Passivity-Based Hybrid Systems Approach to Repetitive Learning Control for FES-Cycling with Control Input Saturation

Functional electrical stimulation (FES)-cycling is an effective method of rehabilitation for people with neuromuscular disorders. Muscle stimulation and electric motor inputs are designed to complement the rider's volitional pedaling, but open challenges remain in the analysis of the stability and robustness of the human-machine system under the influence of switching between muscle and motor inputs. Discontinuous switching between muscle stimulation inputs and motor input motivates the use of a hybrid systems analysis, reducing gain conditions compared to a switched systems analysis and yielding robustness to disturbances. In this paper, repetitive learning control (RLC)-based feedforward terms for each muscle group and electric motor are designed to improve cadence tracking and reduce high-gain feedback terms that can cause chattering effects. Muscle stimulation limits are systematically considered for the safety and comfort of the rider, and a cadence controller is designed integrating RLC and robust control terms to account for input saturation. A passivity-based analysis ensures the hybrid system is flow output strictly passive from the rider's volitional effort to the tracking error output. Moreover, the position and cadence tracking errors are shown to asymptotically converge based on a Lyapunov-like stability analysis.