[Kevin Sevcik]

I concur with Joe. It's a rather classic sort of controls problem, and it's a lot easier to keep the thing balanced if you know the angle that it's at. To this end you need a gyro or yaw rate sensor. Preferably a gyro so you don't have to assmue it's starting in any particular orientation. Preferably both cause with both and an accelerometer or encoder on the wheels so you can get a state space controller going. A state space controller will sort of automatically stabilize the system if it's at all possible.

After that, it depends on just how unstable the construction is and the specs of your motors.