Stochastic optimal open-loop control as a theory of force and impedance planning via muscle co-contraction.

Bastien Berret,Frédéric Jean

doi:10.1371/journal.pcbi.1007414

Abstract

Understanding the underpinnings of biological motor control is an important issue in movement neuroscience. Optimal control theory is a leading framework to rationalize this problem in computational terms. Previously, optimal control models have been devised either in deterministic or in stochastic settings to account for different aspects of motor control (e.g. average behavior versus trial-to-trial variability). While these approaches have yielded valuable insights about motor control, they typically fail in explaining muscle co-contraction. Co-contraction of a group of muscles associated to a motor function (e.g. agonist and antagonist muscles spanning a joint) contributes to modulate the mechanical impedance of the neuromusculoskeletal system (e.g. joint viscoelasticity) and is thought to be mainly under the influence of descending signals from the brain. Here we present a theory suggesting that one primary goal of motor planning may be to issue feedforward (open-loop) motor commands that optimally specify both force and impedance, according to noisy neuromusculoskeletal dynamics and to optimality criteria based on effort and variance. We show that the proposed framework naturally accounts for several previous experimental findings regarding the regulation of force and impedance via muscle co-contraction in the upper-limb. Stochastic optimal (closed-loop) control, preprogramming feedback gains but requiring on-line state estimation processes through long-latency sensory feedback loops, may then complement this nominal feedforward motor command to fully determine the limb's mechanical impedance. The proposed stochastic optimal open-loop control theory may provide new insights about the general articulation of feedforward/feedback control mechanisms and justify the occurrence of muscle co-contraction in the neural control of movement.

Highlights

Optimal control theory is a leading framework for understanding biological motor behavior in computational terms [1,2,3,4]
A new theoretical framework to model human movement planning has been presented. It provides a specific emphasis on the elaboration of optimal feedforward motor commands for the control of noisy neuromusculoskeletal systems
Depending on the task constraints and uncertainty, a significant feedforward co-contraction or stiffening of the joints/hand may become the optimal strategy. This prediction was very consistent as we found it for both joint-level and muscle-level descriptions of the musculoskeletal dynamics as well as for various noise models

Summary

Introduction

Optimal control theory is a leading framework for understanding biological motor behavior in computational terms [1,2,3,4]. The minimum jerk and minimum torque change models are well-known representatives of this line of research [5, 6], which provided researchers with simple models accounting for the formation of average trajectories (e.g. bell-shaped velocity profiles in reaching tasks). This laid the foundations for more advanced studies like inverse optimal control ones, where the goal is to recover relevant optimality criteria from (averaged) experimental motion data [7, 8]. The SOC theory led to a number of valuable predictions among which the minimal intervention principle, stating that errors are corrected on-line only when they affect the goal of the task [9]

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