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 natu ral and is likely to enjoy energy optimality Investiga tion of such motions may potentially lead us to strate gies useful for controlling active walking machines In this paper we demonstrate that the nonlinear dy namics of a simple passive compass gait biped robot can exhibit periodic and stable limit cycle Kinemat ically 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 sta ble gait with unequal step lengths We also present an active control scheme which enlarges the basin of at traction of the passive limit cycle