基于对偶四元数的编队飞行卫星相对位姿描述及算法研究

摘要

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.%针对编队飞行微小卫星,突破轨道姿态分而治之的传统模式,利用对偶四元数,提出了主从星间的相对位置和姿态统一描述方法,建立了对偶四元数卫星编队运动学模型.该方法区别于描述刚体纯旋转变换的四元数方法,将主从星的本体系之间坐标变换的旋转和平移过程进行融合、统一,并具有非常简洁的形式.同时,给出了求解模型的算法,解算出主从星间的相对位置和姿态.仿真结果表明该模型及算法科学合理,能够满足编队飞行的测控要求.