Interpreting the kinematic theory of rapid human movement as an optimal control theory

Human rapid movements often exhibit stereotypical patterns and invariants, which are essential for understanding movement control. The Kinematic Theory posits that invariances observed in velocity profiles are inherent to the structure of the neuromuscular system. In contrast, optimal control theory assumes that invariances result from optimality. Although the lognormal velocity profiles proposed by the Kinematic Theory produce the most realistic rapid movements, they have yet to be examined from an optimality standpoint. Our objective was to investigate the implication of velocity profile lognormality through the lens of optimal control theory. To this end, we analyzed commonly used kinematic control strategies using the lognormal parameters of the Kinematic Theory to identify the key factors contributing to rapid movement cost: energy efficiency, movement smoothness, and time. We then constructed an original composite cost function and applied it to predict the control strategy of an arm model (1 or 2 degrees of freedom) during a rapid extension. Our composite cost function successfully produced asymmetric velocity profiles that resemble a lognormal profile more closely than other control strategies, although the beginning of the movement remains too rapid. We further examined our composite function using experimental data of one participant performing 29 fast arm extensions. We showed that the optimal end-effector velocity profile matched the experimental measurements as closely as a lognormal profile. By analyzing the optimal predictions of the velocity profile, we drew links between the components of the composite function and the lognormal parameters. Finally, we proposed strategies to further improve the optimal control predictions.