EXTREMA: Ballistic capture sets at Mars with initial epoch December 9, 2023
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EXTREMA (short for Engineering Extremely Rare Events in Astrodynamics for Deep-Space Missions in Autonomy) enables self-driving spacecraft, challenging the current paradigm under which spacecraft are piloted in the interplanetary space. Deep-space guidance, navigation, and control applied in a complex scenario is the subject of EXTREMA, which wants to engineer ballistic capture in a totally autonomous fashion. EXTREMA is erected on three pillars. Pillar 1 is on autonomous navigation. Pillar 2 involves autonomous guidance and control. Pillar 3 deals with autonomous ballistic capture, the focus of this work. The project has been awarded a European Research Council (ERC) Consolidator Grant in 2019. In Pillar 3 it is investigated how a spacecraft can attain ballistic capture in autonomy. Ballistic capture is an event that occurs in extremely-rare occasions, and requires acquiring a proper state (position, velocity) far away from the target planet [1]. Massive numerical simulations are required to find the specific conditions that support capture [2]. On average, 1 out of 10,000 conditions explored by the algorithm grants capture [3]. The union of these points defines the capture set, which in turn is used to find the capture corridors: these are streams of orbits that can be targeted far away from the planet and that guarantee ballistic capture. The data set is made of two items containing initial conditions of weakly-stable, unstable, crash, moon-crash, and capture sets at Mars. The first is a text file containing initial conditions used to compute time regressions. The second item is a text file containing 100,000 initial conditions generated randomly in the search space and used to compute the quality criterion of the differential algebra mapping. All initial conditions have initial epoch 09 DEC 2023 00:45:18.363 (UTC). The grid of initial conditions is built to maximize the capture ratio for Mars (see Figure 10 in [3]). Initial conditions are propagated in high-fidelity. The equations of motion of the restricted n-body problem including solar radiation pressure are considered. For additional information about the EXTREMA project visit the page extrema.polimi.it. The data set is associated to the following journal article: Article: Stable sets mapping with Taylor differential algebra with application to ballistic capture orbits around Mars Journal: Celestial Mechanics and Dynamical Astronomy Authors: Thomas Caleb (corresponding author: thomas.caleb@student.isae-supaero.fr), Gianmario Merisio, Pierluigi di Lizia, and Francesco Topputo DOI: 10.1007/s10569-022-10090-8 <strong>References</strong><br> [1] F. Topputo and E. Belbruno,'Earth–Mars transfers with ballistic capture', Celestial Mechanics and Dynamical Astronomy, Vol. 121, No. 4, 2015, pp. 329–346. DOI: 10.1007/s10569-015-9605-8.<br> [2] F. Topputo and E. Belbruno, 'Computation of weak stability boundaries: Sun–Jupiter system', Celestial Mechanics and Dynamical Astronomy, Vol. 105, No. 1-3, 2009, pp. 3–17. DOI: 10.1007/s10569-009-9222-5.<br> [3] Z.-F. Luo and F. Topputo, 'Analysis of ballistic capture in Sun–planet models', Advances in Space Research, Vol. 56, No. 6, 2015, pp. 1030–1041. DOI: 10.1016/j.asr.2015.05.042.
EXTREMA（全称为Engineering Extremely Rare Events in Astrodynamics for Deep-Space Missions in Autonomy，即面向自主深空任务的天体动力学极端稀有事件构建项目）旨在研发自主运行航天器，打破当前星际空间航天器需人工操控的主流范式。该项目的研究主题为复杂场景下的深空制导、导航与控制，目标是以完全自主的方式实现弹道捕获（ballistic capture）技术的工程化应用。本项目依托三大支柱展开：支柱1聚焦自主导航，支柱2涵盖自主制导与控制，支柱3则针对自主弹道捕获开展研究——这也是本项工作的核心。该项目于2019年荣获欧洲研究理事会（European Research Council, ERC）巩固级资助。 在支柱3的研究中，团队将探索航天器如何自主实现弹道捕获。弹道捕获是一类极为罕见的航天事件，需在远离目标行星的位置获取恰当的状态参数（位置、速度）[1]。为筛选出满足捕获条件的特定参数组合，需开展大规模数值模拟[2]。统计结果显示，算法探索的每10000组参数中，仅1组可实现捕获[3]。上述参数的集合构成捕获集，借此可进一步推导捕获走廊：即一系列可在远离目标行星的位置发起、并能确保实现弹道捕获的轨道流。 本数据集包含两类数据，均为火星轨道相关的弱稳定、不稳定、坠毁、月球坠毁以及捕获集初始条件。第一类为文本文件，内含用于计算时间回归的初始条件；第二类为文本文件，包含在搜索空间内随机生成的100000组初始条件，用于计算微分代数映射（differential algebra mapping）的质量准则。所有初始条件的初始历元均为2023年12月9日00:45:18.363（协调世界时UTC）。该初始条件网格的构建目标是最大化火星捕获率（详见文献[3]中的图10）。初始条件采用高保真度传播方式，所考虑的运动方程为包含太阳辐射压（solar radiation pressure）的限制性n体问题（restricted n-body problem）方程。 如需了解EXTREMA项目的更多详情，可访问官网extrema.polimi.it。本数据集关联以下期刊论文： > 论文标题：《基于泰勒微分代数的稳定集映射及其在火星弹道捕获轨道中的应用》（Stable sets mapping with Taylor differential algebra with application to ballistic capture orbits around Mars） > 期刊：《天体力学与动力学天文学》（Celestial Mechanics and Dynamical Astronomy） > 作者：Thomas Caleb（通讯作者邮箱：thomas.caleb@student.isae-supaero.fr）、Gianmario Merisio、Pierluigi di Lizia、Francesco Topputo > DOI：10.1007/s10569-022-10090-8 ### 参考文献 [1] F. Topputo与E. Belbruno，《地球-火星轨道转移的弹道捕获方法》，《天体力学与动力学天文学》，第121卷第4期，2015年，第329-346页。DOI: 10.1007/s10569-015-9605-8. [2] F. Topputo与E. Belbruno，《弱稳定边界的计算：太阳-木星系统》，《天体力学与动力学天文学》，第105卷第1-3期，2009年，第3-17页。DOI: 10.1007/s10569-009-9222-5. [3] Z.-F. Luo与F. Topputo，《太阳-行星模型下的弹道捕获分析》，《空间研究进展》，第56卷第6期，2015年，第1030-1041页。DOI: 10.1016/j.asr.2015.05.042.
