Stabilization of the Passive Biped Dynamic Locomotion Using the Controlled Poincaré Map

Abstract

This paper discusses the stabilization of the passive dynamic walking (PDW) of the compass-gait biped robot using an explicit analytical classical expression of the controlled Poincarémap. We introduced the first-order Taylor series approximation to design a conventional expression of the controlled Poincaré map. In order to stabilize the passive bipedal gaits, we determine the period-l fixed point of the (uncontrolled) Poincarémap and we develop the linearized map around such fixed point. We adopt a state-feedback control law to stabilize this fixed point. In the end, in order to show the efficiency and the validity of the designed controlled Poincaré map in the stabilization of the passive biped dynamic locomotion of the compass robot, we present some simulation results.