访问多个特定相对位置的航天器轨道设计

在航天器轨道设计问题中，将惯性空间中经典的吉布斯三矢量定轨方法拓展到相对运动空间中，给出了一种相对运动条件下的三矢量定轨方法。针对已知轨道的目标航天器，以及二个或三个给定的空间相对位置，基于相对运动方程，提出了设计跟随航天器飞行轨道的数值方法。以轨道面共面或异面，以及目标航天器轨道形状为椭圆或圆，将问题分为四种情况进行约束条件和自由变量个数的分析讨论。对于自由变量个数多于约束方程的情况，额外给定周期重访约束，将各种情况下的特定相对位置访问问题转化为一至二维的非线性方程(组)求解问题。对一维方程求解采用分段黄金分割+割线法进行快速求解；对二维方程组通过网格法搜索迭代初值并通过牛顿迭代快速求解。进一步基于线性模型的解，采用微分修正方法求解了各情况下J2摄动模型下的结果。数值算例验证了提出方法的正确性及有效性。

Spacecraft Orbit Design for Visiting Multiple Specific Relative Positions

The classical Gibbs method for orbit determination from three position vectors in inertial space is extended to the relative motion space, and a three vector orbit determination method under relative motion condition is presented. For two or three given space relative positions to the target spacecraft, a numerical method for designing the orbit of the chaser spacecraft is proposed based on the linear relative motion equations. Taking account of the coplanar or non coplanar orbits, and the circular or elliptical orbit of the target spacecraft, the problem is divided into four cases to analyze and discuss the constraints and the number of free variables. When the number of free variables is greater than that of the constraint equations, the periodic revisit constraint is given additionally, and the specific relative positions visit problem in various cases is transformed into a one or two dimensional nonlinear equation(s). The one dimensional equation is solved quickly by subsection golden section with secant method. For two dimensional equations, the initial values of iteration are searched by grid method and the equation is solved quickly by Newton iteration. Furthermore, based on the solution of the linear model, the differential correction method is used to solve the results of the J 2 perturbation model in each case. Numerical examples are given to verify the correctness and effectiveness of the proposed method.