An analytical study of simple hopping robots with vertical and forward motion

Discrete dynamical systems theory is applied to the analysis of simplified hopping robot models which are analogous to M.H. Raibert´s (1986) experimental machines. A two-dimensional model is presented which includes both forward and vertical hopping dynamics and a foot placement algorithm. These systems are analyzed using a Poincare return map, and hopping behavior is investigated by constructing the return map bifurcation diagrams with respect to system parameters. The bifurcation diagrams exhibit period doubling which results in unexpected hopping behavior