Visual Servoing Based on Theory of Transformation Group

In this paper we propose a new method of modern visual servoing based on the use of the entire image or its components and their group transformation as a direct control feedback. Describes the Idea of the method, the basic formulas and mathematical modeling experiment on motion control of a mobile robot. Visual servoing is used instead robot coordinates features in the image of the external environment. Mismatch in the dynamics between the images is defined by binding their continuous transformation. As such transformations can be used by a group of plane motions, affine and projective groups. To find such a transformation we use frequency methods based on the representation theory of groups and spatial methods based on optical flow or local correlations of image domains. The resulting mismatch of images is transformed into coordinates, speed or torque actuators of the robot. Next, conventional control algorithms based on the inverse problems of dynamics are used.