Orbital Facility Location Problem for Satellite Constellation Servicing Depots

Abstract

This work proposes an adaptation of the facility location problem for the optimal placement of on-orbit servicing depots for satellite constellations in high-altitude orbit. The high-altitude regime, such as medium Earth orbit, is a unique dynamic environment where low-thrust propulsion systems can provide the necessary thrust to conduct plane-change maneuvers between the various orbital planes of the constellation. As such, on-orbit servicing architectures involving servicer spacecraft that conduct roundtrips between servicing depots and the client satellites of the constellation may be conceived. To this end, a new orbital facility location problem formulation is proposed based on binary linear programming, in which the costs of operating and allocating the facility(ies) to satellites are optimized in terms of the sum of the effective mass to low Earth orbit (EMLEO). The low-thrust transfers between the facilities and the clients are computed using a parallel implementation of a Lyapunov feedback controller. The total launch cost of the depot, along with its servicers, propellant, and payload, is taken into account as the cost to establish a given depot. The proposed approach is applied to designing an on-orbit servicing depot architecture for the Galileo and the GPS constellations.