  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.
