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Asymptotically Stable Running for a Five-Link, Four-Actuator, Planar Bipedal Robot

IRCCyN, Ecole Centrale de Nantes, UMR CNRS 6597, BP 92101, 1 rue de la Noë, 44321 Nantes, cedex 03, France, Christine.Chevallereau{at}irccyn.ec-nantes.fr

E. R. Westervelt

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210, USA

J. W. Grizzle

Control Systems Laboratory, EECS Department, University of Michigan, Ann Arbor, MI 48109-2122, USA

Provably asymptotically stable running gaits are developed for the five-link, four-actuator bipedal robot, RABBIT. A controller is designed so that the Poincaré return map associated with periodic running gaits can be computed on the basis of a model with impulse effects that, previously, had been used only for the design of walking gaits. This feedback design leads to the notion of a hybrid zero dynamics for running, which in turn allows the existence and stability of running gaits to be determined on the basis of a scalar map. The main results are illustrated via simulations performed on models with known parameters and on models with parameter uncertainty and structural changes. Animations of the resulting running motions are available on the web.

Key Words: biped robots • hybrid systems • hybrid zero dynamics • nonlinear control • periodic orbits • Poincaré return maps • zero dynamics

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