Adaptive fuzzy backstepping controller design for uncertain underactuated robotic systems

In this paper, the control problem of underactuated systems with mismatched and matched uncertainties is addressed. Adaptive fuzzy backstepping controller is proposed to solve the problem, ensuring the robustness against uncertainties and disturbances. Taking a general class of underactuated robotic systems into account, the nonlinear dynamical equations are first transformed to the so-called cascade form and then, an adaptive-based controller is constructed using the capability of fuzzy logic to tackle the perturbations. From the analytic point of view, the closed loop stability is ensured using the Lyapunov stability theorem. To demonstrate the effectiveness of the method, the proposed controller has been applied to a two-wheeled self-balancing robot with three degrees of freedom, and also to a pendubot with two degrees of freedom. In order to highlight the superiority of the proposed algorithm, the performance is compared with that of an existing robust strategy.