Peer-to-peer refueling for circular satellite constellations

The scheduling problem arising from refueling multiple satellites in a circular constellation is studied. It is assumed that no fuel is 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 (P2P) 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 constelliation 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.