Koopman-Based Model Predictive Control of Functional Electrical Stimulation for Ankle Dorsiflexion and Plantarflexion Assistance

Abstract: Functional Electrical Stimulation (FES) can be an effective tool to augment paretic muscle function and restore normal ankle function. Our approach incorporates a real-time, data-driven Model Predictive Control (MPC) scheme, built upon a Koopman operator theory (KOT) framework. This framework adeptly captures the complex nonlinear dynamics of ankle motion in a linearized form, enabling application of linear control approaches for highly nonlinear FES-actuated dynamics. Utilizing inertial measurement units (IMUs), our method accurately predicts the FES-induced ankle movements, while accounting for nonlinear muscle actuation dynamics, including the muscle activation for both plantarflexors, and dorsiflexors (Tibialis Anterior (TA)). The linear prediction model derived through KOT allowed us to formulate the MPC problem with linear state space dynamics, enhancing the real-time feasibility, precision and adaptability of the FES driven control. The effectiveness and applicability of our approach have been demonstrated through comprehensive simulations and experimental trials, including three participants with no disability and a participant with Multiple Sclerosis. Our findings highlight the potential of a KOT-based MPC approach for FES based gait assistance that offers effective and personalized assistance for individuals with gait impairment conditions.