Limit cycles and their stability in a passive bipedalgaitAmbarish

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. The energy required to maintain the steady motion comes from the conversion of the biped's gravitational potential energy as it descends. 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 show that the stability of the periodic motion of a simple passive biped robot which is able to walk with the so-called "compass gait". 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 is inspired by passivity.