Towards mastery of complex visuo-motor transformations

In this paper we review and integrate a set of findings on learning the transformation of a sliding first-order lever, a type of tool with a prominent role in minimal access surgery. Its kinematic transformation is characterized by the so-called fulcrum effect, the inversion of the movement direction of the tip of the lever relative to that of the hand for rotations. A second characteristic is gain anisotropy, which results in curved paths of the tip of the lever for straight paths of the hand and vice versa. An internal model of the kinematic transformation is acquired during practice, the accuracy of which can be assessed in visual open-loop test trials. The accuracy of the acquired internal model is enhanced when visual closed-loop control during practice is impeded, and the accuracy of the internal model is reduced when closed-loop control during practice is facilitated. The internal model consists of a rapidly acquired line-symmetric approximation to the transformation of the sliding lever and a slowly acquired fine tuning. The fine tuning is local, that is, it is specific for the region of the workspace encountered during practice. The internal model is transferred to other regions of the workspace, but not adjusted to the fine tuning appropriate for these regions. Whereas the symmetry approximation is most likely explicit, the fine tuning seems to be represented implicitly. Findings on the straightness of the paths of the tip of the lever and the hand suggest that the internal model of the transformation is confined to initial and final positions of aimed movements, whereas their path is not strictly controlled, but affected by the dynamic transformation of the tool. Only when visual closed-loop control is possible, the path of the effective part of the tool is straightened. These characteristics of the internal model of the sliding first-order lever and its acquisition may be partly specific to sufficiently complex extrinsic transformations that arise from mechanical or electronic extensions of the body.