Stochastic optimal open-loop control as a theory of force and impedance planning via muscle co-contraction
Authors: Berret Bastien , Jean Frédéric 
Published: September 2019

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 explain a common phenomenon known as muscle co-contraction. Co-contraction of agonist and antagonist muscles contributes to modulate the mechanical impedance of the neuromusculoskeletal system (e.g. joint stiffness) 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 the 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. Optimal feedback (closedloop) 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 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.

Author summary

This study presents a novel computational theory to explain the planning of force and impedance (e.g. stiffness) in the neural control of movement. It assumes that one main goal of motor planning is to elaborate feedforward motor commands that determine both the force and the impedance required for the task at hand. These feedforward motor commands (i.e. that are defined prior to movement execution) are designed to minimize effort and variance costs considering the uncertainty arising from sensorimotor noise. A major outcome of this mathematical framework is the explanation of a long-known phenomenon called muscle co-contraction (i.e. the concurrent contraction of opposing muscles). Muscle co-contraction has been shown to occur in many situations but previous modeling works struggled to account for it. Although effortful, co-contraction contributes to increase the robustness of motor behavior (e.g. small variance) upstream of sophisticated optimal feedback control processes that require state estimation from delayed sensory feedback to function. This work may have implications regarding our understanding of the neural control of movement in computational terms. It also provides a theoretical ground to explain how to optimally plan force and impedance within a general and versatile framework.