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Mass-Optimal Low-Thrust Forced Periodic Trajectories in the Earth-Moon CR3BP

Colby C. Merrill, Jackson Kulik, Matthew J. Bryan, Dmitry Savransky

TL;DR

In the Earth–Moon CR3BP, the work extends trajectory design to mass-optimal, thrust-limited forced periodic orbits using low-thrust propulsion. It develops a direct-collocation workflow within ASSET/PSIOPT, seeds mass-optimal solutions from energy-optimal ones, and characterizes the thrust-limited reachable set with a PSO-based boundary search, complemented by a linear energy-based ellipsoid as a comparison. Key findings show mass-optimal trajectories with modest per-orbit $\Delta V$ (roughly $10$–$12$ m/s) and bang-bang thrust profiles, and a nonlinear thrust-limited reachable set that, when projected onto the $xy$-plane, broadly resembles but extends beyond the linear energy-limited set. This approach broadens practical Cislunar mission design by enabling more mass-efficient, robust periodic trajectories under realistic thrust constraints and provides a framework for reachability analysis in nonlinear orbital dynamics.

Abstract

In Cislunar space, spacecraft are able to exploit naturally periodic orbits, which provide operational reliability. However, these periodic orbits only exist in a limited volume. Enabled by low-thrust propulsion, spacecraft can produce a greater number of periodic trajectories in Cislunar space. We describe a methodology for producing mass-optimal trajectories that enforce periodic structure in the circular-restricted three body problem and study the thrust-limited reachable set around a reference trajectory. In this study, we find that the thrust-limited mass-optimal reachable set is a superset of the energy-limited energy-optimal reachable set in the xy-plane.

Mass-Optimal Low-Thrust Forced Periodic Trajectories in the Earth-Moon CR3BP

TL;DR

In the Earth–Moon CR3BP, the work extends trajectory design to mass-optimal, thrust-limited forced periodic orbits using low-thrust propulsion. It develops a direct-collocation workflow within ASSET/PSIOPT, seeds mass-optimal solutions from energy-optimal ones, and characterizes the thrust-limited reachable set with a PSO-based boundary search, complemented by a linear energy-based ellipsoid as a comparison. Key findings show mass-optimal trajectories with modest per-orbit (roughly – m/s) and bang-bang thrust profiles, and a nonlinear thrust-limited reachable set that, when projected onto the -plane, broadly resembles but extends beyond the linear energy-limited set. This approach broadens practical Cislunar mission design by enabling more mass-efficient, robust periodic trajectories under realistic thrust constraints and provides a framework for reachability analysis in nonlinear orbital dynamics.

Abstract

In Cislunar space, spacecraft are able to exploit naturally periodic orbits, which provide operational reliability. However, these periodic orbits only exist in a limited volume. Enabled by low-thrust propulsion, spacecraft can produce a greater number of periodic trajectories in Cislunar space. We describe a methodology for producing mass-optimal trajectories that enforce periodic structure in the circular-restricted three body problem and study the thrust-limited reachable set around a reference trajectory. In this study, we find that the thrust-limited mass-optimal reachable set is a superset of the energy-limited energy-optimal reachable set in the xy-plane.

Paper Structure

This paper contains 12 sections, 33 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Dynamics
  4. Optimization
  5. Generation of Mass-Optimal Trajectories
  6. Reachable Set Definitions
  7. Energy-Limited Reachable Set
  8. Particle Swarm Optimization
  9. Results
  10. Mass-Optimal Forced Periodic Trajectories
  11. Reachable Set Comparison
  12. Conclusions

Figures (4)

  • Figure 1: An example of the PSO algorithm.
  • Figure 2: An example of energy-optimal and mass-optimal trajectories where the timing of the thrusting maxima are dissimilar between the two cases.
  • Figure 3: An example of energy-optimal and mass-optimal trajectories where the timing of the thrusting maxima are similar between the two cases.
  • Figure 4: A comparison of the reachable sets for energy-optimal and mass-optimal trajectories in the $xy$-plane.