Adaptive Fractional-Order Super-Twisting Sliding Mode Controller for Lower Limb Rehabilitation Exoskeleton in Constraint Circumstances Based on the Grey Wolf Optimization Algorithm

Abstract

In this work, a lower limb exoskeleton with uncertainties and external disturbances under constrained motion has been controlled by developing a model-free adaptive optimal fractional-ordersuper-twisting sliding mode (AOFSTSM) controller. Contrary to popular existing modeling methods, the modeling of the lower limb exoskeleton has been accomplished in the case of contact with the ground. A fractional-order operator and super-twisting sliding mode control have been combined to achieve an excellent tracking performance, chatter-free control inputs, and robustness to external disturbances and uncertainties. The controller structure is model-independent which has been derived without needing to know the dynamics of the system. An adaptive control strategy has been adopted as an approximating method to evaluate the uncertain dynamics of the system without the necessity for knowing the prior knowledge of the upper bounds. A grey wolf optimization technique has been used to find the optimal values of controller parameters. The stability of the overall system has been investigated and derived from the Lyapunov stability criterion. To validate the effectiveness of our proposed controller structure, a series of comparative simulations have been conducted with optimal fractional-order super-twisting sliding mode (OFSTSM) controller and fractional-order super-twisting sliding mode (FSTSM) controller. The comparative simulations have been also carried out with other types of recently existing control methods and recently existing optimization algorithms. The results of numerical simulations indicate the superiority of the AOFSTSM controller over other types of recently existing optimization algorithms and controllers in terms of tracking error and robustness towards the uncertainties and external disturbances.