2 1/2 D visual servoing with central catadioptric cameras

In this paper, we present how the 2 1/2 D visual servoing scheme can be used with omnidirectional cameras. Motivated by the growing interest for omnidirectional sensors on robotic applications and particularly on vision-based control, we extend this framework to the entire class of central catadioptric systems. Indeed, conventional cameras suffer from restricted field of view. Central catadioptric systems have larger fields of view thus overcoming the visibility problem encountered when using conventional cameras. The 2 1/2 D visual servoing is based on the estimation of the partial camera displacement between two views, given by the current and desired images. Geometrical relationships are exploited to enable a partial Euclidean reconstruction by decoupling the interaction between translation and rotation components of a homography matrix. First we describe how to obtain a generic homography matrix for central catadioptric cameras from the projection model of an entire class of camera. Then the information obtained from the homography is used to develop a 2 1/2 D visual servoing scheme.