Image-based visual servoing is a flexible and robust technique to control a robot and guide it to a desired position only by using two-dimensional visual data. However, it is well known that the classical visual servoing based on the 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 1800 around the optical axis. This paper proposes a new formulation of visual servoing, based on a 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 the 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 initial and desired image-plane positions of feature points.

This paper proposes preferential direction control for visual servoing based on orthogonal curvilinear coordinate systems. In this paper, we present a generalized formulation of visual servoing based on curvilinear coordinate systems, which guarantees to converge an error between initial and desired positions of image feature points. Simulation results show that the formulation is effective to control the trajectories of feature points in preferred directions by applying to several curvilinear coordinate systems. Furthermore, we demonstrate that the preferential direction control goes well even if a different coordinate system can be adopted for each feature point. The mixed approaches with different coordinate systems can be applied to control a camera to keep image features within the field of view.

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.

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.