# Self-Organizing Control of Mega Constellations for Continuous Earth Observation
## 1 Introduction  
In recent years, mega constellations consisting of thousands of satellites have received widespread attention due to their potential to provide high-speed and full-coverage telecommunication services. Commercial companies, such as SpaceX and OneWeb, have made their plans public to deploy mega constellations in low Earth orbits [1]. SpaceX have launched nearly 2000 Starlink satellites and started to provide global communication and Internet services. China plans to construct two Guowang low-Earth-orbit constellations, totaling 12,992 satellites for telecommunication services [2]. Such giant constellations are wonderful choices for performing Earth observation missions. Since they evenly distribute at low Earth orbits all over the globe, they can be used to collect huge amounts of data on gravity [3] and atmosphere [4] for analysis, and they can obtain high-resolution Earth images in real time [5]. Among these remote sensing missions, the priority is to provide continuous global coverage. Limited by the computation load of analytic and grid methods, traditional coverage analysis methods are suitable for constellations with less than 100 satellites [6; 7; 8]. For the requirement of quick analysis of mega constellations, [PERSON] et al. studied the geometric configuration of constellation projection points on Earth's surface [9]. The multi-satellite coverage problem is decomposed into a one-satellite coverage problem to solve both continuous and discontinuous coverageproblems. [PERSON] et al. proposed a continuous coverage analysis method based on 2D map theory [10]. The proposed method avoids redundant calculation of intersatellite positions and positions between the satellites and ground targets so that the time complexity does not increase significantly with the increase in satellites. [PERSON] et al. presented a systematic method for the design of continuous global coverage Walker and street-of-coverage constellations, by taking seven critical constellation properties (coverage, robustness, self-induced collision avoidance, launch, build-up, station-keeping, and end-of-life disposal) as design criteria [11]. However, the above studies rely on the overall motion information of the constellation, which will result in central ground control. To that end, this paper innovatively introduces the self-organizing concept of mega constellation control, and the emphasis is on maintaining continuous coverage. Two traditional constellation maintenance methods are the absolute station-keeping method and the relative station-keeping method [12; 13; 14]. For mega constellations, the former will result in frequent on-orbit maneuvers, while the latter relies on the overall configuration information, which is also inefficient because of the huge number of satellites. In this paper, self-organizing control indicates a decentralized and distributed control mechanism that requires the relative motion information of neighbor satellites only. By that means, constellation control will not be affected by the failure or development of constellation satellites. Artificial potential function (APF) is a commonly used self-organizing control method for its clear mathematical descriptions. Trajectories based on APF control are not planned explicitly but rather are shaped by the potential field in reaction to the changing environment. APF control has shown its potential in many close proximity scenarios, including satellite cluster reconfiguration [15; 16], collision avoidance [17], satellite rendezvous and docking [18; 19], etc. [PERSON] improved the APF from Cartesian coordinate form to relative orbital elements (ROEs) form so that the relative orbital dynamics can be reflected in APF control [20]. Our previous work realized reconfiguration, bounded flight, and collision avoidance for satellite clusters by means of ROE-based APF control [21; 22]. However, the relative motion distance between constellation satellites is much larger than that of close clusters.