matlab机器人工具箱matlabroboticstoolboxdemo.docx
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matlab机器人工具箱matlabroboticstoolboxdemo
MATLABROBOTTOOL
rtdemo演示
一、rtdemo机器人工具箱演示
>>rtdemo
%
二、transfermations坐标转换
%Inthefieldofroboticstherearemanypossiblewaysofrepresenting
%positionsandorientations,butthehomogeneoustransformationiswell
%matchedtoMATLABspowerfultoolsformatrixmanipulation.
%
%HomogeneoustransformationsdescribetherelationshipsbetweenCartesian
%coordinateframesintermsoftranslationandorientation.
%Apuretranslationof0.5mintheXdirectionisrepresentedby
transl（0.5,0.0,0.0）
ans=
1.0000000.5000
01.000000
001.00000
0001.0000
%
%arotationof90degreesabouttheYaxisby
roty（pi/2）
ans=
0.000001.00000
01.000000
-1.000000.00000
0001.0000
%
%andarotationof-90degreesabouttheZaxisby
rotz（-pi/2）
ans=
0.00001.000000
-1.00000.000000
001.00000
0001.0000
%
%thesemaybeconcatenatedbymultiplication
t=transl（0.5,0.0,0.0）*roty（pi/2）*rotz（-pi/2）
t=
0.00000.00001.00000.5000
-1.00000.000000
-0.0000-1.00000.00000
0001.0000
%
%Ifthistransformationrepresentedtheoriginofanewcoordinateframewithrespect
%totheworldframeorigin（0,0,0）,thatneworiginwouldbegivenby
t*[0001]'
ans=
0.5000
0
0
1.0000
pause%anykeytocontinue
%
%theorientationofthenewcoordinateframemaybeexpressedintermsof
%Eulerangles
tr2eul（t）
ans=
01.5708-1.5708
%
%orroll/pitch/yawangles
tr2rpy（t）
ans=
-1.57080.0000-1.5708
pause%anykeytocontinue
%
%Itisimportanttonotethattranformmultiplicationisingeneralnot
%commutativeasshownbythefollowingexample
rotx（pi/2）*rotz（-pi/8）
ans=
0.92390.382700
-0.00000.0000-1.00000
-0.38270.92390.00000
0001.0000
rotz（-pi/8）*rotx（pi/2）
ans=
0.92390.0000-0.38270
-0.38270.0000-0.92390
01.00000.00000
0001.0000
%
%
pause%anykeytocontinue
echooff
三、Trajectory齐次方程
%Thepathwillmovetherobotfromitszeroangleposetotheupright（or
%READY）pose.
%
%Firstcreateatimevector,completingthemotionin2secondswitha
%sampleintervalof56ms.
t=[0:
.056:
2];
pause%hitanykeytocontinue
%
%Apolynomialtrajectorybetweenthe2posesiscomputedusingjtraj（）
%
q=jtraj（qz,qr,t）;
pause%hitanykeytocontinue
%
%Forthisparticulartrajectorymostofthemotionisdonebyjoints2and3,
%andthiscanbeconvenientlyplottedusingstandardMATLABoperations
subplot（2,1,1）
plot（t,q（:
2））
title（'Theta'）
xlabel（'Time（s）'）;
ylabel（'Joint2（rad）'）
subplot（2,1,2）
plot（t,q（:
3））
xlabel（'Time（s）'）;
ylabel（'Joint3（rad）'）
pause%hitanykeytocontinue
%
%Wecanalsolookatthevelocityandaccelerationprofiles.Wecould
%differentiatetheangletrajectoryusingdiff（）,butmoreaccurateresults
%canbeobtainedbyrequestingthatjtraj（）returnangularvelocityand
%accelerationasfollows
[q,qd,qdd]=jtraj（qz,qr,t）;
%
%whichcanthenbeplottedasbefore
subplot（2,1,1）
plot（t,qd（:
2））
title（'Velocity'）
xlabel（'Time（s）'）;
ylabel（'Joint2vel（rad/s）'）
subplot（2,1,2）
plot（t,qd（:
3））
xlabel（'Time（s）'）;
ylabel（'Joint3vel（rad/s）'）
pause
（2）
%andthejointaccelerationprofiles
subplot（2,1,1）
plot（t,qdd（:
2））
title（'Acceleration'）
xlabel（'Time（s）'）;
ylabel（'Joint2accel（rad/s2）'）
subplot（2,1,2）
plot（t,qdd（:
3））
xlabel（'Time（s）'）;
ylabel（'Joint3accel（rad/s2）'）
pause%anykeytocontinue
echooff
四、forwardkinematics运动学正解
%ForwardkinematicsistheproblemofsolvingtheCartesianpositionand
%orientationofamechanismgivenknowledgeofthekinematicstructureand
%thejointcoordinates.
%
%ConsiderthePuma560exampleagain,andthejointcoordinatesofzero,
%whicharedefinedbyqz
qz
qz=
000000
%
%Theforwardkinematicsmaybecomputedusingfkine（）withanappropropriate
%kinematicdescription,inthiscase,thematrixp560whichdefines
%kinematicsforthe6-axisPuma560.
fkine（p560,qz）
ans=
1.0000000.4521
01.00000-0.1500
001.00000.4318
0001.0000
%
%returnsthehomogeneoustransformcorrespondingtothelastlinkofthe
%manipulator
pause%anykeytocontinue
%
%fkine（）canalsobeusedwithatimesequenceofjointcoordinates,or
%trajectory,whichisgeneratedbyjtraj（）
%
t=[0:
.056:
2];%generateatimevector
q=jtraj（qz,qr,t）;%computethejointcoordinatetrajectory
%
%thenthehomogeneoustransformforeachsetofjointcoordinatesisgivenby
T=fkine（p560,q）;
%
%whereTisa3-dimensionalmatrix,thefirsttwodimensionsarea4x4
%homogeneoustransformationandthethirddimensionistime.
%
%Forexample,thefirstpointis
T（:
:
1）
ans=
1.0000000.4521
01.00000-0.1500
001.00000.4318
0001.0000
%
%andthetenthpointis
T（:
:
10）
ans=
1.0000-0.000000.4455
-0.00001.00000-0.1500
001.00000.5068
0001.0000
pause%anykeytocontinue
%
%Elements（1:
3,4）correspondtotheX,YandZcoordinatesrespectively,and
%maybeplottedagainsttime
subplot（3,1,1）
plot（t,squeeze（T（1,4,:
）））
xlabel（'Time（s）'）;
ylabel（'X（m）'）
subplot（3,1,2）
plot（t,squeeze（T（2,4,:
）））
xlabel（'Time（s）'）;
ylabel（'Y（m）'）
subplot（3,1,3）
plot（t,squeeze（T（3,4,:
）））
xlabel（'Time（s）'）;
ylabel（'Z（m）'）
pause%anykeytocontinue
%
%orwecouldplotXagainstZtogetsomeideaoftheCartesianpathfollowed
%bythemanipulator.
%
subplot（1,1,1）
plot（squeeze（T（1,4,:
））,squeeze（T（3,4,:
）））;
xlabel（'X（m）'）
ylabel（'Z（m）'）
grid
pause%anykeytocontinue
echooff
四、Animation动画
clf
%
%Thetrajectorydemonstrationhasshownhowajointcoordinatetrajectory
%maybegenerated
t=[0:
.056:
2]';%generateatimevector
q=jtraj（qz,qr,t）;%generatejointcoordinatetrajectory
%
%theoverloadedfunctionplot（）animatesastickfigurerobotmoving
%alongatrajectory.
plot（p560,q）;
%Thedrawnlinesegmentsdonotnecessarilycorrespondtorobotlinks,but
%jointheoriginsofsequentiallinkcoordinateframes.
%
%Asmallright-anglecoordinateframeisdrawnontheendoftherobottoshow
%thewristorientation.
%
%Ashadowappearsonthegroundwhichhelpstogivesomebetterideaofthe
%3Dobject.
pause%anykeytocontinue
%
%Wecanalsoplaceadditionalrobotsintoafigure.
%
%Let'smakeacloneofthePumarobot,butchangeitsnameandbaselocation
p560_2=p560;
p560_2.name='anotherPuma';
p560_2.base=transl（-0.5,0.5,0）;
holdon
plot（p560_2,q）;
pause%anykeytocontinue
%Wecanalsohavemultipleviewsofthesamerobot
clf
plot（p560,qr）;
figure
plot（p560,qr）;
view（40,50）
plot（p560,q）
pause%anykeytocontinue
%
%Sometimesit'susefultobeabletomanuallydrivetherobotaroundto
%getanunderstandingofhowitworks.
drivebot（p560）
%
%usethesliderstocontroltherobot（infactbothviews）.Hittheredquit
%buttonwhenyouaredone.
echooff
五、InverseKinematics运动学逆解
%
%Inversekinematicsistheproblemoffindingtherobotjointcoordinates,
%givenahomogeneoustransformrepresentingthelastlinkofthemanipulator.
%ItisveryusefulwhenthepathisplannedinCartesianspace,forinstance
%astraightlinepathasshowninthetrajectorydemonstration.
%
%Firstgeneratethetransformcorrespondingtoaparticularjointcoordinate,
q=[0-pi/4-pi/40pi/80]
q=
0-0.7854-0.785400.39270
T=fkine（p560,q）;
%
%Nowtheinversekinematicprocedureforanyspecificrobotcanbederived
%symbolicallyandingeneralanefficientclosed-formsolutioncanbe
%obtained.Howeverwearegivenonlyageneralizeddescriptionofthe
%manipulatorintermsofkinematicparameterssoaniterativesolutionwill
%beused.Theprocedureisslow,andthechoiceofstartingvalueaffects
%searchtimeandthesolutionfound,sinceingeneralamanipulatormay
%haveseveralposeswhichresultinthesametransformforthelast
%link.Thestartingpointforthefirstpointmaybespecified,orelseit
%defaultstozero（whichisnotaparticularlygoodchoiceinthiscase）
qi=ikine（p560,T）;
qi'
ans=
-0.0000
-0.7854
-0.7854
-0.0000
0.3927
0.0000
%
%Comparedwiththeoriginalvalue
q
q=
0-0.7854-0.785400.39270
%
%Asolutionisnotalwayspossible,forinstanceifthespecifiedtransform
%describesapointoutofreachofthemanipulator.Asmentionedabove
%thesolutionsarenotnecessarilyunique,andtherearesingularities
%atwhichthemanipulatorlosesdegreesoffreedomandjointcoordinates
%becomelinearlydependent.
pause%anykeytocontinue
%
%Toexaminetheeffectatasingularityletsrepeatthelastexamplebutfora
%differentpose.Atthe`ready'positiontwoofthePuma'swristaxesare
%alignedresultinginthelossofonedegreeoffreedom.
T=fkine（p560,qr）;
qi=ikine（p560,T）;
qi'
ans=
-0.0000
1.5238
-1.4768
-0.0000
-0.0470
0.0000
%
%whichisnotthesameastheoriginaljointangle
qr
qr=
01.5708-1.5708000
pause%anykeytocontinue
%
%Howeverbothresultinthesameend-effectorposition
fkine（p560,qi）-fkine（p560,qr）
ans=
1.0e-015*
0-0.0000-0.0902-0.0694
0.00000-0.00000
0.09020.000000.1110
0000
pause%anykeytocontinue
%Inversekinematicsmayalsobecomputedforatrajectory.
%IfwetakeaCartesianstraightlinepath
t=[0:
.056:
2];%createatimevector
T1=transl（0.6,-0.5,0.0）%definethestartpoint
T1=
1.0000000.6000
01.00000-0.5000
001.00000
0001.0000
T2=transl（0.4,0.5,0.2）%anddestination
T
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