A Probabilistic Analysis of Muscle Force Uncertainty for Control

Background: We control the movements of our body and limbs through our muscles. However, the forces produced by our muscles depend unpredictably on the commands sent to them. This uncertainty has two sources: irreducible noise in the motor system's processes (i.e., motor noise) and variability in the relationship between muscle commands and muscle outputs (i.e., model uncertainty). Any controller, neural or artificial, benefits from estimating these uncertainties when choosing commands. Methods: To examine these benefits, we used an experimental preparation of the rat hindlimb to electrically stimulate muscles and measure the resulting isometric forces. We compare a functional electric stimulation (FES) controller that represents and compensates for uncertainty in muscle forces with a standard FES controller that neglects uncertainty. Results: Accounting for uncertainty substantially increased the precision of force control. Conclusion: Our study demonstrates the theoretical and practical benefits of representing muscle uncertainty when computing muscle commands. Significance: The findings are relevant beyond FES as they highlight the benefits of estimating statistical properties of muscles for both artificial controllers and the nervous system.