A model for quadrupedal running-in-place in the plane

A model for quadrupedal running-in-place is presented which consists of a body supported by massless springy legs which are driven by simple local feedback. Two periodic solutions exist which correspond to the pronk and bound gaits for four-legged robots and animals. Return maps are described for bounding and a restricted version of pronking. The maps must be solved numerically. The bound is stable for a sufficiently small body inertia, but the pronk is unstable. A simple additional centralized control is found to be sufficient to locally stabilize the pronk. Plots of the maps´ equilibria as a function of system parameters are presented