Optimal reconfiguration of satellite constellations with the auction algorithm

Traditionally, satellite constellation design has focused on optimizing global, zonal or regional coverage with a minimum number of satellites. In some instances, however, it is desirable to deploy a constellation in stages to gradually expand capacity. This requires launching additional satellites and reconfiguring the existing on-orbit satellites. Also, a constellation might be retasked and reconfigured after it is initially fielded for operational reasons. This paper presents a methodology for optimizing orbital reconfigurations of satellite constellations. The work focuses on technical aspects for transforming an initial constellation A into a new constellation, B, typically with a larger number of satellites. A general framework was developed to study the orbital reconfiguration problem. The framework was applied to low Earth orbit constellations of communication satellites. This paper specifically addresses the problem of determining the optimal assignment for transferring on-orbit satellites in constellation A to constellation B such that the total AV for the reconfiguration is minimized. It is shown that the auction algorithm, used for solving general network flow problems, can efficiently and reliably determine the optimum assignment of satellites of A to slots of B. Based on this methodology, reconfiguration maps can be created, which show the energy required for transforming one constellation into another as a function of type (Street-of-Coverage, Walker, Draim), altitude, ground elevation angle and fold of coverage. Suggested extensions of this work include quantification of the tradeoff between reconfiguration time and Delta V, multiple successive reconfigurations, balancing propellant consumption within the constellation during reconfiguration as well as using reconfigurability as an objective during initial constellation design. (c) 2007 Elsevier Ltd. All rights reserved.