抄録
Various approaches have been followed to date in the theoretical analysis and modeling of human motor functions. Most notable are notions taken from the fields of control engineering, information theory, and various computational approaches. However, several aspects of motor behaviour have not been dealt with in a satisfactory way so far. For example, the spaces of motor degrees of freedom are customarily considered to be linear even when they are not, and their geometric structure is often ignored. In order to address these issues we apply some general and powerful tools from Differential Geometry. We demonstrate their usefulness to the field by examining several questions that have arisen in the study of the oculomotor system and smooth movements of the hand. In particular, we have achieved the following results: the clarification of aspects relating to eye rotations and the control strategy known as Donders' law and Listing's law; the identification of binocular motor space as the Lie algebra so (4); reproduction of binocular fixation point trajectories in the horizontal plane of regard using a simple kinematic model; by viewing the trajectories traced by the hand as curves in the affine plane, an empirical relation between the geometry and kinematics of smooth hand motion has been shown to imply that the hand moves at approximately constant affine speed; from this behavioural relation we further derived a constraint on neural cortical dynamics under the hypothesis of neural population vector coding. All in all, the geometric methods described here have enabled us to analyse and elucidate several aspects of motor performance, planning and control, and their possible corresponding representations in the brain. We expect that such geometric methods will be increasingly used and that they will have an important role in future research of human motor control.
