An "Interesting" Strange Attractor in the Dynamics of a Hopping Robot

Abstract

This article applies discrete dynamical systems theory to the dynamic analysis of a simplified vertical hopping robot model that is analogous to Raibert's hopping machines. A Poincaré return map is developed to capture the dynamic behavior, and two basic nondimensional parameters that influence the systems dynamics are iden tified. The hopping behavior of the system is investigated by constructing the bifurcation diagrams of the Poincaré return map. The bifurcation diagrams show a period-dou bling cascade leading to a regime of chaotic behavior, where a "strange attractor" is developed. An interesting feature of the dynamics is that the strange attractor can be controlled and eliminated by tuning an appropriate parameter corresponding to the duration of applied hop ping thrust. Physically, the collapse of the strange attrac tor leads to a globally stable period-1 orbit, which guar antees a stable uniform hopping motion.