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

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 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 summaryThis 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 f...

Antagonistic Co-contraction Can Minimize Muscular Effort in Systems with Uncertainty

“…Our results show that co-contraction, contrary to what is often thought (Falconer and Winter, 1985;Winter, 2005), is not inefficient, and that it is not chosen out of necessity (Hogan, 1984;Berret and 15/21 Jean, 2020), but also because it minimizes effort of movement in systems with uncertainty. Previous experimental work also showed already that uncertainty is taken into account when making movement decisions (Kim and Collins, 2015;Hiley and Yeadon, 2013;Donelan et al, 2004), and our results confirm this in simulation as well.…”

“…Hogan [16] proposed that co-contraction is required because the time delay in the nervous system does not allow a human to rely solely on reactive control, and therefore a combination of energy-efficient reactive and inefficient co-contraction is required [16]. This was confirmed using stochastic open-loop optimal control by Berret and Jean [25]. However, Berret and Jean did not allow feedback control.…”

Behavioral and physiological correlates of kinetically tracking a chaotic target

“…Motor learning of a task generally results in the reduction of the position feedback gain [ 38 ], which can be estimated from the force F through a spring-like linear control model [ 39 ]. F has a velocity-dependent component due to the robot’s viscous friction opposing the participant’s motion ( Eq 2 ), which must be removed from F to estimate the linear control model.…”

“…Generally, the learning of a model is associated with a reduction in the position feedback gain, reflecting the fact that participants can use the force more resourcefully while achieving constant or even improved tracking accuracy [ 38 ]. Most of the force could be explained by the viscous friction opposing the participant’s motion, but the residual force could not be explained by a linear control model consisting of a spring and a damper [ 39 , 51 ], nor was it improved by adding quadratic or cross-terms.…”

On Computer Mouse Pointing Model Online Identification and Endpoint Prediction

“…For the new model, the endpoint is well predicted at the velocity peak, but the idea of improving the correction phase dynamics to make it accurate even earlier is nevertheless relevant. How to correctly describe the ballistic phase in the model is a question for future research, for example, some interesting ideas were published recently in [45]. Using more data from trials of well-experienced users can provide a better understanding of the model's accuracy and limitations.…”