基于MATLAB的PUMA560机器人运动仿真与轨迹规划5.docx
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基于MATLAB的PUMA560机器人运动仿真与轨迹规划5.docx
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基于MATLAB的PUMA560机器人运动仿真与轨迹规划5
Themovementsimulationandtrajectoryplanningof
PUMA560robot
Shibozhao
Abstract:
Inthisessay,weadoptmodelingmethodtostudyPUMA560robotintheuseofRoboticsToolboxbasedonMATLAB.Wemainlyfocusonthreeproblemsinelude:
theforwardkinematies,inversekinematiesandtrajectoryplanning.Atthesametime,wesimulateeachproblemabove,observethemovementofeachjointandexplainthereasonfortheselectionofsomeparameters.Finally,weverifythefeasibilityofthemodelingmethod.
Keywords:
PUMA560robot;kinematics;RoboticsToolbox;Thesimulation;
I.Introduction
Asautomationbecomesmoreprevalentinpeop'life,robotbeginsmorefurthertochangepeoplesworld.Therefore,weareobligedtostudythemechanismofrobot.Howtomove,howtodeterminethepositionoftargetandtherobotitself,andhowtodeterminetheanglesofeachpointneededtoobtaintheposition.Inordertostudyrobotmorevalidly,weadoptrobotsimulationandobject-orientedmethodtosimulatetherobotkinematiccharacteristics.Wehelpresearchersunderstandtheconfigurationandlimitoftherobotsvvorkingspaceandrevealthemechanismofreasonablemovementandcontrolalgorithm.Wecanlettheusertoseetheeffectofthedesign,andtimelyfindouttheshortcomingsandtheinsufficiency,whichhelpusavoidtheaccidentandunnecessarylossesonoperatingentity.ThispaperestablishesamodelforRobotPUMA560byusingRoboticsToolbox,andstudytheforwardkinematicsandinversekinematicsoftherobotandtrajectoryplanningproblem.
II.TheintroductionoftheparametersforthePUMA560robot
PUMA560robotisproducedbyUnimationCompanyandisdefinedas6degreesoffreedomrobot.Itconsists6degreesoffreedomrotaryjoints(Thestructurediagramisshowninfigure1).Referringtothehumanbodystructure,thefirstjoin(J1)calledwaistjoints.Thesecondjoin(J2)calledshoulderjoint.Thethirdjoint(J3)calledelbowjoints.ThejointsJ4J5,J6,arecalledwristjoints.Where,thefirstthreejointsdeterminethepositionofwristrefereneepoint.Thelatterthreejointsdeterminetheorientationofthewrist.TheaxisofthejointJ1locatedverticaldirection.TheaxisdirectionofjointJ2,J3ishorizontalandparallel,a3metersapart.JointJ1,J2axisareverticalintersectionandjointJ3,J4axisareverticalcrisscross,distaneeofa4.Thelatterthreejointsaxeshaveanintersectionpointwhichisalsooriginpointfor{4},{5},{6}coordinate.(Eachlinkcoordinatesystemisshowninfigure2)
【4】
Figithestructureofpuma560
WhenPUMA560Robotisintheinitialstate,thecorrespondinglinkparametersareshowedintable1.a2=0.4381m,a3=0.0203m,d2=0.1491m,d40.4331m
Theexpressionofparameters:
Letlengthofthebar:
=representthedistaneebetweenzi4andzialongxi4.
Torsionangle:
i4denotetheanglerevolvingx^fromtozi.
ThemeasuringdistaneebetweenxiJtandxialongziisdi.
Jointangle^istheanglerevoIvingfrom%4toXialongZi.
⑷
Table1theparametersofpuma560
link
:
ij/()
a/()
R/()
di/(m)
Range
1
0
0
90
0
-160~160
2
-90
0
0
0.1491
-225~45
3
0
0.4318
-90
0
-45~225
4
-90
-0.0213
0
0.4331
-110~170
5
90
0
0
0
-100~100
6
-90
0
0
0
-266~266
III.ThemovementanalysisofPuma560robot
3.1Forwardkinematic
Definition:
Forwardkinematicsproblemistosolvetheposeofend-effectercoordinaterelativetothebasecoordinatewhengiventhegeometricparametersoflinkandthetranslationofjoint.Letmakethingsclearly
Whatyouaregiven:
thelengthofeachlinkandtheangleofeachjoint
Whatyoucanfind:
thepositionofanypoint(i.e.its(x,y,z/,1,)coordinate)
3.2Thesolutionofforwardkinematics
Method:
Algebraicsolution
Principal:
x=k(q)Thekinematicmodelofarobotcanbewrittenlikethis,whereqdenotesthevectorofjointvariable,xdenotesthevectoroftaskvariable,k()isthedirectkinematicfunctionthatcanbederivedforanyrobotstructure.
Theoriginofk(q)
Eachjointisassignedacoordinateframe.UsingtheDenavit-Hartenbergnotation,youneed4parameters咚,a,日,d)todescribehowaframe()relatestoapreviousframe(i-1)i:
T.Fortwoframespositionedinspace,thefirstcanbemovedintocoincideneewiththesecondbyasequeneeof4operations:
1.RotatearoundtheXijaxisbyananglei」.
2.TranslatealongtheXi』axisbyadistaneei^.
3.Rotatearoundthenewzaxisbyanangle.
4.Translatealongthenewzaxisbyadistance.
3.3lnversekinematic
Definition:
RobotinversekinematiCSproblemisthatresolveeachjointvariablesoftherobotbasedongiventhepositionanddirectionoftheend-effecterorofthelink(ItcanshowaspositionmatrixT).AsforPUMA560Robot,variable円二6needtobe
resolved.
Letmakethingsclearly:
Whatyouaregiven:
Thelengthofeachlinkandthepositionofsomepointontherobot.
Whatyoucanfind:
Theanglesofeachjointneededtoobtainthatposition.
3.4Thesolutionofinversekinematics
Method:
Algebraicsolution
Principal:
x=j(q)q
WhereJ二fk/:
qistherobotJacobian.JacobiancanbeseenasamappingfromJointvelocityspacetoOperationalvelocityspace.
3.5Thetrajectoryplanningofrobotkinematics
Thetrajectoryplanningofrobotkinematicsmainlystudiesthemovementofrobot.Ourgoalistoletrobotmovesalonggivenpath.Wecandividethetrajectoryofrobotsintotwokinds.Oneispointtopointwhiletheotheristrajectorytracking.Theformerisonlyfocusonspecificlocationpoint.Thelattercaresthewholepath.
Trajectorytrackingisbasedonpointtopoint,buttherouteisnotdetermined.So,trajectorytrackingonlycanensuretherobotsarrivesthedesiredposeintheendposition,butcannotensureinthewholetrajectory.Inordertolettheend-effecterarrivingdesiredpath,wetrytoletthedistancebetweentwopathsassmallaspossiblewhenweplanCartesianspacepath.Inaddition,inordertoeliminateposeandpositionuncertaintybetweentwopathpoints,weusuallydomotivationplanamongeveryjointsundergangcontrol.Inaword,leteachjointhassamerundurationwhenwedotrajectoryplanninginjointspace.
Atsametime,inordertomakethetrajectoryplanningmoresmoothly,weneedtoapplytheinterpolatingmethod.
Method:
polynomialinterpolating[1]
Given:
boundarycondition
飞(0)6g
9(tf)9f
(0)0
J,(tf)=0L
Output:
jointspacetrajectorytbetweentwopoints
23
rt=a。
a2tast
Polynomialcoefficientcanbecomputedasfollows:
0)=%
a^=0
3
a22(71f-V0)
tf
2
a3二--Tf-^o)
tf
(1.3)
(1.4)
(1.5)
(1.6)
IV.KinematicsimulationbasedonMATLAB
•Howtouselink
InRoboticsToolbox,function'nk'isusedtocreateabar.Therearetwomethods.OneistoadoptstandardD-HparametersandtheotheristoadoptmodifiedD-Hparameters,whichcorrespondtotwocoordinatesystems.WeadoptmodifiedD-Hparametersinourpaper.Thefirst4elementsinFunctionlink'areaa,0d.Thelastelementis0(representRotationaljoint)or1(representtranslationjoint).Thefinalparameteroflinkisw/hinbafneansstandardormodified.Thedefaultisstandard.
Therefore,ifyouwanttobuildyourownrobot,youmayusefunctionlink'.Youcancallitlikethis:
'L1=link([00pi00],'modified');
•Thestepofsimulationis:
Step1:
Firstofall,accordingtothedatafromTable1,webuildsimulationprogramoftherobot(showninAppendixrob1.m).
Step2:
Present3Dfigureoftherobot(showninFig4).Thisisathree-dimensionalfigurewhentherobotlocatedtheinitialposition(齐=0).Wecanadjustthepositionofthesliderincontrolpaneltomakethejointrotation(inFig5),justlikecontrollingrealrobot.
Step3PointAlocatedatinitialposition.ItcandedescribedasqA=[0,0,0,0,0,0].ThetargetpointisPointB.ThejointrotationanglecanbeexpressedasqB=[0,-0.7854,-0.7854,0,0.392,0].Wecanachievethesolutionofforward
kinematicsandobtaintheend-effecterposerelativetothebasecoordinatesystemis(0.737,0.149,0.326),relativetothethreeaxesofrotationangleisthe(0,0,-1).Therobot'sthrdmensionalposeinqBisshowninFig6.
Step4:
Accordingtothehomogeneoustransformationmatrix,wecanobtaineachjointvariablefromtheinitialpositiontothespecifiedlocation
Step5SimulatetrajectoryfrompointAtopointB.Thesimulationtimeis10s.Timeintervalis0.1s.Then,wecanpicturelocationimage,theangularvelocityandangularaccelerationimage(shownasFig8)whichdescribeeachjointtransformsovertimefromPointAtoPointB.Inthispaper,weonlypresentthepictureofjoint3.ByusingthefunctionT=fkine(r,q)',weobtainT'athree-dimensionalmatrix.Thefirsttwodimensionalmatrixrepresentthecoordinatechangewhilethelastdimensionistimet'
0.8
0.6
0.4
0.2
Fig4
0
-0.2
-0.4
-0.6
0
Fig5
1
0.8
0.6
0.4
0.2
0.5
Z0
-0.5
-1
1
Figure1
S3
zhaoshibo
lx:
ax:
0737
y:
0.149
z:
0326
0.92+
ay:
0.000
az:
-Q.3B2
I
1「1
:
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”A
+\\、亠M
11
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fl.
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11
q2
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":
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*%
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q4
d
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-Q73&4
qe
q5
Q.392
A
il
Fig7
345678910
timet/s
2
o
5-1
o
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dar/orana
o
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8910
34567
timet/s
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timet/s
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//nnrLa—nHecca
Fig8
VTheproblemduringthesimulation
•Thereasonforselectionofsomeparameter
Theparameteroflink:
Fromkinematicsimulationandprog
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