Abstract Despite the ongoing advancements in low-thrust propulsion technology and the rise of all-electric satellite platforms, low-thrust spacecraft trajectory optimization remains a complex field of research. Shape-based approximations are predominant in interplanetary applications, but they are generally unsuitable for many-revolution trajectories, common in terrestrial applications. Indirect optimization methods allow for global optimization of many-revolution trajectories, but their mathematical complexity generally requires significant simplifications of the dynamical model, and they must be re-derived for any modification to the system dynamics or constraints. Conversely, direct optimization methods exhibit larger convergence radii and are flexible for application in different problems yet suffer from impractical computational times due to large design vectors. This paper presents a methodology for the optimization of low-thrust many-revolution trajectories, employing a hybrid combination of indirect and direct optimization methods. Similar hybrid approaches have been shown to be highly reliable for minimum-time trajectories. This methodology preserves similar performance while additionally enabling minimum-propellant optimization, through a mechanism that allows for coasting (non-thrusting) arcs, as well as targeting of the final geodetic-longitude. To reduce the propagation load of the methodology, we combine an orbital averaging scheme with a differential evolution algorithm, leading to a global optimization process with a practical computational effort. The analytical nature of the methodology reduces the number of optimization variables and its computational counterpart provides unmatchable flexibility for a configurable force and perturbation model as well as operational constraints fulfilment. The approach is applied to an unperturbed and a J2-perturbed GTO-GEO transfer, revealing a 0.03% and a 0.4% error, for time- and propellant-minimization respectively, relative to the reference optimal trajectories. This proves that the method can match the performance of former hybrid approaches while additionally allowing for engine on/off switching. Moreover, the inclusion of the J2 perturbation shows that, in contrast to indirect methods, it can accommodate modifications to the system dynamics without the need to re-derive the optimal control laws. Furthermore, a superior convergence radius of the optimization problem is demonstrated for the hybrid method, with respect to a reference indirect method, through the simultaneous optimization for minimum-propellant expenditure and final geodetic-longitude targeting. This research constitutes a significant advancement for space mission design and satellite operations, because it simultaneously harnesses the advantages of indirect and direct methods with broader flexibility than the popular indirect approaches and enhanced functionality than the former hybrid methods published in literature.

中文翻译：

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用于推进剂最小化的低推力多转轨迹与滑行弧和经度目标的混合优化

摘要 尽管低推力推进技术不断进步和全电动卫星平台的兴起，低推力航天器轨迹优化仍然是一个复杂的研究领域。基于形状的近似在行星际应用中占主导地位，但它们通常不适合多圈轨道，这在陆地应用中很常见。间接优化方法允许对多圈轨迹进行全局优化，但它们的数学复杂性通常需要对动力学模型进行显着简化，并且必须重新推导它们以对系统动力学或约束进行任何修改。反过来，直接优化方法表现出更大的收敛半径，并且可以灵活地应用于不同的问题，但由于设计向量很大，因此计算时间不切实际。本文提出了一种优化低推力多转轨迹的方法，采用间接和直接优化方法的混合组合。类似的混合方法已被证明对于最短时间轨迹是高度可靠的。这种方法保留了相似的性能，同时通过一种允许滑行（非推力）弧线以及以最终大地经度为目标的机制，额外实现了最小推进剂优化。为了减少该方法的传播负载，我们将轨道平均方案与差分进化算法相结合，通过实际的计算工作导致全局优化过程。该方法的分析性质减少了优化变量的数量，其计算对应物为可配置的力和扰动模型以及操作约束实现提供了无与伦比的灵活性。该方法应用于未扰动和 J2 扰动 GTO-GEO 传输，相对于参考最佳轨迹，分别显示 0.03% 和 0.4% 的误差，用于时间和推进剂最小化。这证明该方法可以匹配以前混合方法的性能，同时还允许发动机开/关切换。此外，包含 J2 扰动表明，与间接方法相比，它可以适应系统动力学的修改，而无需重新推导最佳控制规律。此外，通过同时优化最小推进剂消耗和最终大地经度目标，混合方法相对于参考间接方法证明了优化问题的优越收敛半径。这项研究是空间任务设计和卫星操作的重大进步，因为它同时利用了间接和直接方法的优势，比流行的间接方法具有更广泛的灵活性，并且比文献中发表的以前的混合方法具有更强的功能。关于参考间接方法，通过同时优化最小推进剂消耗和最终大地经度目标。这项研究是空间任务设计和卫星操作的重大进步，因为它同时利用了间接和直接方法的优势，比流行的间接方法具有更广泛的灵活性，并且比文献中发表的以前的混合方法具有更强的功能。关于参考间接方法，通过同时优化最小推进剂消耗和最终大地经度目标。这项研究是空间任务设计和卫星操作的重大进步，因为它同时利用了间接和直接方法的优势，比流行的间接方法具有更广泛的灵活性，并且比以前文献中发表的混合方法具有更强的功能。