Visual servoing using eigenspace method and dynamic calculation of interaction matrices

A general scheme to represent the relation between dynamic images and camera motion is presented, and its application to visual servoing proposed. For a specific object, the camera cannot obtain any arbitrary image, so that the possible combination of the camera pose and the obtained image should be constrained on a lower dimensional hyper surface within the product space of all the combinations. 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 analyse the properties of this surface and utilise its tangential property for visual servoing. We propose to use the principal component analysis and to represent images with a composition of small number of "eigen-images" by using the Karhunen-Loeve expansion. We describe that a normal vector of this surface is related to the so-called interaction matrix. We then present a dynamic estimation of the normal vectors to move the robot arm mounting a camera to a goal position where a given goal image will be obtained. Experimental results of visual servoing method show the feasibility and applicability of our proposed approach.