobot

III.PATHPLANNINGGALGORITHM

A.LaplacePotentialGuidance

ThesolutionoftheLaplaceequation

（1）iscalledaHarmonicpotentialfunction,anditsandminimumvaluestakeplaceonlyontheboundary.Intherobotpathgenerationtheboundarymeansobstacleandgoal.Thereforeinsidetheregionwherethepotentialisdefined,nolocalminimumtakesplaceexceptthegoal.Thiseliminatesthedeadlockphenomenonforpathgeneration.

（1）

TheLaplaceequationcanbesolvednumerically.WedefinetwodimensionalLaplaceequationasbelow:

（2）

AndthiswillbeconvertedintothedifferenceequationandthensolvedbyGauss-Seidelmethod.Inequation

（2）ifwetakethecentraldifferenceformulaforsecondderivatives,thefollowingequationwillbeobtained:

（3）

where

，

arethestep（cell）sizesbetweenadjacentnodesforeachx,ydirection.Ifthestepsizeisassumedequalandthefollowingnotationisused:

Thenequation（3）isexpressedinthefollowingmanner:

（4）

Andasaresult,twodimensionalLaplaceequationwillbeconvertedintotheequation（5）asbelow:

（5）

Inthesamemannerasinthethreedimensionalcase,thedifferenceequationforthethreedimensionalLaplaceequationwillbeeasilyobtainedbythefollowing:

（6）

InordertosolvetheaboveequationsweapplyGauss-Seidelmethodandhaveequationsasfollows:

（7）

where

isthecomputationalresultfromthe（n+1）-thiterativecalculationsofthepotential.

Intheabovecomputations,astheboundaryconditions,acertainpositivenumber

isdefinedfortheobstacleand0forthegoal.Andastheinitialconditionsthesamenumber

isalsogivenforallofthefreenodes.Bythisapproachduringiterativecomputationsthevalueoftheboundarynodeswillnotchangeandthevaluesonlyforfreenodeswillbevarying.Applyingthesamepotentialvaluesastheobstacleandinaccordancewiththeiterativecomputationalprocess,thesmallpotentialaroundthegoalwillbegraduallypropagatinglikesurroundingtheobstacle.Thepotentialfieldwillbebuiltbasedontheaboveprocedure.

Usingtheabovepotentialfieldfrom4nodalpointsadjacenttothenodeonwhichthespacerobotexists,thesmallestnodeisselectedforthepointtomoveto.Thisprocedurefinallyleadsthespacerobottothegoalwithoutcollision.

B.SplineInterpolation

Thepathgivenbytheaboveapproachdoesnotassurethesmoothlyconnectedone.Andifthegoalisnotgivenonthenodalpoint,wehavetopartitionthecellsintomuchmoresmallercells.Thiswillincreasethecomputationalloadandtime.

Inordertoeliminatetheabovedrawbacksweproposetheutilizationofsplineinterpolationtechnique.Byassigningthenodalpointsgivenbythesolutiontoviapointsonthepath,wetrytoobtainthesmoothlyconnectedpathwithaccurateinitialandfinalpoints.

InthispaperthecubicsplinewasappliedbyusingMATLABcommand.

C.ConfigurationSpace

WhenweapplytheLaplacepotential,thepathsearchisassuredonlyinthecasewheretherobotisexpressedtobeapointinthesearchingspace.Theconfigurationspace（C-Space）,wheretherobotisexpressedasapoint,isusedforthepathsearch.ToconverttherealspaceintotheC-Spacethecalculationtojudgetheconditionofcollisionisperformedandifthecollisionexists,thecorrespondingpointintheC-spaceisregardedastheobstacle.Inthispaperwhenthepotentialfieldwasgenerated,theconditionsofallthepointsintherealspace,correspondingtoallthenodes,were

calculated.Thejudgmentofintersectionbetweenasegmentconstitutingtherobotarmandasegmentconstitutingtheobstacleateachnodewasmadeandiftheintersectiontakesplace,thisnodeistreatedastheobstacleintheC-Space.

IV.NUMERICALSIMULATIONS

Basedontheaboveapproachthepathplanningforcapturingatargetsatellitewasexaminedusingaspacerobotmodel.Inthispaperweassumethespacerobotwithtwodimensionaland2DOFroboticarmasshowninFig.1.

Thelengthofeachlinkisgivenasfollows:

l1=1.4[m],l2=2.0[m],l3=2.0[m],

andthetargetsatellitewasassumed1msquare.Thegrasphandle,0.1msquare,waslocatedatacenterofonesideofthetarget.Sothishandleisagoalofthepath.

Letusexplainthegeometricalrelationbetweenthespacerobotandthetargetsatellite.Whenweconsidertheoperationaftercapturingthetarget,itisdesirableforthespacerobottohavethelargemanipulability.Thereforeinthispapertheend-effecterwillreachthetargetwhenthemanipulabilityismaximized.Inthe3DOFcase,notdependingonthespacecraftbodyattitude,themanipulabilityismeasuredby

.Andifweassumetheend-effectorofthespacerobotshouldbeverticaltothetarget,thenallofthejointsanglesarepredeterminedasfollows:

Asallthejointsangles