Design of an Adaptive Backstepping Controller for a Two-Degree-of-Freedom Robot with a Simplified Control Law

This paper presents the design of an adaptive backstepping controller for a specific class of cascaded nonlinear systems with affine-in-input structure and known dynamics. The proposed strategy, ensures global asymptotic stability of the closed-loop system under weaker conditions than those required by the conventional backstepping control method. A key advantage of this approach is its simplified control law, achieved by eliminating specific inherent terms found in the standard method. This simplification facilitates more straightforward practical implementation and yields an improved transient response. The method is used to construct an adaptive backstepping controller for a two-degree-of-freedom robot. The proposed controller is designed to guarantee global asymptotic stability while providing precise desired trajectory tracking. Under the assumption of unknown system dynamic parameters, an adaptation law is developed using the backstepping framework. The performance of the proposed method is evaluated through simulations under two scenarios: in the absence of disturbance and in the presence of disturbance. A comprehensive comparison is conducted between the conventional backstepping control, backstepping control with the simplified law, conventional adaptive backstepping control, and the proposed adaptive backstepping control with the simplified law. Simulation results demonstrate that the proposed method not only offers a simpler control structure but also achieves a smoother transient performance with improved convergence. Furthermore, the controller exhibits robustness against bounded disturbances, ensuring the system states remain stable.