A coupled sliding-surface approach for the trajectory control of a flexible-link robot based on a distributed dynamic model

Abstract

This paper proposes a coupled sliding-surface method for the design of trajectory control of a flexible-link robot. First, a sliding surface, coupling the joint velocity with the link bending moment at the joint, is defined based on the energy dynamics of the flexible link. Then a new trajectory–tracking control scheme is designed based on the coupled sliding surface, and extended to an adaptive scheme to cope with parametric uncertainties, where the Lyapunov stability theorem is used as a mathematical design tool. The proposed control is a collocated control designed based on a distributed-parameter dynamic model and hence is free from the so-called spillover instability. Using only the joint actuator, the proposed control guarantees stability throughout the entire trajectory control and asymptotic stability at desired goal positions. The proposed control is a PID control for the rigid dynamics and a proportional control for the flexible dynamics, with feed-forward and dynamics compensation. As a result, the proposed control guarantees zero steady-state joint-tracking errors even in the presence of low-frequency disturbances due to unavoidable mechanical inaccuracies in application. The theoretical results have also been proven by experimental studies.