Instantaneous Center of Rotation for a Differential Drive Robot

[frixis]

Hi,
I want to find the instantaneous center of rotation of a differential drive robot. Assuming I know that the robot will travel with a particular linear and angular velocity (v,w) I can use the equations (given here http://rossum.sourceforge.net/papers/CalculationsForRobotics/CirclePath.htm ).

which come out to be

x_c = x_0 - abs(v/w) sin(\theta_0) y_c = y_0 - abs(v/w) cos(\theta_0)

I'm using the webots simulator and I dumped gps points for the robot moving in a circle (constant v,w (1,1)) and instead of a single x_c and y_c I get a center point for every point. if I plot it out in MATLAB it does not look nice.

Here's an image ...

the red points in the image are the perceived centers

https://docs.google.com/file/d/0BzLnU1-OKHh7dmxvbGU1bDFKcFU/edit?usp=sharing

they just seem to trace the curve itself.

is there some detail I am missing ? I'm really really confused as to what's happening.

help please

I'm trying to figure out the center so I can check whether an obstacle is on this circle or not and whether collision will occur.

 

[Achy47]

Hi there, it looks like you're on the right track with your calculations. However, there are a few things that could be causing the issue you're seeing.

First, make sure that your robot is actually moving in a perfect circle with a constant linear and angular velocity. Any slight variations in the robot's movement could affect the perceived center points.

Second, check your calculations and make sure you're using the correct values for x_0, y_0, and \theta_0. These values should be the initial position and orientation of the robot before it starts moving in a circle.

Lastly, it's possible that there could be some error in the GPS points you've collected. Try collecting more data points and see if the perceived center points start to converge to a single point.

If none of these solutions work, it might be helpful to reach out to the creators of the webots simulator for further assistance. Good luck with your research!