Prescribed performance sliding mode control for wearable exoskeletons with constrained states

A practical fixed-time scheme with prescribed performance is proposed for the rehabilitation tasks of a two degrees-of-freedom upper-limb exoskeleton. Considering the transient and steady requirements, a time-varying function is designed to provide a prescribed upper-bound for the tracking errors and barrier Lyapunov function method is adopted to guarantee the inviolacies of the constraint requirements. Furthermore, to handle the inevitable disturbances from the mechanics and patients, a back-stepping terminal sliding mode controller is established to achieve a fixed-time convergence of the tracking errors with a designable time independent of initial states. In addition, non-smooth filter with a fixed-time form is employed to approximate the derivation of the fictitious control law such that the differential explosion problem can be avoided. Afterwards, the practical fixed-time convergence of the human-robot system is rigorously proved based on Lyapunov theory. Finally, simulation is established in Matlab/Simulink and the results are given to show the effectiveness of the proposed scheme.