Safe and Optimal N-Spacecraft Swarm Reconfiguration in Non-Keplerian Cislunar Orbits

Abstract

This paper presents a novel fuel-optimal guidance and control methodology for spacecraft swarm reconfiguration in Restricted Multi-Body Problems (RMBPs) with a guarantee of passive safety, maintaining miss distance even under abrupt loss of control authority. A new set of constraints exploits a quasi-periodic structure of RMBPs to guarantee passive safety. Particularly, the condition for passive safety is expressed as simple geometric constraints by solving optimal control in Local Toroidal Coordinates, which is based on a local eigenspace of a quasi-periodic motion around the corresponding periodic orbit. The proposed formulation enables a significant simplification of problem structure, which is applicable 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 Bi-Circular 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.