Limit Cycles in a Passive Compass Gait Biped and Passivity-Mimicking Control Laws

It is well-known that a suitably designed unpowered mechanical biped robot can "walk" down an inclined plane with a steady periodic gait. The energy required to maintain the motion comes from the conversion of the biped's gravitational potential energy as it descends. Investigation of such passive natural motions may potentially lead us to strategies useful for controlling active walking machines as well as to understand human locomotion. In this paper we demonstrate the existence and the stability of symmetric and asymmetric passive gaits using a simple nonlinear biped model. Kinematically the robot is identical to a double pendulum (similar to the Acrobot and the Pendubot) and is able to walk with the so-called compass gait. Using the passive behavior as a reference we also investigate the performance of several active control schemes. Active control can enlarge the basin of attraction of passive limit cycles and can create new gaits.