Simplified and effective motor control based on muscle synergies to exploit musculoskeletal dynamics

Abstract

The basic hypothesis of producing a range of behaviors using a small set of motor commands has been proposed in various forms to explain motor behaviors ranging from basic reflexes to complex voluntary movements. Yet many fundamental questions regarding this long-standing hypothesis remain unanswered. Indeed, given the prominent nonlinearities and high dimensionality inherent in the control of biological limbs, the basic feasibility of a low-dimensional controller and an underlying principle for its creation has remained elusive. We propose a principle for the design of such a controller, that it endeavors to control the natural dynamics of the limb, taking into account the nature of the task being performed. Using this principle, we obtained a low-dimensional model of the hindlimb and a set of muscle synergies to command it. We demonstrate that this set of synergies was capable of producing effective control, establishing the viability of this muscle synergy hypothesis. Finally, by combining the low-dimensional model and the muscle synergies we were able to build a relatively simple controller whose overall performance was close to that of the system's full-dimensional nonlinear controller. Taken together, the results of this study establish that a low-dimensional controller is capable of simplifying control without degrading performance.

Fig. 1.

Muscle synergies identified for the control of natural limb dynamics and their closest experimental matches. Only those 10 muscles that were both recorded experimentally and included in the hindlimb model are shown. The activation strength for each muscle within a synergy is indicated by the bar height. Each bar in a synergy is normalized by the vector norm of the synergy. Blue bars are synergies identified by the system-balancing procedures described in the text. Red bars are the best-matching experimental synergies. The 10 muscles are gracilus (GR), semitendinosus (ST), curarlis (CR), gluteus (GL), tensor facia latae (TFL), iliofibularis (Ilf), sartorius (SA), semimembranosus (SM), adductor (ADd), and iliacus internus (Ili).

Fig. 2.

Illustration of the different controller designs considered. (Top) Full-dimensional controller with access to the full state of the system, which can activate each muscle independently (best-case controller). (Middle) Controller with access to the full state but that activates muscles through synergies. (Bottom) Low-dimensional controller (LDC) with access to a low-dimensional state variable and that uses muscle synergies, thereby simplifying control even further.

Fig. 3.

Performance of the four controllers. For comparison, the optimal limb trajectories and commands (for the movement to target 1, the topmost target) for the best-case controller are displayed in each panel (black traces). (A) Optimal limb trajectories for the ND (red) controller (best-case trajectories in black). (Inset) Hindlimb orientation. (B) Thirteen muscle commands for the ND (red) controller and best-case controller (black). (C) Optimal limb trajectories for the JT (blue) controller. (D) Thirteen muscle commands for the JT (blue) controller. (E) Optimal limb trajectories for the low-dimensional controller (LDC) (green). (F) Thirteen muscle commands for the low-dimensional controller (green).

Fig. 4.

Comparison of the performance of controllers in relation to the best-case controller. The amount of explained variance (centered R²) was used to calculate the similarity of the trajectories (A) and commands (B) for each controller to those of the best-case controller. Values are averaged across the six trajectories. Horizontal bars indicate values that are significantly distinct.

Fig. 5.

Assessment of controller dimensionality. The similarity to the best-case controller trajectories (A) and commands (B) of those produced by the low-dimensional controller when its dimension was varied between 4 and 6 is shown. Note that these low-dimensional controllers correspond to controller 4 of Fig. 1, in which both state and control variables are low-dimensional. Horizontal bars indicate values that are significantly distinct.