The Zero Initial Guess Algorithm for Low-Thrust Trajectory Optimization with Its Application in Cislunar Space
Source abstract
Abstract
In this paper, a trajectory optimization method without an initial value guess is proposed. The method employs the Lagrange multipliers from the nonlinear programming process to estimate the costate of the optimal control problem. It utilizes a homotopic process to address the minimum-fuel problem. The estimated costate serves as a useful initial guess for the indirect shooting method, mitigating the initial value sensitivity. The sequential quadratic programming process used in the shooting process avoids the non-optimal results of the direct method. The minimum-time and minimum-fuel low-thrust rendezvous problems on cislunar L1-vicinity, L2-vicinity, and L2-south near rectilinear halo orbits are solved in this paper. The numerical results demonstrate that using low-thrust propulsion can reduce fuel consumption by 42.36% to 84.62% compared with traditional two-impulse maneuvers in the circular restricted three-body rendezvous problem.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Spacecraft Dynamics and Control · Advanced Optimization Algorithms Research · Space Satellite Systems and Control
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Graduate School, Space Engineering University, Beijing 101416, China
Funding
Key Laboratory of Intelligent Space TTC&O
References (40)
Show source-provided references
1. Overview of the Chang’e-4 Mission: Opening the Frontier of Scientific Exploration of the Lunar Far Side10.1007/s11214-021-00793-z ↗
2. Coderre, K.M., Edwards, C., Cichan, T., Richey, D., Shupe, N., Sabolish, D., Ramm, S., Perkes, B., Posey, J., and Pratt, W. (June, January 28). Concept of Operations for the Gateway. Proceedings of the 2018 SpaceOps Conference, Marseille, France.10.2514/6.2018-2464 ↗
3. Eclipse-Conscious Transfer to Lunar Gateway Using Ephemeris-Driven Terminal Coast Arcs10.2514/1.G005920 ↗
4. Rendezvous equations in the vicinity of the second libration point10.2514/3.30263 ↗
5. Linear state-space representation of the dynamics of relative motion, based on restricted three body dynamics
6. Rendezvous targeting and navigation for a translunar halo orbit10.2514/3.21317 ↗
7. Relative Motion Dynamics in the Restricted Three-Body Problem10.2514/1.A34390 ↗
8. Murakami, N., and Yamanaka, K. (2015, January 7–14). Trajectory design for rendezvous in lunar Distant Retrograde Orbit. Proceedings of the 2015 IEEE Aerospace Conference, Big Sky, MT, USA.10.1109/AERO.2015.7119023 ↗
9. Franzini, G., Innocenti, M., and Casasco, M. (2021, January 25–28). An Adjoint-Based Method for Continuous-Thrust Relative Maneuver Computation in the Restricted Three-Body Problem. Proceedings of the 2021 American Control Conference (ACC), New Orleans, LA, USA.10.23919/ACC50511.2021.9482823 ↗
10. Spacecraft trajectory optimization: A review of models, objectives, approaches and solutions10.1016/j.paerosci.2018.07.007 ↗
11. Zuehlke, D., Tiwari, M., Jebari, K., and Kidambi, K.B. (2023). Rendezvous and Proximity Operations in Cislunar Space Using Linearized Dynamics for Estimation. Aerospace, 10.10.3390/aerospace10080674 ↗
12. Formation and Attitude Control for the CanX-4 and CanX-5 Formation Flying Mission10.3182/20110828-6-IT-1002.02870 ↗
13. Thompson, M.R., Forsman, A., Chikine, S., Peters, B.C., Ely, T., Sorensen, D., Parker, J., and Cheetham, B. (2022, January 25–27). Cislunar Navigation Technology Demonstrations on the CAPSTONE Mission. Proceedings of the 2022 International Technical Meeting of The Institute of Navigation, Long Beach, CA, USA.10.33012/2022.18208 ↗
14. Sonwalkar, N., and Matteson, E. (2024, January 8–12). Cislunar Explorers Redesign: Multiple, Independent Technology Demonstrations Reduce Mission Risk. Proceedings of the AIAA SCITECH 2024 Forum, Orlando, FL, USA.10.2514/6.2024-0127 ↗
15. The ESA SMART-1 mission to the Moon with solar electric propulsion10.1016/S0273-1177(99)00544-X ↗
16. Steiger, C., Romanazzo, M., Emanuelli, P.P., Floberghagen, R., and Fehringer, M. (2014, January 5–9). The Deorbiting of ESA’s Gravity Mission GOCE-Spacecraft Operations in Extreme Drag Conditions. Proceedings of the SpaceOps 2014 Conference, Pasadena, CA, USA.10.2514/6.2014-1934 ↗
17. Ignatenko, V., Laurila, P., Radius, A., Lamentowski, L., Antropov, O., and Muff, D. (October, January 26). ICEYE Microsatellite SAR Constellation Status Update: Evaluation of First Commercial Imaging Modes. Proceedings of the IGARSS 2020-2020 IEEE International Geoscience and Remote Sensing Symposium, Waikoloa, HI, USA.10.1109/IGARSS39084.2020.9324531 ↗
18. Wilkie, W.K. (2021, January 11–15). Overview of the NASA Advanced Composite Solar Sail System (ACS3) Technology Demonstration Project. Proceedings of the AIAA Scitech 2021 Forum, Nashville, TN, USA.10.2514/6.2021-1260 ↗
19. Direct Trajectory Optimization Using a Variable Low-Order Adaptive Pseudospectral Method10.2514/1.52136 ↗
20. Costate mapping for indirect trajectory optimization10.1007/s42064-021-0114-0 ↗
21. Low-Thrust Minimum-Fuel Optimization in the Circular Restricted Three-Body Problem10.2514/1.G001080 ↗
22. Homotopic approach to the feedback solution of the orbit pursuit-evasion game10.1016/j.asr.2025.04.044 ↗
23. Low-Thrust Minimum-Fuel Trajectory Optimization Using Multiple Shooting Augmented by Analytical Derivatives10.2514/1.G003473 ↗
24. Alvarado, K.I., and Singh, S.K. (2024). Exploration and Maintenance of Homeomorphic Orbit Revs in the Elliptic Restricted Three-Body Problem. Aerospace, 11.10.3390/aerospace11050407 ↗
25. Practical Techniques for Low-Thrust Trajectory Optimization with Homotopic Approach10.2514/1.52476 ↗
26. Application of the hp-adaptive pseudospectral method in spacecraft orbit pursuit-evasion game10.1016/j.asr.2023.12.024 ↗
27. Low-Thrust Transfers to Southern L 2 Near-Rectilinear Halo Orbits Facilitated by Invariant Manifolds10.1007/s10957-021-01898-9 ↗
28. Analytic construction of periodic orbits about the collinear points10.1007/BF01229511 ↗
29. Exploiting manifolds of L 1 halo orbits for end-to-end Earth–Moon low-thrust trajectory design10.1016/j.actaastro.2021.03.017 ↗
30. Applied Optimal Control: Optimization, Estimation, and Control10.1109/TSMC.1979.4310229 ↗
31. Minimum Time Control of the Restricted Three-Body Problem10.1137/110847299 ↗
32. Costate Computation by a Chebyshev Pseudospectral Method10.2514/1.45154 ↗
33. Costate Estimation using Multiple-Interval Pseudospectral Methods10.2514/1.A32040 ↗
34. Cook, A., Dahlke, J., and Bettinger, R.A. (2023, January 23–27). Preliminary Study of Employing Space-Based Mirrors for Augmented Illumination of Cislunar Resident Space Objects. Proceedings of the AIAA SCITECH 2023 Forum, Online.10.2514/6.2023-0758 ↗
35. Singh, S.K., Taheri, E., Woollands, R., and Junkins, J. (2019, January 21–25). Mission Design for Close-Range Lunar Mapping by Quasi-Frozen Orbits. Proceedings of the 70th International Astronautical Congress, Washington, DC, USA.
36. Near Rectilinear Halo Orbits and Nearby Higher-Period Dynamical Structures: Orbital Stability and Resonance Properties10.1007/s10569-020-09968-2 ↗
37. Particle Swarm Optimization Applied to Space Trajectories10.2514/1.48475 ↗
38. Improved Indirect Method for Air-Vehicle Trajectory Optimization10.2514/1.16228 ↗
39. Taheri, E., and Sowell, S. (2024, January 8–12). Enhanced Finite Fourier Series for Low-Thrust Trajectory design. Proceedings of the AIAA SCITECH 2024 Forum, Orlando, FL, USA.10.2514/6.2024-0634 ↗
40. Shape-Based Approach to Low-Thrust Rendezvous Trajectory Design10.2514/1.36848 ↗