发表机构
Stanford University（斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种统一的偏心相对轨道要素框架，在VNB坐标系中解析几何，提供闭式状态转移矩阵和相位无关的分离界，适用于一般椭圆轨道编队飞行。
AI 中文摘要
准非奇异相对轨道要素（qnsROE）是近圆倾斜轨道编队飞行与交会中最广泛使用的状态表示之一。它们具有闭式摄动状态转移矩阵（STM）和直接的几何映射，这支撑了用于被动安全的偏心率/倾角（E/I）矢量分离。现有的qnsROE偏心扩展在径向-切向-法向坐标系中解析该几何，其中残余半长轴差使E/I分离裕度依赖于相位。本文引入偏心ROE，其在\(e\ o0\)时退化为qnsROE，其一阶几何在速度-法向-副法向（VNB）坐标系中解析，其中长期漂移被限制在速度方向。其一阶位置和速度映射产生闭式、相位无关的副法向-法向分离界，并具有半长轴残差的显式裕度。为相同要素推导了闭式开普勒和长期-\(J_2\) STM以及解耦的脉冲控制输入矩阵，并且这些要素被恢复为VNB坐标系中相对运动笛卡尔方程的物理归一化积分常数。这些结果共同为一般椭圆轨道中的编队飞行提供了统一的ROE框架。
英文摘要
Quasi-nonsingular relative orbital elements (qnsROE) are among the most widely used state representations for formation flying and rendezvous in near-circular inclined orbits. They admit closed-form perturbed state transition matrices (STMs) and a direct geometric mapping, which underpins eccentricity/inclination (E/I)-vector separation for passive safety. Existing eccentric extensions of the qnsROE resolve this geometry in the radial--tangential--normal frame, where a residual semimajor-axis difference makes the E/I separation margin phase dependent. This paper introduces eccentric ROE that reduce to the qnsROE as \(e\to0\) and whose first-order geometry is resolved in the velocity--normal--binormal (VNB) frame, where the secular drift is confined to the velocity direction. Their first-order position and velocity maps yield a closed-form, phase-independent binormal--normal separation bound with an explicit margin for semimajor-axis residuals. Closed-form Keplerian and secular-\(J_2\) STMs and a decoupled impulsive control input matrix are derived for the same elements, and the elements are recovered as the physically normalized integration constants of the Cartesian equations of relative motion in the VNB frame. Together, these results provide a unified ROE framework for formation flying in general elliptic orbits.
Comments33 pages, 6 figures
