Question

I’m on the FIRST robotics team at my high school, and we are working on developing a kiwi drive robot, where there are three omni wheels mounted in a equilateral triangle configuration, like this:

The problem is programming the robot to drive the motors such that that the robot moves in the direction of a given joystick input. For example, to move “up”, motors 1 and 2 would be powered equally, while motor 3 would be off. The joystick position is given as a vector, and I was thinking that if the motors were expressed as vectors too, vector projection might be what I need. However, I’m not sure if this is right, and if it is, how I would apply it. I also have a feeling that there may be multiple solutions to one joystick position. Any help would be greatly appreciated.

Answer 1

I’ve built 9 robots during my time at school (1 FIRST, 8 RoboCup). We used the same omnidrive layout as you do. Beta’s answer looks correct but add rotation to all wheels afterwards:

W1 = -1/2 X - sqrt(3)/2 Y + R 
W2 = -1/2 X + sqrt(3)/2 Y + R
W3 = X + R

[This is Beta’s formula with some added Rotation]

You need to think about the available ranges for your motors. I am guessing it can take a PWM signal of +/-255, so either the input or the output has to be adjusted somewhat. (It’s not that hard…)

A good paper with details

To answer your specific questions: Vector projection is essentially what you are doing here. You apply it by having a matrix M, your input from the joystick I and your output to the motors O. Thus O = M * I;

M = [(-0.5 -sqrt(3)/2    +1)
     (-0.5 +sqrt(3)/2    +1)
     (1     0            +1)]