Diffusion-based learning theory for organizing visuo-motor coordination

A diffusion-based learning theory is presented and applied to organize the visuomotor coordination of an eye-hand system which has redundant motion degree of freedom (dof). This theory considers the spatial optimality of the coordination: to minimize the end-effector position error of the eye-hand system as well as the differentiation of the joint angles with respect to the end-effector positions over all the bounded work space. By introducing variational methods with respect to the space, we derive a partial differential equation (PDE) of the joint angles with respect to the work space. The equation includes a diffusion term. For the given boundary conditions and the initial conditions, it can be solved uniquely, and the solution is a well organized map. From the motor learning point of view, our approach contains both the aspects of supervised learning as well as self-organization. Firstly, we assume that the forward relation from the hand system's joint angles to its end-effector positions can be obtained using supervised learning, and at the boundary of the work space, the supervisor can provide correct joint information. Then, by evolving the diffusion equation, we organize the visuomotor coordination. We show the effectiveness of this approach using a 3-dof scale manipulator. The problems of how to realize the visuomotor map; how to utilize the resultant map in several motions; and what are the influences of the initial conditions on the map formation and the relation to the boundary conditions are also discussed using computer simulations. Our approach has three advantages: (1) it does not require too many trial motions for the eye-hand system; (2) during the map formation process, it requires only the local interactions between each node; and (3) it guarantees the final map's spatial optimality over all the bounded work space.