Compass-Like Biped Robot Part I : Stability and Bifurcation of Passive Gaits

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, step 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. 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 report we demonstrate the existence and the stability of symmetric and asymmetric passive gaits using a simple nonlinear biped robot 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 {\em compass gait}. We also identify period-doubling bifurcation in this passive gait which eventually leads to a chaotic regime for larger slopes.