Autonomous control of a reconfigurable constellation of satellites on geostationary orbit with artificial potential fields

This paper presents a method of controlling a constellation of small satellites in Geostationary Earth Orbit (GEO) such that the constellation is able to reconfigure - changing the angular position of its members relative to the Earth’s surface in order to cluster them above particular target longitudes. This is enabled through the use of an artificial potential function whose minimum value corresponds to a state where the phase angle between each satellite and its intended target is minimised. By linking the tangential low-thrust acceleration of each satellite to this artificial potential function, the altitude of each satellite relative to the nominal GEO altitude is manipulated in order to achieve the required drift rate. A demonstration of the efficacy of the method is given through a simple test case in which a constellation of 90 satellites converge upon 3 equatorial targets, with each target requiring the attention of a varying number of spacecraft from the constellation. The constellation performance is analysed in terms of the time taken for the satellites to converge over their targeted longitudes and the Dv required to actuate the phasing maneuvers. This analysis is performed across a parameter space by varying the number of satellites in the constellation, the number of targeted longitudes, and a parameter representing the maximum acceleration of the thruster