A new formulation of visual servoing based on cylindrical coordinate system with shiftable origin

Image-based visual servoing is a flexible and robust technique to control a robot and guide it to a desired position only by using 2D visual data. However, it is well known that the classical visual servoing based on Cartesian coordinate system has one crucial problem that the camera moves backward at infinity in case that the camera motion from the initial to desired poses is a pure rotation of 180 degrees around the optical axis. This paper proposes a new formulation of visual servoing based on cylindrical coordinate system that can shift the position of the origin. The proposed approach can interpret from a pure rotation around an arbitrary axis to the proper camera rotational motion. It is shown that this formulation contains the classical approach based on Cartesian coordinate system as an extreme case with the origin located at infinity. Furthermore, we propose a decision method of the origin-shift parameters by estimating a rotational motion from the differences between current and desired image-plane positions of feature points.