Finite Dimensional Approximation to Muscular Response in Force-Fatigue Dynamics using Functional Electrical Stimulation

Abstract: Recent dynamical models, based on the seminal work of V. Hill, allow to predict the muscular response to functional electrostimulation (FES), in the isometric and non-isometric cases. The physical controls are modeled as Dirac pulses and lead to a sampled-data control system, sampling corresponding to times of the stimulation, where the output is the muscular force response. Such a dynamics is suitable to compute optimized controls aiming to produce a constant force or force strengthening, but is complex for real time applications. The objective of this article is to construct a finite dimensional approximation of this response to provide fast optimizing schemes, in particular for the design of a smart electrostimulator for muscularreinforcement or rehabilitation. It is an on-going industrial project based on force-fatigue models, validated by experiments.Moreover it opens the road to application of optimal control to track a reference trajectory in the joint angular variable to produce movement in the non-isometric models.