The limit profile of a rapid movement velocity

In motor control, various theories and computational models have been developed to explain and model the stereotypical velocity profiles of skilled rapid movements. According to the fact that these theories aim at describing the same physical pattern (a velocity profile) with different mathematical expressions, some relationships between these various representation schemes should exist. This paper presents a comparative study of two motor control theories that have put forward analytical expressions to describe the stereotypical velocity profiles of rapid movements: the Kinematic Theory and the Minimization Theory. Among the various forms of the latter, the Minimum-Square-Derivatives (MSD) principle and the Minimum-Time model are analyzed. It is shown that their concepts are linked and describe, with different arguments, a paradigm similar to the one used in the Kinematic Theory to model a velocity profile with a Delta-Lognormal equation. This unifying paradigm represents the functioning of a neuromuscular system by the convolution product of an infinite number of subsystem impulse responses. A second finding emerging from the present study is that the analytical models of velocity profiles, as described by the minimum principles under study, correspond, with more or less accuracy, to an approximation of the Delta-Lognormal equation. Overall, the Kinematic Theory can be seen as relying on a general optimization principle and the use of the Minimization Theory in motor control gets new insights.