Abstract: Few computational models have addressed the spatiotemporal features of unconstrained three-dimensional (3D) arm motion. Empirical observations made on hand paths, speed profiles, and arm postures during point-to-point movements led to the assumption that hand path and arm posture are independent of movement speed, suggesting that the geometric and temporal properties of movements are decoupled. In this study, we present a computational model of 3D movements for an arm with four degrees of freedom based on the assumption that optimization principles are separately applied at the geometric and temporal levels of control. Geometric properties (path and posture) are defined in terms of geodesic paths with respect to the kinetic energy metric in the Riemannian configuration space. Accordingly, a geodesic path can be generated with less muscular effort than on any other, nongeodesic path, because the sum of all configuration-speed-dependent torques vanishes. The temporal properties of the movement (speed) are determined in task space by minimizing the squared jerk along the selected end-effector path. The integration of both planning levels into a single spatiotemporal representation simplifies the control of arm dynamics along geodesic paths and results in movements with near minimal torque change and minimal peak value of kinetic energy. Thus, the application of Riemannian geometry allows for a reconciliation of computational models previously proposed for the description of arm movements. We suggest that geodesics are an emergent property of the motor system through the exploration of dynamical space. Our data validated the predictions for joint trajectories, hand paths, final postures, speed profiles, and driving torques.

Abstract: Analogies have been shown to improve motor learning in various tasks and settings. In this study we tested whether applying analogies can shorten the motor learning process and induce insight and skill improvement in tasks that usually demand many hours of practice. Kinematic measures were used to quantify participant's skill and learning dynamics. For this purpose, we used a drawing task, in which subjects drew lines to connect dots, and a mirror game, in which subjects tracked a moving stimulus. After establishing a baseline, subjects were given an analogy, explicit instructions or no further instruction. We compared their improvement in skill (quantified by coarticulation or smoothness), accuracy and movement duration. Subjects in the analogy and explicit groups improved their coarticulation in the target task, while significant differences were found in the mirror game only at a slow movement frequency between analogy and controls.We conclude that a verbal analogy can be a useful tool for rapidly changing motor kinematics and movement strategy in some circumstances, although in the tasks selected it did not produce better performance in most measurements than explicit guidance. Furthermore, we observed that different movement facets may improve independently from others, and may be selectively affected by verbal instructions. These results suggest an important role for the type of instruction in motor learning.