Adaptive backstepping control using combined direct and indirect adaptation for a single-link flexible-joint robot

In this paper, a new tuning functions–based adaptive backstepping controller using combined direct and indirect adaptation for a single–link flexible–joint robot is presented. In this approach, the parameter estimation is driven by a weighted combination of tracking and identification errors. At first, the x–swapping filter identifier with a gradient–type update law is presented for a class of parametric strict–feedback nonlinear systems. Then, the main steps of the controller design for a single–link flexible–joint robot manipulator model are described. The closed–loop error dynamics is shown to be globally stable by using the Lyapunov stability approach. Finally, simulation results are given to illustrate the tracking performance of a single–link flexible–joint robot manipulator with the proposed adaptive control scheme.