基于三次样条函数的小推力再入弹道解析成形方法
Analytical Shaping Method for Low-Thrust Rendezvous Trajectory Using Cubic Spline Functions
摘要：
初步的飞行任务设计需要有效和精确地近似于小推力会合轨道，这种轨道一般可能是三维的，并涉及多次旋转。本文提出了一种新的三次样条函数成形方法，该方法在最优性和计算效率方面都有一定的优势。在预先设定边界条件和三次样条函数段数的前提下，边界状态和转移时间的交会约束均解析满足。然后根据它们是否具有自由优化参数来制定两个特定形状。没有自由参数的形状提供了一个有效的和鲁棒的估计，而另一个允许随后的优化，以满足额外的约束，如对推力大小的约束。结合两个典型的行星际交会任务，即地球-小行星Dionysus的倾斜多圈轨道和样本返回的多圈交会轨道，讨论了该方法与粒子群优化算法相结合的应用。仿真结果表明，该方法在为全局搜索提供良好的估计和为后续的轨迹优化生成合适的初始估计方面优于现有方法。
英文摘要：
Preliminary mission design requires an efficient and accurate approximation to the low-thrust rendezvous trajectories, which might be generally three-dimensional and involve multiple revolutions. In this paper, a new shaping method using cubic spline functions is developed for the analytical approximation, which shows advantages in the optimality and computational efficiency. The rendezvous constraints on the boundary states and transfer time are all satisfied analytically, under the assumption that the boundary conditions and segment numbers of cubic spline functions are designated in advance. Two specific shapes are then formulated according to whether they have free optimization parameters. The shape without free parameters provides an efficient and robust estimation, while the other one allows a subsequent optimization for the satisfaction of additional constraints such as the constraint on the thrust magnitude. Applications of the proposed method in combination with the particle swarm optimization algorithm are discussed through two typical interplanetary rendezvous missions, that is, an inclined multi-revolution trajectory from the Earth to asteroid Dionysus and a multi-rendezvous trajectory of sample return. Simulation examples show that the proposed method is superior to existing methods in terms of providing good estimation for the global search and generating suitable initial guess for the subsequent trajectory optimization.
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