Non-linear model predictive control based trajectory tracking of hand and wrist motion using functional electrical stimulation

Functional Electrical Stimulation (FES) on muscles can recover voluntary motions of the upper limb paralysed patients, enabling them to conduct daily life activities like grasping, holding, etc. FES can stimulate the forearm muscles to track joint trajectory while avoiding hyper-stimulation. While using FES, model-based closed-loop control schemes can track the desired trajectory more effectively than open-loop control strategies. In literature, the model-based technique, namely, the iterative learning control (ILC)-based closed-loop control strategy, is used to track joint motion towards the intended trajectory through FES, utilizing a biomechanical model of the hand and wrist. However, such a technique has limitations pertaining to robust optimal design, identical initialization, sampling, etc. The non-linear model predictive control (NMPC) framework can address these issues, as it is suitable for capturing the system's inherent non-linear dynamics and handling multi-input multi-output (MIMO) systems along with constraints. In this work, two variants of NMPC, with fixed weights (NMPC 1) and fuzzy logic-based auto-tuned weights (NMPC 2) of the cost function, considering an existing planar biomechanical model of the hand and wrist, are proposed and demonstrated in a simulation environment. However, in NMPC 1, the weights of the cost function have to be tuned manually by the hit-and-trial method. To address this issue, NMPC 2 has been developed with fuzzy logic-based adaptive weights in the cost function. The developed controllers actuate individual muscles using FES to simultaneously track the angular positions of three joints: wrist, Metacarpophalangeal (MCP), and Proximal Interphalangeal (PIP) of the non-linear MIMO system (hand and wrist) while considering input constraints. Both controllers' tracking performances are compared against an ILC-based control strategy. The results demonstrate that NMPC 1 and NMPC 2 outperform the ILC-based control approach regarding tracking performance, muscle actuation, and required input stimulation. The later two aspects are expected to reduce the degradation of muscle health while tracking the same desired trajectories. This study also investigates the robustness of the developed controllers after muscle parameter perturbation.