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On an experiential plane, the Frictional Force being independent of area in contact is bothersome. Perhaps the problem has to do with the transition from static friction to kinetic friction (the point at which the surfaces start to slip, which does affect the "traction" the robot has.
Up to the transition, Ff = u Fn, with a large mu, and after the transition, in sliding, the mu becomes lower. In Physics they demonstrate that the total force is independent of area by putting a rectangular block on s table and using a spring balance to measure the force. But no mention was made of the force per unit area, ever.
I'm guessing, but I think the transition is related to the shear force, which has a limit in force/area units (p.s.i., eg).
Perhaps someone in the tire industry could hop in, but when I drove on snow-covered ice, with my rwd Rambler 440 station wagon, I spun the rear wheels on the hill, until I softened the tires by temporarily letting some air out. Perhaps the snow-ice interface reached limiting shear force, and the greater area allowed greater total force, and greater traction resulted. (?)
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