How about gearing your robot reasonably, or if you choose to go Extremely fast, step the voltage that is put into your motor so you do not put as large of a strain on the motor.
If you are geared for, say 15 feet per second, you will most likely pop the 30A breakers as you try to accelerate, if you do it with full voltage. But if you start by applying 1V, then 2, then 3... etc, you will not draw as much current. Simple physics, V = I*R.....
Either that or that oboard can of freeze spray
the 60 amp breaker will handle current draws of MUCH more than 60 amps..... these stats were taken from Woody's speach during kickoff in 2002 -
@200 Amps - Trips in 8 seconds
@100 Amps - Trips in 1 minute, 48 seconds
Just know that you cannot pull too much current for too long. If you design within the limits of current draw, your robot will be fine.