Forward euler equations of motion

  1. 1. The problem statement, all variables and given/known data

    Hi, I'm trying to compute the equations of motion for a car as shown
    in the attached image.

    α = steering angle
    θ = orientation of the car relative to the world coordinate system

    Say you're given the linear velocity v and the steering
    angle α. How do you compute the position and angle θ for a
    particular time?

    Any help appreciated.

    2. Relevant equations

    r = w/α where w=4 is the wheel base.

    3. The attempt at a solution
     
    Last edited: Mar 29, 2009
  2. jcsd
  3. LowlyPion

    LowlyPion 5,328
    Homework Helper

    The attached image is where again?

    As to your interest isn't the steering direction going to relate to the change of θ ?
     
  4. Hi, I forget to attach the image, but I've attached it now.

    Yes I presume the change of orientation is related to the
    steering angle. But how did they get the forward
    kinematic equations on page 3 of this paper?

    http://cswww.essex.ac.uk/staff/hhu/Papers/Journal-RAS-39-3.pdf
     
  5. LowlyPion

    LowlyPion 5,328
    Homework Helper

    Those equations are state equations according to the material based of a sequential k+1 state of the previous position k. They look like position vectors based on the velocity applied to the angle θ and the rate of change of angle a applied to subsequent θ's.
     
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