Low-Thrust Control for IGSO Satellite Constellation Using an Improved Convex Optimization

Satellite constellation orbiting in Inclined Geosynchronous Orbits (IGSO), such as Beidou-3 system (China, 2019) and GSSAP satellites (USA, 2014), provide a promising alternative to the increasingly crowded Geostationary Earth Orbit (GEO) belt as well as an extension to the space situational awareness system. On the other hand, selected highly elliptical orbits at geosynchronous altitude as well as the electric propulsion systems present key tools to obtain a low delta-V budget. However, new challenges arise despite the obvious benefits of low-thrust operations in IGSO constellation. Real and multiple constraints, including shadow constraints, on-off profile of low thrust, result in a narrower solution space and lower optimization efficiency. This paper aims to present an improved convex optimization algorithm towards low-thrust control problems as well as a comparison between the improved convex optimization and the indirect optimization. The convex optimization tool is introduced due to two main benefits: faster computational efficiencies and more reliable accesses to global optimal solution. A semi-analytical orbit propagation tool is first introduced as the preliminaries. Afterwards, the long-term dynamic behaviors beneficial to the frozen orbit design and the end-of-life disposal are analyzed through a phase space study. Then, the indirect optimization method as well as an efficient initial costate guess method is revisited to show the special point, which can help achieve a quick convergence. Finally, the improved convex optimization algorithm, including a linearization step with respect to two special points and a convexification step, is proposed. Simulation are used compare the performances of two methods in both eccentricity vector space and inclination vector space.