Distributed Repetitive Learning Control for Cooperative Cadence Tracking in Functional Electrical Stimulation Cycling

Closed-loop control of functional electrical stimulation coupled with motorized assistance to induce cycling is a rehabilitative strategy that can improve the mobility of people with neurological conditions (NCs). However, robust control methods, which are currently pervasive in the cycling literature, have limited effectiveness due to the use of high stimulation intensity leading to accelerated fatigue during cycling protocols. This paper examines the design of a distributed repetitive learning controller (RLC) that commands an independent learning feedforward term to each of the six stimulated lower-limb muscle groups and an electric motor during the tracking of a periodic cadence trajectory. The switched controller activates lower limb muscles during kinematic efficient regions of the crank cycle and provides motorized assistance only when most needed (i.e., during the portions of the crank cycle where muscles evoke a low torque output). The controller exploits the periodicity of the desired cadence trajectory to learn from previous control inputs for each muscle group and electric motor. A Lyapunov-based stability analysis guarantees asymptotic tracking via an invariance-like corollary for nonsmooth systems. The switched distributed RLC was evaluated in experiments with seven able-bodied individuals and five participants with NCs. A mean root-mean-squared cadence error of 3.58 ± 0.43 revolutions per minute (RPM) (0.07 ± 7.35% average error) and 4.26 ± 0.84 RPM (0.1 ± 8.99% average error) was obtained for the healthy and neurologically impaired populations, respectively.