A direct interpretation of dynamic images and camera motion for vision guided robotics

A general scheme to represent the relation between dynamic images and camera motion is presented. Then, its application to visual servoing is proposed. For a specific object, the possible combination of the camera pose and the obtained image should be constrained on a lover dimensional hyper surface within the product space of whole combination of image data and camera position. The visual servoing, for example, is interpreted as to find a path on this surface leading to a given goal image. Our approach is to analyze the properties of this surface, and utilize its differential or tangential property for visual servoing. For this approach, the dimension of the image information becomes key problem. We propose to use the principal component analysis and to represent images with a composition of small number of "eigenimages" by using K-L (Karhunen-Loeve) expansion. In this paper, we describe, first, that a normal vector of this surface is related to the so-called interaction matrix, and confirm the feasibility of our basic idea for visual servoing with a preliminary experiment. Then, we present a dynamical estimation of the normal vectors to move robot arm mounting a camera to a goal position where a given goal image will be obtained. We also consider the construction of the eigenspace (the eigenimage space) to represent images efficiently and to speedup convergence in the control. Experimental results of visual servoing with proposed method show the feasibility and applicability of our newly proposed approach.