Forward euler equations of motion


by sabatier
Tags: equations, euler, forward, motion
sabatier
sabatier is offline
#1
Mar28-09, 05:36 PM
P: 5
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
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LowlyPion
LowlyPion is offline
#2
Mar28-09, 09:48 PM
HW Helper
P: 5,346
The attached image is where again?

As to your interest isn't the steering direction going to relate to the change of θ ?
sabatier
sabatier is offline
#3
Mar29-09, 02:48 AM
P: 5
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/P...l-RAS-39-3.pdf

LowlyPion
LowlyPion is offline
#4
Mar29-09, 11:22 AM
HW Helper
P: 5,346

Forward euler equations of motion


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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