Holonomic Drive

Today I was talking with some of my team members, from the 'Iobotics robotics team, about what we were going to do at the 2009 Vex Worlds competition. The idea of holonomic (omni directional) drive came up which brought up an interesting discussion on how to do it and which motors to use and at what power. I did some calcualations on velocity of the wheels and the direction that the bot would travel and came out with pretty simple equations. But for power versus direction it would be slightly more complicated, to do. Because the motors need to follow a polar equation of direction theta vs percentage of power r. The wheels which are parallel to each other have the same power no matter the direction. They follow this equation with the front being at theta = 90. for the top left and bottom right the equation is R = cos ( theta - 45) and the other two it is R = sin (theta - 45). Yet these are not the exact equations to follow because power in the 1.5 amp motors isnt directly perportional to the speed of the motors. Also we want max speed to be max speed not a slowed speed especially when driving forward. The equation is not acutally correct also, because this represents top speed being the sum of each motor, but it would be good to follow a continuous algorythm rather than a broken one/piece wise as we would do other wise.

Phew, long post of an incomplete train of thought...
Thanks for reading

Mark.