机器人路径规划毕业论文外文翻译.docx

机器人路径规划毕业论文外文翻译.docx

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机器人路径规划毕业论文外文翻译

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外文文献：

SpaceRobotPathPlanning

forCollisionAvoidance

YuyaYanoshitaandShinichiTsuda

Abstract—Thispaperdealswithapathplanningofspacerobotwhichincludesacollisionavoidancealgorithm.Forthefuturespacerobotoperation,autonomousandself-containedpathplanningismandatorytocaptureatargetwithouttheaidofgroundstation.Especiallythecollisionavoidancewithtargetitselfmustbealwaysconsidered.Oncethelocation,shapeandgrasppointofthetargetareidentified,thosewillbeexpressedintheconfigurationspace.Andinthispaperapotentialmethod.

Laplacepotentialfunctionisappliedtoobtainthepathintheconfigurationspaceinordertoavoidso-calleddeadlockphenomenon.Improvementonthegenerationofthepathobservedbyapplyingpathsmoothingmethod,whichutilizesthesplinefunctioninterpolation.Thisreducesthecomputationalloadandgeneratesthesmoothpathofthespacerobot.Thevalidityofthisapproachisshownbyafewnumericalsimulations.

KeyWords—SpaceRobot,PathPlanning,CollisionAvoidance,PotentialFunction,SplineInterpolation

I.INTRODUCTION

Inthefuturespacedevelopment,thespacerobotanditsautonomywillbekeyfeaturesofthespacetechnology.Thespacerobotwillplayrolestoconstructspacestructuresandperforminspectionsandmaintenanceofspacecrafts.Theseoperationsareexpectedtobeperformedinanautonomous.

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.

Therobotismountedonaspacecraftand-planemotionoftheend-effecter.Inthiscaseweadditionalfreedomofthespacecraftattitudeangleandthiswillbeconsideredtheadditionalrotaryjoint.Thismeansthatthespacerobotisthreelinkedwith3DOF（DegreeOfFreedom）.Thelengthofeachlinkandtheangleofeachrotaryjointaregivenbyand（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-Seidelmethodand+1）-thiterativecalculationsofthepotential.

Intheabovecomputations,astheboundaryconditions,acertainpositivenumberisdefinedfortheobstacleand0forthegoal.Andastheinitialconditionsthesamenumberisalsogivenforallofthefreenodes.Bythisapproachduringiterativecomputationsthevalueoftheboundarynodeswillnotchangeandthevaluesonlyforfreenodeswillbevarying.Applyingthesamepotentialvaluesastheobstacleandinaccordancewiththeiterativecomputationalprocess,thesmallpotentialaroundthegoalwillbegraduallypropagatinglikesurroundingtheobstacle.Thepotentialfieldwillbebuiltbasedontheaboveprocedure.

Usingtheabovepotentialfieldfrom4nodalpointsadjacenttothenodeonwhichthespacerobotexists,thesmallestnodeisselectedforthepointtomoveto.Thisprocedurefinallyleadsthespacerobottothegoalwithoutcollision.

B.SplineInterpolation

Thepathgivenbytheaboveapproachdoesnotassurethesmoothlyconnectedone.Andifthegoalisnotgivenonthenodalpoint,wethecellsintomuchmoresmallercells.Thiswillincreasethecomputationalloadandtime.

Inordertoeliminatetheabovedrawbacksweproposetheutilizationofsplineinterpolationtechnique.Byassigningthenodalpointsgivenbythesolutiontoviapointsonthepath,wetrytoobtainthesmoothlyconnectedpathwithaccurateinitialandfinalpoints.

InthispaperthecubicsplinewasappliedbyusingMATLABcommand.

C.ConfigurationSpace

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

IV.NUMERICALSIMULATIONS

Basedontheaboveapproachthepathplanningforcapturingatargetsatellitewasexaminedusingaspacerobotmodel.Inthispaperweassumethespacerobotwithtwodimensionaland2DOFroboticarmasshowninFig.1.

Thelengthofeachlinkisgivenasfollows:

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

andthetargetsatellitewasassumed1msquare.Thegraspthegeometricalrelationbetweenthespacerobotandthetargetsatellite.Whenweconsidertheoperationaftercapturingthetarget,itisdesirableforthespacerobottothispapertheend-effecterwillreachthetargetwhenthemanipulabilityismaximized.Inthe3DOFcase,notdependingonthespacecraftbodyattitude,themanipulabilityismeasuredby.Andifweassumetheend-effectorofthespacerobotshouldbeverticaltothetarget,thenallofthejointsanglesarepredeterminedasfollows:

Asallthejointsanglesaredetermined,therelativepositionbetweenthespacecraftandthetargetisalsodecideduniquely.Ifthespacecraftisassumedtolocateattheoriginoftheinertialframe（0,0）,thegoalisgivenby（-3.27,-2.00）intheabovecase.Basedonthesepreparations,wecansearchthepathtothegoalbymovingthearmintheconfigurationspace.

Twosimulationsforpathplanningwerecarriedoutandtheresultsareshownbelow.

A.2DOFRobot

Inordertosimplifythesituation,theattitu