Vision-based control for rigid body stabilization

This paper addresses the problem of stabilizing to a desired equilibrium point an eye-in-hand system, which consists of a single camera mounted on a rigid body free to move on SE(3). It is assumed that there is a collection of landmarks fixed in the environment and that the image coordinates of those landmarks are provided to the system by an on-board CCD camera. The proposed method addresses not only the problem of stabilization but also that of maintaining feature visibility along the system’s trajectory. The resulting solution consists of a feedback control law based on the current and desired image coordinates and reconstructed attitude and depth ratio information, which guarantees that (i) the desired equilibrium point is an almost global attractor; (ii) a set of necessary conditions for feature visibility holds throughout the system’s trajectories; and (iii) the image of a predefined feature point is kept inside the camera’s field of view.