Shaping of arm configuration space by prescription of non-Euclidean metrics with applications to human motor control

摘要

The study of the kinematic and dynamic features of human arm movements provides insights into thencomputational strategies underlying human motor control. In this paper a differential geometric approach tonmovement control is taken by endowing arm configuration space with different non-Euclidean metric structuresnto study the predictions of the generalized minimum-jerk (MJ) model in the resulting Riemannian manifoldnfor different types of human arm movements. For each metric space the solution of the generalized MJ modelnis given by reparametrized geodesic paths. This geodesic model is applied to a variety of motor tasks rangingnfrom three-dimensional unconstrained movements of a four degree of freedom arm between pointlike targetsnto constrained movements where the hand location is confined to a surface (e.g., a sphere) or a curve (e.g.,nan ellipse). For the latter speed-curvature relations are derived depending on the boundary conditions imposedn(periodic or nonperiodic) and the compatibility with the empirical one-third power law is shown. Based on thesentheoretical studies and recent experimental findings, I argue that geodesics may be an emergent property of thenmotor system and that the sensorimotor system may shape arm configuration space by learning metric structuresnthrough sensorimotor feedback.