Coordinated Control of Relative Orbit of Co-Location Geostationary Satellites Using Game Theory

In this paper, a new strategy based on differential game theory is proposed to plan optimal maneuvers for collaborative station-keeping of a set of satellites co-located in an orbital slot in geostationary orbit. In this regard, two different system modes have been developed to design the corrective maneuvers of these satellites. It is essential for satellites to maintain a flight configuration, share information, and make common decisions in cooperative mode. A non-cooperative mode involves each satellite making its own decisions based on information received from other satellites. The inter-satellite link is also utilized to increase the automaticity of the satellites, which in turn could lead to reduction of the minimum distance between them, so that more satellites could be located in the orbital slot. Depending on the angle of view required, it is revealed that utilizing the optical inter-satellite link may consume more fuel than the use of the radio link. Additionally, a multi-objective particle swarm optimization (MOPSO) algorithm has been used in this article to calculate the optimal initial position of the satellites based on the co-location requirements and the frequency band used in the inter-satellite link. Simulation results show that the proposed methodology could significantly reduce the fuel consumption of three satellites that should be keep in one orbital slot in comparison with the traditional strategy based on eccentricity/inclination separation. Also, based on the case studies conducted by the authors, it is possible to optimally locate and control 20 satellites in a collective orbital slot without any interference.