OGY-based control of chaos in semi-passive dynamic walking of a torso-driven biped robot

Abstract

This paper aims at controlling chaos exhibited in the semi-passive dynamic walking of a torso-driven biped robot as it goes down an inclined surface. Our control approach is based on the OGY method. The proposed biped robot is a three-degrees-of-freedom planar biped having an impulsive hybrid nonlinear dynamics. For this walker, we use only one torque between the stance leg and the torso in order to control the torso at some desired position and then in order to generate a semi-passive gait. The desired torso angle is considered as the control parameter in our OGY-based control approach. We develop a reduced simple impulsive hybrid linear model by linearizing the impulsive hybrid nonlinear dynamics around a desired period-1 hybrid limit cycle. This conducts to determine an explicit expression of a constrained controlled Poincare map. A linearization of the controlled Poincare map around its fixed point permits to looking for the gain matrix of the stabilizing control law. We show that application of the developed OGY-based control parameter law has controlled the chaotic semi-passive gait.