Two-Relay Controller and Its Application in Snake-Like Robot Motion: An Infinite-Dimensional Setting

Abstract

We proposed a self-oscillation control and its application to the locomotion of a robotic snake system whose model is governed by a partial differential equation. The dynamics of the snake were represented as a one-dimensional hyperbolic partial differential equation. Studies have demonstrated that the motion of a snake on a surface or in the water is like a wave. A boundary two-relay controller was used to induce the self-oscillation in the snake-like robot. We proved, by proposing a strict Lyapunov functional, the asymptotical stability of the closed-loop system. We corroborated the theoretical results by numerical simulations. The results constitute a first step in using a two-relay controller in infinite-dimensional systems.