serialRobotTest.py
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1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2# This is an EXUDYN example
3#
4# Details: Test Example of a serial robot with redundant coordinates
5# NOTE: more efficient version in serialRobotTSD.py and serialRobotKinematicTree.py using TorsionalSpringDamper
6#
7# Author: Johannes Gerstmayr
8# Date: 2020-02-16
9# Revised: 2021-07-09
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
15import exudyn as exu
16from exudyn.utilities import *
17from exudyn.rigidBodyUtilities import *
18from exudyn.robotics import *
19from exudyn.robotics.motion import Trajectory, ProfileConstantAcceleration
20
21import numpy as np
22from numpy import linalg as LA
23
24useGraphics = True #without test
25#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
26#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
27try: #only if called from test suite
28 from modelUnitTests import exudynTestGlobals #for globally storing test results
29 useGraphics = exudynTestGlobals.useGraphics
30except:
31 class ExudynTestGlobals:
32 pass
33 exudynTestGlobals = ExudynTestGlobals()
34#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
35
36SC = exu.SystemContainer()
37mbs = SC.AddSystem()
38
39#useGraphics = False
40if useGraphics:
41 sensorWriteToFile = True
42else:
43 sensorWriteToFile = False
44
45jointWidth=0.1
46jointRadius=0.06
47linkWidth=0.1
48
49graphicsBaseList = [GraphicsDataOrthoCubePoint([0,0,-0.15], [0.4,0.4,0.1], color4grey)]
50graphicsBaseList +=[GraphicsDataCylinder([0,0,0], [0.5,0,0], 0.0025, color4red)]
51graphicsBaseList +=[GraphicsDataCylinder([0,0,0], [0,0.5,0], 0.0025, color4green)]
52graphicsBaseList +=[GraphicsDataCylinder([0,0,0], [0,0,0.5], 0.0025, color4blue)]
53graphicsBaseList +=[GraphicsDataCylinder([0,0,-jointWidth], [0,0,jointWidth], linkWidth*0.5, color4list[0])] #belongs to first body
54
55ty = 0.03
56tz = 0.04
57zOff = -0.05
58toolSize= [0.05,0.5*ty,0.06]
59graphicsToolList = [GraphicsDataCylinder(pAxis=[0,0,zOff], vAxis= [0,0,tz], radius=ty*1.5, color=color4red)]
60graphicsToolList+= [GraphicsDataOrthoCubePoint([0,ty,1.5*tz+zOff], toolSize, color4grey)]
61graphicsToolList+= [GraphicsDataOrthoCubePoint([0,-ty,1.5*tz+zOff], toolSize, color4grey)]
62
63
64#changed to new robot structure July 2021:
65newRobot = Robot(gravity=[0,0,9.81],
66 base = RobotBase(visualization=VRobotBase(graphicsData=graphicsBaseList)),
67 tool = RobotTool(HT=HTtranslate([0,0,0.1]), visualization=VRobotTool(graphicsData=graphicsToolList)),
68 referenceConfiguration = []) #referenceConfiguration created with 0s automatically
69
70newRobot.AddLink(RobotLink(mass=20, COM=[0,0,0], inertia=np.diag([1e-8,0.35,1e-8]), localHT = StdDH2HT([0,0,0,np.pi/2]), visualization=VRobotLink(linkColor=color4list[0])))
71newRobot.AddLink(RobotLink(mass=17.4, COM=[-0.3638, 0.006, 0.2275], inertia=np.diag([0.13,0.524,0.539]), localHT = StdDH2HT([0,0,0.4318,0]), visualization=VRobotLink(linkColor=color4list[1])))
72newRobot.AddLink(RobotLink(mass=4.8, COM=[-0.0203,-0.0141,0.07], inertia=np.diag([0.066,0.086,0.0125]), localHT = StdDH2HT([0,0.15,0.0203,-np.pi/2]), visualization=VRobotLink(linkColor=color4list[2])))
73newRobot.AddLink(RobotLink(mass=0.82, COM=[0,0.019,0], inertia=np.diag([0.0018,0.0013,0.0018]), localHT = StdDH2HT([0,0.4318,0,np.pi/2]), visualization=VRobotLink(linkColor=color4list[3])))
74newRobot.AddLink(RobotLink(mass=0.34, COM=[0,0,0], inertia=np.diag([0.0003,0.0004,0.0003]), localHT = StdDH2HT([0,0,0,-np.pi/2]), visualization=VRobotLink(linkColor=color4list[4])))
75newRobot.AddLink(RobotLink(mass=0.09, COM=[0,0,0.032], inertia=np.diag([0.00015,0.00015,4e-5]), localHT = StdDH2HT([0,0,0,0]), visualization=VRobotLink(linkColor=color4list[5])))
76
77
78# newRobot = Robot(gravity=[0,0,-9.81], referenceConfiguration = [])
79# newRobot.BuildFromDictionary(myRobot) #this allows conversion from old structure
80
81#assumption, as the bodies in the mbs have their COM at the reference position
82#for link in robot['links']:
83# link['COM']=[0,0,0]
84
85#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
86#configurations and trajectory
87q0 = [0,0,0,0,0,0] #zero angle configuration
88
89q1 = [0, np.pi/8, np.pi*0.25, 0,np.pi/8,0] #configuration 1
90q2 = [np.pi/2,-np.pi/8,-np.pi*0.125, 0,np.pi/4,0] #configuration 2
91#q2 = [np.pi*0.45,-np.pi*0.35,-np.pi*0.25, np.pi*0.10,np.pi*0.2,np.pi*0.3] #configuration 2
92#q2 = [pi/2,-pi/8,-pi*0.125,0,pi/4,pi/2] #configuration 2
93
94trajectory=Trajectory(q0, 0)
95if False: #tests for static torque compensation
96 #trajectory.Add(ProfileConstantAcceleration(q0, 1)) #V1.2.37: torques at tEnd= 0.3773259482700045
97 trajectory.Add(ProfileConstantAcceleration(q2, 0.25))
98 trajectory.Add(ProfileConstantAcceleration(q2, 0.75))
99else: #standard test case:
100 trajectory.Add(ProfileConstantAcceleration(q1, 0.25))
101 trajectory.Add(ProfileConstantAcceleration(q2, 0.25))
102 trajectory.Add(ProfileConstantAcceleration(q0, 0.5 ))
103 trajectory.Add(ProfileConstantAcceleration(q0, 1e6))
104
105#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
106#test robot model
107#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
108#control parameters, per joint:
109Pcontrol = np.array([40000, 40000, 40000, 100, 100, 10])
110Dcontrol = np.array([400, 400, 100, 1, 1, 0.05]) #last value 0.05 gives less oscillations as compared to earlier values of 0.1!
111# Pcontrol = 0.01*Pcontrol #soft behavior
112
113
114#++++++++++++++++++++++++++++++++++++++++++++++++
115#base, graphics, object and marker:
116graphicsBaseList = [GraphicsDataOrthoCubePoint([0,0,-0.2], [0.4,0.4,0.1], color4grey)]
117graphicsBaseList +=[GraphicsDataCylinder([0,0,0], [0.5,0,0], 0.0025, color4red)]
118graphicsBaseList +=[GraphicsDataCylinder([0,0,0], [0,0.5,0], 0.0025, color4green)]
119graphicsBaseList +=[GraphicsDataCylinder([0,0,0], [0,0,0.5], 0.0025, color4blue)]
120#oGround = mbs.AddObject(ObjectGround(referencePosition=list(HT2translation(Tcurrent)),
121objectGround = mbs.AddObject(ObjectGround(referencePosition=HT2translation(newRobot.GetBaseHT()),
122 visualization=VObjectGround(graphicsData=graphicsBaseList)))
123
124#baseMarker; could also be a moving base!
125baseMarker = mbs.AddMarker(MarkerBodyRigid(bodyNumber=objectGround, localPosition=[0,0,0]))
126
127
128
129#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
130#build mbs robot model:
131robotDict = newRobot.CreateRedundantCoordinateMBS(mbs, baseMarker=baseMarker)
132
133# !!!!!IMPORTANT!!!!!:
134jointList = robotDict['jointList'] #must be stored there for the load user function
135
136unitTorques0 = robotDict['unitTorque0List'] #(left body)
137unitTorques1 = robotDict['unitTorque1List'] #(right body)
138
139loadList0 = robotDict['jointTorque0List'] #(left body)
140loadList1 = robotDict['jointTorque1List'] #(right body)
141#print(loadList0, loadList1)
142#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
143#control robot
144compensateStaticTorques = True
145def ComputeMBSstaticRobotTorques(newRobot):
146 q=[]
147 for joint in jointList:
148 q += [mbs.GetObjectOutput(joint, exu.OutputVariableType.Rotation)[2]] #z-rotation
149 HT=newRobot.JointHT(q)
150 return newRobot.StaticTorques(HT)
151
152#user function which is called only once per step, speeds up simulation drastically
153def PreStepUF(mbs, t):
154 if compensateStaticTorques:
155 staticTorques = ComputeMBSstaticRobotTorques(newRobot)
156 else:
157 staticTorques = np.zeros(len(jointList))
158 #compute load for joint number
159 for i in range(len(jointList)):
160 joint = i
161 phi = mbs.GetObjectOutput(jointList[joint], exu.OutputVariableType.Rotation)[2] #z-rotation
162 omega = mbs.GetObjectOutput(jointList[joint], exu.OutputVariableType.AngularVelocityLocal)[2] #z-angular velocity
163
164 #[u,v,a] = MotionInterpolator(t, robotTrajectory, joint) #OLD, until V1.1.135
165 [u,v,a] = trajectory.EvaluateCoordinate(t, joint)
166
167
168 torque = -(Pcontrol[joint]*(phi-u) + Dcontrol[joint]*(omega-v)) #negative sign in feedback control!
169 # torque = (Pcontrol[joint]*(phi+u) + Dcontrol[joint]*(omega+v)) #until V1.2.; but static Torque compensation is wrong in this case!
170 torque -= staticTorques[joint] #add static torque compensation
171
172 load0 = torque * unitTorques0[i] #includes sign and correct unit-torque vector
173 load1 = torque * unitTorques1[i] #includes sign and correct unit-torque vector
174
175 # #write updated torque to joint loads, applied to left and right body
176 mbs.SetLoadParameter(loadList0[i], 'loadVector', list(load0))
177 mbs.SetLoadParameter(loadList1[i], 'loadVector', list(load1))
178
179 return True
180
181mbs.SetPreStepUserFunction(PreStepUF)
182
183
184
185#add sensors:
186sJointRot = []
187sJointAngVel = []
188sJointTorque = []
189cnt = 0
190for jointLink in jointList:
191 sJointRot += [mbs.AddSensor(SensorObject(objectNumber=jointLink,
192 storeInternal=True,#fileName="solution/joint" + str(cnt) + "Rot.txt",
193 outputVariableType=exu.OutputVariableType.Rotation,
194 writeToFile = sensorWriteToFile))]
195 sJointAngVel += [mbs.AddSensor(SensorObject(objectNumber=jointLink,
196 storeInternal=True,#fileName="solution/joint" + str(cnt) + "AngVel.txt",
197 outputVariableType=exu.OutputVariableType.AngularVelocityLocal,
198 writeToFile = sensorWriteToFile))]
199 cnt+=1
200
201cnt = 0
202for load0 in robotDict['jointTorque0List']:
203 sJointTorque += [mbs.AddSensor(SensorLoad(loadNumber=load0,storeInternal=True,# fileName="solution/jointTorque" + str(cnt) + ".txt",
204 writeToFile = sensorWriteToFile))]
205 cnt+=1
206
207
208
209mbs.Assemble()
210#mbs.systemData.Info()
211
212SC.visualizationSettings.connectors.showJointAxes = True
213SC.visualizationSettings.connectors.jointAxesLength = 0.02
214SC.visualizationSettings.connectors.jointAxesRadius = 0.002
215
216SC.visualizationSettings.nodes.showBasis = True
217SC.visualizationSettings.nodes.basisSize = 0.1
218SC.visualizationSettings.loads.show = False
219
220SC.visualizationSettings.openGL.multiSampling=4
221
222tEnd = 0.2 #0.2 for testing
223h = 0.001
224
225if useGraphics:
226 tEnd = 0.2
227 #tEnd = 1 #shows exactly static torques ComputeMBSstaticRobotTorques(newRobot) and desired angles (q2) at end
228
229#mbs.WaitForUserToContinue()
230simulationSettings = exu.SimulationSettings() #takes currently set values or default values
231
232simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
233simulationSettings.timeIntegration.endTime = tEnd
234simulationSettings.solutionSettings.solutionWritePeriod = h
235simulationSettings.solutionSettings.sensorsWritePeriod = h
236simulationSettings.solutionSettings.writeSolutionToFile = useGraphics
237# simulationSettings.timeIntegration.simulateInRealtime = True
238# simulationSettings.timeIntegration.realtimeFactor = 0.25
239
240simulationSettings.timeIntegration.verboseMode = 1
241simulationSettings.displayComputationTime = False
242simulationSettings.displayStatistics = False
243simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse
244
245#simulationSettings.timeIntegration.newton.useModifiedNewton = True
246simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = False
247simulationSettings.timeIntegration.generalizedAlpha.useNewmark = simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints
248simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5 #0.6 works well
249
250simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations=True
251
252mbs.SolveDynamic(simulationSettings)
253
254if useGraphics:
255 SC.visualizationSettings.general.autoFitScene=False
256 exu.StartRenderer()
257 if 'renderState' in exu.sys:
258 SC.SetRenderState(exu.sys['renderState'])
259
260
261 mbs.SolutionViewer()
262 exu.StopRenderer()
263
264lastRenderState = SC.GetRenderState() #store model view
265
266#compute final torques:
267measuredTorques=[]
268
269for cnt, sensorNumber in enumerate(sJointTorque):
270 if useGraphics:
271 exu.Print('sensor torque',cnt, '=', mbs.GetSensorValues(sensorNumber))
272 measuredTorques += [1e-2*mbs.GetSensorValues(sensorNumber)[2]]
273
274if useGraphics:
275 for cnt, sensorNumber in enumerate(sJointRot):
276 exu.Print('sensor rot ',cnt, '=', mbs.GetSensorValues(sensorNumber))
277
278
279
280exu.Print("torques at tEnd=", VSum(measuredTorques))
281
282#add larger test tolerance for 32/64bits difference
283exudynTestGlobals.testError = (VSum(measuredTorques) - 0.7681856909852399) #until 2022-04-21: 7680031232063571; until 2021-09-10: 76.8003123206452; until 2021-08-19 (changed robotics.py): 76.80031232091771; old controller: 77.12176106978085) #OLDER results: up to 2021-06-28: 0.7712176106955341; 2020-08-25: 77.13193176752571 (32bits), 2020-08-24: (64bits)77.13193176846507
284exudynTestGlobals.testResult = VSum(measuredTorques)
285
286#exu.Print('error=', exudynTestGlobals.testError)
287
288if useGraphics:
289
290
291 mbs.PlotSensor(sJointTorque, components=2, closeAll=True, yLabel='joint torques (Nm)', title='joint torques')
292
293 mbs.PlotSensor(sJointRot, components=2, yLabel='joint angles (rad)', title='joint angles')
294
295 #V1.2.40, P39: with D[-1]=0.05: since 2022-04-22:
296 # sensor torque 0 = [ 0. 0. -12.68901871]
297 # sensor torque 1 = [-0. -0. 76.45031947]
298 # sensor torque 2 = [-0. -0. 12.97010176]
299 # sensor torque 3 = [ 0.00000000e+00 0.00000000e+00 -8.56924875e-05]
300 # sensor torque 4 = [-0. -0. 0.08725323]
301 # sensor torque 5 = [ 0.0000000e+00 0.0000000e+00 -9.5769297e-07]
302 # sensor rot 0 = [-1.04899069e-15 3.05694259e-19 -3.19543456e-04]
303 # sensor rot 1 = [-4.57411886e-14 -1.77599905e-14 3.63829923e-01]
304 # sensor rot 2 = [ 4.68252006e-14 -1.78150803e-14 7.25569701e-01]
305 # sensor rot 3 = [-1.07990283e-13 1.95010674e-13 2.42757634e-07]
306 # sensor rot 4 = [ 1.07852866e-13 -2.06184741e-13 3.63658987e-01]
307 # sensor rot 5 = [ 1.84235149e-16 -6.26054764e-13 -5.07549126e-08]
308 # torques at tEnd= 0.7681856909852399
309
310 #V1.2.40, P39: with D[-1]=0.1:
311 # sensor torque 0 = [ 0. 0. -12.68901812]
312 # sensor torque 1 = [-0. -0. 76.4503195]
313 # sensor torque 2 = [-0. -0. 12.97010177]
314 # sensor torque 3 = [ 0.0000000e+00 0.0000000e+00 -8.9097007e-05]
315 # sensor torque 4 = [-0. -0. 0.08725323]
316 # sensor torque 5 = [-0.00000000e+00 -0.00000000e+00 1.09612342e-05]
317 # sensor rot 0 = [-1.04899069e-15 3.32799313e-19 -3.19543454e-04]
318 # sensor rot 1 = [-4.59632332e-14 -1.77794520e-14 3.63829923e-01]
319 # sensor rot 2 = [ 4.71643413e-14 -1.78734434e-14 7.25569701e-01]
320 # sensor rot 3 = [-1.07609037e-13 1.95343741e-13 2.42965135e-07]
321 # sensor rot 4 = [ 1.07471637e-13 -2.06279100e-13 3.63658987e-01]
322 # sensor rot 5 = [ 1.84106879e-16 -6.25874352e-13 8.28833899e-08]
323 # torques at tEnd= 0.7681857824086907
324
325 #V1.2.37, P37: ==> uses wrong static torque compensation
326 # sensor torque 0 = [ 0. 0. -12.67938332]
327 # sensor torque 1 = [-0. -0. 76.42613004]
328 # sensor torque 2 = [-0. -0. 12.96641046]
329 # sensor torque 3 = [ 0.00000000e+00 0.00000000e+00 -8.93114211e-05]
330 # sensor torque 4 = [-0. -0. 0.08723331]
331 # sensor torque 5 = [-0.0000000e+00 -0.0000000e+00 1.1143982e-05]
332 # sensor rot 0 = [ 1.60812265e-16 -2.71050543e-20 3.19257214e-04]
333 # sensor rot 1 = [ 5.06049354e-14 -1.91882065e-14 -3.63432530e-01]
334 # sensor rot 2 = [-4.07000942e-14 3.58791681e-14 -7.25182770e-01]
335 # sensor rot 3 = [ 9.91554982e-13 4.63740157e-13 -2.41708605e-07]
336 # sensor rot 4 = [-9.26617234e-13 3.52539928e-13 -3.63103888e-01]
337 # sensor rot 5 = [ 9.21913969e-18 3.74700271e-16 -8.34127775e-08]
338 # torques at tEnd= 0.7680031232065901