.. _examples-serialrobottsd: ***************** serialRobotTSD.py ***************** You can view and download this file on Github: `serialRobotTSD.py `_ .. code-block:: python :linenos: #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # This is an EXUDYN example # # Details: Example of a serial robot with redundant coordinates # # Author: Johannes Gerstmayr # Date: 2020-02-16 # Revised: 2021-07-09 # # 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.itemInterface import * from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities import exudyn.graphics as graphics #only import if it does not conflict from exudyn.rigidBodyUtilities import * from exudyn.graphicsDataUtilities import * from exudyn.robotics import * from exudyn.robotics.motion import Trajectory, ProfileConstantAcceleration, ProfilePTP import numpy as np from numpy import linalg as LA from math import pi SC = exu.SystemContainer() mbs = SC.AddSystem() sensorWriteToFile = True #++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ mode='newDH' jointWidth=0.1 jointRadius=0.06 linkWidth=0.1 graphicsBaseList = [graphics.Brick([0,0,-0.15], [0.12,0.12,0.1], graphics.color.grey)] graphicsBaseList +=[graphics.Cylinder([0,0,0], [0.5,0,0], 0.0025, graphics.color.red)] graphicsBaseList +=[graphics.Cylinder([0,0,0], [0,0.5,0], 0.0025, graphics.color.green)] graphicsBaseList +=[graphics.Cylinder([0,0,0], [0,0,0.5], 0.0025, graphics.color.blue)] graphicsBaseList +=[graphics.Cylinder([0,0,-jointWidth], [0,0,jointWidth], linkWidth*0.5, graphics.colorList[0])] #belongs to first body ty = 0.03 tz = 0.04 zOff = -0.05 toolSize= [0.05,0.5*ty,0.06] graphicsToolList = [graphics.Cylinder(pAxis=[0,0,zOff], vAxis= [0,0,tz], radius=ty*1.5, color=graphics.color.red)] graphicsToolList+= [graphics.Brick([0,ty,1.5*tz+zOff], toolSize, graphics.color.grey)] graphicsToolList+= [graphics.Brick([0,-ty,1.5*tz+zOff], toolSize, graphics.color.grey)] #changed to new robot structure July 2021: newRobot = Robot(gravity=[0,0,9.81], base = RobotBase(visualization=VRobotBase(graphicsData=graphicsBaseList)), tool = RobotTool(HT=HTtranslate([0,0,0.1]), visualization=VRobotTool(graphicsData=graphicsToolList)), referenceConfiguration = []) #referenceConfiguration created with 0s automatically #modDHKK according to Khalil and Kleinfinger, 1986 link0={'stdDH':[0,0,0,pi/2], 'modDHKK':[0,0,0,0], 'mass':20, #not needed! 'inertia':np.diag([1e-8,0.35,1e-8]), #w.r.t. COM! in stdDH link frame 'COM':[0,0,0]} #in stdDH link frame link1={'stdDH':[0,0,0.4318,0], 'modDHKK':[0.5*pi,0,0,0], 'mass':17.4, 'inertia':np.diag([0.13,0.524,0.539]), #w.r.t. COM! in stdDH link frame 'COM':[-0.3638, 0.006, 0.2275]} #in stdDH link frame link2={'stdDH':[0,0.15,0.0203,-pi/2], 'modDHKK':[0,0.4318,0,0.15], 'mass':4.8, 'inertia':np.diag([0.066,0.086,0.0125]), #w.r.t. COM! in stdDH link frame 'COM':[-0.0203,-0.0141,0.07]} #in stdDH link frame link3={'stdDH':[0,0.4318,0,pi/2], 'modDHKK':[-0.5*pi,0.0203,0,0.4318], 'mass':0.82, 'inertia':np.diag([0.0018,0.0013,0.0018]), #w.r.t. COM! in stdDH link frame 'COM':[0,0.019,0]} #in stdDH link frame link4={'stdDH':[0,0,0,-pi/2], 'modDHKK':[0.5*pi,0,0,0], 'mass':0.34, 'inertia':np.diag([0.0003,0.0004,0.0003]), #w.r.t. COM! in stdDH link frame 'COM':[0,0,0]} #in stdDH link frame link5={'stdDH':[0,0,0,0], 'modDHKK':[-0.5*pi,0,0,0], 'mass':0.09, 'inertia':np.diag([0.00015,0.00015,4e-5]), #w.r.t. COM! in stdDH link frame 'COM':[0,0,0.032]} #in stdDH link frame linkList=[link0, link1, link2, link3, link4, link5] for link in linkList: newRobot.AddLink(RobotLink(mass=link['mass'], COM=link['COM'], inertia=link['inertia'], localHT=StdDH2HT(link['stdDH']), )) cnt = 0 for link in newRobot.links: color = graphics.colorList[cnt] color[3] = 0.75 #make transparent link.visualization = VRobotLink(jointRadius=jointRadius, jointWidth=jointWidth, showMBSjoint=False, linkWidth=linkWidth, linkColor=color, showCOM= True ) cnt+=1 #++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #configurations and trajectory q0 = [0,0,0,0,0,0] #zero angle configuration #this set of coordinates only works with TSD, not with old fashion load control: # q1 = [0, pi/8, pi*0.75, 0,pi/8,0] #configuration 1 # q2 = [pi,-pi, -pi*0.5,1.5*pi,-pi*2,pi*2] #configuration 2 # q3 = [3*pi,0,-0.25*pi,0,0,0] #zero angle configuration #this set also works with load control: q1 = [0, pi/8, pi*0.5, 0,pi/8,0] #configuration 1 q2 = [0.8*pi,-0.8*pi, -pi*0.5,0.75*pi,-pi*0.4,pi*0.4] #configuration 2 q3 = [0.5*pi,0,-0.25*pi,0,0,0] #zero angle configuration #trajectory generated with optimal acceleration profiles: trajectory = Trajectory(initialCoordinates=q0, initialTime=0) trajectory.Add(ProfileConstantAcceleration(q3,0.25)) trajectory.Add(ProfileConstantAcceleration(q1,0.25)) trajectory.Add(ProfileConstantAcceleration(q2,0.25)) trajectory.Add(ProfileConstantAcceleration(q0,0.25)) #traj.Add(ProfilePTP([1,1],syncAccTimes=False, maxVelocities=[1,1], maxAccelerations=[5,5])) # x = traj.EvaluateCoordinate(t,0) #++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #test robot model #++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #control parameters, per joint: fc=1 Pcontrol = np.array([40000, 40000, 40000, 100, 100, 10]) Dcontrol = np.array([400, 400, 100, 1, 1, 0.1]) Pcontrol = fc*Pcontrol Dcontrol = fc*Dcontrol #soft: # Pcontrol = [4000, 4000, 4000, 100, 100, 10] # Dcontrol = [40, 40, 10, 1, 1, 0.1] #desired angles: qE = q0 qE = [pi*0.5,-pi*0.25,pi*0.75, 0,0,0] tStart = [0,0,0, 0,0,0] duration = 0.1 jointList = [0]*newRobot.NumberOfLinks() #this list must be filled afterwards with the joint numbers in the mbs! def ComputeMBSstaticRobotTorques(newRobot): q=[] for joint in jointList: q += [mbs.GetObjectOutput(joint, exu.OutputVariableType.Rotation)[2]] #z-rotation HT=newRobot.JointHT(q) return newRobot.StaticTorques(HT) #++++++++++++++++++++++++++++++++++++++++++++++++ #base, graphics, object and marker: objectGround = mbs.AddObject(ObjectGround(referencePosition=HT2translation(newRobot.GetBaseHT()), #visualization=VObjectGround(graphicsData=graphicsBaseList) )) #baseMarker; could also be a moving base! baseMarker = mbs.AddMarker(MarkerBodyRigid(bodyNumber=objectGround, localPosition=[0,0,0])) #++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #build mbs robot model: robotDict = newRobot.CreateRedundantCoordinateMBS(mbs, baseMarker=baseMarker) jointList = robotDict['jointList'] #must be stored there for the load user function unitTorques0 = robotDict['unitTorque0List'] #(left body) unitTorques1 = robotDict['unitTorque1List'] #(right body) loadList0 = robotDict['jointTorque0List'] #(left body) loadList1 = robotDict['jointTorque1List'] #(right body) #print(loadList0, loadList1) #++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #control robot compensateStaticTorques = True torsionalSDlist = [] for i in range(len(jointList)): joint = jointList[i] rot0 = mbs.GetObject(joint)['rotationMarker0'] rot1 = mbs.GetObject(joint)['rotationMarker1'] markers = mbs.GetObject(joint)['markerNumbers'] nGeneric=mbs.AddNode(NodeGenericData(initialCoordinates=[0], numberOfDataCoordinates=1)) #for infinite rotations tsd = mbs.AddObject(TorsionalSpringDamper(markerNumbers=markers, nodeNumber=nGeneric, rotationMarker0=rot0, rotationMarker1=rot1, stiffness=Pcontrol[i], damping=Dcontrol[i], visualization=VTorsionalSpringDamper(drawSize=0.1) )) torsionalSDlist += [tsd] #user function which is called only once per step, speeds up simulation drastically def PreStepUF(mbs, t): if compensateStaticTorques: staticTorques = ComputeMBSstaticRobotTorques(newRobot) #print("tau=", staticTorques) else: staticTorques = np.zeros(len(jointList)) [u,v,a] = trajectory.Evaluate(t) #compute load for joint number for i in range(len(jointList)): joint = jointList[i] phi = mbs.GetObjectOutput(joint, exu.OutputVariableType.Rotation)[2] #z-rotation omega = mbs.GetObjectOutput(joint, exu.OutputVariableType.AngularVelocityLocal)[2] #z-angular velocity #[u1,v1,a1] = MotionInterpolator(t, robotTrajectory, i) u1 = u[i] v1 = v[i] tsd = torsionalSDlist[i] mbs.SetObjectParameter(tsd, 'offset', u1) mbs.SetObjectParameter(tsd, 'velocityOffset', v1) mbs.SetObjectParameter(tsd, 'torque', staticTorques[i]) #additional torque from given velocity return True mbs.SetPreStepUserFunction(PreStepUF) #add sensors: cnt = 0 jointTorque0List = [] for i in range(len(jointList)): jointLink = jointList[i] tsd = torsionalSDlist[i] #using TSD: sJointRot = mbs.AddSensor(SensorObject(objectNumber=tsd, fileName="solution/joint" + str(i) + "Rot.txt", outputVariableType=exu.OutputVariableType.Rotation, writeToFile = sensorWriteToFile)) sJointAngVel = mbs.AddSensor(SensorObject(objectNumber=jointLink, fileName="solution/joint" + str(i) + "AngVel.txt", outputVariableType=exu.OutputVariableType.AngularVelocityLocal, writeToFile = sensorWriteToFile)) sTorque = mbs.AddSensor(SensorObject(objectNumber=tsd, fileName="solution/joint" + str(i) + "Torque.txt", outputVariableType=exu.OutputVariableType.TorqueLocal, writeToFile = sensorWriteToFile)) jointTorque0List += [sTorque] mbs.Assemble() #mbs.systemData.Info() SC.visualizationSettings.connectors.showJointAxes = True SC.visualizationSettings.connectors.jointAxesLength = 0.02 SC.visualizationSettings.connectors.jointAxesRadius = 0.002 SC.visualizationSettings.nodes.showBasis = True SC.visualizationSettings.nodes.basisSize = 0.1 SC.visualizationSettings.loads.show = False SC.visualizationSettings.openGL.multiSampling=4 tEnd = 1.25 h = 0.002 #SC.renderer.DoIdleTasks() simulationSettings = exu.SimulationSettings() #takes currently set values or default values simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h) simulationSettings.timeIntegration.endTime = tEnd simulationSettings.solutionSettings.solutionWritePeriod = h*1 simulationSettings.solutionSettings.sensorsWritePeriod = h*10 simulationSettings.solutionSettings.binarySolutionFile = True #simulationSettings.solutionSettings.writeSolutionToFile = False # simulationSettings.timeIntegration.simulateInRealtime = True # simulationSettings.timeIntegration.realtimeFactor = 0.25 simulationSettings.timeIntegration.verboseMode = 1 # simulationSettings.displayComputationTime = True simulationSettings.displayStatistics = True simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse #simulationSettings.timeIntegration.newton.useModifiedNewton = True simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True simulationSettings.timeIntegration.generalizedAlpha.useNewmark = simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints simulationSettings.timeIntegration.newton.useModifiedNewton = True simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations=True SC.visualizationSettings.general.autoFitScene=False SC.visualizationSettings.window.renderWindowSize=[1920,1200] useGraphics = False if useGraphics: SC.renderer.Start() if 'renderState' in exu.sys: SC.renderer.SetState(exu.sys['renderState']) SC.renderer.DoIdleTasks() mbs.SolveDynamic(simulationSettings, showHints=True) if useGraphics: SC.visualizationSettings.general.autoFitScene = False SC.renderer.Stop() mbs.SolutionViewer() lastRenderState = SC.renderer.GetState() #store model view #compute final torques: measuredTorques=[] for sensorNumber in jointTorque0List: measuredTorques += [abs(mbs.GetSensorValues(sensorNumber))] exu.Print("torques at tEnd=", VSum(measuredTorques)) if True: import matplotlib.pyplot as plt import matplotlib.ticker as ticker plt.rcParams.update({'font.size': 14}) plt.close("all") doJointTorques = False if doJointTorques: for i in range(6): data = np.loadtxt("solution/jointTorque" + str(i) + ".txt", comments='#', delimiter=',') plt.plot(data[:,0], data[:,3], PlotLineCode(i), label="joint torque"+str(i)) #z-rotation plt.xlabel("time (s)") plt.ylabel("joint torque (Nm)") ax=plt.gca() # get current axes ax.grid(True, 'major', 'both') ax.xaxis.set_major_locator(ticker.MaxNLocator(10)) ax.yaxis.set_major_locator(ticker.MaxNLocator(10)) plt.tight_layout() ax.legend(loc='center right') plt.show() # plt.savefig("solution/robotJointTorques.pdf") doJointAngles = True if doJointAngles: plt.close("all") for i in range(6): data = np.loadtxt("solution/joint" + str(i) + "Rot.txt", comments='#', delimiter=',') # data = np.loadtxt("solution/joint" + str(i) + "AngVel.txt", comments='#', delimiter=',') plt.plot(data[:,0], data[:,1], PlotLineCode(i), label="joint"+str(i)) #z-rotation plt.xlabel("time (s)") plt.ylabel("joint angle (rad)") ax=plt.gca() ax.grid(True, 'major', 'both') ax.xaxis.set_major_locator(ticker.MaxNLocator(10)) ax.yaxis.set_major_locator(ticker.MaxNLocator(10)) plt.tight_layout() ax.legend() plt.rcParams.update({'font.size': 16}) plt.show() # plt.savefig("solution/robotJointAngles.pdf")