Proving asymptotic stability of dynamic walking for a five-link biped robot with feet

During the dynamic walking of biped robots, the underactuated rotating DOF emerges between the support foot and the ground. This makes the biped model hybrid and dimension-variant. In this paper, we present the definition of orbit stability for dimension-variant hybrid systems (DVHS). Based on the work of Grizzle et al. (2001), we generalize Poincaré theorem to a class of DVHS, and this result is then used to study asymptotically stable dynamic walking for a five-link planar biped robot with flat feet. Time-invariant gait planning and nonlinear control strategy, which is organized around the hybrid zero dynamics of Westervelt et al. (2003), is also introduced to realize dynamic walking with feet. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved, and the effectiveness of the proposed method is illustrated.