Forward euler equations of motion

[sabatier]

Homework Statement

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.

Homework Equations

r = w/α where w=4 is the wheel base.

The Attempt at a Solution

 

[LowlyPion]

The attached image is where again?

As to your interest isn't the steering direction going to relate to the change of θ ?

 

[sabatier]

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

 

[LowlyPion]

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.