Some screenshots (note that the car is not actually going to be a sphere, but I needed something quick to represent the car):
Click to enlarge
Because the car is eventually going to be hovering, the driving control doesn't have to be as accurate to real life as it would if the car had wheels. So I added some dampening to the sideways motion (Essentially lateral friction to keep the car from moving sideways, unless it's skidding), but didn't have to do a full-on friction model. Plus, the car has a force-field (or whatever they will call those things in the future), so the walls actually bounce the car more like a pinball bumper than in a realistic fashion (the force field applies some bounce force).
Anyway, now that I have the cars driving, it's time for the next huge step: Driver AI.
Note that I have absolutely no idea at all how to write an AI to drive around my loopy sorts of courses. Time to do some research!