Finite-time stabilization of periodic orbits for under-actuated biped walking with hybrid zero dynamics

Abstract

This paper is concerned with the problem of finite-time stable walking for a 5-link under-actuated biped robot. Due to instantaneous change of 2 legs and complex dynamics during the walking process, the robot can be regarded as a nonlinear impulsive system. In order to make impulsive control of the robotic system, it is modeled as a rigid kinematic chain with Lagrange equations, which is strong coupling and hybrid. A novel finite-time feedback controller is proposed to realize finite-time stability of the nonlinear impulsive system. The controller is designed based on finite-time stabilizing control Lyapunov function (FTS-CLF) and hybrid zero dynamics (HZD). By establishing a finite-time stable periodic orbit, the controller can make the output of virtual constraints converge to zero rapidly. Restricted Poincare return map is then utilized to analyze the finite-time stability of nonlinear impulsive system. It ensures that the flow of the continuous subsystem can pass through the impact cross section. Additionally, a periodic walking gait planning is further investigated, and the existence of the gait is proved, which satisfy the joint trajectory tracking. Finally, the effectiveness of the mentioned method is illustrated by simulations.