Limit cycles and their stability in a passive bipedal gait

It is well-known that a suitably designed unpowered mechanical biped robot can "walk" down an inclined plane with a steady gait. The characteristics of the gait (e.g., velocity, time period, step length) depend on the geometry and the inertial properties of the robot and the slope of the plane. A passive motion has the distinction of being "natural" and is likely to enjoy energy optimality. Investigation of such motions may potentially lead us to strategies useful for controlling active walking machines. In this paper we demonstrate that the nonlinear dynamics of a simple passive "compass gait" biped robot can exhibit periodic and stable limit cycle. Kinematically the robot is identical to a double pendulum (or its variations such as the Acrobot and the Pendubot). Simulation results also reveal the existence of a stable gait with unequal step lengths. We also present an active control scheme which enlarges the basin of attraction of the passive limit cycle.