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Functional electrical stimulation (FES) can be used as a neuroprosthesis in which muscles are stimulated by electrical pulses to compensate for the loss of voluntary movement control. Modulating the stimulation intensities to reliably generate movements is a challenging control problem. This paper introduces a feedback controller for a multi-muscle FES system to control hand movements in a 2-D (table-top) task space. This feedback controller is based on a recent human motor control model, which uses muscle synergies to simplify its calculations and improve the performance. This synergy-based controller employs direct relations between the muscle synergies and the produced hand force, therefore allowing for the real-time calculation of six muscle stimulation levels required to reach an arbitrary target. The experimental results show that this control scheme can perform arbitrary point-to-point reaching tasks in the 2-D task space in real time, with an average of ~2 cm final hand position error from the specified targets. The success of this prototype demonstrates the potential of the proposed method for the feedback control of functional tasks with FES.

This article investigates the application of optimal feedback control to trajectory planning in voluntary human arm movements. A nonlinear model predictive controller (NMPC) with a finite prediction horizon was used as the optimal feedback controller to predict the hand trajectory planning and execution of planar reaching tasks. The NMPC is completely predictive, and motion tracking or electromyography data are not required to obtain the limb trajectories. To present this concept, a two degree of freedom musculoskeletal planar arm model actuated by three pairs of antagonist muscles was used to simulate the human arm dynamics. This study is based on the assumption that the nervous system minimizes the muscular effort during goal-directed movements. The effects of prediction horizon length on the trajectory, velocity profile, and muscle activities of a reaching task are presented. The NMPC predictions of the hand trajectory to reach fixed and moving targets are in good agreement with the trajectories found by dynamic optimization and those from experiments. However, the hand velocity and muscle activations predicted by NMPC did not agree as well with experiments or with those found from dynamic optimization.

Static optimization (SO) has been used extensively to solve the muscle redundancy problem in inverse dynamics (ID). The major advantage of this approach over other techniques is the computational efficiency. This study discusses the possibility of applying SO in forward dynamics (FD) musculoskeletal simulations. The proposed approach, which is entitled forward static optimization (FSO), solves the muscle redundancy problem at each FSO time step while tracking desired kinematic trajectories. Two examples are showcased as proof of concept, for which results of both dynamic optimization (DO) and FSO are presented for comparison. The computational costs are also detailed for comparison. In terms of simulation time and quality of muscle activation prediction, FSO is found to be a suitable method for solving forward dynamic musculoskeletal simulations.

This paper presents a new model-based method to define muscle synergies. Unlike the conventional factorization approach, which extracts synergies from electromyographic data, the proposed method employs a biomechanical model and formally defines the synergies as the solution of an optimal control problem. As a result, the number of required synergies is directly related to the dimensions of the operational space. The estimated synergies are posture-dependent, which correlate well with the results of standard factorization methods. Two examples are used to showcase this method: a two-dimensional forearm model, and a three-dimensional driver arm model. It has been shown here that the synergies need to be task-specific (i.e., they are defined for the specific operational spaces: the elbow angle and the steering wheel angle in the two systems). This functional definition of synergies results in a low-dimensional control space, in which every force in the operational space is accurately created by a unique combination of synergies. As such, there is no need for extra criteria (e.g., minimizing effort) in the process of motion control. This approach is motivated by the need for fast and bio-plausible feedback control of musculoskeletal systems, and can have important implications in engineering, motor control, and biomechanics.