Chaotic motions in the dynamics of a hopping robot

Discrete dynamical systems theory is applied to the dynamic stability analysis of a simplified hopping robot. A Poincarereturn map is developed to capture the system dynamic behavior, and two basic nondimensional parameters which influence the systems dynamics are identified. The hopping behavior of the system is investigated by constructing the bifurcation diagrams of the Poincarereturn map with respect to these parameters. The bifurcation diagrams show a period-doubling cascade leading to a regime of chaotic behavior, where a strange attractor is developed. One 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 hopping thrust. Physically, the collapse of the strange attractor leads to globally stable uniform hopping motion.