[MrForbes]

there might be an error in your formula...the factor of 0.5 for weight distribution over the rear wheels ignores weight transfer when pushing. If you put a scale up against a wall, and have the robot push against that, you might discover the real number to be higher than you thought.

This weight transfer thing plays an important role in drag racing, cars that are set up right have the front wheels just skimming the track at launch, all the vehicle weight is on the rear wheels.

In robot pushing matches, a similar thing happens, but for a different reason. Draw a free body diagram of the robot, with the pushing point centered on the bumper zone, see what happens.