Forward euler equations of motion

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Homework Help Overview

The discussion revolves around computing the equations of motion for a car, specifically focusing on the relationship between the steering angle and the car's orientation over time. The original poster seeks assistance in determining the position and angle based on given linear velocity and steering angle.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between the steering angle and the change in orientation. Questions arise regarding the derivation of forward kinematic equations from a referenced paper.

Discussion Status

The discussion is ongoing, with participants providing insights into the nature of the equations and their relation to state transitions. Some guidance has been offered regarding the interpretation of the equations, but no consensus has been reached.

Contextual Notes

There is mention of an attached image that is critical for understanding the problem context, which was initially omitted by the original poster. The reference to a specific paper suggests that external resources are being considered for further clarification.

sabatier
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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

 
Last edited:
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The attached image is where again?

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