Abstract

Hybrids systems are combinations of continuous and discrete systems. The bouncing ball is an extensively studied hybrid system, for which many solid Lyapunov-based tools are now available. Toward applying these tools to walking robots, where a hybrid dynamical system framework is also a natural fit, the rimless wheel provides a salient dynamic model because it shares commonalities with both bouncing balls and two-legged robots. While much of existing locomotion research is based on Poincaré analysis, in this paper we also study the rimless wheel using Lyapunov-based tools. Our results motivate future use of Poincaré maps for certain hybrid systems and Lyapunov-based tools for more complicated walkers.