Automatic Control of Cycling Induced by Functional Electrical Stimulation With Electric Motor Assistance

Cycling induced by automatic control of functional electrical stimulation provides a means of therapeutic exercise and functional restoration for people affected by paralysis. During cycling induced by functional electrical stimulation, various muscle groups are stimulated according to the cycle crank angle; however, because of kinematic constraints on the cycle-rider system, stimulation is typically only applied in a subsection of the crank cycle. Therefore, these systems can be considered as switched control systems with autonomous, state-dependent switching with potentially unstable modes. Previous studies have included an electric motor in the system to provide additional control authority, but no studies have considered the effects of switched control in the stability analysis of the motorized functional electrical stimulation cycling system. In this paper, a model of the motorized cycle-rider system with functional electrical stimulation is developed that includes the effects of a switched control input. A novel switching strategy for the electric motor is designed to only provide assistance in the regions of the crank cycle where the kinematic effectiveness of the rider's muscles is low. A switched sliding-mode controller is designed, and global, exponentially stable tracking of a desired crank trajectory is guaranteed via Lyapunov methods for switched systems, despite parametric uncertainty in the nonlinear model and unknown, time-varying disturbances. Experimental results from five able-bodied, passive riders are presented to validate the control design, and the developed control system achieves an average cadence tracking error of $0.00\pm 2.91$ revolutions per minute for a desired trajectory of 50 revolutions per minute.