Moving a mecanum wheel robot programmatically

I want to build a mecanum type robot and instead of using a joystick to control it, I want to send it commands programmatically. In other words, if I calculate a directional angle that I want it to move in, how do I figure out what direction and PWM signals to send to each of the four motors?

Let's say 90 degrees is forward, 0 is right, 180 is left and 270 (or -90) is backwards. Any other angle would move it somewhere between these quadrants. I believe that the PWM signal would vary the speed of the wheel and that by giving the 4 wheels the correct direction and speed, it should move exactly as I want it to.

Do I need to control each wheel separately or do i control them in pairs?

Scott

Interesting project, controlling the movements by remote.
More information is needed about the robot. Are the wheels turning, except for rotating?

My thinking is to start with a kit like this from Superdroids.

Ok, but I don't want to spend time and effort do find out what possibilities that kit have. That work You do and then come back with questions giving the important facts.

Steering a wheel based robot has been done in thousands using different kits, most of them different in one or more ways. Maybe some member has used just this kit. I haven't. Next round.