Abstract
According to Fitts’ Law, the time (MT) to move to a target is a linear function of the logarithm of the ratio between the target’s distance and width. Although Fitts’ Law accurately predicts MTs for direct movements, it does not accurately predict MTs for indirect movements, as when an obstacle intrudes on the direct movement path. To address this limitation, Jax et al. (2007) added an obstacle-intrusion term to Fitts’ Law. They accurately predicted MTs around obstacles in two-dimensional (2-D) workspaces, but their model had one more parameter than Fitts’ Law did and was merely descriptive. In this study, we addressed these concerns by turning to the mechanistic, posture-based (PB) movement planning model. The PB-based model accounted for almost as much MT variance in a 3-D movement task as the model of Jax et al., with only two parameters, the same number of parameters as in Fitts’ Law.
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Notes
In the foregoing, B must be at least as large as the distance the obstacle intrudes (OI) into the workspace. For convenience of exposition, we assume that B simply equals OI.
The six positional degrees of freedom of a rigid object are the x, y, and z values of a reference point within the object such as its center of gravity, and the object’s pitch, roll, and yaw.
It is not unusual for a target to be an obstacle. When reaching for a glass, for example, the glass is an obstacle vis à vis the dorsal side of the hand and fingers. This is why the hand must move around the glass before closing in on it. The PB model was designed to generate such behaviors and simulates them accurately (Rosenbaum et al. 2001).
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Vaughan, J., Barany, D.A., Sali, A.W. et al. Extending Fitts’ Law to three-dimensional obstacle-avoidance movements: support for the posture-based motion planning model. Exp Brain Res 207, 133–138 (2010). https://doi.org/10.1007/s00221-010-2431-z
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DOI: https://doi.org/10.1007/s00221-010-2431-z