A Muscle Synergy-Inspired Adaptive Control Scheme for a Hybrid Walking Neuroprosthesis

Abstract

A hybrid neuroprosthesis that uses an electric motor-based wearable exoskeleton and functional electrical stimulation (FES) has a promising potential to restore walking in persons with paraplegia. A hybrid actuation structure introduces effector redundancy, making its automatic control a challenging task because multiple muscles and additional electric motor need to be coordinated. Inspired by the muscle synergy principle, we designed a low dimensional controller to control multiple effectors: FES of multiple muscles and electric motors. The resulting control system may be less complex and easier to control. To obtain the muscle synergy-inspired low dimensional control, a subject-specific gait model was optimized to compute optimal control signals for the multiple effectors. The optimal control signals were then dimensionally reduced by using principal component analysis to extract synergies. Then, an adaptive feedforward controller with an update law for the synergy activation was designed. In addition, feedback control was used to provide stability and robustness to the control design. The adaptive-feedforward and feedback control structure makes the low dimensional controller more robust to disturbances and variations in the model parameters and may help to compensate for other time-varying phenomena (e.g., muscle fatigue). This is proven by using a Lyapunov stability analysis, which yielded semi-global uniformly ultimately bounded tracking. Computer simulations were performed to test the new controller on a 4-degree of freedom gait model.

Keywords: adaptive control; functional electrical stimulation; hybrid neuroprosthesis; non-linear control; time-invariant synergies.

Figures

Figure 1

A four-link gait model based of a subject wearing a hybrid neuroprosthesis while using a walker. The model has 10 inputs, including FES of six muscles (antagonistic hip, knee, and ankle muscle pairs in the swing leg), three electric motors acting on each joint of swing leg (Th, Tk, Ta), and a walker moment acting on the stance leg (Mw). The step length is defined as the distance from stance toe to swing toe.

Figure 2

Optimal gait trajectories for a step size of 0.4 m in 0.75 s.

Figure 3

Optimal inputs to the walker moment, electric motors, and stimulation channels to reproduce the optimal gait trajectories.

Figure 4

This plot indicates how much of the data variability would be accounted for based on the number of synergies considered. Rule of thumb would indicate using three synergies, but since the controller is not solely dependent on the feedforward component less synergies can be used.

Figure 5

(A) Two synergies, w1 and w2. (B) The corresponding time-varying activation coefficients, c1 and c2, of synergies, w1 and w2.

Figure 6

Four cases for gait control using a hybrid neuroprosthesis. Case 1 only used the feedforward synergies, Case 2 used the adapted feedforward synergies, Case 3 considered both the adapted feedforward synergies and feedback control, and Case 4 used the full optimal inputs and feedback control. Note that the profile from the third and fourth cases almost perfectly overlaps the desired profiles.

Figure 7

Control inputs for Cases 1 and 2 of the simulations. Note that the control input profile shapes, after PCA decomposition, in Case 1 may not be similar to the optimal inputs in Figure 3.

Figure 8

Control inputs for Case 3 of the simulations. The feedback’s contribution was used only in the walker moment and motor torques.

Figure 9

Control inputs for Case 4 of the simulations. The feedback’s contribution was used only in the walker moment and motor torques.

Figure 10

The gait sequence for the four cases, a step length of 0.4 m with a step duration of 0.75 s was used. Since the errors for the third and fourth cases are so close their gait sequences look identical.