Walking Stabilization of the Passive Bipedal Compass robot using a Second Explicit Expression of the Controlled Poincaré Map

Abstract

This paper illustrates a stabilization approach of the passive bipedal locomotion of the compass-gait biped model based on an exclusively developed enhanced design of the closed form of the Controlled Poincaré Map (CPM). The followed technique relies on transforming the impulsive hybrid nonlinear dynamics of the passive motion into a linear form around a period-1 limit cycle. Forward, we simplify the complicated resulted expression using the second order of the Taylor Series. This technique, enables us to design a closed form of the CPM. The control of the passive bipedal locomotion starts with the identification of the period-1 fixed point of the non-CPM and continues with the determination of the linearized PM around such fixed point. Next, a feedback controller is adopted to stabilize this identified fixed point. Some simulation results are provided at the end to illustrate the efficiency of the control process of the passive walking motion of the compass-gait robot model.