Closed-loop neural networkbased nmes control for human limb tracking

Abstract—Closed-loop control of skeletal muscle is complicated by the nonlinear muscle force to length and velocity relationships and the inherent unstructured and time-varying uncertainties in available models. Some pure feedback methods have been devel-oped with some success, but the most promising and popular con-trol methods for neuromuscular electrical stimulation (NMES) are neural network (NN)-based methods. Efforts in this paper focus on the use of a NN feedforward controller that is augmented with a continuous robust feedback term to yield an asymptotic result (in lieu of typical uniformly ultimately bounded stability). Specifically, an NN-based controller and Lyapunov-based stability analysis are provided to enable semi-global asymptotic tracking of a desired limb time-varying trajectory (i.e., non-isometric contractions). The developed controller is applied as an amplitude modulated voltage to external electrodes attached to the distal-medial and proximal-lateral portion of the quadriceps femoris muscle group in non-im-paired volunteers. The added value of incorporating a NN feed-forward term is illustrated through experiments that compare the developed controller with and without the NN feedforward com-ponent. Index Terms—Asymptotic stability, closed-loop control of func-tional electrical stimulation (FES), neural networks (NNs), neuro-muscular electrical stimulation (NMES), non-isometric contrac-tions, nonlinear control, robust integral of the sign of the error (RISE)-based feedback. I