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ROSMobileManipulator.py

You can view and download this file on Github: ROSMobileManipulator.py

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN python example
#
# Details:  This example shows how to communicate between an Exudyn simulation and ROS
#           To make use of this example, you need to 
#           install ROS (ROS1 noetic) including rospy (see rosInterface.py)
#           prerequisite to use: 
#           use a bash terminal to start the roscore with: 
#               roscore 
#           then run the simulation:
#               python 3 ROSMobileManipulator.py
#           You can use the prepared ROS node, ROSControlMobileManipulator to control the simulation
#           use a bash terminal to start the recommended file  (see folder Examples/supplementary):
#               python3 ROSControlMobileManipulator.py
#           For even more ROS functionality create a ROS package (e.q. myExudynInterface) in a catkin workspace, 
#           copy files ROSMobileManipulator.py, ROSbodykairos.stl and ROSControlMobileManipulator.py in corresponding folders within the package
#           For more functionality see also: ROSMassPoint.py, ROSBringupTurtle.launch, ROSControlTurtleVelocity.py from the EXUDYN examples folder
# 
# Author:   Martin Sereinig, Peter Manzl 
# Date:     2023-05-31 (created)
# last Update: 2023-09-11
# 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.
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

# general imports
import numpy as np
import roboticstoolbox as rtb
from spatialmath import SE3

# exudyn imports
import exudyn as exu 
from exudyn.utilities import *
from exudyn.itemInterface import *
from exudyn.rigidBodyUtilities import *
from exudyn.graphicsDataUtilities import *
from exudyn.robotics import *
from exudyn.robotics.models import ManipulatorUR5, LinkDict2Robot
from exudyn.robotics.motion import Trajectory, ProfileConstantAcceleration, ProfilePTP
import exudyn.robotics.rosInterface as exuROS #exudyn ROS interface class
import exudyn.robotics.mobile as mobile

# ROS imports
from geometry_msgs.msg import Twist
from geometry_msgs.msg import Pose
from std_msgs.msg import String


# here build inherited class and using within a simple exudyn simulation of one mass spring-damper 
class MyExudynROSInterface(exuROS.ROSInterface):
    def __init__(self):
        # use initialisation of super class
        # this initialize a rosnode with name
        super().__init__(name='ROSMobileManipulator')
        # initialization of all standard publisher done by super class
        # use standard publisher functions form super class
        # initialize all subscriber 
        # suitable callback function is auto generated by superclass (using lambda function)
        # twist subscriber: cmd_vel
        twistSubsrciberBase = '' 
        twistSubsrciberTopic = 'cmd_vel'     # topic to subscribe 
        self.cmd_vel = Twist()              # data type of topic, must be named: self.twistSubscriberTopic
        self.myTwistSubscriber = self.InitSubscriber(twistSubsrciberBase,twistSubsrciberTopic,Twist)
        # string subsriber: my_string
        stringSubsrciberBase = ''
        stringSubsrciberTopic = 'my_string'     # topic to subscribe 
        self.my_string = String()              # data type of topic, must be named: self.twistSubscriberTopic
        self.myStringSubscriber = self.InitSubscriber(stringSubsrciberBase,stringSubsrciberTopic,String)
        # string subsriber: my_pose
        poseSubsrciberBase = ''
        poseSubsrciberTopic = 'my_pose'     # topic to subscribe 
        self.my_pose = Pose()              # data type of topic, must be named: self.twistSubscriberTopic
        self.myPoseSubscriber = self.InitSubscriber(poseSubsrciberBase,poseSubsrciberTopic,Pose)        


debugFlag = False  # turn prints on and off

# function to check (exudyn) module version 
def checkInstall(moduleName): 
    import importlib
    found = importlib.util.find_spec(moduleName) is not None
    if not(found): 
        print('Error! Please install the module {} Version 1.7 or higher using \npip install {}==1.7'.format(moduleName, moduleName))
        return False
    else: 
        return True

# function to control the mobile manipulator behavior 
def functionStateMachine(t, posPlatform, ThetaPlatform, PosObj, armStatus, myState, myDict):
    # initialize variables
    v = [0.0,0.0,0]
    # with None no arm movement is performed
    TArm = None
    grasp = None
    # check robotC control string send via ROS
    robotControlString = myROSInterface.my_string.data
    if debugFlag:
        if robotControlString!='':
            print('robot control string: ', robotControlString)
        else:
            print('no robot control string')
    if robotControlString == 'ms':
        TArm = None
        grasp = None
        # get velocity data from ROS /cmd_vel topic, please use: rostopic pub -r 100 /cmd_vel geometry_msgs/Twist "..."
        rosLinearVelo = myROSInterface.cmd_vel.linear
        rosAngularVelo = myROSInterface.cmd_vel.angular 
        v = [rosLinearVelo.x, rosLinearVelo.y, rosAngularVelo.z]
    elif robotControlString == 'a':
        # state for arm movement 
        v = [0.0,0.0,0]
        ArmPosition = [myROSInterface.my_pose.position.x, myROSInterface.my_pose.position.y, myROSInterface.my_pose.position.z]
        ArmOrientationQ = [myROSInterface.my_pose.orientation.w, myROSInterface.my_pose.orientation.x, myROSInterface.my_pose.orientation.y, myROSInterface.my_pose.orientation.z]
        ArmOrientationR = EulerParameters2RotationMatrix(ArmOrientationQ)
        # build homogenous transformation from rotation matrix existing rotation matrix
        TArmRot = np.eye(4)
        TArmRot[0:3,0:3] = ArmOrientationR
        TArm = HTtranslate(ArmPosition) @ TArmRot
    elif robotControlString == 'mk':
        # state for external cmd_vel (keyboard or other node)
        # get velocity data from ROS /cmd_vel topic, please use: rostopic pub -r 100 /cmd_vel geometry_msgs/Twist "..." but send via keyboard node
        rosLinearVelo = myROSInterface.cmd_vel.linear
        rosAngularVelo = myROSInterface.cmd_vel.angular 
        v = [rosLinearVelo.x, rosLinearVelo.y, rosAngularVelo.z]
    else:
        # print('no valid control string received')
        v = [0.0, 0.0, 0.0]
        TArm = None
        grasp = None
    return v, TArm, grasp, myState, myDict

# set simulation system
SC = exu.SystemContainer()
mbs = SC.AddSystem()
# function to simulate the mobile manipulator 
def SimulationMobileRobot(funcStatMachine,myROSInterface, p0=[0,0], theta0=0, flagFixObject=False, flagOnlyGrasp=False, verboseMode = 0, sensorWriteToFile = False): 
    compensateStaticTorques = False
    mobRobSolutionPath = 'solution/'
    hstepsize = 5e-3 # step size 
    tEnd = 100 # simulation time 
    comShift=[0,0,-0.1]
    debugPlatformOffset = 125*9.81 /10**(6)
    constrainedAxesSet=[0,0,0,0,0,0]
    offsetUserFunctionParametersSet=[0,0,0,0,0,0]
    debugOffsetNumber= debugPlatformOffset

    #ground body and marker
    gGround = GraphicsDataCheckerBoard(point = [0,0,0], size=8, nTiles = 12) # (centerPoint=[4,4,-0.001],size=[12,12,0.002], color=color4lightgrey[0:3]+[0.5])
    graphicsGroundList =[gGround]
    coordinateSystemGround = False
    if coordinateSystemGround:
        graphicsGroundList += [GraphicsDataCylinder([0,0,0], [0.5,0,0], 0.0035, color4red)]            # base coordinate system x
        graphicsGroundList +=[GraphicsDataCylinder([0,0,0], [0,0.5,0], 0.0035, color4green)]          # base coordinate system y
        graphicsGroundList +=[GraphicsDataCylinder([0,0,0], [0,0,0.5], 0.0035, color4blue)]           # base coordinate system z
    oGround = mbs.AddObject(ObjectGround(visualization=VObjectGround(graphicsData=graphicsGroundList)))
    markerGround = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=[0,0,0]))
    comShiftPlatform = [0,0,0]

    # define mobile manipulator KAIROS     
    mobileRobot = { 'gravity':                  [0,0,-9.81],                # gravity in m/s^2
                    'platformDimensions':       [0.575, 0.718 , 0.2495],    # [width, length, hight]   [0.575, 0.718 , 0.495]
                    'platformMass':             125-18.4,                   # platform mass- manipulator mass 
                    'platformInitialPose':      HTtranslate([p0[0],p0[1],(0.495+(-0.12))]) @ HTrotateZ(theta0),  # platform initial pose as HT middle of platform (box representation) 
                    'platformInitialOmega':     [0,0,0],                # platform initial rotational velocity around x,y,z axis
                    'platformInitialVelocity':  [0,0,0],                # platform initial translational velocity in x,y,z direction
                    'platformCOM':              comShift,               # center of mass shift to base coordinate system
                    'comShiftPlatform':         comShiftPlatform,       # the shift of the platform alone
                    'platformBaseCoordinate':   [0.0 ,0.0 ,0.0],        # geometric center  in middle of platform                   
                    'platformInertia':          InertiaCuboid,          # platform inertia w.r.t. COM!                    
                    'platformRepresentation':   'box',                  # 'box' or 'stl' graphical representation of the mobile platform 
                    'platformStlFile':          'ROSbodykairos.stl',    # path to the used stl file 
                    'friction':                 [1 ,0.0, 0.0],          # [dryFriction1, dryFriction2,rollFriction]= [0.4,0.0075,0.05] for LeoBot (Master Thesis Manzl)
                    'viscousFrictionWheel':     [0.1, 0.1],             # orthotropic damping in the rotated roller frame; see also Exudyn documentation of 
                    'frictionAngle':            np.pi/4 ,               # friction angle theta=pi/4 for mecanum wheel, theta=0 for standard wheel  
                    'wheelType':                0,                      # 0=wheelType wheel o-config, 1=mecanum wheel x-config, 2=standard wheel  (always in bottom view)
                    'wheelBase':                0.430,                  # distance between center of wheels (wheel axes) between front and back  
                    'wheelTrack':               0.390,                  # distance between center of wheels between left and right 
                    'wheelRoh':                 200*8,                  # density of wheel in kg/m^3
                    'wheelRadius':              0.254/2,                # radius of wheel in m 
                    'wheelWidth':               0.1,                    # width of wheel in m, just for graphics     
                    'wheelMass':                8,                      # Mass of one mecanum wheel, leobot measured
                    'wheelInertia':             InertiaCylinder,        # inertia for infinitely small ring:
                    'wheelNumbers':             4,                      # number of wheels on platform
                    'wheelContactStiffness':    10**(6), 
                    'wheelContactDamping':      50*np.sqrt(10**(5)), 
                    'serialRobotMountpoint':    HTtranslate([0.178 , 0, 0.12]), 
                    'proportionalZone':         1e-2,                   # friction regularization
                    'debugOffset':              debugOffsetNumber
                    }  

    #################### Build mobile robot and add it to existing mbs
    mobileRobotBackDic = mobile.mobileRobot2MBS(mbs, mobileRobot, markerGround)
    mbs.variables['mobileRobotBackDic'] = mobileRobotBackDic # to be able to use all variables in all functions (make it global useable)
    # add mbs.variable for ROS sensor
    mbs.variables['nodeNumber'] = mobileRobotBackDic['nPlatformList'][0] # just needed if nodeNumber is used for sensor information 
    # for shorter writing: 
    Lx = mobileRobot['wheelTrack']
    Ly = mobileRobot['wheelBase']
    R = mobileRobot['wheelRadius']
    #initialize mobile platform kinematics 
    platformKinematics = mobile.MobileKinematics(R,Lx,Ly,wheeltype=0)

    def UFoffset(mbs,t,itemIndex,offsetUserFunctionParameters):
        return offsetUserFunctionParameters
    mbs.SetObjectParameter(mobileRobotBackDic['oPlatformList'][0],'offsetUserFunctionParameters',offsetUserFunctionParametersSet)
    mbs.SetObjectParameter(mobileRobotBackDic['oPlatformList'][0],'offsetUserFunction',UFoffset)
    mbs.SetObjectParameter(mobileRobotBackDic['oPlatformList'][0],'constrainedAxes',constrainedAxesSet)
    ######################## Sensor data from mobile platform ###
    WheelSpringDamper = [0]*4
    MotorDataNode = [0]*4
    cWheelBrakes = [0]*4
    for i in range(4):     
        RM0 = mbs.GetObject(mobileRobotBackDic['oAxlesList'][i])['rotationMarker0']
        RM1 = mbs.GetObject(mobileRobotBackDic['oAxlesList'][i])['rotationMarker1']

    # wheel controller for KAIROS Platform  
        paramOpt = {'kMotor': 100, 'fact_dMotor': 0.5} 
        kWheelControl = paramOpt['kMotor'] 
        dWheelControl = kWheelControl * paramOpt['fact_dMotor']
        MotorDataNode[i] = mbs.AddNode(NodeGenericData(numberOfDataCoordinates = 1, initialCoordinates=[0]))
        WheelSpringDamper[i] = mbs.AddObject(TorsionalSpringDamper(name='Wheel{}Motor'.format(i), 
                                            markerNumbers=[mobileRobotBackDic['mAxlesList'][i], mobileRobotBackDic['mWheelsList'][i]],
                                            nodeNumber= MotorDataNode[i], # for continuous Rotation
                                            stiffness = kWheelControl, damping =  dWheelControl, offset = 0,
                                            rotationMarker0=RM0, 
                                            rotationMarker1=RM1))
        cWheelBrakes[i] = mbs.AddObject(GenericJoint(markerNumbers=
                                                [mobileRobotBackDic['mAxlesList'][i], mobileRobotBackDic['mWheelsList'][i]], 
                                                constrainedAxes = [0]*6, 
                                                rotationMarker0=RM0, 
                                                rotationMarker1=RM1, 
                                                ))
        mbs.variables['flagBrakeActive'] = False

    # wheel user function  
    mbs.variables['signWheels'] = [-1,1,1,-1]
    mbs.variables['t0'] = 0
    mbs.variables['phiWheel'] = [0,0,0,0]
    vMax = 3.0
    wMax = vMax / mobileRobot['wheelRadius'] # m/s
    mbs.variables['wHistory'] = [[],[],[],[]] # for debug 
    def PreStepUFWheel(mbs, t, w= [0,0,0,0]):
        if t == 0: 
            return True
        dt =  mbs.sys['dynamicSolver'].it.currentStepSize 
        dwMax = wMax * dt

        if debugFlag: print('dwMax = ', dwMax)

        for i in range(4):
            wOld = mbs.GetObjectParameter(WheelSpringDamper[i], 'velocityOffset')
            if w[i] > wOld + dwMax: 
                w[i] = wOld + dwMax 
            elif w[i] < wOld - dwMax: 
                w[i] = wOld - dwMax 
            mbs.variables['phiWheel'][i] += (t-mbs.variables['t0'])*w[i] #* mbs.variables['signWheels'][i]
            mbs.SetObjectParameter(WheelSpringDamper[i], 'offset', mbs.variables['phiWheel'][i])
            mbs.SetObjectParameter(WheelSpringDamper[i], 'velocityOffset', w[i])
            mbs.variables['wHistory'][i] += [w[i]]
            # mbs.SetObjectParameter(WheelSpringDamper[i], 'offset', SmoothStep(t, 0.5 , 2, 0, 1)*t * mbs.variables['signWheels'][i])    
        mbs.variables['t0'] = t
        return True
    sPlatformPosition = mbs.AddSensor(SensorMarker(name='platformpos',markerNumber=mobileRobotBackDic['mPlatformList'][-1], 
                                                        fileName=mobRobSolutionPath + '/rollingDiscCarPos.txt', 
                                                        outputVariableType = exu.OutputVariableType.Position, writeToFile = sensorWriteToFile,storeInternal=True))
    sPlatformVelocity = mbs.AddSensor(SensorMarker(name='platformvelo',markerNumber=mobileRobotBackDic['mPlatformList'][-1], 
                                                        fileName=mobRobSolutionPath + '/rollingDiscCarVel.txt', 
                                                        outputVariableType = exu.OutputVariableType.Velocity, writeToFile = sensorWriteToFile,storeInternal=True))   
    sPlatformOrientation = mbs.AddSensor(SensorBody(name='platformRot',bodyNumber=mobileRobotBackDic['bPlatformList'][0], 
                                                        fileName=mobRobSolutionPath + '/rollingDiscCarOrientation.txt', 
                                                        outputVariableType = exu.OutputVariableType.Rotation , writeToFile = sensorWriteToFile))
    mbs.variables['sensorList'] = [sPlatformPosition, sPlatformOrientation]
    # ad manipulator to model 
    if 1: 
        mode='newDH'
        qOffset = [-np.pi * 1/4, 0,0,0,0,0]
        q0 = [-3*np.pi/4, np.pi - 1e-15  , np.pi*1.5/2 ,0- 1e-15 ,0- 1e-15 ,0- 1e-15 ] #zero angle configuration
        tx = 0.03
        zOff = -0.2
        toolSize= [tx*0.5, 0.06,0.12]
        r6 = 0.04
        graphicsToolList = []
        graphicsToolList += [GraphicsDataCylinder(pAxis=[0,0,zOff], vAxis= [0,0,np.abs(zOff)*0.8], radius=r6, color=color4red)]
        graphicsToolList+= [GraphicsDataOrthoCubePoint([ tx,0, 0], toolSize, color4grey)]
        graphicsToolList+= [GraphicsDataOrthoCubePoint([-tx,0, 0], toolSize, color4grey)]
        graphicsToolList+= [GraphicsDataOrthoCubePoint([0,0, -0.05], [tx*5,0.09,0.04], color4grey)]
        graphicsToolList += [GraphicsDataBasis(length=0.2)]
        basePoseHT=mobileRobot['platformInitialPose'] @ mobileRobot['serialRobotMountpoint'] @ HTrotateZ(qOffset[0]) #robot base position and orientation  

        # manipulator input with included function from exudyn robotics models
        myRobotList = ManipulatorUR5()
        robot = Robot(gravity=[0,0,-9.81],
            base = RobotBase(HT=basePoseHT), #visualization=VRobotBase(graphicsData=graphicsBaseList)),
            tool = RobotTool(HT=HTtranslate([0,0,0.155]), #  @ HTrotateZ(np.pi/2), 
                            visualization=VRobotTool(graphicsData=graphicsToolList)),
            referenceConfiguration = q0) #referenceConfiguration created with 0s automatically
        robot = LinkDict2Robot(myRobotList, robotClass=robot)
        #control parameters, per joint:
        fc=0.5
        Pcontrol = np.array([4000, 4000, 4000, 100, 100, 100])
        Dcontrol = np.array([60,   60,   60,   6,   6,   0.6])
        Pcontrol = fc*Pcontrol
        Dcontrol = fc*Dcontrol

        # change predefined control parameters
        for i in range(robot.NumberOfLinks()):
            robot.links[i].PDcontrol = (Pcontrol[i], Dcontrol[i])
        #trajectory generated with optimal acceleration profiles:
        trajectory = Trajectory(initialCoordinates=q0, initialTime=0)
        trajectory.Add(ProfileConstantAcceleration(q0,0.5))
        jointList = [0]*robot.NumberOfLinks() #this list must be filled afterwards with the joint numbers in the mbs!
        def ComputeMBSstaticRobotTorques(robot):
            q=[]
            for joint in jointList:
                q += [mbs.GetObjectOutput(joint, exu.OutputVariableType.Rotation)[2]] #z-rotation
            HT=robot.JointHT(np.array(q)+qOffset)
            return robot.StaticTorques(HT)

        #++++++++++++++++++++++++++++++++++++++++++++++++
        #base, graphics, object and marker:
        #baseMarker; could also be a moving base according to doc but found no examples!
        baseMarker = mobileRobotBackDic['mPlatformList'][-1] # mbs.AddMarker(MarkerBodyRigid(bodyNumber=objectGround, localPosition=[0,0,0]))
        sArmTorque = [0,0,0,0,0,0]

        #++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
        #build mbs robot model:

        robotDict = robot.CreateRedundantCoordinateMBS(mbs, baseMarker=baseMarker)
        jointList = robotDict['jointList'] #must be stored there for the load user function
        torsionalSDlist = robotDict['springDamperList']

        for i in range(len(robotDict['springDamperList'])): 
            sArmTorque[i] = mbs.AddSensor(SensorObject(objectNumber= robotDict['springDamperList'][i], 
                                        fileName=mobRobSolutionPath+ '/ArmMotorTorque'+str(i) + '.txt', 
                                        outputVariableType = exu.OutputVariableType.TorqueLocal, writeToFile=sensorWriteToFile))
            # mbs.SetObjectParameter(torsionalSDlist[i], 'offset', q0[i] + qOffset[i])
        mEndeffektor = mbs.AddMarker(MarkerBodyRigid(name='Endeffektor', bodyNumber=robotDict['bodyList'][-1], localPosition=[0,0,0.157]))
        sEndeffektor = mbs.AddSensor(SensorMarker(markerNumber=mEndeffektor, writeToFile=False, outputVariableType=exu.OutputVariableType.Position))
        # robotics toolbox by Peter Corke 
        UR5_rtb = rtb.models.DH.UR5()
        UR5_rtb.tool = SE3([0,0,0.2])
        def getNewTraj(TArm, qLast): 
            vm = [np.pi * 1.1/2]*6
            am = [5 * 0.6]*6
            nAttempts = 10
            qNew = UR5_rtb.ikine_LM(TArm, q0 = qLast) # , q0=qLast-qOffset)
            iAttempt = 1
            if not(qNew.success): 
                for iAttempt in range(1, nAttempts): 
                    # randomize initial angles to try to get a solution for the inverse kinematics
                    qNew = UR5_rtb.ikine_LM(TArm, q0 = (np.random.random(6)-1)*np.pi*2) # , q0=qLast-qOffset)
                    if qNew.success: 
                        break
                if not(qNew.success): 
                    print('Inverse Kinematics could not be solved after {} attempts. \nPlease check if the given Pose \n{}\nis in the workspace.'.format(iAttempt, TArm))
                    return None, None
            teMax = 0       
            qNew = qNew.q # - qOffset
            for i in range(len(qNew)): 
                te = abs(qNew[i] - qLast[i])/vm[i] + vm[i]/am[i]
                if te > teMax: 
                    teMax = te
            print('Planned new PTP motion after {} attempts from:\n{}\nto\n{}\nin {}s. '.format(iAttempt, np.round(qLast, 2), np.round(qNew, 2), np.round(teMax, 2)))
            # qNew[1] += np.pi*2
            return qNew, teMax

        def activateBrakes(cJoints, oTSD, flag): 
            for i in range(len(cJoints)): 
                # mbs.SetObjectParameter(cJoints[i], 'constrainedAxes', [0,0,0,0,0,1*bool(flag)])
                if flag: # deactivate motors 
                    mbs.SetObjectParameter(oTSD[i], 'stiffness', 100)
                    mbs.SetObjectParameter(oTSD[i], 'damping', 5)
                else: 
                    mbs.SetObjectParameter(oTSD[i], 'stiffness', kWheelControl)
                    mbs.SetObjectParameter(oTSD[i], 'damping', dWheelControl)

            print('un'*bool(not(flag)) + 'locking wheels')
            return True

        hObj = 0.08
        xTable, yTable, hTable = 0.2, 0.4, 0.645
        if flagFixObject: 
            PosObj = [3.0,1.0, hTable + hObj/2] # for testing of grasp
        else: 
            PosObj = (np.random.rand(3)-0.5) * [0.4,0.8,0] + [1.5 ,0, hTable + hObj/2]

        graphicsTarget = GraphicsDataCylinder(pAxis = [0,0,-hObj/2], vAxis = [0,0,hObj ], radius = 0.02, color=color4lightgreen)
        inertiaTarget = InertiaCylinder(500, hObj , 0.02, 2)
        nObj, bObj = AddRigidBody(mainSys = mbs, 
                    inertia = inertiaTarget, 
                    nodeType = str(exu.NodeType.RotationEulerParameters), 
                    position = PosObj, 
                    rotationMatrix = np.eye(3),
                    angularVelocity =  [0,0,0],
                    velocity= [0,0,0],
                    gravity = [0,0,0], 
                    graphicsDataList = [graphicsTarget])
        mObj = mbs.AddMarker(MarkerBodyRigid(bodyNumber=bObj))
        cGrasp = mbs.AddObject(RigidBodySpringDamper(markerNumbers=[mEndeffektor, mObj], stiffness = np.eye(6)*1e3, damping = np.eye(6)*1e2, 
                                                    visualization={'show': False, 'drawSize': -1, 'color': [0]*4}, activeConnector=False))
        graphicsTable = GraphicsDataOrthoCubePoint(centerPoint = [0,0,0], size = [xTable, yTable, hTable], color=color4darkgrey2)

        nTable, bTable = AddRigidBody(mainSys = mbs, 
                        inertia = inertiaTarget, 
                        nodeType = str(exu.NodeType.RotationEulerParameters), 
                        position = list(PosObj[0:2]) + [hTable/2], 
                        rotationMatrix = np.eye(3),
                        angularVelocity =  [0,0,0],
                        velocity= [0,0,0],
                        gravity = [0,0,0], 
                        graphicsDataList = [graphicsTable])

        mbs.variables['myDict'] = {}

        #prestep user functions
        for i in range(6): 
            mbs.variables['qDebug{}'.format(i)] = []
        mbs.variables['state'] = 0
        mbs.variables['trajectory'] = trajectory
        #user function which is called only once per step, speeds up simulation drastically

        def PreStepUF(mbs, t):
            if compensateStaticTorques:
                staticTorques = ComputeMBSstaticRobotTorques(robot)
            else:
                staticTorques = np.zeros(len(jointList))

            PosPlatform =  mbs.GetSensorValues(mbs.variables['sensorList'][0]) - [0.178, 0 , 0 ]#mbs.variables['sensorRecord{}'.format(mbs.variables['sensorRecorders'][0])]
            ThetaPlatform = mbs.GetSensorValues(mbs.variables['sensorList'][1])[-1]

            phi = np.zeros(len(robot.links))
            for i in range(len(robot.links)): 
                    phi[i] = mbs.GetObjectOutput(jointList[i], exu.OutputVariableType.Rotation)[2] #z-rotation

            if t > mbs.variables['trajectory'][-1]['finalTime']: 
                armStatus = 1 # current trajectory finished
            else: 
                armStatus = 0

            # here functionstatemachine in preStepUserFunction call 
            vel, TArm, grasp, mbs.variables['state'], mbs.variables['myDict'] = funcStatMachine(t, PosPlatform, ThetaPlatform, 
                                                    PosObj, armStatus, mbs.variables['state'], mbs.variables['myDict'])
            if type(TArm) == np.ndarray: 
                TArm = SE3(TArm)
            if mbs.variables['state'] == -1: 
                mbs.SetRenderEngineStopFlag(True)
                print('finished Statemachine. ')

            # platform kinematics calculation 
            w = platformKinematics.getWheelVelocities(vel)

            if TArm != None: 
                lastTraj = mbs.variables['trajectory'][-1]
                qLast = lastTraj['coordinateSets'][-1] # the last desired joint angles
                tLast = lastTraj['finalTime'] # 
                qNew, Ttraj = getNewTraj(TArm, qLast)
                if type(qNew) != type(None): 
                    mbs.variables['trajectory'].Add(ProfileConstantAcceleration(qLast,t-tLast+0.1))
                    mbs.variables['trajectory'].Add(ProfileConstantAcceleration(qNew,Ttraj))
                # print('\n\nTTraj is: \n{}\n\n'.format(np.round(Tj, 3)))

            if grasp:
                pEE = mbs.GetSensorValues(sEndeffektor)
                distanceGrasp = pEE - PosObj - [0,0,0]
                # print('distance grasp = ', distanceGrasp)
                if np.linalg.norm(distanceGrasp) < 0.1: # distance of grasp to  
                    print('grasp successful!')    
                    # activate constraint for grasp 
                    RotEE = mbs.GetNodeOutput(robotDict['nodeList'][-1], exu.OutputVariableType.RotationMatrix).reshape([3,3])
                    mbs.SetObjectParameter(cGrasp, 'rotationMarker1', RotEE)
                    # mbs.SetObjectParameter(cGrasp, '', RotEE) # position

                    # mbs.SetObjectParameter(cGrasp, 'constrainedAxes', [1]*6)
                    # mbs.SetObjectParameter(cGrasp, '', [1]*6)
                    mbs.SetObjectParameter(cGrasp, 'activeConnector', True)
                    offset_local = list(RotEE @ distanceGrasp) 
                    offset_local[1] = 0
                    mbs.SetObjectParameter(cGrasp, 'offset', offset_local + [0,0,0]) # list(RotEE @ distanceGrasp) + [0,0,-hObj*0])
                else: 
                    print('grasping the object was not successful. Calculated distacne = {}'.format(np.round(distanceGrasp, 3)))
            [u,v,a] = mbs.variables['trajectory'].Evaluate(t)
            for i in range(len(robot.links)):
                tsd = torsionalSDlist[i]
                mbs.SetObjectParameter(tsd, 'offset', u[i] + qOffset[i])
                mbs.SetObjectParameter(tsd, 'velocityOffset', v[i])
                mbs.SetObjectParameter(tsd, 'torque', staticTorques[i]) #additional torque from given velocity 
            # send velocity data to ROS
            myROSInterface.PublishTwistUpdate(mbs,t)
            # send position data to ROS 
            myROSInterface.PublishPoseUpdate(mbs,t)
            PreStepUFWheel(mbs, t, w)

            if np.linalg.norm(w) < 1e-5 and t > 0.5:
                if not(mbs.variables['flagBrakeActive']): 
                    activateBrakes(cWheelBrakes, WheelSpringDamper, True)
                    mbs.variables['flagBrakeActive'] = True                  
            else: 
                if mbs.variables['flagBrakeActive']: 
                    activateBrakes(cWheelBrakes, WheelSpringDamper, False)
                    mbs.variables['flagBrakeActive'] = False      

            return True

    mbs.SetPreStepUserFunction(PreStepUF)
    SC.visualizationSettings.interactive.trackMarker = mobileRobotBackDic['mPlatformList'][0]
    # start simulation: 
    mbs.Assemble()
    PreStepUF(mbs, 0)

    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
    SC.visualizationSettings.openGL.shadow = 0.5
    SC.visualizationSettings.openGL.light0position = [0, -2, 10, 0]
    SC.visualizationSettings.openGL.shadowPolygonOffset = 0.1
    #mbs.WaitForUserToContinue()

    simulationSettings = exu.SimulationSettings() #takes currently set values or default values
    simulationSettings.timeIntegration.numberOfSteps = int(tEnd/hstepsize)
    simulationSettings.timeIntegration.endTime = tEnd
    simulationSettings.solutionSettings.solutionWritePeriod = hstepsize #0.005
    simulationSettings.solutionSettings.sensorsWritePeriod = hstepsize # 0.005
    simulationSettings.solutionSettings.binarySolutionFile = False
    simulationSettings.solutionSettings.writeSolutionToFile = False

    simulationSettings.timeIntegration.simulateInRealtime = True
    #simulationSettings.timeIntegration.realtimeFactor = 0.25
    simulationSettings.timeIntegration.verboseMode = verboseMode
    #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.spectralRadius = 0.5 # 0.25
    simulationSettings.timeIntegration.discontinuous.maxIterations = 3
    simulationSettings.timeIntegration.adaptiveStepRecoveryIterations = 10
    simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations= True # False

    simulationSettings.displayComputationTime = True
    simulationSettings.displayStatistics = True
    #simulationSettings.linearSolverType = exu.LinearSolverType.EigenSpars


    SC.visualizationSettings.general.autoFitScene=False
    SC.visualizationSettings.general.renderWindowString = 'Mobile Robot Simulation'
    SC.visualizationSettings.window.renderWindowSize=[1920,1200]
    SC.visualizationSettings.window.startupTimeout=5000
    SC.visualizationSettings.interactive.selectionLeftMouse = False
    SC.visualizationSettings.interactive.selectionRightMouse = False

    SC.visualizationSettings.openGL.initialModelRotation =RotationMatrixZ(-0.2) @ RotationMatrixX(np.pi/2.7)  #
    SC.visualizationSettings.openGL.initialZoom = 1.5
    SC.visualizationSettings.openGL.initialCenterPoint = [0, 2, 0] # -1.7, -2, -2]
    # SC.visualizationSettings.contour.outputVariable = exu.OutputVariableType.Displacement
    # SC.visualizationSettings.contour.outputVariableComponent = 2 #0=x, 1=y, 2=z
    exu.StartRenderer()
    mbs.WaitForUserToContinue()
    exu.SolveDynamic(mbs, simulationSettings, showHints=True, storeSolver = True)
    #mbs.WaitForRenderEngineStopFlag()
    exu.StopRenderer()

    # for debug 
    if debugFlag: 
        import matplotlib.pyplot as plt
        for i in range(4): 
            plt.plot(mbs.variables['wHistory'][i], label='wheel ' + str(i+1))
        plt.legend()
        plt.show()
        mbs.PlotSensor(sensorNumbers=[sPlatformPosition], components=[0,1,2], labels=['x(m); ','y','z'], colorCodeOffset=2, closeAll=False)
        mbs.PlotSensor(sensorNumbers=[sPlatformVelocity], components=[0,1,2], labels=['vx(m); ','vy','vz'], colorCodeOffset=2, closeAll=False)
    return mbs

# main function 
if __name__ == '__main__': 
    if not(checkInstall('exudyn')): 
        print('Error! Simulation can not be started!')
        import sys
        sys.exit()

    print('Starting Simulation...')
    # initialize ROS interface from own subclass
    myROSInterface = MyExudynROSInterface()
    # start simulation
    SimulationMobileRobot(functionStateMachine,myROSInterface,p0=[0,0],flagFixObject=True)