Target sequence optimization for multiple debris rendezvous using low thrust based on characteristics of SSO

Abstract

A method is proposed to select the target sequence for a J 2-perturbed multiple debris rendezvous mission aimed at removing dozens of debris from several thousand debris candidates running on sun-synchronous orbits (SSO). The solving methodology proceeds in two steps: Firstly, the variance of the right ascension of ascending node (RAAN) of the debris group is used for narrowing down the potential debris candidate; secondly, the debris of the candidate group that has closest RAAN to the current debris is chosen as the next debris. The low thrust near-minimum-fuel trajectories of each rendezvous leg are obtained by the indirect optimization method. The proposed approach is demonstrated for the problem of the 8th China Trajectory Optimization Competition (CTOC). The radar cross section (RCS) of the debris is also considered in the first step since the primary performance index of the competition is to maximize the total RCS of the debris visited. The results show that the proposed approach achieves better performance within a competition period. Of the many rendezvous sequences found, the best one submitted for the competition obtained a total RCS of 184 by accomplishing rendezvous with 70 debris within a transfer duration of one year.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    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 

  2. [2]

    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): 648–653.

    Article  Google Scholar 

  3. [3]

    Liou, J. C. An active debris removal parametric study for LEO environment remediation. Advances in Space Research, 2011, 47(11): 1865–1876.

    Article  Google Scholar 

  4. [4]

    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 

  5. [5]

    Shan, M., 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 

  6. [6]

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

    MathSciNet  Article  MATH  Google Scholar 

  7. [7]

    Cerf, M. Multiple space debris collecting mission: Optimal mission planning. Journal of Optimization Theory and Applications, 2015, 167(1): 195–218.

    MathSciNet  Article  MATH  Google Scholar 

  8. [8]

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

    Article  Google Scholar 

  9. [9]

    Casalino, L., Pastrone, D. Active debris removal missions with multiple targets. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference, 2014.

    Google Scholar 

  10. [10]

    Bonnal, C., Ruault, J. M., Desjean, M. C. Active debris removal: Recent progress and current trends. Acta Astronautica, 2013, 85: 51–60.

    Article  Google Scholar 

  11. [11]

    Haberkorn, T., Martinon, P., Gergaud, J. Low thrust minimum-fuel orbital transfer: A homotopic approach. Journal of Guidance, Control, and Dynamics, 2004, 27(6): 1046–1060.

    Article  Google Scholar 

  12. [12]

    Zhang, J., Parks, G. T., Luo, Y.-Z., Tan, G.-J. Multispacecraft refueling optimization considering the J2 perturbation and window constraints. Journal of Guidance, Control, and Dynamics, 2013, 37(1): 111–122.

    Article  Google Scholar 

  13. [13]

    Zhao, S., Gurfil, P., Zhang, J. Optimal servicing of geostationary satellites considering Earth’s triaxiality and Lunisolar effects. Journal of Guidance, Control, and Dynamics, 2016, 39(10): 2219–2231.

    Article  Google Scholar 

  14. [14]

    Yang, Z., Luo, Y.-Z., Zhang, J., Tang, G.-J. Homotopic perturbed Lambert algorithm for long-duration rendezvous optimization. Journal of Guidance, Control, and Dynamics, 2015, 38(11): 2215–2223.

    Article  Google Scholar 

  15. [15]

    Zhang, J., Zhao, S., Zhang, Y. Autonomous guidance for rendezvous phasing based on special-pointbased maneuvers. Journal of Guidance, Control, and Dynamics, 2015, 38(4): 578–586.

    MathSciNet  Article  Google Scholar 

  16. [16]

    Ely, T. A. Transforming mean and osculating elements using numerical methods. The Journal of the Astronautical Sciences, 2015, 62(1): 21–43.

    Article  Google Scholar 

  17. [17]

    Brouwer, D. Solution of the problem of artificial satellite theory without drag. Astronomical Journal, 1959, 64: 378–397.

    MathSciNet  Article  Google Scholar 

  18. [18]

    Kozai, Y. The motion of a close earth satellite. Astronomical Journal, 1959, 64: 367–377.

    MathSciNet  Article  Google Scholar 

  19. [19]

    Jiang, F., Baoyin, H., Li, J. Practical techniques for low-thrust trajectory optimization with homotopic approach. Journal of Guidance, Control, and Dynamics, 2012, 35(1): 245–258.

    Article  Google Scholar 

  20. [20]

    Bryson, A. E. Applied Optimal Control: Optimization, Estimation and Control. Revised Printing.Washington, DC: Hemisphere Publishing, 1975: 42–89.

    Google Scholar 

  21. [21]

    Russell, R. P. Primer vector theory applied to global low-thrust trade studies. Journal of Guidance, Control, and Dynamics, 2007, 30(2): 460–472.

    MathSciNet  Article  Google Scholar 

  22. [22]

    Zhang, C., Topputo, F., Bernelli-Zazzera, F., Zhao, Y.-S. Low-thrust minimum-fuel optimization in the circular restricted three-body problem. Journal of Guidance, Control, and Dynamics, 2015, 38(8): 1501–1510.

    Article  Google Scholar 

  23. [23]

    Martinon, P., Gergaud, J. Using switching detection and variational equations for the shooting method. Optimal Control Applications and Methods, 2007, 28(2): 95–116.

    MathSciNet  Article  Google Scholar 

  24. [24]

    Fehlberg, E. Classical fifth-, sixth-, seventh-, and eighth-order Runge-Kutta formulas with step size control. NASATR R-287, 1968.

    Google Scholar 

  25. [25]

    Zhao, S., Zhang, J. Minimum-fuel station-change for geostationary satellites using low-thrust considering perturbations. Acta Astronautica, 2016, 127: 296–307.

    Article  Google Scholar 

Download references

Acknowledgements

We are very grateful to the organizers of the 8th China Trajectory Optimization Competition for the interesting and complex problem. Most methods presented in this paper were developed under the National Natural Science Foundation of China (Nos. 11172036, 11572037, and 11402021) and the Excellent Young Scholars Research Fund of Beijing Institute of Technology (No. 2015YG0101).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Shuge Zhao.

Additional information

Shuge Zhao received his B.S. degree in detection, guidance, and control techniques from Shenyang Ligong University, Shenyang, China, in 2009, M.S. degree in control science and engineering from Beihang University, Beijing, China, in 2012, and Ph.D. degree in flight vehicle design from Beijing Institute of Technology, Beijing, China, in 2016. From 2016, he is a postdoctoral fellow at the Second Research Academy of China Aerospace Science and Industry Corporation. His research interests include orbital dynamics and control, and spacecraft trajectory optimization.

Jingrui Zhang received her B.S. and M.S. degrees in automation instrument and flight mechanics from Harbin Institute of Technology, Harbin, China, in 1996 and 1998, respectively, and Ph.D. degree in automatic control from the University of Picardie-Jule Verne, Picardie, France, in 2002. From 2002 to 2004, she was a postdoctoral fellow at the Department of Mechanical Engineering, Tsinghua University, Beijing, China. She is currently a professor at Beijing Institute of Technology, Beijing, China. Her research interests include rapid maneuver and stabilization of spacecraft attitude control, formation flying, and rendezvous and docking.

Kaiheng Xiang received his B.S. and Ph.D. degrees in flight vehicle design from Beihang University, Beijing, China, in 1993 and 1999, respectively. From 2000 to 2002, he was a postdoctoral fellow at the China Academy of Space Technology, Beijing, China. He is currently a research fellow at the Second Research Academy of China Aerospace Science and Industry Corporation, Beijing, China. His research interests include orbital dynamics and the system design of spacecraft.

Rui Qi received his B.S. and Ph.D. degrees in flight vehicle design from Beihang University, Beijing, China, in 2008 and 2013, respectively. From May 2015 to May 2016, he was a visiting professor at McGill University, working with Professor Arun Misra on the study of active debris removal using tethered space-tug. He is currently an assistant professor at Beijing Institute of Technology, Beijing, China. His research interests include active debris removal, formation flying, and orbital mechanics.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhao, S., Zhang, J., Xiang, K. et al. Target sequence optimization for multiple debris rendezvous using low thrust based on characteristics of SSO. Astrodyn 1, 85–99 (2017). https://doi.org/10.1007/s42064-017-0007-4

Download citation

Keywords

  • multiple debris rendezvous
  • sun-synchronous orbits (SSO)
  • low thrust
  • optimal control