Fast adaptive fuzzy terminal sliding mode control of synergistic movement of the hip and knee joints (air-stepping) using functional electrical stimulation: A simulation study

Abstract

Functional electrical stimulation (FES) is a practical method for rehabilitation and increasing the level of movement in paraplegic subjects. So far, various control methods such as the combination of fuzzy adaptive or neural network with classic sliding mode control have been used for generating FES control signals. Such hybrid methods have led to the chattering phenomenon, the singularity of the control signal, and low speed of the controller outside and on the sliding surface. In the current study, a fast adaptive fuzzy terminal sliding mode controller (FAFTSMC) for a musculoskeletal model of the hindlimb, including six muscles joined to a planar model of two-link rigid robotic manipulator is presented for controlling the air stepping through FES. To reduce the control complexity considerably, a decentralized FAFTSMC consisted of a set of independent multi-input multi-output (MIMO) controllers where each subsystem is controlled by a stand-alone controller, is used to control the tracking problem. Outside the sliding surface, a novel fast terminal reachability law is used to force the dynamics of the system to move toward the sliding surface. In the sliding phase, a continuous fast terminal sliding surface is designed for the convergence of the tracking error and its first derivative to a neighborhood of zero in a finite time without any occurrence of the chattering or singularity in the control effort. A fuzzy adaptive estimator is employed to identify nonlinear time-varying dynamics of the process model. The stability of the closed-loop system is proved using the Lyapunov method. Simulation results of the control algorithm show that the hip and knee joint reference trajectories can be tracked with the fast adaptive fuzzy terminal sliding mode controller with an excellent precision.