serialRobotInteractiveLimits.py

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  1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  2# This is an EXUDYN example
  3#
  4# Details:  Example of a serial robot with redundant coordinates
  5#
  6# Author:   Johannes Gerstmayr
  7# Date:     2020-02-16
  8# Revised:  2023-03-22
  9# Note:     This example uses the redundant mbs approach; The kinematic tree approach would be much faster!
 10#
 11# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
 12#
 13#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 14
 15
 16import exudyn as exu
 17from exudyn.itemInterface import *
 18from exudyn.utilities import *
 19from exudyn.rigidBodyUtilities import *
 20from exudyn.graphicsDataUtilities import *
 21from exudyn.robotics import *
 22from exudyn.robotics.motion import Trajectory, ProfileConstantAcceleration, ProfilePTP
 23from exudyn.interactive import InteractiveDialog
 24
 25import numpy as np
 26from numpy import linalg as LA
 27from math import pi
 28
 29SC = exu.SystemContainer()
 30mbs = SC.AddSystem()
 31
 32sensorWriteToFile = True
 33
 34mbs.variables['controlActive'] = 1 #flag to deactivate control
 35#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 36
 37#now in the new structure
 38
 39mode='newDH'
 40
 41graphicsBaseList = [GraphicsDataOrthoCubePoint([0,0,-0.4], [0.12*1,0.12*1,0.6], color4grey)]
 42graphicsBaseList +=[GraphicsDataCylinder([0,0,0], [0.5,0,0], 0.0025, color4red)]
 43graphicsBaseList +=[GraphicsDataCylinder([0,0,0], [0,0.5,0], 0.0025, color4green)]
 44graphicsBaseList +=[GraphicsDataCylinder([0,0,0], [0,0,0.5], 0.0025, color4blue)]
 45graphicsBaseList +=[GraphicsDataCylinder([0,0,-0.1], [0,0,0.1], 0.05, color4blue)]
 46graphicsBaseList +=[GraphicsDataCheckerBoard([0,0,-0.7], [0,0,1], size=2)]
 47#newRobot.base.visualization['graphicsData']=graphicsBaseList
 48
 49ty = 0.03
 50tz = 0.04
 51zOff = -0.05
 52toolSize= [0.05,0.5*ty,0.06]
 53graphicsToolList = [GraphicsDataCylinder(pAxis=[0,0,zOff], vAxis= [0,0,tz], radius=ty*1.5, color=color4red)]
 54graphicsToolList+= [GraphicsDataOrthoCubePoint([0,ty,1.5*tz+zOff], toolSize, color4grey)]
 55graphicsToolList+= [GraphicsDataOrthoCubePoint([0,-ty,1.5*tz+zOff], toolSize, color4grey)]
 56
 57
 58#changed to new robot structure July 2021:
 59newRobot = Robot(gravity=[0,0,0*9.81],
 60              base = RobotBase(visualization=VRobotBase(graphicsData=graphicsBaseList)),
 61              tool = RobotTool(HT=HTtranslate([0,0,0.1]), visualization=VRobotTool(graphicsData=graphicsToolList)),
 62             referenceConfiguration = []) #referenceConfiguration created with 0s automatically
 63
 64#modDHKK according to Khalil and Kleinfinger, 1986
 65link0={'stdDH':[0,0,0,pi/2],
 66       'modDHKK':[0,0,0,0],
 67        'mass':20,  #not needed!
 68        'inertia':np.diag([1e-8,0.35,1e-8]), #w.r.t. COM!
 69        'COM':[0,0,0]}
 70
 71link1={'stdDH':[0,0,0.4318,0],
 72       'modDHKK':[0.5*pi,0,0,0],
 73        'mass':17.4,
 74        'inertia':np.diag([0.13,0.524,0.539]), #w.r.t. COM!
 75        'COM':[-0.3638, 0.006, 0.2275]}
 76
 77link2={'stdDH':[0,0.15,0.0203,-pi/2],
 78       'modDHKK':[0,0.4318,0,0.15],
 79        'mass':4.8,
 80        'inertia':np.diag([0.066,0.086,0.0125]), #w.r.t. COM!
 81        'COM':[-0.0203,-0.0141,0.07]}
 82
 83link3={'stdDH':[0,0.4318,0,pi/2],
 84       'modDHKK':[-0.5*pi,0.0203,0,0.4318],
 85        'mass':0.82,
 86        'inertia':np.diag([0.0018,0.0013,0.0018]), #w.r.t. COM!
 87        'COM':[0,0.019,0]}
 88
 89link4={'stdDH':[0,0,0,-pi/2],
 90       'modDHKK':[0.5*pi,0,0,0],
 91        'mass':0.34,
 92        'inertia':np.diag([0.0003,0.0004,0.0003]), #w.r.t. COM!
 93        'COM':[0,0,0]}
 94
 95link5={'stdDH':[0,0,0,0],
 96       'modDHKK':[-0.5*pi,0,0,0],
 97        'mass':0.09,
 98        'inertia':np.diag([0.00015,0.00015,4e-5]), #w.r.t. COM!
 99        'COM':[0,0,0.032]}
100linkList=[link0, link1, link2, link3, link4, link5]
101
102for link in linkList:
103    newRobot.AddLink(RobotLink(mass=link['mass'],
104                               COM=link['COM'],
105                               inertia=link['inertia'],
106                               localHT=StdDH2HT(link['stdDH']),
107                               ))
108
109cnt = 0
110for link in newRobot.links:
111    color = color4list[cnt]
112    color[3] = 0.75 #make transparent
113    link.visualization = VRobotLink(jointRadius=0.06, jointWidth=0.08, showMBSjoint=True, linkWidth=0.05,
114                                    linkColor=color, showCOM= False )
115    cnt+=1
116
117#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
118#configurations and trajectory
119q0 = [0,0,0,0,0,0] #zero angle configuration
120
121# q1 = [0, pi/8, pi*0.75, 0,pi/8,0] #configuration 1
122# q2 = [pi,-pi, -pi*0.5,1.5*pi,-pi*2,pi*2] #configuration 2
123# q3 = [3*pi,0,-0.25*pi,0,0,0] #zero angle configuration
124
125#trajectory generated with optimal acceleration profiles:
126trajectory = Trajectory(initialCoordinates=q0, initialTime=0)
127# trajectory.Add(ProfileConstantAcceleration(q3,0.25))
128# trajectory.Add(ProfileConstantAcceleration(q1,0.25))
129# trajectory.Add(ProfileConstantAcceleration(q2,0.25))
130trajectory.Add(ProfileConstantAcceleration(q0,0.25))
131#traj.Add(ProfilePTP([1,1],syncAccTimes=False, maxVelocities=[1,1], maxAccelerations=[5,5]))
132
133# x = traj.EvaluateCoordinate(t,0)
134
135
136#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
137#test robot model
138#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
139#control parameters, per joint:
140fc=1
141Pcontrol = 0.1*np.array([40000, 40000, 40000, 10*100, 10*100, 10*10])
142Dcontrol = np.array([400,   400,   100,   10*1,   10*1,   10*0.1])
143Pcontrol = fc*Pcontrol
144Dcontrol = fc*Dcontrol
145#soft:
146#Pcontrol = [4000, 4000, 4000, 100, 100, 10]
147#Dcontrol = [40,   40,   10,   1,   1,   0.1]
148
149#desired angles:
150qE = q0
151qE = q0
152tStart = [0,0,0, 0,0,0]
153duration = 0.1
154
155
156jointList = [0]*newRobot.NumberOfLinks() #this list must be filled afterwards with the joint numbers in the mbs!
157
158def ComputeMBSstaticRobotTorques(newRobot):
159    q=[]
160    for joint in jointList:
161        q += [mbs.GetObjectOutput(joint, exu.OutputVariableType.Rotation)[2]] #z-rotation
162    HT=newRobot.JointHT(q)
163    return newRobot.StaticTorques(HT)
164
165#++++++++++++++++++++++++++++++++++++++++++++++++
166#base, graphics, object and marker:
167
168objectGround = mbs.AddObject(ObjectGround(referencePosition=HT2translation(newRobot.GetBaseHT()),
169                                      #visualization=VObjectGround(graphicsData=graphicsBaseList)
170                                          ))
171
172
173#baseMarker; could also be a moving base!
174baseMarker = mbs.AddMarker(MarkerBodyRigid(bodyNumber=objectGround, localPosition=[0,0,0]))
175
176
177
178#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
179#build mbs robot model:
180robotDict = newRobot.CreateRedundantCoordinateMBS(mbs, baseMarker=baseMarker)
181
182jointList = robotDict['jointList'] #must be stored there for the load user function
183
184unitTorques0 = robotDict['unitTorque0List'] #(left body)
185unitTorques1 = robotDict['unitTorque1List'] #(right body)
186
187loadList0 = robotDict['jointTorque0List'] #(left body)
188loadList1 = robotDict['jointTorque1List'] #(right body)
189#print(loadList0, loadList1)
190
191
192#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
193#add CartesianSpringDamper for mouse drag
194gripperBody=robotDict['bodyList'][-1]
195gripperLength = 0.1 #in z-direction
196markerGripper = mbs.AddMarker(MarkerBodyPosition(bodyNumber=gripperBody, localPosition=[0,0,gripperLength]))
197markerGround0 =  mbs.AddMarker(MarkerBodyPosition(bodyNumber=objectGround))
198
199# def UFcartesianSD(mbs, t, itemNumber, displacement, velocity, stiffness, damping, offset):
200#     if mbs.variables['controlActive']:
201#         return [0,0,0]
202#     else:
203#         p = SC.GetCurrentMouseCoordinates(True) #True=OpenGL coordinates; 2D
204#         A = np.array(SC.GetRenderState()['modelRotation'])
205#         # print('p=',p)
206#         # print('u=',displacement)
207#         p3D = A@np.array([p[0],p[1],0.])
208
209#         dp = displacement-p3D
210#         f = [stiffness[0]*dp[0], stiffness[1]*dp[1], stiffness[2]*dp[2]]
211#         return f
212
213
214kSD = 50000*0.1
215dSD = kSD*0.01 #damping included in robot
216gripperSD = mbs.AddObject(CartesianSpringDamper(markerNumbers=[markerGround0, markerGripper],
217                                                stiffness=[kSD,kSD,kSD],
218                                                damping=[dSD,dSD,dSD],
219                                                #springForceUserFunction=UFcartesianSD,
220                                                visualization=VCartesianSpringDamper(show=False), #do not show, looks weird
221                                                ))
222mbs.variables['gripperSD'] = gripperSD
223
224#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
225#test for joint limits:
226limits = []
227def UFtsd(mbs, t, itemNumber, rotation, angularVelocity, stiffness, damping, offset):
228    f = 0.
229    if False and mbs.variables['controlActive']:
230        f = stiffness*rotation + damping*angularVelocity
231    else:
232        limTSD = limits[itemNumber]
233        if rotation > limTSD[1]:
234            f = 50*stiffness*(rotation-limTSD[1])**2 + stiffness*(rotation-offset) + damping*angularVelocity
235        elif rotation < limTSD[0]:
236            f = -50*stiffness*(rotation-limTSD[0])**2 + stiffness*(rotation-offset) + damping*angularVelocity
237        else:
238            f = stiffness*(rotation-offset) + damping*angularVelocity
239    return f
240
241useUserFunction = 1
242if not useUserFunction:
243    UFtsd = 0
244
245#control robot
246compensateStaticTorques = False
247torsionalSDlist = []
248nGenericList = []
249limits = [[0.,0.]]*mbs.systemData.NumberOfObjects()
250limits += [[-0.75*pi,0.75*pi],
251           [ 0.0*pi,1.0*pi],
252           [-1.0*pi,0.4*pi],
253           [-0.5*pi,0.5*pi],
254           [-0.5*pi,0.5*pi],
255           [-0.5*pi,0.5*pi],
256           ]
257for i in range(len(jointList)):
258    joint = jointList[i]
259    rot0 = mbs.GetObject(joint)['rotationMarker0']
260    rot1 = mbs.GetObject(joint)['rotationMarker1']
261    markers = mbs.GetObject(joint)['markerNumbers']
262
263    nGeneric=mbs.AddNode(NodeGenericData(initialCoordinates=[0],
264                                         numberOfDataCoordinates=1)) #for infinite rotations
265    nGenericList += [nGeneric]
266    tsd = mbs.AddObject(TorsionalSpringDamper(markerNumbers=markers,
267                                        nodeNumber=nGeneric,
268                                        rotationMarker0=rot0,
269                                        rotationMarker1=rot1,
270                                        stiffness=Pcontrol[i],
271                                        damping=Dcontrol[i],
272                                        springTorqueUserFunction=UFtsd,
273                                        visualization=VTorsionalSpringDamper(drawSize=0.1)
274                                        ))
275    torsionalSDlist += [tsd]
276
277
278#user function which is called only once per step, speeds up simulation drastically
279def PreStepUF(mbs, t):
280
281    # print('nG=',end='')
282    # for i in nGenericList:
283    #     q = mbs.GetNodeOutput(i, exu.OutputVariableType.Coordinates)
284    #     print(round(q,4),', ',end='')
285    # print('')
286
287    #additional static torque compensation; P and D control in TSD:
288    if not mbs.variables['controlActive']:
289        p = SC.GetCurrentMouseCoordinates(True) #True=OpenGL coordinates; 2D
290        A = np.array(SC.GetRenderState()['modelRotation'])
291        p3D = A@np.array([p[0],p[1],0.])
292
293        offset = p3D
294        mbs.SetObjectParameter(mbs.variables['gripperSD'], 'offset', offset)
295        mbs.SetObjectParameter(mbs.variables['gripperSD'], 'activeConnector', True)
296    else:
297        mbs.SetObjectParameter(mbs.variables['gripperSD'], 'activeConnector', False)
298
299    #with control:
300    if compensateStaticTorques:
301        staticTorques = ComputeMBSstaticRobotTorques(newRobot)
302        #print("tau=", staticTorques)
303    else:
304        staticTorques = np.zeros(len(jointList))
305
306
307    [u,v,a] = trajectory.Evaluate(t)
308
309    fact = 1.
310    if mbs.variables['controlActive']==2:
311        fact =1. #0.1 #soft reset ...
312
313    #compute load for joint number
314    for i in range(len(jointList)):
315        joint = jointList[i]
316        phi = mbs.GetObjectOutput(joint, exu.OutputVariableType.Rotation)[2] #z-rotation
317        omega = mbs.GetObjectOutput(joint, exu.OutputVariableType.AngularVelocityLocal)[2] #z-angular velocity
318        #[u1,v1,a1] = MotionInterpolator(t, robotTrajectory, i)
319        tsd = torsionalSDlist[i]
320        if mbs.variables['controlActive'] or i>=3:
321            mbs.SetObjectParameter(tsd, 'torque', staticTorques[i]) #additional torque from given velocity; positive sign from Exudyn 1.2.38 onwards
322            mbs.SetObjectParameter(tsd, 'stiffness', Pcontrol[i]*fact)
323            mbs.SetObjectParameter(tsd, 'damping', Dcontrol[i]*1)
324
325    # with mouse drag:
326    for i in range(len(jointList)):
327        if not (mbs.variables['controlActive'] or i>=3):
328            tsd = torsionalSDlist[i]
329            #keep damping, but deactivate stiffness
330            mbs.SetObjectParameter(tsd, 'torque', 0)
331            #mbs.SetObjectParameter(tsd, 'stiffness', 0)
332            mbs.SetObjectParameter(tsd, 'damping', Dcontrol[i]*0.1) #keep small damping to improve drag!
333
334    return True
335
336mbs.SetPreStepUserFunction(PreStepUF)
337
338
339# mbs.variables['q0Current'] = q0[0]
340for i in range(6):
341    mbs.variables['q{}Current'.format(i)] = q0[i]
342
343#add sensors:
344cnt = 0
345for i in range(len(jointList)):
346    jointLink = jointList[i]
347    tsd = torsionalSDlist[i]
348    sJointRot = mbs.AddSensor(SensorObject(objectNumber=tsd,
349                               fileName="solution/joint" + str(cnt) + "Rot.txt",
350                               outputVariableType=exu.OutputVariableType.Rotation,
351                               writeToFile = sensorWriteToFile))
352    sJointAngVel = mbs.AddSensor(SensorObject(objectNumber=jointLink,
353                               fileName="solution/joint" + str(cnt) + "AngVel.txt",
354                               outputVariableType=exu.OutputVariableType.AngularVelocityLocal,
355                               writeToFile = sensorWriteToFile))
356    cnt+=1
357
358cnt = 0
359jointTorque0List = []
360for load0 in robotDict['jointTorque0List']:
361    sTorque = mbs.AddSensor(SensorLoad(loadNumber=load0, fileName="solution/jointTorque" + str(cnt) + ".txt",
362                                       writeToFile = sensorWriteToFile))
363    jointTorque0List += [sTorque]
364    cnt+=1
365
366
367
368
369def GetPoseString(q):
370    strx = '   x = ['
371    strphi = 'phi = ['
372    HT = newRobot.JointHT(q)[-1]
373    t = np.round(HT[0:3,-1], 4)
374    R = HT[0:3,0:3]
375    phi = np.round(RotationMatrix2RotXYZ(R),3)
376
377    for i in range(2):
378        strx += '{},\t'.format(t[i])
379        strphi += '{},\t'.format(phi[i])
380
381    strx += '{}]'.format(t[-1])
382    strphi += '{}]'.format(phi[-1])
383    diffLen = len(strx) - len(strphi)
384    if diffLen > 0:
385        strphi += ' '*diffLen
386    elif diffLen < 0:
387        strx += ' '*diffLen
388
389    return strx + '\n' + strphi
390
391#define items for dialog
392fAngle=2.
393dialogItems = [{'type':'label', 'text':'Angle 1', 'grid':(0,0,2), 'options':['L']},
394               {'type':'slider', 'range': (-fAngle*3.14, fAngle*3.14), 'value':q0[0], 'steps':628, 'variable':'q0Current', 'grid':(0,1)},
395               {'type':'label', 'text':'Angle 2:', 'grid':(1,0)},
396               {'type':'slider', 'range': (-fAngle*3.14, fAngle*3.14), 'value':q0[1], 'steps':628, 'variable':'q1Current', 'grid':(1,1)},
397               {'type':'label', 'text':'Angle 3:', 'grid':(2,0)},
398               {'type':'slider', 'range': (-fAngle*3.14, fAngle*3.14), 'value':q0[2], 'steps':628, 'variable':'q2Current', 'grid':(2,1)},
399               {'type':'label', 'text':'Angle 4:', 'grid':(3,0)},
400               {'type':'slider', 'range': (-fAngle*3.14, fAngle*3.14), 'value':q0[3], 'steps':628, 'variable':'q3Current', 'grid':(3,1)},
401               {'type':'label', 'text':'Angle 5:', 'grid':(4,0)},
402               {'type':'slider', 'range': (-fAngle*3.14, fAngle*3.14), 'value':q0[4], 'steps':628, 'variable':'q4Current', 'grid':(4,1)},
403               {'type':'label', 'text':'Angle 6:', 'grid':(5,0)},
404               {'type':'slider', 'range': (-fAngle*3.14, fAngle*3.14), 'value':q0[5], 'steps':628, 'variable':'q5Current', 'grid':(5,1)},
405               {'type': 'label', 'text': 'Position:', 'grid': (6,0)},
406               {'type': 'label', 'text': '{}'.format(GetPoseString(q0)), 'grid': (6,1)},
407               {'type':'radio', 'textValueList':[('Mouse drag',0),('Control on',1),('Reset',2)], 'value':1, 'variable':'controlActive',
408                'grid': [(7,0),(7,1),(7,2)]}
409               #{'type':'button', 'text':'test button','callFunction':ButtonCall, 'grid':(7,0,2)},
410               ]
411
412
413mbs.Assemble()
414#mbs.systemData.Info()
415
416SC.visualizationSettings.connectors.showJointAxes = True
417SC.visualizationSettings.connectors.jointAxesLength = 0.02
418SC.visualizationSettings.connectors.jointAxesRadius = 0.002
419
420SC.visualizationSettings.nodes.showBasis = True
421SC.visualizationSettings.nodes.basisSize = 0.1
422SC.visualizationSettings.loads.show = False
423
424SC.visualizationSettings.openGL.multiSampling=4
425SC.visualizationSettings.openGL.shadow=0.3
426SC.visualizationSettings.openGL.perspective=0.7
427
428tEnd = 1.25
429h = 0.0005
430
431#mbs.WaitForUserToContinue()
432simulationSettings = exu.SimulationSettings() #takes currently set values or default values
433
434simulationSettings.solutionSettings.solutionInformation = 'Hanging Robot Interactive Example'
435
436
437simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
438simulationSettings.timeIntegration.endTime = tEnd
439simulationSettings.solutionSettings.solutionWritePeriod = h*1
440simulationSettings.solutionSettings.sensorsWritePeriod = h*10
441simulationSettings.solutionSettings.binarySolutionFile = True
442simulationSettings.timeIntegration.verboseMode = 0
443#simulationSettings.solutionSettings.writeSolutionToFile = False
444# simulationSettings.timeIntegration.simulateInRealtime = True
445# simulationSettings.timeIntegration.realtimeFactor = 0.25
446simulationSettings.solutionSettings.writeInitialValues = False
447
448simulationSettings.displayComputationTime = False
449simulationSettings.displayStatistics = False
450# simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse
451# simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations=False
452
453#simulationSettings.timeIntegration.newton.useModifiedNewton = True
454simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = False
455simulationSettings.timeIntegration.generalizedAlpha.useNewmark = simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints
456simulationSettings.timeIntegration.newton.useModifiedNewton = True
457
458SC.visualizationSettings.window.renderWindowSize=[1920,1200]
459SC.visualizationSettings.general.graphicsUpdateInterval=0.005
460
461#this is an exemplariy simulation function, which adjusts some values for simulation
462def SimulationUF(mbs, dialog):
463    q = []
464    for i in range(6):
465        qi = mbs.variables['q{}Current'.format(i)] #not possible to update this variable
466        #qi = dialog.sliderVariables[i].get()
467        mbs.SetObjectParameter(torsionalSDlist[i],'offset',qi)
468        theta = mbs.GetObjectOutput(torsionalSDlist[i],exu.OutputVariableType.Rotation)
469        #q += [mbs.variables['q{}Current'.format(i)]]
470        q += [1.*theta] #current rotation
471    #dialog.dialogItems[-1]['text'] = GetPoseString(q)
472
473    if mbs.variables['controlActive'] == 2:
474        for i in range(6):
475            q[i] = 0
476            mbs.variables['q{}Current'.format(i)] = 0
477            dialog.widgets[2*i+1].set(q[i])
478
479    dialog.labelStringVariables[-1].set(GetPoseString(q))
480
481    if not mbs.variables['controlActive']:
482        for i in range(6):
483            #dialog.sliderVariables[i].set(q[i])
484            dialog.widgets[2*i+1].set(q[i])
485    #print(q)
486
487SC.visualizationSettings.general.autoFitScene = False #use loaded render state
488exu.StartRenderer()
489if 'renderState' in exu.sys:
490    SC.SetRenderState(exu.sys[ 'renderState' ])
491
492dialog = InteractiveDialog(mbs=mbs, simulationSettings=simulationSettings,
493                           simulationFunction=SimulationUF,
494                           title='Interactive window',
495                           dialogItems=dialogItems, period=0.01, realtimeFactor=4, #realtime is only approx. (does not include time lost for computation ==> 2 is a good choice)
496                           runOnStart=True,
497                           addLabelStringVariables=True,
498                           #addSliderVariables=True
499                           )
500                           # plots=plots, fontSize=12)
501
502exu.StopRenderer()
503
504if 0:
505    if useGraphics:
506        exu.StartRenderer()
507        if 'renderState' in exu.sys:
508            SC.SetRenderState(exu.sys['renderState'])
509        mbs.WaitForUserToContinue()
510
511    mbs.SolveDynamic(simulationSettings, showHints=True)
512
513
514    if useGraphics:
515        SC.visualizationSettings.general.autoFitScene = False
516        exu.StopRenderer()
517
518
519    mbs.SolutionViewer()
520
521    lastRenderState = SC.GetRenderState() #store model view
522
523    #compute final torques:
524    measuredTorques=[]
525    for sensorNumber in jointTorque0List:
526        measuredTorques += [mbs.GetSensorValues(sensorNumber)[2]]
527    exu.Print("torques at tEnd=", VSum(measuredTorques))
528
529
530
531    if True:
532        import matplotlib.pyplot as plt
533        import matplotlib.ticker as ticker
534        plt.rcParams.update({'font.size': 14})
535        plt.close("all")
536
537        doJointTorques = False
538        if doJointTorques:
539            for i in range(6):
540                data = np.loadtxt("solution/jointTorque" + str(i) + ".txt", comments='#', delimiter=',')
541                plt.plot(data[:,0], data[:,3], PlotLineCode(i), label="joint torque"+str(i)) #z-rotation
542
543            plt.xlabel("time (s)")
544            plt.ylabel("joint torque (Nm)")
545            ax=plt.gca() # get current axes
546            ax.grid(True, 'major', 'both')
547            ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
548            ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
549            plt.tight_layout()
550            ax.legend(loc='center right')
551            plt.show()
552            # plt.savefig("solution/robotJointTorques.pdf")
553
554        doJointAngles = True
555        if doJointAngles:
556            plt.close("all")
557
558            for i in range(6):
559                data = np.loadtxt("solution/joint" + str(i) + "Rot.txt", comments='#', delimiter=',')
560                plt.plot(data[:,0], data[:,1], PlotLineCode(i), label="joint"+str(i)) #z-rotation
561
562            plt.xlabel("time (s)")
563            plt.ylabel("joint angle (rad)")
564            ax=plt.gca()
565            ax.grid(True, 'major', 'both')
566            ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
567            ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
568            plt.tight_layout()
569            ax.legend()
570            plt.rcParams.update({'font.size': 16})
571            plt.show()
572            # plt.savefig("solution/robotJointAngles.pdf")