# Orbital Facility Location Problem for Satellite Constellation Servicing Depots

## TL;DR

This paper adapts the Facility Location Problem to optimize the placement of on-orbit servicing depots for satellite constellations in high-altitude orbits, considering transfer costs, launch costs, and orbital dynamics.

## Contribution

It introduces an orbital facility location model using binary linear programming and Lyapunov feedback control for transfer calculations, tailored for high-altitude satellite servicing.

## Key findings

- Optimized depot placement for Galileo and GPS constellations.
- Demonstrated cost-effective on-orbit servicing architectures.
- Validated approach with real satellite constellation data.

## 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 (MEO), is a unique dynamical environment where existing 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 round-trips between servicing depots and the client satellites of the constellation may be conceived. To this end, orbital facility location problem is a binary linear program, where the costs of operating and allocating the facility(ies) to satellites are considered in terms of the sum of Equivalent Mass to Low Earth Orbit (EMLEO), is proposed. 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 are taken into account as the cost to establish a given depot. The proposed approach is applied to designing on-orbit servicing depots for the Galileo and the GPS constellations.