Lyapunov-based versus Poincaré map analysis of the rimless wheel

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.