Learning to Reach: A Mathematical Model

This article presents a mathematical model of the development of reaching that assumes that the major problem facing infants is their lack of lower level motor control and that infants learn to adjust their reaching strategies as a consequence of their previous experience and to match their current level of control. The model hypothesizes that infant reaches are a series of submovements, with the goal being to get the hand to the target in the face of errors in executed submovements. To relate actual infant reaches to this model, reaching data were decomposed into submovements, using a polynomial fitting algorithm that assumed minimum-jerk submovements. The model makes quantitative predictions about the course of development that are supported by existing results. The validity of the model's underlying assumptions was assessed by comparing the directional variability of the submovements with the variability assumed in the model.