Optimal low thrust transfers among asteroid belt asteroids.

This dataset contains > 3,000,000 optimal low-thrust transfers between asteroids in the belt. It was created from the asteroids data released during the 12th edition of the Global Trajectory optimization competitions (see the official GTOC portal) and considering a spacecraft having an initial mass ms in the range [700, 8000] kg, a maximum thrust TM = 0.6 N with a specific impule Isp = 4000 s, resulting in possible initial acceleration levels in the range [7.5 1e-5, 8.6 1e-4] m/s^2. The dataset was developed in the context of our contribution to the International Symposium on Space Flight Dynamics 2024 (ISSFD). Starting from a sampled asteroid couple (As Af), and an initial mass ms: The minimum time transfer tof_min is found solving the corresponding optimal control problem (in a Keplerian dynamics) and the resulting transfer recorded in a first dataset. In some cases, for several fixed tof > tof_min the maximum final mass transfer is found solving the corresponding optimal control problem and the resulting transfer recorded in a second dataset. Each line in the csv dataset correspond to a specific optimal transfer (randevouz) and contains the following information: [xs, ys, zs, vxs, vys, vzs, xf, yf, zf, vxf, vyf, vzf, ms, tof, mf, MIMA, MIMA2, MIMA3, mfms_approx] , i.e. the starting (s) spacecarft state, the final (f) spacecraft state, the starting spacecraft mass ms, the time of flight tof and the final mass mf. Several analytical approximations are also reported: MIMA, MIMA2, MIMA3, mfms_approx. The analytical approximation MIMA is derived and published in: Hennes, D., Izzo, D., & Landau, D. (2016, December). Fast approximators for optimal low-thrust hops between main belt asteroids. In 2016 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 1-7). IEEE. A second improved version (MIMA2) is derived and published in: Izzo, D., Märtens, M., L. Beauregard ..., G. Acciarini et al. "Asteroid Mining: ACT&Friends’ Results for the GTOC 12 Problem." to appear in Astrodynamics (Springer). and the final one, MIMA3, is derived and published in: G. Acciarini, Beauregard L. and Izzo, D., Computing low-thrust transfers in the asteroid belt, a comparison between astrodynamical manipulations and a machine learning approach. ISSFD conference, Darmstadt, 2024. The MIMAs approximate the maximum initial mass a spacecarft can have to perform a given fixed time transfer (that also is, in the optimal time of flight transfer dataset ms). For these transfers no coast arc exists. In all other cases, a related analytical approach can be used to approximate mf. The result, when available is added to the dataset as mfms_approx (approximating the ratio mf/ms, an approximation for the final mass can be retreived multiplying by ms) NOTE: the MIMAs and mfms_approx sometimes fail numerically or conceptually in which case a nan is reported or a 'nonsensical' number (e.g. lower than the actual starting mass).

本数据集包含超过300万次主带小行星间的最优低推力转移轨道。本数据集基于第12届全球轨道优化竞赛（Global Trajectory Optimization Competitions，简称GTOC，可参见官方GTOC门户）发布的小行星数据构建，同时考虑了初始质量$m_s$介于700~8000 kg、最大推力$T_M=0.6$ N、比冲$I_{sp}=4000$ s的航天器，由此得到的初始加速度范围为$7.5 imes10^{-5} sim 8.6 imes10^{-4}$ m/s²。

本数据集的开发工作是针对我们向2024年国际空间飞行动力学研讨会（International Symposium on Space Flight Dynamics，简称ISSFD）提交的研究成果展开的。

首先从采样得到的小行星对$(A_s, A_f)$与初始质量$m_s$出发，通过求解对应最优控制问题（基于开普勒动力学）得到最小时间转移轨道$t_{of,min}$，并将该转移轨道的相关信息存入第一数据集。在部分场景中，针对多个大于$t_{of,min}$的固定飞行时间$t_{of}$，通过求解对应最优控制问题得到最大终质量转移轨道，并将相关信息存入第二数据集。

该CSV数据集的每一行对应一次特定的最优转移交会（rendezvous）任务，包含以下字段：$[x_s, y_s, z_s, v_{x_s}, v_{y_s}, v_{z_s}, x_f, y_f, z_f, v_{x_f}, v_{y_f}, v_{z_f}, m_s, t_{of}, m_f, ext{MIMA}, ext{MIMA2}, ext{MIMA3}, ext{mfms\_approx}]$，即航天器的初始位置$(x_s,y_s,z_s)$与初始速度$(v_{x_s},v_{y_s},v_{z_s})$、最终位置$(x_f,y_f,z_f)$与最终速度$(v_{x_f},v_{y_f},v_{z_f})$、航天器初始质量$m_s$、飞行时间$t_{of}$与最终质量$m_f$。此外还包含多个解析近似结果：$ ext{MIMA}$、$ ext{MIMA2}$、$ ext{MIMA3}$以及$ ext{mfms\_approx}$。

解析近似方法$ ext{MIMA}$的推导与发表文献如下：Hennes, D., Izzo, D. 与 Landau, D.（2016年12月）《主带小行星间最优低推力跳跃轨道的快速近似方法》，收录于2016年IEEE计算智能研讨会（IEEE Symposium Series on Computational Intelligence，简称SSCI），第1-7页，IEEE出版社。

第二种改进版本$ ext{MIMA2}$的推导与发表文献如下：Izzo, D., Märtens, M., L. Beauregard等，"小行星采矿：ACT&团队针对GTOC第12届竞赛问题的研究成果"，将发表于《Astrodynamics》（Springer出版社）。

最终版本$ ext{MIMA3}$的推导与发表文献如下：G. Acciarini、Beauregard L.与Izzo, D.，《小行星带低推力转移轨道计算：天体动力学操控与机器学习方法的对比》，2024年达姆施塔特ISSFD会议。

$ ext{MIMA}$系列方法用于近似航天器执行给定固定时间转移轨道时所能承载的最大初始质量（在最小飞行时间转移轨道数据集的场景中，该初始质量即为$m_s$）。对于这类转移轨道，不存在滑行弧段。在其余场景中，可采用相关解析方法近似计算最终质量$m_f$。若该近似结果可用，则将其以$ ext{mfms\_approx}$的形式存入数据集（$ ext{mfms\_approx}$为$m_f$与$m_s$的比值近似，最终质量的近似值可通过乘以$m_s$得到）。

注意：$ ext{MIMA}$系列方法与$ ext{mfms\_approx}$有时会出现数值或概念上的失效，此时将返回$ ext{NaN}$（非数值）或无意义的数值（例如小于实际初始质量的值）。

搜集汇总

背景与挑战

背景概述

该数据集包含超过300万条小行星带小行星间的最优低推力转移数据，基于全球轨迹优化竞赛数据创建，适用于航天器初始质量700-8000公斤、推力0.6N的场景。数据集分为最小时间转移和固定时间最大质量转移两部分，每条记录包含航天器状态、质量和飞行时间等详细信息，并附有分析近似方法，旨在支持小行星带低推力转移研究和优化。