So at first I thought lets make a wheel out of magnets. I quickly took a step back and said, that won't work, because you simply wont move lol.
Actually, I think it WILL roll. For example, as long as the magnetic force is perpendicular to the direction of movement, 15 Lbs of magnetic pull shouldn't be any different than 15 Lbs of weight.
And, hard wheels will have less friction (as long as you're not running over debris). But, the magnetic pull should (hopefully) be more than the 15 Lb weight, and the actual weight will be added to the pull.
I'd say it's worthy of an experiment (maybe with one magnetic wheel, or on a small scale).
Our competitions are held in an arena made up of a steel floor...
The 1st experiment should be to make sure the floor is not made from non-magnetic stainless steel. 
That is when I thought, why not "embed" electromagnets into a wheel.
Although that's a very cool idea I have a feeling that it won't make an efficient motor.