Calculating the trajectory of a robot

[eNathan]

Greetings PF,

I'm a computer science student who is tasked with a robotics project. I've got a 2-wheeled robot (there's a 3rd dummy wheel on the back to prevent it from falling over) that turns like a tank, by means of turning one wheel faster than the other. If both wheels are the same speed, it goes forward. I've only studied basic mechanical physics and calculus.

The problem is this: Suppose the robot's floor is represented by a simple X Y plane, and the robot is currently at a specific point on the plane. The robot has 2 wheels of some diameter, spaced apart by each other by some distance. If the left wheel has some constant rotational velocity, and the right wheel has some constant rotational velocity, what displacement will the robot undergo after some period of time and what direction will it be facing?

I know that you can construct such a function. Since I'm not a physics major I'm really struggling with this. I know that if you give the wheels different speeds (rotational velocity) and let it just go, it will basically go in a big circle. If I can, for instance, compute the radius of this representative circle, I know the robot will just follow along the arch and the rest of the computation should be easy. I don't know how to proceed from there though..

Any help would be awesomely appreciated!

 

[mfb]

Both wheels will make circles, and the ratio of their radii is the same as the ratio of the wheel velocities (assuming no slipping). You know the distance between the wheels, that allows to calculate those numbers. I don't know which point you choose as "the robot position", but if it is in between the robot radius will be the average of the two wheel values.