Impulsive control and stability analysis of biped robot based on virtual constraint and adaptive optimization

Abstract

This article is concerned with the problem of asymptotically stable periodic walking for a five‐link underactuated biped robot. Because of instantaneous change of two 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 state feedback controller is proposed to generate a closed‐loop periodic walking gait and track the desired trajectory of each joint. This controller is designed based on virtual constraint and hybrid zero dynamics. When the holonomic constraint of each actuator is zeroed by the controller, it can be regarded as an output. By using this method, the computation of the standard 5 degree of freedom (DOF) robot model can be reduced to 1 DOF. In addition, an adaptive optimization scheme is further investigated, which solves the problem of model parameter uncertainty. Finally, simulations are presented to illustrate the effectiveness of the proposed method.