.. _testmodels-mecanumwheelrollingdisctest: ****************************** mecanumWheelRollingDiscTest.py ****************************** You can view and download this file on Github: `mecanumWheelRollingDiscTest.py `_ .. code-block:: python :linenos: #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # This is an EXUDYN example # # Details: mecanum wheels modeled by ObjectConnectorRollingDiscPenalty # specific friction angle of rolling disc is used to model rolls of mecanum wheels # formulation is still under development and needs more testing # # Author: Johannes Gerstmayr # Date: 2020-06-19 # # 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. # #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ import exudyn as exu from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities import exudyn.graphics as graphics #only import if it does not conflict import numpy as np useGraphics = True #without test #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel: try: #only if called from test suite from modelUnitTests import exudynTestGlobals #for globally storing test results useGraphics = exudynTestGlobals.useGraphics except: class ExudynTestGlobals: pass exudynTestGlobals = ExudynTestGlobals() #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ SC = exu.SystemContainer() mbs = SC.AddSystem() g = [0,0,-9.81] #gravity in m/s^2 doBreaking = False #++++++++++++++++++++++++++++++ #wheel parameters: rhoWheel = 500 #density kg/m^3 rWheel = 0.4 #radius of disc in m wWheel = 0.2 #width of disc in m, just for drawing p0Wheel = [0,0,rWheel] #origin of disc center point at reference, such that initial contact point is at [0,0,0] initialRotationCar = RotationMatrixZ(0) v0 = -5*0 #initial car velocity in y-direction omega0Wheel = [v0/rWheel,0,0] #initial angular velocity around z-axis #v0 = [0,0,0] #initial translational velocity #exu.Print("v0Car=",v0) #++++++++++++++++++++++++++++++ #car parameters: p0Car = [0,0,rWheel] #origin of disc center point at reference, such that initial contact point is at [0,0,0] lCar = 3 #y-direction wCar = 3 #x-direction hCar = rWheel #z-direction mCar = 500 omega0Car = [0,0,0] #initial angular velocity around z-axis v0Car = [0,-v0,0] #initial velocity of car center point #inertia for infinitely small ring: inertiaWheel = InertiaCylinder(density=rhoWheel, length=wWheel, outerRadius=rWheel, axis=0) #exu.Print(inertiaWheel) inertiaCar = InertiaCuboid(density=mCar/(lCar*wCar*hCar),sideLengths=[wCar, lCar, hCar]) #exu.Print(inertiaCar) graphicsCar = graphics.Brick(centerPoint=[0,0,0],size=[wCar-1.1*wWheel, lCar, hCar], color=graphics.color.steelblue) [nCar,bCar]=AddRigidBody(mainSys = mbs, inertia = inertiaCar, nodeType = str(exu.NodeType.RotationEulerParameters), position = p0Car, rotationMatrix = initialRotationCar, angularVelocity = omega0Car, velocity=v0Car, gravity = g, graphicsDataList = [graphicsCar]) nWheels = 4 markerWheels=[] markerCarAxles=[] oRollingDiscs=[] sAngularVelWheels=[] # car setup: # ^Y, lCar # | W2 +---+ W3 # | | | # | | + | car center point # | | | # | W0 +---+ W1 # +---->X, wCar #ground body and marker gGround = graphics.Brick(centerPoint=[4,4,-0.001],size=[12,12,0.002], color=graphics.color.lightgrey[0:3]+[0.2]) oGround = mbs.AddObject(ObjectGround(visualization=VObjectGround(graphicsData=[gGround]))) markerGround = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=[0,0,0])) if useGraphics: sCarVel = mbs.AddSensor(SensorBody(bodyNumber=bCar, storeInternal=True, #fileName='solution/rollingDiscCarVel.txt', outputVariableType = exu.OutputVariableType.Velocity)) sPos=[] sTrail=[] sForce=[] for iWheel in range(nWheels): frictionAngle = 0.25*np.pi #45° if iWheel == 0 or iWheel == 3: #difference in diagonal frictionAngle *= -1 #additional graphics for visualization of rotation (JUST FOR DRAWING!): graphicsWheel = [graphics.Brick(centerPoint=[0,0,0],size=[wWheel*1.1,0.7*rWheel,0.7*rWheel], color=graphics.color.lightred)] nCyl = 12 rCyl = 0.1*rWheel for i in range(nCyl): #draw cylinders on wheels iPhi = i/nCyl*2*np.pi pAxis = np.array([0,rWheel*np.sin(iPhi),-rWheel*np.cos(iPhi)]) vAxis = [0.5*wWheel*np.cos(frictionAngle),0.5*wWheel*np.sin(frictionAngle),0] vAxis2 = RotationMatrixX(iPhi)@vAxis rColor = graphics.color.grey if i >= nCyl/2: rColor = graphics.color.darkgrey graphicsWheel += [graphics.Cylinder(pAxis=pAxis-vAxis2, vAxis=2*vAxis2, radius=rCyl, color=rColor)] dx = -0.5*wCar dy = -0.5*lCar if iWheel > 1: dy *= -1 if iWheel == 1 or iWheel == 3: dx *= -1 kRolling = 1e5 dRolling = kRolling*0.01 initialRotation = RotationMatrixZ(0) #v0Wheel = Skew(omega0Wheel) @ initialRotationWheel @ [0,0,rWheel] #initial angular velocity of center point v0Wheel = v0Car #approx. pOff = [dx,dy,0] #add wheel body [n0,b0]=AddRigidBody(mainSys = mbs, inertia = inertiaWheel, nodeType = str(exu.NodeType.RotationEulerParameters), position = VAdd(p0Wheel,pOff), rotationMatrix = initialRotation, #np.diag([1,1,1]), angularVelocity = omega0Wheel, velocity=v0Wheel, gravity = g, graphicsDataList = graphicsWheel) #markers for rigid body: mWheel = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b0, localPosition=[0,0,0])) markerWheels += [mWheel] mCarAxle = mbs.AddMarker(MarkerBodyRigid(bodyNumber=bCar, localPosition=pOff)) markerCarAxles += [mCarAxle] lockedAxis0 = 0 if doBreaking: lockedAxis0 = 1 #if iWheel==0 or iWheel==1: freeAxis = 1 #lock rotation mbs.AddObject(GenericJoint(markerNumbers=[mWheel,mCarAxle],rotationMarker1=initialRotation, constrainedAxes=[1,1,1,lockedAxis0,1,1])) #revolute joint for wheel #does not work, because revolute joint does not accept off-axis #kSuspension = 1e4 #dSuspension = kSuspension*0.01 #mbs.AddObject(CartesianSpringDamper(markerNumbers=[mWheel,mCarAxle],stiffness=[0,0,kSuspension],damping=[0,0,dSuspension])) nGeneric = mbs.AddNode(NodeGenericData(initialCoordinates=[0,0,0], numberOfDataCoordinates=3)) oRolling = mbs.AddObject(ObjectConnectorRollingDiscPenalty(markerNumbers=[markerGround, mWheel], nodeNumber = nGeneric, discRadius=rWheel, dryFriction=[1.,0.], dryFrictionAngle=frictionAngle, dryFrictionProportionalZone=1e-1, rollingFrictionViscous=0.2*0, contactStiffness=kRolling, contactDamping=dRolling, visualization=VObjectConnectorRollingDiscPenalty(discWidth=wWheel, color=graphics.color.blue))) oRollingDiscs += [oRolling] strNum = str(iWheel) sAngularVelWheels += [mbs.AddSensor(SensorBody(bodyNumber=b0, storeInternal=True,#fileName='solution/rollingDiscAngVelLocal'+strNum+'.txt', outputVariableType = exu.OutputVariableType.AngularVelocityLocal))] if useGraphics: sPos+=[mbs.AddSensor(SensorBody(bodyNumber=b0, storeInternal=True,#fileName='solution/rollingDiscPos'+strNum+'.txt', outputVariableType = exu.OutputVariableType.Position))] sTrail+=[mbs.AddSensor(SensorObject(name='Trail'+strNum,objectNumber=oRolling, storeInternal=True,#fileName='solution/rollingDiscTrail'+strNum+'.txt', outputVariableType = exu.OutputVariableType.Position))] sForce+=[mbs.AddSensor(SensorObject(objectNumber=oRolling, storeInternal=True,#fileName='solution/rollingDiscForce'+strNum+'.txt', outputVariableType = exu.OutputVariableType.ForceLocal))] torqueFactor = 100 def UFBasicTorque(mbs, t, torque): if t < 0.2: return torque else: return [0,0,0] #takes as input the translational and angular velocity and outputs the velocities for all 4 wheels #wheel axis is mounted at x-axis; positive angVel rotates CCW in x/y plane viewed from top # car setup: # ^Y, lCar # | W2 +---+ W3 # | | | # | | + | car center point # | | | # | W0 +---+ W1 # +---->X, wCar #values given for wheel0/3: frictionAngle=-pi/4, wheel 1/2: frictionAngle=pi/4; dryFriction=[1,0] (looks in lateral (x) direction) #==>direction of axis of roll on ground of wheel0: [1,-1] and of wheel1: [1,1] def MecanumXYphi2WheelVelocities(xVel, yVel, angVel, R, Lx, Ly): LxLy2 = (Lx+Ly)/2 mat = (1/R)*np.array([[ 1,-1, LxLy2], [-1,-1,-LxLy2], [-1,-1, LxLy2], [ 1,-1,-LxLy2]]) return mat @ [xVel, yVel, angVel] #compute velocity trajectory def ComputeVelocity(t): vel = [0,0,0] #vx, vy, angVel; these are the local velocities!!! f=1 if t < 4: vel = [f,0,0] elif t < 8: vel = [0,f,0] elif t < 16: vel = [0,0,0.125*np.pi] elif t < 20: vel = [f,0,0] return vel pControl = 500 #compute controlled torque; torque[0] contains wheel number def UFtorque(mbs, t, torque): iWheel = int(torque[0]) #wheel number v = ComputeVelocity(t) #desired velocity vDesired = MecanumXYphi2WheelVelocities(v[0],v[1],v[2],rWheel,wCar,lCar)[iWheel] vCurrent = mbs.GetSensorValues(sAngularVelWheels[iWheel])[0] #local x-axis = wheel axis cTorque = pControl*(vDesired-vCurrent) #print("W",iWheel, ": vDes=", vDesired, ", vCur=", vCurrent, ", torque=", cTorque) return [cTorque,0,0] if False: mbs.AddLoad(Torque(markerNumber=markerWheels[0],loadVector=[ torqueFactor,0,0], bodyFixed = True, loadVectorUserFunction=UFBasicTorque)) mbs.AddLoad(Torque(markerNumber=markerWheels[1],loadVector=[-torqueFactor,0,0], bodyFixed = True, loadVectorUserFunction=UFBasicTorque)) mbs.AddLoad(Torque(markerNumber=markerWheels[2],loadVector=[-torqueFactor,0,0], bodyFixed = True, loadVectorUserFunction=UFBasicTorque)) mbs.AddLoad(Torque(markerNumber=markerWheels[3],loadVector=[ torqueFactor,0,0], bodyFixed = True, loadVectorUserFunction=UFBasicTorque)) if True: for i in range(4): mbs.AddLoad(Torque(markerNumber=markerWheels[i],loadVector=[ i,0,0], bodyFixed = True, loadVectorUserFunction=UFtorque)) #mbs.AddSensor(SensorObject(objectNumber=oRolling, fileName='solution/rollingDiscTrailVel.txt', # outputVariableType = exu.OutputVariableType.VelocityLocal)) mbs.Assemble() simulationSettings = exu.SimulationSettings() #takes currently set values or default values tEnd = 0.5 if useGraphics: tEnd = 0.5 #24 h=0.002 simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h) simulationSettings.timeIntegration.endTime = tEnd #simulationSettings.solutionSettings.solutionWritePeriod = 0.01 simulationSettings.solutionSettings.sensorsWritePeriod = 0.002 simulationSettings.timeIntegration.verboseMode = 0 simulationSettings.displayComputationTime = False simulationSettings.displayStatistics = False simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5#0.5 simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations=True simulationSettings.timeIntegration.newton.useModifiedNewton = True simulationSettings.timeIntegration.discontinuous.ignoreMaxIterations = False #reduce step size for contact switching simulationSettings.timeIntegration.discontinuous.iterationTolerance = 0.1 SC.visualizationSettings.nodes.show = True SC.visualizationSettings.nodes.drawNodesAsPoint = False SC.visualizationSettings.nodes.showBasis = True SC.visualizationSettings.nodes.basisSize = 0.015 #create animation: if useGraphics: SC.visualizationSettings.window.renderWindowSize=[1920,1080] SC.visualizationSettings.openGL.multiSampling = 4 if False: simulationSettings.solutionSettings.recordImagesInterval = 0.05 SC.visualizationSettings.exportImages.saveImageFileName = "animation/frame" if useGraphics: exu.StartRenderer() mbs.WaitForUserToContinue() mbs.SolveDynamic(simulationSettings) p0=mbs.GetObjectOutputBody(bCar, exu.OutputVariableType.Position, localPosition=[0,0,0]) exu.Print('solution of mecanumWheelRollingDiscTest=',p0[0]) #use x-coordinate exudynTestGlobals.testError = p0[0] - (0.2714267238324345) #2020-06-20: 0.2714267238324345 exudynTestGlobals.testResult = p0[0] if useGraphics: SC.WaitForRenderEngineStopFlag() exu.StopRenderer() #safely close rendering window! ##++++++++++++++++++++++++++++++++++++++++++++++q+++++++ #plot results if useGraphics: mbs.PlotSensor(sTrail, componentsX=[0]*4, components=[1]*4, title='wheel trails', closeAll=True, markerStyles=['x ','o ','^ ','D '], markerSizes=12) mbs.PlotSensor(sForce, components=[1]*4, title='wheel forces')