Robust Control of the Human Trunk Posture Using Functional Neuromuscular Stimulation: A Simulation Study

Abstract

The trunk movements of an individual paralyzed by spinal cord injury (SCI) can be restored by functional neuromuscular stimulation (FNS), which applies low-level current to the motor nerves to activate the paralyzed muscles to generate useful torques, to actuate the trunk. FNS can be modulated to vary the biotorques to drive the trunk to follow a user-defined reference motion and maintain it at a desired postural set-point. However, a stabilizing modulation policy (i.e., control law) is difficult to derive as the biomechanics of the spine and pelvis are complex and the neuromuscular dynamics are highly nonlinear, nonautonomous, and input redundant. Therefore, a control method that can stabilize it with FNS without knowing the accurate skeletal and neuromuscular dynamics is desired. To achieve this goal, we propose a control framework consisting of a robust control module that generates stabilizing torques while an artificial neural network-based mapping mechanism with an anatomy-based updating law ensures that the muscle-generated torques converge to the stabilizing values. For the robust control module, two sliding-mode robust controllers (i.e., a high compensation controller and an adaptive controller), were investigated. System stability of the proposed control method was rigorously analyzed based on the assumption that the skeletal dynamics can be approximated by Euler-Lagrange equations with bounded disturbances, which enables the generalization of the control framework. We present experiments in a simulation environment where an anatomically realistic three-dimensional musculoskeletal model of the human trunk moved in the anterior- posterior and medial-lateral directions while perturbations were applied. The satisfactory simulation results suggest the potential of this control technique for trunk tracking tasks in a typical clinical environment.

Fig. 1

The figure shows how the human trunk motions are generated by FNS-induced torques. Principally, activating different muscle nerves can result in motions at different directions, which also obey the rules of vector composition.

Fig. 2

This figure shows the human trunk model. (a) Skeletal model: it shows the main links and regions. (b) Neuromuscular model: it shows how the muscle activation causes the torques that generate joint motions.

Fig. 3

Joint angles in human trunk model

Fig. 4

Activating semimembranosus can cause the pelvic pitch to increase along the positive direction (counterclockwise if right side is pointing out of the paper); activating both the right (R) and left (L) erector spinae simultaneously can cause the lumbar pitch to increase, while activating R erector spinae increases the lumbar roll and L decreases lumbar roll

Fig. 5

The integrated control loop

Fig. 6

The figure shows the reference (ref) trajectory tracking performance, where the motion driven by the high compensation (high comp.) controller and the motion driven by the adaptive (adapt.) controller are plotted. Angular trajectories of the trunk joints without perturbation.

Fig. 7

Angular trajectories of the trunk joints with perturbation which were added to lumbar pitch at 5.5 s and lumbar roll at 8.5 s

Fig. 8

This figure shows the posture changes corresponding to Fig. 6. The left model depicts the motion driven by the high compensation (high comp.) controller while the right is the adaptive (adapt.) controller.

Fig. 9

The figure shows the torques determined by the controller and the torques caused by the FNS

Fig. 10

The figures show the FNS-caused muscle activation. The muscles were divided into four groups, i.e., group 1: GM 1-3 and AM, group 2: SM, SA and IL, group 3: ES, RA and PS, group 4: EO, IO and QL. The right (R) and left (L) were also separated for the evaluation.

Fig. 11

This figure shows the A.I.I. (average of R and L) of the muscles under different controllers