Fuzzy adaptive fractional-order nonsingular terminal sliding mode control for robotic manipulators: Online uncertainty estimation and fast tracking

Abstract This paper proposes an adaptive fractional-order nonsingular terminal sliding mode control framework for trajectory tracking of robotic manipulators under unknown disturbances and model uncertainties. First, a fractional-order dynamic model is derived to more accurately capture the complex electromechanical behavior of the manipulator compared with conventional integer-order models. A fast terminal sliding surface is then introduced, which remains free of singularities and overcomes certain limitations inherent in standard sliding mode control. The inclusion of a fractional-order operator in the sliding surface provides an additional tuning parameter, which enhances the system's disturbance rejection capability. To ensure robust closed-loop performance without prior knowledge of uncertainty bounds, a fuzzy logic estimator is developed to approximate the unknown upper bounds of disturbances and modeling errors online. These estimated bounds are then employed in the switching control law, eliminating the need for conservative pre-selected bounds. The resulting controller achieves high tracking accuracy, rapid finite-time convergence, and significant chattering reduction. Finite-time stability and convergence of the tracking error are rigorously established using the Lyapunov direct method. Numerical simulation results confirm the effectiveness of the proposed scheme. The controller demonstrates excellent tracking precision, fast transient response, and substantial chattering attenuation, outperforming the considered benchmark controllers.