Classic model for friction does not depend on surface area.
maximum friction force F is given by the equation:
F=u*N
where
u is the coefficient of friction between the two objects and
N is the normal force between them.
in our case the net force that the floor is applying to the robot (the normal force) is the weight of the robot.
so:
F=u*W in our case.
so as you can classic friction does not depend on surface area.
if you were to model each wheel individually you would get a lower normal force (roughly the weight of the robot divided by the number of wheels) on each wheel so that
N=W/n (W=total weight, n=number of wheels.)
so the force from each wheel would be F'=u*W/N
and we have n wheels so we get a total force of: F=F'*n=n*u*w/n=u*W
magic!
classic theory of friction breaks down in a lot of cases (for example spikes on a carpet), but should be very close to the reality in this year's game.
-Leav