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Equations of motion

  1. Mar 30, 2009 #1
    1. The problem statement, all variables and given/known data
    A simple car with 4 wheels for use in a computer game. Front wheels turn only.
    Derive the equations of motion for the car.

    Car is controlled by setting its speed s, and steering angle phi.
    The forward Euler method is used to compute the forward kinematics.

    At time t the position vector is x, the orientation is theta.
    Given the speed and steering angle, we want to compute
    the updated values of x and theta for time t = t + delta t.
    The car travels a distance s*(delta t) along the arc of a circle.
    The radius of the circle (turning radius) is (steering angle)/4.
    (where steering angle is in radians).

    Derive the equations for the updated position and orientation
    of the car.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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