  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.
