A Tube-based Model Predictive Control Method for Joint Angle Tracking with Functional Electrical Stimulation and An Electric Motor Assist

摘要

During functional electrical stimulation (FES), muscle force saturation and a user's tolerance levels of stimulation intensity limit a controller's ability to deliver the desired amount of stimulation, which, if unaddressed, degrade the performance of high-gain feedback control strategies. Additionally, these strategies may overstimulate the muscles, which further contribute to the rapid onset of muscle fatigue. Cooperative control of FES with an electric motor assist may allow stimulation levels within the imposed limits, reduce overall stimulation duty cycle, and compensate for the muscle fatigue. Model predictive controller (MPC) is one such optimal control strategy to achieve these control objectives of the combined hybrid system. However, the traditional MPC method for the hybrid system requires exact model knowledge of the dynamic system, i.e., cannot handle modeling uncertainties, and the recursive feasibility has been shown only for limb regulation problems. So far, extending the current results to a limb tracking problem has been challenging. In this paper, a novel tube-based MPC method for tracking control of a human limb angle by cooperatively using FES and electric motor inputs is derived. A feedback controller for the electrical motor assist is designed such that it reduces the error between the nominal MPC and the output of the actual hybrid system. Further, a terminal controller and terminal constraint region are derived to show the recursive feasibility of the robust MPC scheme. Simulation results were performed on a single degree of freedom knee extension model. The results show robust performance despite modeling uncertainties.