A Control Model: An Alternative Interpretation of Fitts' Law

Fitts' law has been universally cited as an index of difficulty or predictor of movement time (MT) for rapid aiming tasks since it was first published in 1954 (Fitts 1954). Many researchers report a remarkable correlation of Fitts' law and the observed movement times in aiming tasks. Other researchers report discrepancies, however, between observed movement time and the law, especially at low and high movement times, which correspond, respectively, to short movements to a large target, and long movements to a small target. These discrepancies suggest that while the law predicts MT well for some human motions, the true basis for the law may not be known, and, as a consequence, that there may exist conditions where its application is appropriate and yet others where different laws should be used. Fitts suggested the law as a model of the rate-limit of human information processing and movement. But this rate-limit model is not the only interpretation possible. Rapid movement of the hand to a target can be modeled from a different view-point: namely, as a control system. This paper gives the analytical results for several models: a first order model where it is assumed that the hand velocity can be directly controlled, and a second order model where it is assumed that the hand acceleration can be directly controlled. The results show that the first and second order models with the linear control-law produce a MT function with the exact form of the Fitts' law, and yet it has nothing to do with information theory.