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 in 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 image coordinates and reconstructed depth information that guarantees: i) almost global asymptotic stability of the desired equilibrium point; ii) positive invariance of a conveniently defined subset of SE(3), to enforce feature visibility; and iii) exponential stability of an error vector directly defined in the image plane.