Optimal Low-Thrust Transfers Between Relative Planar and Spatial Quasi-Satellite Orbits in the Earth–Moon System

Pushparaj, Nishanth; Hiraiwa, Naoki; Hayashi, Yuta; Bando, Mai

Abstract

This paper investigates the design of optimal low-thrust transfers between relative planar and spatial quasi-satellite orbits (QSOs) in the Earth–Moon system under the Circular Restricted Three-Body Problem (CR3BP). A key contribution is the adaptation of a trajectory optimization framework, previously applied to halo orbit transfers, to accommodate the unique challenges of QSO families, especially the transition between planar and spatial configurations. The method employs a refined beam search strategy to construct diverse initial guess chains, which are then optimized via a successive convexification algorithm tailored for the spatial dynamics of QSOs. Additionally, a linear–quadratic regulator (LQR)-based control scheme is implemented to ensure long-term station-keeping of the final 3D-QSO. Simulation results demonstrate the feasibility of connecting planar and spatial QSOs with minimum-fuel trajectories while maintaining bounded terminal deviations, offering new tools for future Earth–Moon logistics and navigation infrastructure. Key findings include the successful design of low-thrust transfer trajectories between planar QSOs and 1:5 3D-QSOs, with a minimum total Δ𝑉
of 195.576 m/s over a time of flight (ToF) of 261 days, and a minimum ToF of 41 days with a total Δ𝑉
of 270.507 m/s. Additionally, the application of LQR control demonstrated the ability to maintain 1:5 3D-QSO families around the Moon with less than 12 mm/s Δ𝑉
over two months. This research provides valuable insights into the optimization of low-thrust transfer trajectories and the application of advanced control techniques for space missions, particularly those targeting lunar and planetary satellite exploration.

Citation

Pushparaj, N., Hiraiwa, N., Hayashi, Y., & Bando, M. (2025). Optimal Low-Thrust Transfers Between Relative Planar and Spatial Quasi-Satellite Orbits in the Earth–Moon System. Aerospace, 12(6), Article 524. https://doi.org/10.3390/aerospace12060524

• Journal Article Type: Article
• Acceptance Date: Jun 8, 2025
• Online Publication Date: Jun 10, 2025
• Publication Date: Jun 10, 2025
• Deposit Date: Jun 11, 2025
• Publicly Available Date: Jun 12, 2025
• Journal: Aerospace
• Electronic ISSN: 2226-4310
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 6
• Article Number: 524
• DOI: https://doi.org/10.3390/aerospace12060524
• Keywords: CRTBP; periodic orbits; QSO; optimization
• Public URL: https://nottingham-repository.worktribe.com/output/50171022
• Publisher URL: https://www.mdpi.com/2226-4310/12/6/524