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Re: New wheels / floor and encoders for position.
You could use a combination of encoders and an accelerometer to create a traction control system. Traction control works by transferring power to the wheel(s) that is not slipping (ex. if you're driving a car and one of your powered wheels is on ice and the other is on pavement). This wont work when all your drive wheels are on the same surface.
Preventing your driver from spinning out the wheels is the best that you can do (this will provide rolling friction rather than sliding friction). Anti-lock braking wouldn't be a bad idea either.
As far as telling where you are at, a system using an accelerometer and gyro should do the job.
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