Adaptive Fuzzy High-Order Super-Twisting Sliding Mode Controller for Uncertain Robotic Manipulator

This paper presents a novel adaptive fuzzy high-order super-twisting sliding mode controller, based on the modified super-twisting control (STC), to achieve accurate trajectory tracking for a robotic manipulator with unknown structured uncertainties, parametric uncertainties, and time-varying external disturbances. Initially, a non-linear homogeneous sliding manifold is designed to achieve finite-time convergence, better robustness, and good transient characteristics. Afterwards, conventional STC is modified with the new sliding surface that eliminates the limitation of STC application only on relative degree 1 systems. Moreover, two adaptive fuzzy systems are designed to replace the STC signals for handling the chattering problem and overestimating the controller gains. These fuzzy systems are continuously adjusted by two adaptation laws that are deduced from the Lyapunov stability theory. These adaptive laws need only a sliding surface variable as an input and generate the optimal controller gains as an output. The finite-time convergence and stability of the proposed controller is analyzed by the homogeneous Lyapunov stability theory. Finally, to show the efficacy of the proposed method, the controller is simulated on a 2-degree-of-freedom planar robotic manipulator to obtain the accurate trajectory tracking. Simulation results demonstrate the superiority of the proposed control scheme in the presence of structured and unstructured uncertainties