Robert Ringrose of MIT demo’ed a very cool design at AAAI97. His Hopper robot leg stands on its own, and, when activated, hops straight up and down, maintaining its balance. It corrects its balance if you shove it to one side. It can be adjusted to hop forward, backward left, right, etc., simply by changing its center of gravity. The hopper will move in the direction of its mass.This robot needs no brain. It is stabilized by physics. Hopping is a very stable motion. The rotary motion of the motor is turned into a sinusoidal motion which is in series with the spring.  

Stabilizing pitch is a little bit of a problem. If your foot is too small, you’ll fall over. Curvature of the foot is a critical measurement. If your foot is too flat, a strong correction (caused by a tiny shove) would generate a dynamically progressive instability. But if your foot is properly curved, it will balance like a weeble.

Historically, it’s been considered that a walking gait has been a very difficult problem to solve. However, the hopping robot shows that if you build it right, you don’t have a problem to solve. Ringrose pointed out that two biped hoppers (four legs)with a twisting base would be an inherently stable machine, whether it trots, paces, bounds or gallops.