Peer-to-Peer Refueling for Circular Satellite Constellations

In this paper, we study the scheduling problem arising from refueling multiple satellites in a circular constellation. It is assumed that there is no fuel delivered to the constellation from an external source. Instead, all satellites in the constellation are assumed to be capable of refueling each other (peer-to-peer refueling). The total time to complete the rendezvous maneuvers including the refueling itself is specified. During the refueling period each satellite may conduct a fuel exchange with at most one other satellite. Whenever two satellites perform a fuel transfer only one is active, that is, only one of the two satellites initiates an orbital transfer to rendezvous with the inactive satellite. After the transfer of fuel is completed, the active satellite returns to its original orbital slot. The goal is to equalize the fuel among the satellites in the constellation after one refueling period, while minimizing the total fuel consumed during the orbital transfers. It is shown that this problem can be formulated as a maximum-weight matching problem on the reduced constellation graph, which can be solved using standard numerical methods. Numerical results indicate the benefits of a P2P strategy over a single-spacecraft refueling strategy for constellations with a large number of satellites.