I just saw a cool one in FAO Swartz: a $70US radio-controlled robot with
dynamic stability! The main part of the device is a gyroscope w/vertical
axis (made to look like a flying saucer), with a short body and two
sphere-shaped wheels below. That's right, TWO wheels, and if you turn off
the gyroscope, the thing falls right over. They didn't have a
demonstration model out to play with, so I don't know if there's any
active feedback, or if they just rely on the user to place it upright at
the start.
Hmmm. If it's initially lying on its side, and if the wheels can push it
along and rotate it the right way, will it precess into a standing
position without manual help?