A Stability Mechanism of the Fixed Point in Passive Walking

Abstract

A passive walker can walk down shallow slope with no energy source other than gravity. This motion is very attractive because its gait is really natural and ideal. Moreover, the walker can exhibit a stable limit cycle. Dynamics of passive walking is very interesting target and important for understanding human locomotion and developing the biped robots. Though the passive walkers are mechanically simple, they are a sort of hybrid systems with the switching condition which combines the nonlinear differential equations describing the swing motion and the leg-exchange. This makes it difficult to analyze. In this paper, we focus on the mechanism of stability of fixed points in passive walking. For the sake of simplicity and clarity as possible, we use a biped model known as the simplest walking model and treat the inter-leg angle at heel-strike as a variable. The equations of stability condition are derived from the eigenvalues of discrete dynamical system. We demonstrate a physical structure which forms the fixed points and a mechanism of its stability.