Holometric Drive Pseudocode?

[sakekasi]

As an off season project, I am working on a holometric drivetrain system with a mechanic on my team. A holometric drive has 4 omni wheels at 45 degree angles to a square frame and can go in any direction using vector cancellation.

I was wondering how I would compute the speeds to power the wheels at given the x and y components of the vector that indicates the desired motion of the robot.

Any ideas?

Thanks in advance.