de Almeida A K, Vaillant T, de Oliveira V M, Barbosa D, Maia D, Aljbaae S, Coelho B, Bergano M, Pandeirada J, Prado A F B A, Guerman A, Correia A C M
CICGE, DGAOT, FCUP, Vila Nova de Gaia, Portugal.
CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516, Coimbra, Portugal.
Sci Rep. 2024 Mar 29;14(1):7479. doi: 10.1038/s41598-024-57986-z.
Maneuvering a spacecraft in the cislunar space is a complex problem, since it is highly perturbed by the gravitational influence of both the Earth and the Moon, and possibly also the Sun. Trajectories minimizing the needed fuel are generally preferred in order to decrease the mass of the payload. A classical method to constrain maneuvers is mathematically modeling them using the Two Point Boundary Value Problem (TPBVP), defining spacecraft positions at the start and end of the trajectory. Solutions to this problem can then be obtained with optimization techniques like the nonlinear least squares conjugated with the Theory of Functional Connections (TFC) to embed the constraints, which recently became an effective method for deducing orbit transfers. In this paper, we propose a tangential velocity (TV) type of constraints to design orbital maneuvers. We show that the technique presented in this paper can be used to transfer a spacecraft (e.g. from the Earth to the Moon) and perform gravity assist maneuvers (e.g. a swing-by with the Moon). In comparison with the TPBVP, solving the TV constraints via TFC offers several advantages, leading to a significant reduction in computational time. Hence, it proves to be an efficient technique to design these maneuvers.
在地月空间操纵航天器是一个复杂的问题，因为它受到地球和月球，甚至可能还有太阳的引力影响而高度摄动。为了减少有效载荷的质量，通常优先选择使所需燃料最小化的轨道。一种约束机动的经典方法是使用两点边值问题（TPBVP）对其进行数学建模，定义航天器在轨道起点和终点的位置。然后可以使用诸如与函数连接理论（TFC）共轭的非线性最小二乘法等优化技术来获得该问题的解，以嵌入约束条件，这最近成为推导轨道转移的一种有效方法。在本文中，我们提出了一种切向速度（TV）类型的约束来设计轨道机动。我们表明，本文提出的技术可用于转移航天器（例如从地球到月球）并执行引力辅助机动（例如绕月摆动）。与TPBVP相比，通过TFC求解TV约束具有几个优点，可显著减少计算时间。因此，它被证明是设计这些机动的一种有效技术。
