Lyapunov-based Approach to Reactive Step Generation for Push Recovery of Biped Robots via Hybrid Tracking Control of DCM

Abstract

This paper addresses reactive generation of step time and location of biped robots for balance recovery against a severe push. Key idea is to reformulate the balance recovery problem into a tracking problem for "hybrid" inverted pendulum model of the biped, where taking a new step implicitly yields a discrete jump of the tracking error. This interpretation offers a Lyapunov-based approach to reactive step generation, which is possibly more intuitive and easier to analyze than large-scaled or nonlinear optimization-based approaches. With the continuous error dynamics for the divergent component of motion (DCM), our strategy for step generation is to decrease the "post-step" Lyapunov level for DCM error at each walking cycle, until it eventually becomes smaller than a threshold so that no more footstep needs to be adjusted. We show that implementation of this idea while obeying physical constraints can be done by employing a hybrid tracking controller (together with a reference model) as our reactive step generator, consisting of a simple DCM-based continuous controller and a small-sized quadratic programming-based discrete controller. The validity of the proposed scheme is verified by simulation results.