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Timeline Club: An optimization algorithm for solving multiple debris removal missions of the time-dependent traveling salesman problem model

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Abstract

With the increase of space debris, space debris removal has gradually become a major issue to address by worldwide space agencies. Multiple debris removal missions, in which multiple debris objects are removed in a single mission, are an economical approach to purify the space environment. Such missions can be considered typical time-dependent traveling salesman problems (TDTSPs). In this study, an intelligent global optimization algorithm called Timeline Club Optimization (TCO) is proposed to solve multiple debris removal missions of the TDTSP model. TCO adopts the traditional ant colony optimization (ACO) framework and replaces the pheromone matrix of the ACO with a new structure called the Timeline Club. The Timeline Club records which debris object to be removed next at a certain moment from elitist solutions and decides the probability criterion to generate debris sequences in new solutions. Two hypothetical scenarios, the Iridium-33 mission and the GTOC9 mission, are considered in this study. Simulation results show that TCO offers better performance than those of beam search, ant colony optimization, and the genetic algorithm in multiple debris removal missions of the TDTSP model.

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References

  1. Kessler, D. J., Cour-Palais, B. G. Collision frequency of artificial satellites: The creation of a debris belt. Journal of Geophysical Research: Space Physics, 1978, 83(A6): 2637–2646.

    Article  Google Scholar 

  2. Kessler, D. J., Johnson, N. L., Liou, J. C., Matney, M. The Kessler Syndrome: Implications to future space operations. In: Proceedings of the 33rd Annual AAS Rocky Mountain Guidance and Control Conference, 2010: AAS 10–016.

  3. Barbee, B. W., Alfano, S., Piñon, E., Gold, K., Gaylor, D. Design of spacecraft missions to remove multiple orbital debris objects. In: Proceedings of the 2011 Aerospace Conference, 2011: 1–14.

  4. Liou, J. C., Johnson, N. L. Instability of the present LEO satellite populations. Advances in Space Research, 2008, 41(7): 1046–1053.

    Article  Google Scholar 

  5. Uriot, T., Izzo, D., Simões, L. F., Abay, R., Einecke, N., Rebhan, S., Martinez-Heras, J., Letizia, F., Siminski, J., Merz, K. Spacecraft collision avoidance challenge: Design and results of a machine learning competition. Astrodynamics, 2021, https://doi.org/10.1007/s42064-021-0101-5.

  6. Liou, J. C., Johnson, N. L., Hill, N. M. Controlling the growth of future LEO debris populations with active debris removal. Acta Astronautica, 2010, 66(5–6): 648–653.

    Article  Google Scholar 

  7. Houpert, A. A space based radar on a micro-satellite for in situ detection of small orbital debris. Acta Astronautica, 1999, 44(7–12): 313–321.

    Article  Google Scholar 

  8. Zhao, H. P., Fu, X. J., Gao, M. G., Ding, S. Research on the visibility of low-orbit debris using space-borne radar. IET Radar, Sonar & Navigation, 2015, 9(1): 31–37.

    Article  Google Scholar 

  9. Culp, R. D., Gravseth, I. J. Space-debris identification using optical calibration of common spacecraft materials. Journal of Spacecraft and Rockets, 1996, 33(2): 262–266.

    Article  Google Scholar 

  10. Shan, M. H., Guo, J., Gill, E. Review and comparison of active space debris capturing and removal methods. Progress in Aerospace Sciences, 2016, 80: 18–32.

    Article  Google Scholar 

  11. Ishige, Y., Kawamoto, S., Kibe, S. Study on electro-dynamic tether system for space debris removal. Acta Astronautica, 2004, 55(11): 917–929.

    Article  Google Scholar 

  12. Zhong, R., Zhu, Z. H. Dynamics of nanosatellite deorbit by bare electrodynamic tether in low earth orbit. Journal of Spacecraft and Rockets, 2013, 50(3): 691–700.

    Article  Google Scholar 

  13. Borja, J. A., Tun, D. Deorbit process using solar radiation force. Journal of Spacecraft and Rockets, 2006, 43(3): 685–687.

    Article  Google Scholar 

  14. Phipps, C. R., Albrecht, G., Friedman, H., Gavel, D., George, E. V., Murray, J., Ho, C., Priedhorsky, W., Michaelis, M. M., Reilly, J. P. ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser. Laser and Particle Beams, 1996, 14(1): 1–44.

    Article  Google Scholar 

  15. Phipps, C. R. A laser-optical system to re-enter or lower low Earth orbit space debris. Acta Astronautica, 2014, 93: 418–429.

    Article  Google Scholar 

  16. Zhao, S. G., Zhang, J. R., Xiang, K. H., Qi, R. Target sequence optimization for multiple debris rendezvous using low thrust based on characteristics of SSO. Astrodynamics, 2017, 1(1): 85–99.

    Article  Google Scholar 

  17. Cook, W. J. In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation. Princeton University Press, 2012.

  18. Federici, L., Zavoli, A., Colasurdo, G. A time-dependent TSP formulation for the design of an active debris removal mission using simulated annealing. 2019: arXiv: 1909.10427[math.OC]. Available at https://arxiv.org/abs/1909.10427.

  19. Cerf, M. Multiple space debris collecting mission—Debris selection and trajectory optimization. Journal of Optimization Theory and Applications, 2013, 156(3): 761–796.

    Article  MathSciNet  MATH  Google Scholar 

  20. Zuiani, F., Vasile, M. Preliminary design of debris removal missions by means of simplified models for low-thrust, many-revolution transfers. 2012: arXiv: 1207.3749[math.OC]. Available at https://arxiv.org/abs/1207.3749.

  21. Braun, V., Lüpken, A., Flegel, S., Gelhaus, J., Möckel, M., Kebschull, C., Wiedemann, C., Vörsmann, P. Active debris removal of multiple priority targets. Advances in Space Research, 2013, 51(9): 1638–1648.

    Article  Google Scholar 

  22. Li, H. Y., Chen, S. Y., Baoyin, H. X. J2-perturbed multitarget rendezvous optimization with low thrust. Journal of Guidance, Control, and Dynamics, 2017, 41(3): 802–808.

    Article  Google Scholar 

  23. Olympio, J. T., Frouvelle, N. Space debris selection and optimal guidance for removal in the SSO with low-thrust propulsion. Acta Astronautica, 2014, 99: 263–275.

    Article  Google Scholar 

  24. Barea, A., Urrutxua, H., Cadarso, L. Large-scale object selection and trajectory planning for multi-target space debris removal missions. Acta Astronautica, 2020, 170: 289–301.

    Article  Google Scholar 

  25. Madakat, D., Morio, J., Vanderpooten, D. Biobjective planning of an active debris removal mission. Acta Astronautica, 2013, 84: 182–188.

    Article  Google Scholar 

  26. Bérend, N., Olive, X. Bi-objective optimization of a multiple-target active debris removal mission. Acta Astronautica, 2016, 122: 324–335.

    Article  Google Scholar 

  27. Stuart, J., Howell, K., Wilson, R. Application of multi-agent coordination methods to the design of space debris mitigation tours. Advances in Space Research, 2016, 57(8): 1680–1697.

    Article  Google Scholar 

  28. Shen, H. X., Zhang, T. J., Casalino, L., Pastrone, D. Optimization of active debris removal missions with multiple targets. Journal of Spacecraft and Rockets, 2017, 55(1): 181–189.

    Article  Google Scholar 

  29. Missel, J., Mortari, D. Path optimization for space sweeper with sling-sat: A method of active space debris removal. Advances in Space Research, 2013, 52(7): 1339–1348.

    Article  Google Scholar 

  30. Izzo, D., Getzner, I., Hennes, D., Simoes, L. F. Evolving solutions to TSP variants for active space debris removal. In: Proceedings of the Genetic and Evolutionary Computation Conference, 2015: 1207–1214.

  31. Jing, Y., Chen, X. Q., Chen, L. H. Biobjective planning of GEO debris removal mission with multiple servicing spacecrafts. Acta Astronautica, 2014, 105(1): 311–320.

    Article  Google Scholar 

  32. Daneshjou, K., Mohammadi-Dehabadi, A. A., Bakhtiari, M. Mission planning for on-orbit servicing through multiple servicing satellites: A new approach. Advances in Space Research, 2017, 60(6): 1148–1162.

    Article  Google Scholar 

  33. Di Carlo, M., Romero Martin, J. M., Vasile, M. Automatic trajectory planning for low-thrust active removal mission in low-earth orbit. Advances in Space Research, 2017, 59(5): 1234–1258.

    Article  Google Scholar 

  34. Dorigo, M., Maniezzo, V., Colorni, A. Ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics Part B, Cybernetics, 1996, 26(1): 29–41.

    Article  Google Scholar 

  35. Dorigo, M., Gambardella, L. M. Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1997, 1(1): 53–66.

    Article  Google Scholar 

  36. Holland, J. H. Adaption in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence. The MIT Press, 1975.

  37. Kanazaki, M., Yamada, Y., Nakamiya, M. Trajectory optimization of a satellite for multiple active space debris removal based on a method for the traveling serviceman problem. In: Proceedings of the 21st Asia Pacific Symposium on Intelligent and Evolutionary Systems, 2017: 61–66.

  38. Liu, Y., Yang, J. N., Wang, Y. Z., Pan, Q., Yuan, J. P. Multi-objective optimal preliminary planning of multi-debris active removal mission in LEO. Science China Information Sciences, 2017, 60(7): 1–10.

    Google Scholar 

  39. Chen, Y., Bai, Y. Z., Zhao, Y., Wang, Y., Chen, X. Q. Optimal mission planning of active space debris removal based on genetic algorithm. IOP Conference Series: Materials Science and Engineering, 2020, 715: 012025.

    Article  Google Scholar 

  40. Li, H. Y., Baoyin, H. X. Optimization of multiple debris removal missions using an evolving elitist club algorithm. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(1): 773–784.

    Article  Google Scholar 

  41. Alfriend, K. T., Lee, D. J., Creamer, N. G. Optimal servicing of geosynchronous satellites. Journal of Guidance, Control, and Dynamics, 2006, 29(1): 203–206.

    Article  Google Scholar 

  42. Shen, H. X., Casalino, L. Simple ΔV approximation for optimization of debris-to-debris transfers. Journal of Spacecraft and Rockets, 2020, 58(2): 575–580.

    Article  Google Scholar 

  43. Melgarejo, P. A., Laborie, P., Solnon, C. A time-dependent no-overlap constraint: Application to urban delivery problems. In: Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2015. Lecture Notes in Computer Science, Vol. 9075. Michel, L. Ed. Springer, Cham, 2015: 1–17.

    Chapter  MATH  Google Scholar 

  44. Balakrishnan, N., Lucena, A., Wong, R. T. Scheduling examinations to reduce second-order conflicts. Computers & Operations Research, 1992, 19(5): 353–361.

    Article  MATH  Google Scholar 

  45. Miranda-Bront, J. J., Méndez-Díaz, I., Zabala, P. Facets and valid inequalities for the time-dependent travelling salesman problem. European Journal of Operational Research, 2014, 236(3): 891–902.

    Article  MathSciNet  MATH  Google Scholar 

  46. Ban, H. B. The hybridization of ACO + GA and RVNS algorithm for solving the time-dependent traveling salesman problem. Evolutionary Intelligence, 2020: 1–20.

  47. Izzo, D. Problem description for the 9th Global Trajectory Optimisation Competition. Technical Report. Advanced Concepts Team, European Space Agency, Netherlands, Noordwijk AZ, 2017.

    Google Scholar 

  48. Petropoulos, A., Grebow, D., Jones, D., Lantoine, G., Nicholas, A., Roa, J., Senent, J., Stuart, J., Arora, N., Pavlak, T., et al. GTOC9: Methods and results from the Jet Propulsion Laboratory team. Acta Futura, 2018, 11: 25–35.

    Google Scholar 

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Acknowledgements

This research was supported by the National Key R&D Program of China (No. 2019YFA0706500).

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Correspondence to Hexi Baoyin.

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Nan Zhang received his bachelor degree in engineering mechanics, in 2019, from Tsinghua University, Beijing, China. He was a visiting student at Lunar and Planetary Laboratory in the University of Arizona from October 2018 to February 2019. He is now pursuing his Ph.D. degree in School of Aerospace Engineering, Tsinghua University. His research interests are focused on intelligent optimization algorithms for multitarget detection and trajectory optimization.

Zhong Zhang received his bachelor degree in aerospace engineering from Tsinghua University, Beijing, China, in 2019. He is currently a Ph.D. student in School of Aerospace Engineering, Tsinghua University. His research interests fall under the combinatorial optimization problems.

Hexi Baoyin, professor in School of Aerospace Engineering, Tsinghua University. His current research interests include orbit theory in irregular gravitational fields and interplanetary mission analysis and optimization.

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Zhang, N., Zhang, Z. & Baoyin, H. Timeline Club: An optimization algorithm for solving multiple debris removal missions of the time-dependent traveling salesman problem model. Astrodyn 6, 219–234 (2022). https://doi.org/10.1007/s42064-021-0107-z

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