Quasi-Euler representation and attitude reachability criteria of camera motion for computer vision

Abstract

Two attitude kinetic models of a camera, including absolute and relative motions, are established in form of quaternion in this paper. Based on the two models, new variables, Quasi-Euler angles are derived with a quaternion matrix transformation for camera's large angle attitude maneuver problem. Because the Quasi-Euler Angles-based attitude representation of the camera is single-valued, the problem of non-single-valued due to traditional quaternion representation is avoided; and Quasi-Euler Angles-based attitude representation is suitable for absolute and relative attitude motions of the camera. Furthermore, we prove that the camera attitude can reach the predefined orientation at the terminal time and stabilize on it as long as Quasi-Euler angles and their first-order time derivatives, called Quasi-Euler angle velocities, are equal to zeros for the absolute motion and the relative motion.