Bifurcation and chaos in a simple passive bipedal gait

This paper proposes an analysis of the behavior of perhaps the simplest biped robot: the compass gait model. It has been shown previously that such a robot can walk down a slope indefinitely without any actuation. Passive motions of this nature are of particular interest since they may lead us to strategies for controlling active walking machines as well as to a better understanding of human locomotion. We show here that, depending on the parameters of the system, passive compass gait may exhibit 1-periodic, 2ⁿ-periodic and chaotic gaits proceeding from cascades of period-doubling bifurcations. Since compass equations are quite involved (they combine nonlinear differential and algebraic equations in a 4-dimensional space), our investigations rely, in part, on numerical simulations