Abstract For most atmospheric or exo-atmospheric spacecraft flight scenarios, a well-designed trajectory is usually a key for stable flight and for improved guidance and control of the vehicle. Although extensive research work has been carried out on the design of spacecraft trajectories for different mission profiles and many effective tools were successfully developed for optimizing the flight path, it is only in the recent five years that there has been a growing interest in planning the flight trajectories with the consideration of multiple mission objectives and various model errors/uncertainties. It is worth noting that in many practical spacecraft guidance, navigation and control systems, multiple performance indices and different types of uncertainties must frequently be considered during the path planning phase. As a result, these requirements bring the development of multi-objective spacecraft trajectory optimization methods as well as stochastic spacecraft trajectory optimization algorithms. This paper aims to broadly review the state-of-the-art development in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning techniques for spacecraft flight operations. A brief description of the mathematical formulation of the problem is firstly introduced. Following that, various optimization methods that can be effective for solving spacecraft trajectory planning problems are reviewed, including the gradient-based methods, the convexification-based methods, and the evolutionary/metaheuristic methods. The multi-objective spacecraft trajectory optimization formulation, together with different class of multi-objective optimization algorithms, is then overviewed. The key features such as the advantages and disadvantages of these recently-developed multi-objective techniques are summarised. Moreover, attentions are given to extend the original deterministic problem to a stochastic version. Some robust optimization strategies are also outlined to deal with the stochastic trajectory planning formulation. In addition, a special focus will be given on the recent applications of the optimized trajectory. Finally, some conclusions are drawn and future research on the development of multi-objective and stochastic trajectory optimization techniques is discussed.

中文翻译：

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航天器飞行轨迹设计优化技术综述

摘要 对于大多数大气层或大气层外的航天器飞行场景，设计良好的轨迹通常是稳定飞行和改进飞行器制导和控制的关键。尽管针对不同任务剖面的航天器轨迹设计进行了广泛的研究工作，并成功开发了许多用于优化飞行路径的有效工具，但直到最近五年才对计划飞行产生了越来越大的兴趣。考虑多个任务目标和各种模型错误/不确定性的轨迹。值得注意的是，在许多实际的航天器制导、导航和控制系统中，在路径规划阶段必须经常考虑多种性能指标和不同类型的不确定性。因此，这些需求带来了多目标航天器轨迹优化方法以及随机航天器轨迹优化算法的发展。本文旨在广泛回顾航天器飞行操作的数值多目标轨迹优化算法和随机轨迹规划技术的最新发展。首先介绍问题的数学公式的简要描述。随后，回顾了可以有效解决航天器轨迹规划问题的各种优化方法，包括基于梯度的方法、基于凸化的方法和进化/元启发式方法。多目标航天器轨迹优化公式，然后概述了不同类别的多目标优化算法。总结了这些最近开发的多目标技术的优点和缺点等关键特征。此外，注意将原始确定性问题扩展到随机版本。还概述了一些稳健的优化策略来处理随机轨迹规划公式。此外，还将特别关注优化轨迹的近期应用。最后，得出了一些结论，并讨论了多目标和随机轨迹优化技术的未来研究。注意将原始确定性问题扩展到随机版本。还概述了一些稳健的优化策略来处理随机轨迹规划公式。此外，还将特别关注优化轨迹的近期应用。最后，得出了一些结论，并讨论了多目标和随机轨迹优化技术的未来研究。注意将原始确定性问题扩展到随机版本。还概述了一些稳健的优化策略来处理随机轨迹规划公式。此外，还将特别关注优化轨迹的近期应用。最后，得出了一些结论，并讨论了多目标和随机轨迹优化技术的未来研究。