Dynamic Stability Analysis of a Trotting Quadruped Robot Based on Switching Control

Abstract

This paper presents a dynamic stability analysis method for a trotting quadruped robot on unknown rough terrains, which is based on the Lyapunov theory of a switching system. Firstly, the dynamical model of a trotting quadruped robot is built as a nonlinear switching system. In the stance phase, the dynamical model of a body and two stance legs is approximated as a compound model including a seven-link mechanism and a linear inverted pendulum. Furthermore, as a result of the switching process, the trotting quadruped robot becomes a non-autonomous system. Secondly, a contact force distribution/control strategy is proposed, based on adaptive sliding mode to guarantee the position and orientation of the seven-link mechanism asymptotically stable in the stance phase. With the proposed strategy, a common Lyapunov function is designed in order to validate the uniform asymptotic stability of the body's height and orientation variations. Then, the landing positions of the swing legs are calculated, based on the linear inverted pendulum model in order to make the horizontal position error of the robot converge to a bounded region. Finally, quadruped trotting experiments are performed in order to validate the effectiveness of the proposed methods.