mecanumWheelRollingDiscTest.py
You can view and download this file on Github: mecanumWheelRollingDiscTest.py
1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2# This is an EXUDYN example
3#
4# Details: mecanum wheels modeled by ObjectConnectorRollingDiscPenalty
5# specific friction angle of rolling disc is used to model rolls of mecanum wheels
6# formulation is still under development and needs more testing
7#
8# Author: Johannes Gerstmayr
9# Date: 2020-06-19
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 *
17
18import numpy as np
19
20useGraphics = True #without test
21#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
22#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
23try: #only if called from test suite
24 from modelUnitTests import exudynTestGlobals #for globally storing test results
25 useGraphics = exudynTestGlobals.useGraphics
26except:
27 class ExudynTestGlobals:
28 pass
29 exudynTestGlobals = ExudynTestGlobals()
30#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
31
32SC = exu.SystemContainer()
33mbs = SC.AddSystem()
34
35g = [0,0,-9.81] #gravity in m/s^2
36
37doBreaking = False
38
39#++++++++++++++++++++++++++++++
40#wheel parameters:
41rhoWheel = 500 #density kg/m^3
42rWheel = 0.4 #radius of disc in m
43wWheel = 0.2 #width of disc in m, just for drawing
44p0Wheel = [0,0,rWheel] #origin of disc center point at reference, such that initial contact point is at [0,0,0]
45initialRotationCar = RotationMatrixZ(0)
46
47v0 = -5*0 #initial car velocity in y-direction
48omega0Wheel = [v0/rWheel,0,0] #initial angular velocity around z-axis
49
50#v0 = [0,0,0] #initial translational velocity
51#exu.Print("v0Car=",v0)
52
53#++++++++++++++++++++++++++++++
54#car parameters:
55p0Car = [0,0,rWheel] #origin of disc center point at reference, such that initial contact point is at [0,0,0]
56lCar = 3 #y-direction
57wCar = 3 #x-direction
58hCar = rWheel #z-direction
59mCar = 500
60omega0Car = [0,0,0] #initial angular velocity around z-axis
61v0Car = [0,-v0,0] #initial velocity of car center point
62
63#inertia for infinitely small ring:
64inertiaWheel = InertiaCylinder(density=rhoWheel, length=wWheel, outerRadius=rWheel, axis=0)
65#exu.Print(inertiaWheel)
66
67inertiaCar = InertiaCuboid(density=mCar/(lCar*wCar*hCar),sideLengths=[wCar, lCar, hCar])
68#exu.Print(inertiaCar)
69
70graphicsCar = GraphicsDataOrthoCubePoint(centerPoint=[0,0,0],size=[wCar-1.1*wWheel, lCar, hCar],
71 color=color4steelblue)
72[nCar,bCar]=AddRigidBody(mainSys = mbs,
73 inertia = inertiaCar,
74 nodeType = str(exu.NodeType.RotationEulerParameters),
75 position = p0Car,
76 rotationMatrix = initialRotationCar,
77 angularVelocity = omega0Car,
78 velocity=v0Car,
79 gravity = g,
80 graphicsDataList = [graphicsCar])
81
82nWheels = 4
83markerWheels=[]
84markerCarAxles=[]
85oRollingDiscs=[]
86sAngularVelWheels=[]
87
88# car setup:
89# ^Y, lCar
90# | W2 +---+ W3
91# | | |
92# | | + | car center point
93# | | |
94# | W0 +---+ W1
95# +---->X, wCar
96
97#ground body and marker
98gGround = GraphicsDataOrthoCubePoint(centerPoint=[4,4,-0.001],size=[12,12,0.002], color=color4lightgrey[0:3]+[0.2])
99oGround = mbs.AddObject(ObjectGround(visualization=VObjectGround(graphicsData=[gGround])))
100markerGround = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=[0,0,0]))
101
102if useGraphics:
103 sCarVel = mbs.AddSensor(SensorBody(bodyNumber=bCar, storeInternal=True, #fileName='solution/rollingDiscCarVel.txt',
104 outputVariableType = exu.OutputVariableType.Velocity))
105
106sPos=[]
107sTrail=[]
108sForce=[]
109
110
111for iWheel in range(nWheels):
112 frictionAngle = 0.25*np.pi #45°
113 if iWheel == 0 or iWheel == 3: #difference in diagonal
114 frictionAngle *= -1
115
116 #additional graphics for visualization of rotation (JUST FOR DRAWING!):
117 graphicsWheel = [GraphicsDataOrthoCubePoint(centerPoint=[0,0,0],size=[wWheel*1.1,0.7*rWheel,0.7*rWheel], color=color4lightred)]
118 nCyl = 12
119 rCyl = 0.1*rWheel
120 for i in range(nCyl): #draw cylinders on wheels
121 iPhi = i/nCyl*2*np.pi
122 pAxis = np.array([0,rWheel*np.sin(iPhi),-rWheel*np.cos(iPhi)])
123 vAxis = [0.5*wWheel*np.cos(frictionAngle),0.5*wWheel*np.sin(frictionAngle),0]
124 vAxis2 = RotationMatrixX(iPhi)@vAxis
125 rColor = color4grey
126 if i >= nCyl/2: rColor = color4darkgrey
127 graphicsWheel += [GraphicsDataCylinder(pAxis=pAxis-vAxis2, vAxis=2*vAxis2, radius=rCyl,
128 color=rColor)]
129
130
131 dx = -0.5*wCar
132 dy = -0.5*lCar
133 if iWheel > 1: dy *= -1
134 if iWheel == 1 or iWheel == 3: dx *= -1
135
136 kRolling = 1e5
137 dRolling = kRolling*0.01
138
139 initialRotation = RotationMatrixZ(0)
140
141 #v0Wheel = Skew(omega0Wheel) @ initialRotationWheel @ [0,0,rWheel] #initial angular velocity of center point
142 v0Wheel = v0Car #approx.
143
144 pOff = [dx,dy,0]
145
146
147 #add wheel body
148 [n0,b0]=AddRigidBody(mainSys = mbs,
149 inertia = inertiaWheel,
150 nodeType = str(exu.NodeType.RotationEulerParameters),
151 position = VAdd(p0Wheel,pOff),
152 rotationMatrix = initialRotation, #np.diag([1,1,1]),
153 angularVelocity = omega0Wheel,
154 velocity=v0Wheel,
155 gravity = g,
156 graphicsDataList = graphicsWheel)
157
158 #markers for rigid body:
159 mWheel = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b0, localPosition=[0,0,0]))
160 markerWheels += [mWheel]
161
162 mCarAxle = mbs.AddMarker(MarkerBodyRigid(bodyNumber=bCar, localPosition=pOff))
163 markerCarAxles += [mCarAxle]
164
165 lockedAxis0 = 0
166 if doBreaking: lockedAxis0 = 1
167 #if iWheel==0 or iWheel==1: freeAxis = 1 #lock rotation
168 mbs.AddObject(GenericJoint(markerNumbers=[mWheel,mCarAxle],rotationMarker1=initialRotation,
169 constrainedAxes=[1,1,1,lockedAxis0,1,1])) #revolute joint for wheel
170
171 #does not work, because revolute joint does not accept off-axis
172 #kSuspension = 1e4
173 #dSuspension = kSuspension*0.01
174 #mbs.AddObject(CartesianSpringDamper(markerNumbers=[mWheel,mCarAxle],stiffness=[0,0,kSuspension],damping=[0,0,dSuspension]))
175
176 nGeneric = mbs.AddNode(NodeGenericData(initialCoordinates=[0,0,0], numberOfDataCoordinates=3))
177 oRolling = mbs.AddObject(ObjectConnectorRollingDiscPenalty(markerNumbers=[markerGround, mWheel], nodeNumber = nGeneric,
178 discRadius=rWheel, dryFriction=[1.,0.], dryFrictionAngle=frictionAngle,
179 dryFrictionProportionalZone=1e-1,
180 rollingFrictionViscous=0.2*0,
181 contactStiffness=kRolling, contactDamping=dRolling,
182 visualization=VObjectConnectorRollingDiscPenalty(discWidth=wWheel, color=color4blue)))
183 oRollingDiscs += [oRolling]
184
185 strNum = str(iWheel)
186 sAngularVelWheels += [mbs.AddSensor(SensorBody(bodyNumber=b0, storeInternal=True,#fileName='solution/rollingDiscAngVelLocal'+strNum+'.txt',
187 outputVariableType = exu.OutputVariableType.AngularVelocityLocal))]
188
189 if useGraphics:
190 sPos+=[mbs.AddSensor(SensorBody(bodyNumber=b0, storeInternal=True,#fileName='solution/rollingDiscPos'+strNum+'.txt',
191 outputVariableType = exu.OutputVariableType.Position))]
192
193 sTrail+=[mbs.AddSensor(SensorObject(name='Trail'+strNum,objectNumber=oRolling, storeInternal=True,#fileName='solution/rollingDiscTrail'+strNum+'.txt',
194 outputVariableType = exu.OutputVariableType.Position))]
195
196 sForce+=[mbs.AddSensor(SensorObject(objectNumber=oRolling, storeInternal=True,#fileName='solution/rollingDiscForce'+strNum+'.txt',
197 outputVariableType = exu.OutputVariableType.ForceLocal))]
198
199
200torqueFactor = 100
201def UFBasicTorque(mbs, t, torque):
202 if t < 0.2:
203 return torque
204 else:
205 return [0,0,0]
206
207#takes as input the translational and angular velocity and outputs the velocities for all 4 wheels
208#wheel axis is mounted at x-axis; positive angVel rotates CCW in x/y plane viewed from top
209# car setup:
210# ^Y, lCar
211# | W2 +---+ W3
212# | | |
213# | | + | car center point
214# | | |
215# | W0 +---+ W1
216# +---->X, wCar
217#values given for wheel0/3: frictionAngle=-pi/4, wheel 1/2: frictionAngle=pi/4; dryFriction=[1,0] (looks in lateral (x) direction)
218#==>direction of axis of roll on ground of wheel0: [1,-1] and of wheel1: [1,1]
219def MecanumXYphi2WheelVelocities(xVel, yVel, angVel, R, Lx, Ly):
220 LxLy2 = (Lx+Ly)/2
221 mat = (1/R)*np.array([[ 1,-1, LxLy2],
222 [-1,-1,-LxLy2],
223 [-1,-1, LxLy2],
224 [ 1,-1,-LxLy2]])
225 return mat @ [xVel, yVel, angVel]
226
227#compute velocity trajectory
228def ComputeVelocity(t):
229 vel = [0,0,0] #vx, vy, angVel; these are the local velocities!!!
230 f=1
231 if t < 4:
232 vel = [f,0,0]
233 elif t < 8:
234 vel = [0,f,0]
235 elif t < 16:
236 vel = [0,0,0.125*np.pi]
237 elif t < 20:
238 vel = [f,0,0]
239 return vel
240
241pControl = 500
242#compute controlled torque; torque[0] contains wheel number
243def UFtorque(mbs, t, torque):
244 iWheel = int(torque[0]) #wheel number
245
246 v = ComputeVelocity(t) #desired velocity
247 vDesired = MecanumXYphi2WheelVelocities(v[0],v[1],v[2],rWheel,wCar,lCar)[iWheel]
248 vCurrent = mbs.GetSensorValues(sAngularVelWheels[iWheel])[0] #local x-axis = wheel axis
249
250 cTorque = pControl*(vDesired-vCurrent)
251 #print("W",iWheel, ": vDes=", vDesired, ", vCur=", vCurrent, ", torque=", cTorque)
252
253 return [cTorque,0,0]
254
255if False:
256 mbs.AddLoad(Torque(markerNumber=markerWheels[0],loadVector=[ torqueFactor,0,0], bodyFixed = True, loadVectorUserFunction=UFBasicTorque))
257 mbs.AddLoad(Torque(markerNumber=markerWheels[1],loadVector=[-torqueFactor,0,0], bodyFixed = True, loadVectorUserFunction=UFBasicTorque))
258 mbs.AddLoad(Torque(markerNumber=markerWheels[2],loadVector=[-torqueFactor,0,0], bodyFixed = True, loadVectorUserFunction=UFBasicTorque))
259 mbs.AddLoad(Torque(markerNumber=markerWheels[3],loadVector=[ torqueFactor,0,0], bodyFixed = True, loadVectorUserFunction=UFBasicTorque))
260
261if True:
262 for i in range(4):
263 mbs.AddLoad(Torque(markerNumber=markerWheels[i],loadVector=[ i,0,0], bodyFixed = True, loadVectorUserFunction=UFtorque))
264
265#mbs.AddSensor(SensorObject(objectNumber=oRolling, fileName='solution/rollingDiscTrailVel.txt',
266# outputVariableType = exu.OutputVariableType.VelocityLocal))
267
268
269mbs.Assemble()
270
271simulationSettings = exu.SimulationSettings() #takes currently set values or default values
272
273tEnd = 0.5
274if useGraphics:
275 tEnd = 0.5 #24
276
277h=0.002
278
279simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
280simulationSettings.timeIntegration.endTime = tEnd
281#simulationSettings.solutionSettings.solutionWritePeriod = 0.01
282simulationSettings.solutionSettings.sensorsWritePeriod = 0.002
283simulationSettings.timeIntegration.verboseMode = 0
284simulationSettings.displayComputationTime = False
285simulationSettings.displayStatistics = False
286
287simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
288simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
289simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5#0.5
290simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations=True
291
292simulationSettings.timeIntegration.newton.useModifiedNewton = True
293simulationSettings.timeIntegration.discontinuous.ignoreMaxIterations = False #reduce step size for contact switching
294simulationSettings.timeIntegration.discontinuous.iterationTolerance = 0.1
295
296SC.visualizationSettings.nodes.show = True
297SC.visualizationSettings.nodes.drawNodesAsPoint = False
298SC.visualizationSettings.nodes.showBasis = True
299SC.visualizationSettings.nodes.basisSize = 0.015
300
301#create animation:
302if useGraphics:
303 SC.visualizationSettings.window.renderWindowSize=[1920,1080]
304 SC.visualizationSettings.openGL.multiSampling = 4
305 if False:
306 simulationSettings.solutionSettings.recordImagesInterval = 0.05
307 SC.visualizationSettings.exportImages.saveImageFileName = "animation/frame"
308
309if useGraphics:
310 exu.StartRenderer()
311 mbs.WaitForUserToContinue()
312
313mbs.SolveDynamic(simulationSettings)
314
315p0=mbs.GetObjectOutputBody(bCar, exu.OutputVariableType.Position, localPosition=[0,0,0])
316exu.Print('solution of mecanumWheelRollingDiscTest=',p0[0]) #use x-coordinate
317
318exudynTestGlobals.testError = p0[0] - (0.2714267238324345) #2020-06-20: 0.2714267238324345
319exudynTestGlobals.testResult = p0[0]
320
321
322if useGraphics:
323 SC.WaitForRenderEngineStopFlag()
324 exu.StopRenderer() #safely close rendering window!
325
326##++++++++++++++++++++++++++++++++++++++++++++++q+++++++
327#plot results
328if useGraphics:
329
330
331 mbs.PlotSensor(sTrail, componentsX=[0]*4, components=[1]*4, title='wheel trails', closeAll=True,
332 markerStyles=['x ','o ','^ ','D '], markerSizes=12)
333 mbs.PlotSensor(sForce, components=[1]*4, title='wheel forces')