Explanation of Fitts' law in Reaching Movement based on Human Arm Dynamics

Why does Fitts’ law fit various human behavioural data well even though it is not a model based on human physical dynamics? To clarify this, we derived the relationships among the factors applied in Fitts’ law—movement duration and spatial endpoint error—based on a multi-joint forward- and inverse-dynamics models in the presence of signal-dependent noise. As a result, the relationship between them was modelled as an inverse proportion. To validate whether the endpoint error calculated by the model can represent the endpoint error of actual movements, we conducted a behavioural experiment in which centre-out reaching movements were performed under temporal constraints in four directions using the shoulder and elbow joints. The result showed that the distributions of model endpoint error closely expressed the observed endpoint error distributions. Furthermore, the model was found to be nearly consistent with Fitts’ law. Further analysis revealed that the coefficients of Fitts’ law could be expressed by arm dynamics and signal-dependent noise parameters. Consequently, our answer to the question above is: Fitts’ law for reaching movements can be expressed based on human arm dynamics; thus, Fitts’ law closely fits human’s behavioural data under various conditions.