Data-driven Model Predictive Control for Drop Foot Correction

Functional Electrical Stimulation (FES) is an effective method to restore the normal range of ankle motion in people with Drop Foot. This paper aims to develop a real-time, data-driven Model Predictive Control (MPC) scheme of FES for drop foot correction (DFC). We utilize a Koopman operator-based framework for system identification required for setting up the MPC scheme. Using the Koopman operator we can fully capture the nonlinear dynamics through an infinite dimensional linear operator describing the evolution of functions of state space. We use inertial measurement units (IMUs) for collecting the foot pitch and roll rate state information to build an approximate linear predictor for FES actuated ankle motion. In doing so, we also account for the implicit muscle actuation dynamics which are dependent on the activation and fatigue levels of the Tibialis Anterior (TA) muscle contribution during ankle motion, and hence, develop a relationship between FES input parameters and ankle motion, tailored to an individual user. The approximation, although computationally expensive, leads to reformulating the optimization problem as a quadratic program for the MPC problem. Further, we show the closed-loop system’s recursive feasibility and asymptotic stability analysis. Simulation and experimental results from a subject with Multiple Sclerosis show the effectiveness of the data-driven MPC scheme of FES for DFC.