  This paper addresses the computation of Delta-V-optimal, safe, relative orbit
reconfigurations for satellite formations in a centralized fashion. The
formations under consideration comprise an uncontrolled chief spacecraft flying
with an arbitrary number, N, of deputy satellites, where each deputy is
equipped with a single electric thruster. Indeed, this represents a
technological solution that is becoming widely employed by the producers of
small-satellite platforms. While adopting a single electric thruster does
reduce the required power, weight, and size of the orbit control system, it
comes at the cost of rendering the satellite under-actuated. In this setting,
the satellite can provide a desired thrust vector only after an attitude
maneuver is carried out to redirect the thruster nozzle opposite to the desired
thrust direction. In order to further extend the applicability range of such
under-actuated platforms, guidance strategies are developed to support
different reconfiguration scenarios for N-satellite formations. This paper
starts from a classical non-convex quadratically constrained trajectory
optimization formulation, which passes through multiple simplifications and
approximations to arrive to two novel convex formulations, namely a
second-order cone programming formulation, and a linear programming one. Out of
five guidance formulations proposed in this article, the most promising three
were compared through an extensive benchmark analysis that is applied to
fifteen of the most widely-used solvers. This benchmark experiment provides
information about the key distinctions between the different problem
formulations, and under which conditions each one of them can be recommended.
