[patrickrd]

Everybody has really good points. Unfortunately, as many have said, F=mu*N is only a model of friction, and often not very good.

I did a lot of experimentation on this a few months ago and can offer some vague yet useful advice. It's vague because models for any two given surface can be extremely different in behavior than other surfaces.
- Friction increases with normal force
- Friction increases when you dig into the carpet
- Disqualification probability increases when you have sharp edges that dig into the carpet. However this is also a good way to get better traction.
- Sharp, hard material that has very small grooves (or cleats) that dig into the carpet gets better traction. Think soccer cleats. Flexible material (such as rubber) gives into the carpet and does worse. Idea is to maximize pressure by the carpets on the cleats so the cleats can dig as far into the ground as possible.
- Surface area generally has negligable effect on traction... but in general more surface area causes more traction, up to a point before it starts getting worse.
- Effective coefficient of friction decreases as normal force increases... mu goes downwards to some constant as normal force goes to infinity. The more the two dig into each other, the less mu is a "constant".
- EXPERIMENT. The best way to maximize your traction is to make a simple apparatus where you can apply a constant normal force, and measure the amount of tangential force to make a wheel slip. Test different ideas. Use a normal force that your robot will typically provide (e.g. 30-35 lbs).