Safe and Optimal <i>N</i> -Spacecraft Swarm Reconfiguration in Non-Keplerian Cislunar Orbits

This paper presents a novel fuel-optimal guidance and control methodology for spacecraft swarm reconfiguration in Restricted Multi-Body Problems (RMBPs) with considerations of passive safety, maintaining miss distance even under abrupt loss of control authority. The problem is casted as a optimal control problem in local toroidal coordinates, which is based on a local eigenspace of a quasi-periodic motion around the corresponding periodic orbit. This formulation enables a significant simplification of a novel set of passive safety constraints that leverages the quasi-periodic structure of RMBPs suited to large-scale swarm reconfiguration in cislunar orbits. The method is demonstrated in the Circular Restricted Three-Body Problem, the Elliptic Restricted Three-Body Problem, and the Bicircular Restricted Four-Body Problem. Furthermore, the optimized control profiles are validated in the full-ephemeris dynamics model. By extending and generalizing well-known concepts of relative orbital elements within the restricted two-body problem to the three- and four-body problems, this paper lays the foundation for practical control schemes of relative motion in cislunar space.