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

TL;DR

This work develops a fuel-efficient, passively safe method for reconfiguring swarms of spacecraft in non-Keplerian cislunar environments by exploiting quasi-periodic relative motion on a Quasi-Periodic Invariant Torus. Central to the approach is the Local Toroidal Coordinates (LTC), a mode-isolating frame that simplifies safety constraints and enables decentralized, per-pair optimization within an MPC-enabled, all-ephemeris validation loop. Relative dynamics are formulated in the velocity-based VNB frame across CR3BP, ER3BP, and BCR4BP, with a rigorous safety analysis linking LTC geometry to KOZs and first-order QPRO constraints. Results show that LTC-based OCPs can efficiently produce one-revolution passive-safe transfers with small fuel costs, robustly extending to multi-spacecraft swarms and full-ephemeris dynamics, albeit with some MPC sensitivity to NRHO perturbations. The work lays a practical foundation for scalable, safe swarming in cislunar RMBPs and points to future integration of station-keeping and observability-driven optimization for even more robust mission design.

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.

Figures (19)

• Figure 1: Coordinate frames and vectors used in this work.
• Figure 2: Local eigenspace of the monodromy matrix: central mode in the R2BP and the oscillatory mode in the CR3BP.
• Figure 3: Periodic and quasi-periodic motion in the R2BP and RMBP.
• Figure 4: Nonsingular local toroidal coordinates $[ \alpha, \beta, h]$ and geometric local toroidal coordinates $[ \varepsilon, \theta, h]$
• Figure 5: First-order QPRIT (gray surface) and 50 invariant circles (blue ellipses) of CR3BP $L_2$ South 9:2 (synodic) NRHO in co-moving frames ($\varepsilon$=200 m, fixed point at apolune).