Module: robotics.mobile

The utilities contains functionality for mobile robots based on the EXUDYN example MecanumWheel RollingDiscPenality specific friction angle of rolling disc is used to model rolls of mecanum wheels

  • Author: Martin Sereinig, Peter Manzl and Johannes Gerstmayr

  • Date: 2021-10-01 Updated: 2023-09-15

  • Notes: formulation is still under development

Function: mobileRobot2MBS

mobileRobot2MBS(mbs, mobileRobot, markerGround, flagGraphicsRollers = True, *args, **kwargs)

  • function description:
    add items to existing mbs to build up a mobile robot platform,
    there are options that can be passed as args / kwargs, which can contains options as described below.
    The robot platform is built out of rigid bodies where the wheels can be modeled as rolling discs
    (mecanum wheel x/o configuration) or with a detailed mecanum wheel simulation approach
  • input:
    mbs: the multibody system which will be extended
    markerGround: a rigid body marker, at which the robot will be placed (usually ground)
    mobileRobot: a dictionary including all information about the mobile robot platform
  • output:
    the function returns a dictionary containing nodes, body, object and marker numbers of individual mobile robot parts
    nPlatformList, bPlatformList, oPlatformList, mPlatformList; nodes, bodies, objects and marker of the platform [nPlattform] [bPlattform] [oPlattform] []
    oAxisList, mAxlesList; objects and marker of the axles [a1, a2, a3, a4]
    nWheelsList, bWheelsList, oRollingDiscsList, mWheelsList; nodes, bodys, objects and markers of the four wheels [w1, w2, w3, w4]
  • notes:
    for coordinate system, see Python function definition

Relevant Examples (Ex) and TestModels (TM) with weblink to github:

Function: Generatrix2Polynomial

Generatrix2Polynomial(param, GeneratrixFunction, tol = 1e-14, nFit = 101, nTest = 1001)

  • function description:
    create a polynomial describing a generatrix function
  • input:
    param: list containing data (lRoll, aPoly, …)
  • author:
    Peter Manzl
    **note: create and fit a polynomial of an order high enough to approximate the given GeneratrixFunction
    with a given tolerance. The error is measured as the Chebyshev distance.

Function: GeneratrixRoll

GeneratrixRoll(u, param)

  • function description:
    generatrix function for a roll of a Mecanum wheel
  • input:
    u: parameter, max. +- pi/2
    param['r']: radius of the associated Mecanum wheel
    param['delta']: angle of the rolls rotation axis to the wheels rotation axis
    param['dRoll']: smallest distance of roll axis to the wheel axis
  • output:
    x and y values for the function in the local frame. The rotation around the
    local x-yxis creates the surface of the roll.
  • author:
    Peter Manzl
  • notes:
    parametric equation, x,y are the generatrix of the roll in
    its local frame with the axis of rotation x, see .

Function: FunDiffPoly

FunDiffPoly(x, a)

  • function description:
    calculates the derivative of the polynomial \(a0*x^n + ...\)
  • input:
    x: value at which the polynomial is evaluated
    a: coefficients
  • output:
    f:
  • author:
    Peter Manzl
    **note: helper function polynomial describing a generatrix function

Function: FunDDiffPoly

FunDDiffPoly(x, a)

  • function description:
    calculates the second derivative of a polynomial
  • input:
    x: value at which the polynomial is evaluated
    a: coefficients
  • output:
    f:
  • author:
    Peter Manzl
    **note: helper function polynomial describing a generatrix function

CLASS MobileKinematics (in module robotics.mobile)

class description:

calculate 4 wheel velocities for a mecanum wheel driven platform with given platform velocities

  • author:
    Peter Manzl, Johannes Gerstmayr
  • notes:
    still under development; wheel axis is mounted at y-axis; positive angVel rotates CCW in x/y plane viewed from top; for coordinate system, see Python class definition

Class function: __init__

__init__(self, R, lx, ly, flagAdjusted = False, lcx = 0, lcy = 0, wheeltype = 0)

  • classFunction:
    initialize mobileKinematics class
  • input:
    R: wheel radius
    lx: wheel track width
    ly: wheel base
    wheeltype: 1=x-config (bad), 0=o-config (good)
  • author:
    Peter Manzl

Class function: getWheelVelocities

getWheelVelocities(self, vDes)

  • classFunction:
    calculate wheel velocities from Cartesian velocities
  • input:
    vDes: desired velocity [vx, vy, omega] in the robot’s local frame
    vx: platform translational velocity in local x direction
    vy: platform translational velocity in local y direction
    omega: platform rotational velocity around local z axis
  • output:
    w: wheel velocities w=[w0,w1,w2,w3]
  • author:
    Peter Manzl

Class function: getCartesianVelocities

getCartesianVelocities(self, w)

  • classFunction:
    calculate Cartesian velocities from wheel velocities
  • input:
    w: wheel velocities w=[w0,w1,w2,w3]
  • output:
    v: Cartesian velocity [vx, vy, omega] in the robot’s local frame
    vx: platform translational velocity in local x direction
    vy: platform translational velocity in local y direction
    omega: platform rotational velocity around local z axis
  • author:
    Peter Manzl

Relevant Examples (Ex) and TestModels (TM) with weblink to github: