On stabilization of bipedal robots during disturbed standing using the concept of Lyapunov exponents

Abstract

In this work, we investigate the balance control of disturbed bipedal standing. A simple PD-based switching state feedback control is proposed, which can stabilize the biped at the upright position while satisfying the constraints between the feet and the ground. The stability of such a control system is analyzed using the concept of Lyapunov exponents, and a stability region (domain of attraction) is determined. Since Lyapunov exponents are calculated numerically, several methods are employed to improve the numerical accuracy and the computing efficiency. Furthermore, the stability region is compared and agrees well with the one from the previous work that predicts the feasible movement during which balance of human standing can be maintained. This agreement shows the potential of the concept of Lyapunov exponents to be used as a measure of balance control of human standing. The work contributes to bipedal balance control, which is important in the development of bipedal walking machines