Rotation-oriented visual servoing based on cylindrical coordinates

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 visual servoing has one classical 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 optical axis. It has been considered so far that the problem can not be essentially solved by the simplest conventional approach. This paper shows that the problem can be solved as simply as the conventional approach by introducing cylindrical coordinates into the formulation of visual servoing. Furthermore, we propose a new hybrid visual servoing that can control properly even in the situation coupling between translational and rotational motions by using a linear combination of velocity screws obtained from the Cartesian and cylindrical approaches with the rate of magnitudes of these translational velocities in z direction as a weight. This hybrid approach is modified to keep all feature points within the field of view by combining with another weight that is defined by a sigmoid function of the shortest distance to the edge of the image plane from the feature point.