A General Optimal Control Model of Human Movement Patterns II: Rapid, Targeted Hand Movements (Fitts Law)

TL;DR

This paper presents a principled optimal control model of rapid, targeted hand movements that naturally reproduces Fitts law and explains movement patterns, including differences observed in older adults with cognitive impairments.

Contribution

It introduces a jerk-control based optimal control model that enforces smooth muscle forces and derives Fitts law from movement energy and accuracy trade-offs.

Findings

Model reproduces Fitts law accurately.

Explains movement differences in cognitively impaired older adults.

Links movement constants to energy and momentum concepts.

Abstract

Rapid, targeted hand movements exhibit a regular movement pattern described by Fitts law. We develop a model of these movements in which this movement pattern results from an optimal control model describing rapid hand movements and a utility model describing the speed/accuracy trade-off between moving the hand rapidly to the target and hitting the target accurately. The optimal control model is constructed using principled approach in which we forbid the muscle forces to exhibit any discontinuities and require the cost to be expressed in terms of a psychophysical representation of the movement. This yields a yank-control or jerk-control model of the movement which exhibits two constants of the motion that are closely related to the energy and momentum in classical mechanics. We force the optimal control model to obey Fitts law by requiring a particular relationship hold between the constants of the motion and the size of the target and show that the resulting model compares well to a standard expression of Fitts law obtained empirically using observations of computer mouse movements. We then proceed to further show how this relationship may be obtained as the result of a simple models of the movement accuracy and the speed/accuracy trade-off. We use the movement accuracy model to analyze observed differences in computer mouse movement patterns between older adults with mild cognitive impairment and intact older adults. We conclude by looking at how a subject might carry out in practice the optimization implicit in resolving the speed/accuracy trade-off in our model.