Skip to main content
SpringerLink
Log in

Cislunar Satellite Constellation Design via Integer Linear Programming

  • Original Article
  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

Cislunar space domain awareness is of increasing interest to the international community as Earth-Moon traffic is projected to increase, which raises the problem of placing space-based sensors optimally in a constellation to satisfy the space domain awareness demand in cislunar space. This demand profile can vary over space and time, making the design optimization problem challenging. This paper tackles the problem of satellite constellation design for spatio-temporally varying coverage demand by leveraging an integer linear programming formulation. The developed optimization formulation assumes the circular restricted 3-body dynamics and attempts to minimize the number of satellites required for the requested demand profile.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

Data availability

Not applicable.

References

  1. Folta, D.C., Pavlak, T.A., Haapala, A.F., Howell, K.C.: Preliminary design considerations for access and operations in Earth-Moon L1/L2 orbits. In: AAS/AIAA Spaceflight Mechanics Meeting (2013)

  2. Haapala, A., Vaquero, M., Pavlak, T., Howell, K.C., Folta, D.C.: Trajectory selection strategy for tours in the Earth-Moon system. In: AAS/AIAA Astrodynamics Specialist Conference, Hilton Head, South Carolina (2013)

  3. Cunio, P.M., Bever, M.J., Flewelling, B.R.: Payload and constellation design for a solar exclusion-avoiding cislunar SSA fleet. In: Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS) (2020)

  4. Thompson, M.R., Ré, N.P., Meek, C., Cheetham, B.: Cislunar orbit determination and tracking via simulated space-based measurements. In: Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, HI (2021)

  5. Wilmer, A.P., Bettinger, R.A., Little, B.D.: Cislunar periodic orbits for earth-moon L1 and L2 Lagrange point surveillance. J. Spacecr. Rocket. 59(6), 1809–1820 (2022)

    Article  Google Scholar 

  6. Dahlke, J.A., Wilmer, A.P., Bettinger, R.A.: Preliminary comparative assessment of L2 and L3 surveillance using select cislunar periodic orbits. In: AAS/AIAA Astrodynamics Specialist Conference, pp. 1–19 (2022)

  7. Zimovan, E.M., Howell, K.C., Davis, D.C.: Near rectilinear halo orbits and their application in cis-lunar space. In: 3rd IAA Conference on Dynamics and Control of Space Systems, Moscow, Russia, vol. 20, p. 40 (2017)

  8. Frueh, C., Howell, K., DeMars, K., Bhadauria, S., Gupta, M.: Cislunar space traffic management: surveillance through Earth-Moon resonance orbits. In: 8th European Conference on Space Debris (2021)

  9. Gupta, M., Howell, K.C., Frueh, C.: Constellation design to support cislunar surveillance leveraging sidereal resonant orbits. In: 33rd AAS/AIAA Space Flight Mechanics Meeting, Austin, Texas (2023)

  10. Klonowski, M., Holzinger, M.J., Fahrner, N.O.: Optimal cislunar architecture design using Monte Carlo tree search methods. J. Astronaut. Sci. 70(3), 17 (2023)

    Article  Google Scholar 

  11. Vendl, J.K., Holzinger, M.J.: Cislunar periodic orbit analysis for persistent space object detection capability. J. Spacecr. Rocket. 58(4), 1174–1185 (2021)

    Article  Google Scholar 

  12. Visonneau, L., Shimane, Y., Ho, K.: Optimizing multi-spacecraft cislunar space domain awareness systems via hidden-genes genetic algorithm. J. Astronaut. Sci. 70, 22 (2023)

    Article  Google Scholar 

  13. Lee, H.W., Shimizu, S., Yoshikawa, S., Ho, K.: Satellite constellation pattern optimization for complex regional coverage. J. Spacecr. Rocket. 57(6), 1309–1327 (2020)

    Article  Google Scholar 

  14. Krag, W.E.: Visible magnitude of typical satellites in synchronous orbits. NASA STI/Recon Technical Report N 75 (1974)

  15. Vaquero, M., Senent, J.: Poincare: a multi-body, multi-system trajectory design tool. In: 7th International Conference on Astrodynamics Tools and Techniques, pp. 1-12. Jet Propulsion Laboratory, National Aeronautics and Space Administration Oberpfaffenhofen, Pasadena, CA (2018)

  16. Broucke, R.A.: Periodic orbits in the restricted three body problem with Earth-Moon masses. Technical report (1968)

  17. Rackauckas, C., Nie, Q.: DifferentialEquations.jl—a performant and feature-rich ecosystem for solving differential equations in Julia. J. Open Res. Softw. 5, 1 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge support for this research from the Air Force Office of Scientific Research (AFOSR), as part of the Space University Research Initiative (SURI), grant FA9550-22-1-0092 (grant principal investigator: J. Crassidis from University at Buffalo, The State University of New York).

Author information

Authors and Affiliations

  1. Aerospace Engineering, Georgia Institute of Technology, 270 Ferst Drive, Atlanta, GA, 30332, USA

    Malav Patel, Yuri Shimane & Koki Ho

  2. Mechanical, Materials and Aerospace Engineering, West Virginia University, 1306 Evansdale Drive, Morgantown, WV, 26506, USA

    Hang Woon Lee

Authors
  1. Malav Patel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuri Shimane
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hang Woon Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Koki Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Koki Ho.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no Conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This paper is a substantially revised version of Paper AAS 23-358 presented at the AAS/AIAA Astrodynamics Specialist Conference, Big Sky, MT, in Aug. 2023. The added content includes new analysis, case studies, and results.

Appendices

Appendix A: Optimizing the Constellation Pattern Vector

Algorithm 1 presents pseudocode for the formulation. In this work, we utilize Gurobi MATLAB for computation. Computation is done with an M1 Pro CPU using 8 high-performance cores. Algorithm run time is < 300 s for each \(N \in \{1, 2, 4, 8, 16\}\).

figure a

Algorithm 1

Appendix B: CR3BP System Parameters and Candidate Orbit Initial Conditions

System parameters for the Earth-Moon CR3BP with the Sun as illumination source are presented in Tables 1 and 2. Initial conditions for candidate orbits are shown below in Table 3. Orbits were generated via a single shooting differential corrections algorithm written in Julia. We use the Vern7 ODE propagator (available in the Julia DifferentialEquations [17] module) in this algorithm.

Table 1 CR3BP parameters
Full size table
Table 2 Illumination parameters
Full size table
Table 3 Candidate orbit initial conditions
Full size table

Appendix C: Coverage Requirement Generation

Algorithm 2 provides pseudocode for the coverage requirement satisfying the criteria outlined in Sect. 4.1.

figure b

Algorithm 2

Appendix D: Extended Results

Figures 23 and 24 show the constellations and indicator maps of all the optimization runs for each \(N \in \{1, 2, 4, 8, 16\}\). Table 4 shows the phasing of the constellations relative to seed satellites.

Fig. 23
figure 23

Optimized constellations for given number of departure windows

Full size image
Table 4 Constellation phasing relative to seed satellites
Full size table
Fig. 24
figure 24

Constellation robustness binary maps

Full size image

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Patel, M., Shimane, Y., Lee, H.W. et al. Cislunar Satellite Constellation Design via Integer Linear Programming. J Astronaut Sci 71, 26 (2024). https://doi.org/10.1007/s40295-024-00445-8

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40295-024-00445-8

Keywords

Search

Navigation