Model Predictive Control of a Feedback-Linearized Hybrid Neuroprosthetic System With a Barrier Penalty

Abstract

Functional electrical stimulation (FES) is prescribed as a treatment to restore motor function in individuals with neurological impairments. However, the rapid onset of FES-induced muscle fatigue significantly limits its duration of use and limb movement quality. In this paper, an electric motor-assist is proposed to alleviate the fatigue effects by sharing work load with FES. A model predictive control (MPC) method is used to allocate control inputs to FES and the electric motor. To reduce the computational load, the dynamics is feedback linearized so that the nominal model inside the MPC method becomes linear. The state variables: the angular position and the muscle fatigue are still preserved in the transformed state space to keep the optimization meaningful. Because after feedback linearization the original linear input constraints may become nonlinear and state-dependent, a barrier cost function is used to overcome this issue. The simulation results show a satisfactory control performance and a reduction in the computation due to the linearization.

A Computer Simulation Study on Movement Control by Functional Electrical Stimulation Using Optimal Control Technique with Simplified Parameter Estimation

“…Tracking control performance was evaluated by the relative error (NMAE) calculated from the mean absolute error (MAE) for time intervals 2-30 s as expressed in Eqs. ( 14)- (15).…”

“…Moreover, another issue is the nonlinear MPC has a heavy computational load to perform the optimization process. Other studies use a combination of input-output feedback linearization and a linear MPC [15], [16] to reduce the computational load of nonlinear MPC. Although MPC-based FES controllers in previous studies showed high tracking control accuracy and the learning process is not necessary, they need many initial parameters adjustment for the prediction model used in MPC for individual patients in each control trial.…”

Continuous-Time Nonlinear Model Predictive Tracking Control with Input Constraints Using Feedback Linearization

“…Carron et al applied the combination to a compliant 6-DOF robotic arm, where an inverse dynamics FL was used to obtain a discrete-time linar model, the extended Kalman filter was used to estimate the states, and a discrete-time MPC was incorporated with the model [11]. Bao et al presented the combination to a hybrid neuroprosthetic system, where an FL was used to reduce computational loads, and then an MPC was applied through a barrier cost function to deal with the nonlinear input constrains, originally converted from linear ones [12]. Chen et al presented the combination in cascade and applied it to the control of automotive fuel cell oxygen excess ratio, where an FL cascaded with a continuous-time MPC was used to perform anti-disturbance control.…”

Shared Control of a Powered Exoskeleton and Functional Electrical Stimulation Using Iterative Learning

“…Optimal control is also a suitable approach for cooperative control of FES and an electric motor in the hybrid exoskeleton. Kirsch et al (2018) , Bao et al (2016) , and Bao et al (2019) optimally controlled a one–degree-of-freedom (DOF) hybrid leg extension machine using a nonlinear model predictive control (NMPC) method to modulate FES and electric motor assistance as per the FES-induced fatigue dynamics. However, a muscle fatigue–based dynamic effort distribution between FES and an electric motor has not been attempted in functionally relevant and multi-DOF lower-limb movements.…”