a b s t r a c tMinimizing the amount of electrical stimulation can potentially mitigate the adverse effects of muscle fatigue during functional electrical stimulation (FES) induced limb movements. A gradient projectionbased model predictive controller is presented for optimal control of a knee extension elicited via FES. A control Lyapunov function was used as a terminal cost to ensure stability of the model predictive control. The controller validation results show that the algorithm can be implemented in real-time with a steadystate RMS error of less than 2°. The experiments also show that the controller follows step changes in desired angles and is robust to external disturbances.

A hybrid neuroprosthesis that combines human muscle power, elicited through functional electrical stimulation (FES), with a powered orthosis may be advantageous over a sole FES or a powered exoskeleton-based rehabilitation system. The hybrid system can conceivably overcome torque reduction due to FES-induced muscle fatigue by complementarily using torque from the powered exoskeleton. The second advantage of the hybrid system is that the use of human muscle power can supplement the powered exoskeleton's power (motor torque) requirements; thus, potentially reducing the size and weight of a walking restoration system. To realize these advantages, however, it is unknown how to concurrently optimize desired control performance and allocation of control inputs between FES and electric motor. In this paper, a model predictive control-based dynamic control allocation (DCA) is used to allocate control between FES and the electric motor that simultaneously maintain a desired knee angle. The experimental results, depicting the performance of the DCA method while the muscle fatigues, are presented for an able-bodied participant and a participant with spinal cord injury. The experimental results showed that the motor torque recruited by the hybrid system was less than that recruited by the motor-only system, the algorithm can be easily used to allocate more control input to the electric motor as the muscle fatigues, and the muscle fatigue induced by the hybrid system was found to be less than the fatigue induced by sole FES. These results validate the aforementioned advantages of the hybrid system; thus implying the hybrid technology's potential use in walking rehabilitation.

A hybrid neuroprosthesis that uses an electric motor-based wearable exoskeleton and functional electrical stimulation (FES) has a promising potential to restore walking in persons with paraplegia. A hybrid actuation structure introduces effector redundancy, making its automatic control a challenging task because multiple muscles and additional electric motor need to be coordinated. Inspired by the muscle synergy principle, we designed a low dimensional controller to control multiple effectors: FES of multiple muscles and electric motors. The resulting control system may be less complex and easier to control. To obtain the muscle synergy-inspired low dimensional control, a subject-specific gait model was optimized to compute optimal control signals for the multiple effectors. The optimal control signals were then dimensionally reduced by using principal component analysis to extract synergies. Then, an adaptive feedforward controller with an update law for the synergy activation was designed. In addition, feedback control was used to provide stability and robustness to the control design. The adaptive-feedforward and feedback control structure makes the low dimensional controller more robust to disturbances and variations in the model parameters and may help to compensate for other time-varying phenomena (e.g., muscle fatigue). This is proven by using a Lyapunov stability analysis, which yielded semi-global uniformly ultimately bounded tracking. Computer simulations were performed to test the new controller on a 4-degree of freedom gait model.

Electromechanical delay (EMD) and uncertain nonlinear muscle dynamics can cause destabilizing effects and performance loss during closed-loop control of neuromuscular electrical stimulation (NMES). Linear control methods for NMES often perform poorly due to these technical challenges. A new predictor-based closed-loop controller called proportional integral derivative controller with delay compensation (PID-DC) is presented in this paper. The PID-DC controller was designed to compensate for EMDs during NMES. Further, the robust controller can be implemented despite uncertainties or in the absence of model knowledge of the nonlinear musculoskeletal dynamics. Lyapunov stability analysis was used to synthesize the new controller. The effectiveness of the new controller was validated and compared with two recently developed nonlinear NMES controllers, through a series of closed-loop control experiments on four able-bodied human subjects. Experimental results depict statistically significant improved performance with PID-DC. The new controller is shown to be robust to variations in an estimated EMD value.

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