Title: Analytical Shaping Method for Low-Thrust Rendezvous Trajectory Using Cubic Spline Functions Show Chinese title

Title: 用于使用三次样条函数的低推力交会轨迹的解析造型方法

Abstract: 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. Show Chinese abstract

Abstract: 初步任务设计需要对低推力会合轨迹进行高效且准确的近似，这些轨迹可能是三维的，并涉及多次绕行。 在本文中，开发了一种使用三次样条函数的新造型方法用于解析近似，该方法在最优性和计算效率方面表现出优势。 在假设边界条件和三次样条函数的段数预先指定的情况下，所有关于边界状态和转移时间的会合约束都能被解析地满足。 然后根据是否具有自由优化参数来制定两种特定形状。 没有自由参数的形状提供了高效且稳健的估计，而另一种形状则允许后续优化以满足其他约束条件，例如推力大小的约束。 通过两个典型的星际会合任务，即从地球到小行星Dionysus的倾斜多次绕行轨迹以及样本返回的多次会合轨迹，讨论了所提出方法与粒子群优化算法结合的应用。 仿真示例显示，所提出的方法在为全局搜索提供良好估计以及为后续轨迹优化生成合适的初始猜测方面优于现有方法。