Abstract: A unified representation of relative position and attitude based on dual\|quaternion is presented for small satellite formation flight, which is a breakthrough in traditional pattern for treating orbit and attitude of satellite separately. A satellite formation kinematics model is constructed by using dual\|quaternion. Differing from the quaternion solution adopted to express the pure rotation transform of rigid body, the dual\|quaternion scheme is adopted to describe the coordinate transform among satellite reference frames by fusing the measurements of rotational and translational processes, and it has very simple form. A corresponding algorithm is presented for solving the model, and relative position and attitude between satellites are resolved. Simulation shows that the model and the proposed algorithm are scientific and effective, and meet the demand for measurement and control for satellite formation flight.

Key words: Satellite formation flight, Relative position and attitude, Dual-quaternion, Unified representation