A Non-Linear Control Method to Compensate for Muscle Fatigue during Neuromuscular Electrical Stimulation

Neuromuscular electrical stimulation (NMES) is a promising technique to artificially activate muscles as a means to potentially restore the capability to perform functional tasks in persons with neurological disorders. A pervasive problem with NMES is that overstimulation of the muscle (among other factors) leads to rapid muscle fatigue, which limits the use of clinical and commercial NMES systems. The objective of this article is to develop an NMES controller that incorporates the effects of muscle fatigue during NMES-induced non-isometric contraction of the human quadriceps femoris muscle. Our previous work that used the RISE class of non-linear controllers cannot accommodate fatigue and muscle activation dynamics. A totally new control design approach and associated stability proof is required to derive a new class of NMES control design that accounts for muscle fatigue dynamics and a first-order activation dynamics, in addition to the second-order musculoskeletal dynamics. Motivated from a control method for robotic systems in a strict-feedback form, a backstepping based-non-linear NMES controller was designed to accommodate for the additional muscle activation dynamics. Further, experimentally identified estimates of the fatigue and activation dynamics were incorporated in the control design. The developed controller uses a neural networkbased estimate of the musculoskeletal dynamics and error due to fatigue estimation. A globally uniformly ultimately bounded stability is proven the new controller that accounts for an uncertain non-linear muscle model and bounded non-linear disturbances (e.g., spasticity and changing load dynamics). The developed controller was validated through experiments on the left and right legs of 3 able-bodied subjects and was compared with a proportional-derivative (PD) controller and a PD augmented with a neural network. The statistical analysis showed improved control performance compared with the PD controller.