An evaluation of the minimum-jerk and minimum torque-change principles at the path, trajectory, and movement-cost levels

In the present study we evaluated the minimum-jerk and the minimum torque-change model at the path, trajectory, and movement-cost levels. To date, most evaluations of these models have mainly been restricted to path comparisons. Assessments of the time courses of realized jerk and torque changes are surprisingly lacking. Moreover, the extent to which the presumed optimized parameters change as a function of the duration and other temporal features of aiming movements has never been investigated, most probably because the models presuppose movement time. In order to fill this gap, we analyzed a subset of the data of an earlier experiment in which 12 participants performed leftward and rightward planar pointing movements. Hand displacements and joint excursions were recorded with a 3D motion-tracking system and subsequently evaluated by means of model-based analyses. The results show that despite a good agreement between observed paths and predicted paths; especially by the minimum torque-change model, the time courses of jerk and torque changes of observed and modeled movements differed considerably. These differences could mainly be attributed to asymmetrical properties of the time functions of slow movements. Variations of movement costs as a function of movement time and skewness of tangential velocity profiles show that, especially at high movement speed, costs increase exponentially with departures of symmetry. It is concluded that trajectory-formation models have limited explanatory power in situations that require demanding information processing during the homing-in phase of goal-directed movements. However, for slow movements, deviations from the optimal timing profiles require little extra costs in terms of jerk or torque change.