Large constellations assessment and optimization in LEO space debris environment

Recent plans for large constellations in Low-Earth Orbit have opened the debate on both their vulnerability and their influence on the already hazardous space debris environment. In fact, given that large constellations normally employ satellites of small size, there might be situations in which cm-size debris could have enough energy to cause fragmentation of a significant part of these spacecraft upon impact, while smaller debris could affect the functionalities of critical subsystems, even compromising the success of disposal operations planned at end-of-life. In this context, this paper investigates: (1) collisions with large objects that could initiate the fragmentation of a significant part of the satellite, and (2) impacts with small debris that might perforate the spacecraft hull thus causing relevant performance/functionality degradation. These two points are merged in a simple statistical tool for risk assessment, which analyses the effects of the main parameters of the constellations on its vulnerability (i.e. operational life, number of satellites, spacecraft cross section, satellites reliability). In more details, the tool relates impact probability (for both small and large debris) to the ballistic response of spacecraft structures and protections, defining the critical configurations that might compromise the expected disposal operations. This method requires a limited knowledge of the spacecraft internal layout, as it is based on a statistical analysis of impact damage instead of a complete evaluation of the vulnerability of each subsystem. In parallel, non-debris related failures are also investigated and statistic models of spacecraft reliability characteristic are proposed. Among the results, it is shown that reducing the lifetime of individual satellites in a constellation might improve the success rate of post-mission disposal, thanks to the reduction of the spacecraft exposure to the space environment with the consequential degradation of its performance. On the other hand, reducing the lifetime would seriously affect the debris environment: the increase in traffic in the most crowded altitudes would be not counterbalanced by the higher post mission disposal success rate, causing an overall increase of the total number of uncontrolled resident objects.     

低轨巨型星座构型设计与控制研究进展与展望

近年来低轨星座计划发展迅速,低轨巨型星座已成为全球争夺空间战略资源的"新战场".首先,概述了Telesat、OneWeb、Starlink等低轨巨型星座计划的发展现状,以及中国互联网星座计划的基本情况.在此基础上,分别从星座的任务需求、覆盖特性、摄动补偿和备份策略4个方面,综述了星座的构型设计方法及其特点.然后,根据卫...     

基于TLE的Starlink星座第一阶段部署情况分析

近年来,随着卫星技术的快速发展和低轨（low earth orbit,LEO）卫星宽带互联网建设需求的不断增加,低轨大规模星座发展日新月异。针对Starlink星座初始化部署问题,首先论述了“星链”（Starlink）星座现状,分析在轨卫星高度变化。然后利用公开的两行轨道根数（two-line element,TLE）,从卫星发射入轨、轨道面分布两个方面,简要分析了Starlink星座的部署情况,给出升交点的变化规律;同时仿真分析了Starlink星座对地面的覆盖性能。最后,给出星座轨道面和相位分布、故障卫星处置以及可见卫星数量。所分析的结果以期为中国未来部署大规模LEO星座的建设提供借鉴。     

Assessment of the close approach frequency and collision probability for satellites in different configurations of large constellations

The Earth orbital environment is drastically changing due to an intensification of the space activities. In particular, several projects of large constellations, proposed for the next years for communications purpose like global internet access, Internet of Things, or for Earth observations, will lead to the deployment of several thousands of new satellites at an unprecedented rate. It is a crucial challenge for space traffic management, which will deal with a great number of satellite conjunctions, potentially causing a collision with damaging consequences for the constellation itself and the space environment sustainability.In this paper, we investigate the close approach frequency and the cumulative collision probability for each referenced constellation. For this purpose, we compute the orbital evolution of satellites in different constellations during the lifecycle, from the deployment to the decommissioning, and we apply the CUBE algorithm and the Foster method to assess the collision probability with the background space debris population assuming a constant uncertainty in position. We show the variation of risk defined by the close approach frequency and the cumulative collision probability as a function of the proposed configuration. In particular, satellites of the Iridium and Kuiper constellation, but also satellite of the Telesat constellation on polar orbits are the most exposed at a collision. Moreover, the decommissioning phase contribute for a major part to the final cumulative collision probability.     

一种双基站低轨道区域覆盖δ星座设计

在双基站理论研究基础上 ,进行了定倾角区域性覆盖双基站δ星座设计 ,采用倾角为 41°的回归轨道 ,用点覆盖数值仿真的方法设计了对地面站与空间站的一重覆盖与二重覆盖下的星座构型。且星座中各星之间 ,各星与空间站之间均可建立星际链路 ,保证数据在空间站、地面站及星座之间连续传递     

Low Earth orbit constellation design using a multi-objective genetic algorithm for GNSS reflectometry missions

Spaceborne global navigation satellite system reflectometry (GNSS-R) is an innovative bistatic radar remote sensing technique utilizing low Earth orbit (LEO) based GNSS-R instruments to acquire GNSS L-band opportunistic signals for measuring geophysical parameters. A GNSS-R LEO constellation with an optimization design for its specialized missions is very significant and necessary. However, the constellation design involves multi-parameter and multi-objective optimization, and the classical analytic solution is not capable of such a complicated issue. This study proposes a multi-objective LEO constellation design method with a genetic algorithm (GA) and presents a framework for designing two GNSS-R LEO constellations, termed “lower-latitude constellation” for typhoons and hurricanes observation in the tropics and “global constellation” for global geophysical parameter measurements. Then, the observation capability of both designed constellations is evaluated in terms of the number of reflection points, spatial coverage density, and revisit time to verify the GA efficiency in LEO constellation design. Results show that the two designed LEO constellations with high fitness function values possess optimal orbit parameter set configuration and outperform the existing CyGNSS constellations in observation performance. Compared with CyGNSS, the number of reflection points observed by the lower-latitude constellation and the global constellation increases by 38% and 45%, as well as the spatial coverage density increases by 28% and 36%. The revisit time for the lower-latitude constellation is reduced by 0.29 h, whereas the revisit time for the global constellation increases by one hour.     

Orbit Design for Twin-spacecraft Space VLBI

Space Very Long Baseline Interferometry (S-VLBI) is an aperture synthesis technique utilizing an array of radio telescopes including ground telescopes and space orbiting telescopes. It can achieve much higher spatial resolution than that from the ground-only VLBI. In this paper, a new concept of twin spacecraft S-VLBI has been proposed, which utilizes the space-space baselines formed by two satellites to obtain larger and uniform uv coverage without atmospheric influence and hence achieve high quality images with higher angular resolution. The orbit selections of the two satellites are investigated. The imaging performance and actual launch conditions are all taken into account in orbit designing of the twin spacecraft S-VLBI. Three schemes of orbit design using traditional elliptical orbits and circular orbits are presented. These design results can be used for different scientific goals. Furthermore, these designing ideas can provide useful references for the future Chinese millimeter-wave S-VLBI mission.      

基于覆盖圆的太阳同步回归轨道卫星目标轨迹调整方法

遥感卫星星座在环境监测、地理测绘等领域运用中,需要考虑目标轨迹分布的优化问题.轨迹分布与星座的重访能力和进出站间隔保持等应用需求密切相关.目前对星下点轨迹分布的优化和调整还缺乏准确实用的方法,存在卫星数目增多带来的计算量增加问题和对多种需求综合考虑不够的问题.为了克服现有技术的不足,解决太阳同步回归轨道遥感卫星星座的目...     

移动通信卫星经济性分析

由小型近地轨道卫星组成星座,实现移动通信服务,是卫星通信发展的重要方向。近地轨道卫星和地球静止轨道卫星用作移动通信卫星网,各有其优缺点。文章从经济性角度对两类卫星网进行了比较,重点是对不同高度的轨道(包括低、中、地球静止)的移动通信系统的空间部分成本——卫星星座的研制成本与发射成本进行分析比较,给出了具体的运算公式和计算结果。其结论是:轨道高度越低,卫星网的成本越高;地球静止轨道卫星网的成本最低。但是,决定是否发展小型近地轨道通信卫星网,不能仅考虑经济因素,还要考虑对技术进步的推动作用。     

Analysis on navigation accuracy of high orbit spacecraft based on BDS GEO and IGSO satellites

To make up for the insufficiency of earth-based TT&C systems, the use of GNSS technology for high-orbit spacecraft navigation and orbit determination has become a new technology. It is of great value to applying Geosynchronous Earth Orbit (GEO) and Inclined GeoStationary Orbit (IGSO) navigation satellites for supporting the navigation of high-orbit spacecraft since there are three different types of navigation satellites in BeiDou Navigation Satellite System (BDS): Medium Earth Orbit (MEO), GEO and IGSO. This paper conducts simulation experiments based on Two-Line Orbital Element (TLE) data to analyze and demonstrate the role of these satellites in the navigation of high-orbit spacecraft. Firstly, the spacecraft in GEO was used as the target satellite to conduct navigation experiments. Experiments show that for the spacecraft on the GEO orbit, after adding GEO and IGSO respectively on the basis of receiving MEO navigation satellite signals, the accuracies were improved by 7.22 % and 6.06 % respectively. When adding both GEO and IGSO navigation satellites at the same time, the accuracy can reach 16 m. In the second place, navigation and positioning experiments were carried out on three high elliptical orbit (HEO) satellites with different semimajor axis (32037.2 km, 42385.9 km, 67509.6 km). The experiments show that the number of visible satellites has been improved significantly after adding GEO and IGSO navigation satellites at the same time. The visible satellites in these three orbits were improved by 32.84 %, 41.12 % and 37.68 %, respectively compared with only observing MEO satellites.The RMS values of the navigation positioning errors of these three orbits are 25.59 m, 87.58 m and 712.48 m, respectively.     

基于星间测量的卫星星座 自主导航算法

自主导航能力是新一代导航星座的重要特性,利用卫星星间相对测量实现星座自主导航,是实现导航星座自主运行的基础.基于相对测量的导航卫星自主导航问题,将导致测量方程和状态方程的高度非线性,对导航算法提出了新的要求.在总结前人工作的基础上,提出了一种星载导航算法方案:利用三颗卫星之间的相对矢量在惯性空间的投影作为测量量,利用高精度星载轨道预报器作为系统的状态方程,使用SRUKF(Square Root Unscented Kalman Filter)滤波算法同时对三颗卫星的位置进行估计.仿真结果表明,该方案具有可行性,并且当轨道预报器的精度较高时有可能在100d内实现5m的导航精度.      

基于GNSS的高轨卫星定位技术研究

利用全球卫星导航系统(GNSS)进行导航定位具有全球、全天候、实时和高精度的优点,应用于高地球轨道(HEO)卫星的定位,能够提供精确的轨道和姿态确定,并且可以克服目前主要利用地面测控系统对HEO卫星进行定位的设备复杂、投资高等缺点,使得自主导航成为可能.本文对利用GNSS的高轨卫星定位相关技术进行了研究,分析了单一GNSS系统和多个GNSS组合系统的卫星可见性、动态性和几何精度因子(GDOP).通过仿真分析表明,利用组合GNSS系统并通过提高GNSS接收机灵敏度的方法,可以解决GNSS进行HEO卫星定位的相关问题,并能保证HEO卫星定位精度的要求.      

大规模卫星星群域管控策略设计

针对大规模卫星星群单节点管控带来的系统通联性差、地面资源依赖度高等问题,提出了分层管理、域内自治、动态维护的卫星星群分布式域管控策略。首先,设计了衡量卫星节点管控能力的静态指数及动态指数,并提出了多因素加权的星群簇首选择方法。其次,提出了通过逐层择优的方式进行域结构初始化的算法流程。最后,根据星群变化情形,提出了基于事件触发的动态时间片域管控方法,保证了大规模星群在全任务周期内能维持相对稳定的管控构型。仿真结果表明,所提出的域管控策略能够有效完成对目标星群的簇首选择、域初始化及动态维护过程,并保持域结构的稳定。实现了目标星群在空间中的域结构划分管理,使地面直接参与管理的卫星节点数目降至原管理模式的14%,有效解决了星群管控严重依赖地面资源的相关问题。     

遗传算法在星座多星接近轨道优化中的应用

以三颗非共轨的Walker星座卫星为研究对象, 对航天器无需变轨与其接近的可能性进行研究. 将Lambert方法得到的航天器轨道作为初始轨道, 利用遗传算法对初始轨道进行优化. 对初始轨道在参考时刻位置和速度的改变量进行编码,形成对应的种群. 以航天器与星座卫星之间的最近距离为适应度函数, 通过种群的繁殖得到优化结果. 结合仿真算例, 分析了最小二乘算法和遗传算法在轨道优化中的优劣以及接近过程中轨道摄动的影响. 结果表明, 遗传算法适用于所提出的轨道改进问题. 研究结果可为单航天器无需变轨对星座多星接近问题提供理论依据.      

Scheduling algorithms for rapid imaging using agile Cubesat constellations

Distributed Space Missions such as formation flight and constellations, are being recognized as important Earth Observation solutions to increase measurement samples over space and time. Cubesats are increasing in size (27U, ～40?kg in development) with increasing capabilities to host imager payloads. Given the precise attitude control systems emerging in the commercial market, Cubesats now have the ability to slew and capture images within short notice. We propose a modular framework that combines orbital mechanics, attitude control and scheduling optimization to plan the time-varying, full-body orientation of agile Cubesats in a constellation such that they maximize the number of observed images and observation time, within the constraints of Cubesat hardware specifications. The attitude control strategy combines bang-bang and PD control, with constraints such as power consumption, response time, and stability factored into the optimality computations and a possible extension to PID control to account for disturbances. Schedule optimization is performed using dynamic programming with two levels of heuristics, verified and improved upon using mixed integer linear programming. The automated scheduler is expected to run on ground station resources and the resultant schedules uplinked to the satellites for execution, however it can be adapted for onboard scheduling, contingent on Cubesat hardware and software upgrades. The framework is generalizable over small steerable spacecraft, sensor specifications, imaging objectives and regions of interest, and is demonstrated using multiple 20?kg satellites in Low Earth Orbit for two case studies – rapid imaging of Landsat’s land and coastal images and extended imaging of global, warm water coral reefs. The proposed algorithm captures up to 161% more Landsat images than nadir-pointing sensors with the same field of view, on a 2-satellite constellation over a 12-h simulation. Integer programming was able to verify that optimality of the dynamic programming solution for single satellites was within 10%, and find up to 5% more optimal solutions. The optimality gap for constellations was found to be 22% at worst, but the dynamic programming schedules were found at nearly four orders of magnitude better computational speed than integer programming. The algorithm can include cloud cover predictions, ground downlink windows or any other spatial, temporal or angular constraints into the orbital module and be integrated into planning tools for agile constellations.     

基于参考轨道的Walker星座相对相位保持策略

针对高轨道Walker全球星座相对相位保持问题,在分析星座几何结构演化规律基础上,提出了一种基于动态调整参考轨道的星座相对相位保持策略.该参考轨道的半长轴取星座所有卫星的平均轨道半长轴的平均值,通过计算各卫星相对参考轨道的相对相位偏差以及变化率,而后根据有关维持的约束条件来选择合适的卫星进行站点保持,使得所有卫星的相对参考轨道的相位偏差不超过允许值.当一旦有卫星进行了站点保持,则参考轨道就重新统计确定.文章通过一个12颗MEO卫星构成的Walker-δ星座的分析算例,表明这种相对保持策略可以减少星座的站点维持次数.本文提出的方法可以为我国今后卫星导航星座的维持提供参考.     

Downsizing an orbital space robot: A dynamic system based evaluation

Small space robots have the potential to revolutionise space exploration by facilitating the on-orbit assembly of infrastructure, in shorter time scales, at reduced costs. Their commercial appeal will be further improved if such a system is also capable of performing on-orbit servicing missions, in line with the current drive to limit space debris and prolong the lifetime of satellites already in orbit. Whilst there have been a limited number of successful demonstrations of technologies capable of these on-orbit operations, the systems remain large and bespoke. The recent surge in small satellite technologies is changing the economics of space and in the near future, downsizing a space robot might become be a viable option with a host of benefits. This industry wide shift means some of the technologies for use with a downsized space robot, such as power and communication subsystems, now exist. However, there are still dynamic and control issues that need to be overcome before a downsized space robot can be capable of undertaking useful missions. This paper first outlines these issues, before analyzing the effect of downsizing a system on its operational capability. Therefore presenting the smallest controllable system such that the benefits of a small space robot can be achieved with current technologies. The sizing of the base spacecraft and manipulator are addressed here. The design presented consists of a 3 link, 6 degrees of freedom robotic manipulator mounted on a 12U form factor satellite. The feasibility of this 12U space robot was evaluated in simulation and the in-depth results presented here support the hypothesis that a small space robot is a viable solution for in-orbit operations.     

Introducing the law games: Predicting legal liability and fault in satellite operations

Over recent times there has been a rise in the number of objects placed into Earth orbit. With various countries licensing a number of large constellations, the orbital population is set to increase dramatically. A significant number of technical advances have facilitated this and, in the UK and elsewhere, this has been matched by the updating of legislation and an increased policy focus on the need for increased space surveillance and tracking. The rise of large constellations coupled with an increasing number of experimental techniques such as active debris removal or on-orbit servicing procedures means that establishing fault will be crucial if litigation is to be successful. In doing this, any legal proceedings will look at both norms of behaviour, deviation from which will point towards fault and the types and standard of evidence that will be required.This paper will outline these problems in detail. It will be proposed that what is required to map out the contours of liability are both codification of the norms for satellite operations and clarity on protocols for evidence gathering in cases where fault may be contested in orbital operations. This discussion will identify that a way in which this could be achieved is by the use of “space law games”. These are simulations, similar to military war games, in which fictional scenarios could highlight some of the key legal issues that might need to be dealt with. The paper will outline some of the ways in which the law games might work and pose questions as to what data and other considerations will be needed to make such simulations meaningful.