Posture Stabilization Control of a One-Legged Hopping Robot Based on Periodic Discrete-Time System

Abstract

This paper considers the posture stabilization problem of a one-legged planar hopping robot. Stabilizing the posture of the one-legged hopping robot is an essential problem for realizing running legged robots. In this paper, we propose a design method of posture stabilization control of the one-legged hopping robot via periodic linear-quadratic optimal control. We formulated the problem of traveling at a constant horizontal speed in the air while keeping the robot's posture stable as a periodic discrete-time system. The feedback control law is obtained by LQI design for the periodic discrete-time system. The advantage of this method is that it does not need the trajectory planning of the robot. The proposed method can adjust the robot's dynamic characteristics by adequately selecting the weighting matrices of the LQ criterion. The effectiveness of the proposed method is shown by numerical simulations. The simulation results showed that the proposed method enables the stable running of the robot at the specified speed provided that the hopping heights maintained constant appropriately.