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