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We investigated and identified the conditions necessary for asymptotically stable gait generation in compass-like biped robots from the mechanical energy balance point of view. The equilibrium point at impact in a dynamic gait is uniquely determined by two constraint conditions: keeping the restored mechanical energy constant and settling the relative hip-joint angle to the desired value just before impact. The generated bipedal gait with these two constraints then becomes asymptotically stable around the equilibrium point, as shown by a simple recurrence formula of the kinetic energy just before impact. We verified this stable gait generation method using numerical simulation of virtual passive dynamic walking. The result were compared with those for a rimless wheel and an inherent stability principle was derived. Furthermore, we derived a robust control law using a reference mechanical energy trajectory and demonstrated its effectiveness numerically. Finally, we discuss sufficient conditions for the gait stability in more general cases using an index function.

Asymptotically Stable Gait Generation for Compass-like Biped Robot Based on Stability Principle of Rimless Wheel