Egalitarian Peer-to-Peer Satellite Refueling Strategy

Abstract

In this paper we revisit the problem of peer-to-peer refueling of a satellite constellation in orbit with propellant. In particular, we propose the egalitarian peer-to-peer refueling strategy that relaxes the restriction on the active satellites to return to their original orbital slots after all fuel exchanges have been completed. We formulate the problem as a minimum cost flow problem in the so-called constellation network, and minimize the total V subject to flow balance constraints, along with certain additional constraints introduced to avoid conflicts between active and passive satellites. Recognizing that the actual objective is to minimize the total fuel expenditure, instead of V, we also propose a method to improve the results by performing a local search around the minimum-V solution. We also provide explicit upper and lower bounds on the suboptimality of the obtained results. With the help of numerical examples, it is shown that the proposed egalitarian peer-to-peer refueling strategy leads to considerable reduction in terms of the total fuel expenditure over the baseline peer-to-peer strategy.

A Note on Peer-to-Peer Satellite Refueling Strategies

“…Clearly, one could restrict the solutions to be such that starting and ending slots need to be identical, that is, φ i = φ k . Although this would make the problem easy (see Section 3), it has been illustrated that this might lead to suboptimal solutions, i.e., solutions with a larger than necessary fuel cost [2]. Let us consider a triple (i, j, k) and the associated cost c(i, j, k).…”

“…We revisit the peer-to-peer refueling problem, in which the maneuvering satellites are allowed to interchange their orbital positions [2]. We show that the problem is computationally hard, by reducing it to a special case of the three-index assignment problem.…”

“…The following problem was described in Dutta and Tsiotras [2]. Given are n satellites distributed over n slots in a circular orbit.…”

“…Each satellite is denoted as either fuel-deficient, or fuel-sufficient; this depends on whether the satellite has at least a minimum required amount of fuel. The idea put forward in [2] is that the satellites can redistribute the fuel among themselves by engaging in fuel exchange in pairs; for each pair, a satellite moves (performs an orbital transfer) to rendezvous with another satellite, exchanges fuel, and returns back to any available slot. This redistribution of available fuel among the satellites is an integral part of a mixed refueling strategy, which is much more fuel-efficient than supplying fuel via a single service-vehicle, particularly with an increasing number of satellites in the constellation [2].…”

Optimal Scheduling of GEO On-orbit Refuelling with Uncertain Object Satellites

“…Bo et al [6] presented a new refuelling pattern based on formation flying, and proposed two strategies to address the problem. Tsiotras and Dutta [1,[7][8][9][10] focused on OOR missions using peer-to-peer (P2P) strategy. In the investigations mentioned above, the object satellites are always definite, and much work focuses on fuel cost only.…”