A quaternion formulation for homography-based visual servo control

Previous homography-based visual servo controllers have been developed using an error system that contains a singularity resulting from the representation of the rotation matrix. For some aerospace applications such as visual servo control of satellites or air vehicles, the singularity introduced by the rotation representation may be restrictive. To eliminate this singularity, a homography-based visual servo controller is developed in this paper based on an error system composed of the unit quaternion representation. The proposed adaptive controller regulates a camera to a desired position and orientation that is determined from a desired image. A quaternion-based Lyapunov function is developed to facilitate the control design and the stability analysis.