优化低推力轨迹的直接到直接映射

IF 2.7 1区 物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS
David Ottesen, Ryan P. Russell
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引用次数: 0

摘要

优化、多次旋转航天器轨迹的求解具有挑战性。在一类模型中,最佳直接解法和间接解法之间存在联系。对于最小化推力加速度平方的转移,引物矢量理论可将直接的多次脉冲操纵轨迹映射为间接的连续推力加速度等效轨迹。映射算法与如何获得直接解无关,只需要边界值问题求解器及其偏导数。在这项工作中,双体问题使用的是兰伯特求解器。映射很简单,因为冲动机动和共态共享最佳轨迹周围的同一线性空间。数值结果表明,随着脉冲数和段数的增加,直接的海岸-脉冲解收敛于间接的连续解。通过一组改变半长轴、偏心率和倾角的三个多旋转、多段示例,探索了双体设计空间。前两个例子涉及半长轴或偏心率的微小变化,第三个例子是转移到地球同步轨道。使用单个处理器,转数在 10 到 100 圈时的优化运行时间为几秒到几分钟,转数多达 500 圈时的优化运行时间约为一小时。这些推力-加速度-平方解决方案中的任何一个都是很好的候选方案,可以在实际约束条件下开始同调,以解决更高保真的最小化问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Direct-to-indirect mapping for optimal low-thrust trajectories

Optimal, many-revolution spacecraft trajectories are challenging to solve. A connection is made for a class of models between optimal direct and indirect solutions. For transfers that minimize thrust-acceleration-squared, primer vector theory maps direct, many-impulsive-maneuver trajectories to the indirect, continuous-thrust-acceleration equivalent. The mapping algorithm is independent of how the direct solution is obtained and requires only a solver for a boundary value problem and its partial derivatives. A Lambert solver is used for the two-body problem in this work. The mapping is simple because the impulsive maneuvers and co-states share the same linear space around an optimal trajectory. For numerical results, the direct coast-impulse solutions are demonstrated to converge to the indirect continuous solutions as the number of impulses and segments increases. The two-body design space is explored with a set of three many-revolution, many-segment examples changing semimajor axis, eccentricity, and inclination. The first two examples involve a small change to either semimajor axis or eccentricity, and the third example is a transfer to geosynchronous orbit. Using a single processor, the optimization runtime is seconds to minutes for revolution counts of 10 to 100, and on the order of one hour for examples with up to 500 revolutions. Any of these thrust-acceleration-squared solutions are good candidates to start a homotopy to a higher-fidelity minimization problem with practical constraints.

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来源期刊
Astrodynamics
Astrodynamics Engineering-Aerospace Engineering
CiteScore
6.90
自引率
34.40%
发文量
32
期刊介绍: Astrodynamics is a peer-reviewed international journal that is co-published by Tsinghua University Press and Springer. The high-quality peer-reviewed articles of original research, comprehensive review, mission accomplishments, and technical comments in all fields of astrodynamics will be given priorities for publication. In addition, related research in astronomy and astrophysics that takes advantages of the analytical and computational methods of astrodynamics is also welcome. Astrodynamics would like to invite all of the astrodynamics specialists to submit their research articles to this new journal. Currently, the scope of the journal includes, but is not limited to:Fundamental orbital dynamicsSpacecraft trajectory optimization and space mission designOrbit determination and prediction, autonomous orbital navigationSpacecraft attitude determination, control, and dynamicsGuidance and control of spacecraft and space robotsSpacecraft constellation design and formation flyingModelling, analysis, and optimization of innovative space systemsNovel concepts for space engineering and interdisciplinary applicationsThe effort of the Editorial Board will be ensuring the journal to publish novel researches that advance the field, and will provide authors with a productive, fair, and timely review experience. It is our sincere hope that all researchers in the field of astrodynamics will eagerly access this journal, Astrodynamics, as either authors or readers, making it an illustrious journal that will shape our future space explorations and discoveries.
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