Safe rendezvous scenario design for geostationary satellites with collocation constraints

Abstract

Rendezvous on the geostationary orbit (GEO) is much more complex than that on the low earth orbit and has a higher critical requirement for safety performance. This paper presents a safe scenario design method for GEO rendezvous proximity missions where the safety constraint of a collocated satellite is considered. A recently proposed quantitative index considering trajectory uncertainty is introduced to analyze the safety performance of the scenario parameters including the V-bar keeping positions and the fly-by trajectory radius. Furthermore, an exhaustive analysis is performed to find the dangerous regions of the V-bar keeping positions and the appropriate semi-major axis of the fly-by ellipse, considering the safety requirements of both the target and the collocated satellite. A geometry method is then developed for designing a feasible and suboptimal safe rendezvous scenario. The method is tested by designing four rendezvous scenarios with ±V-bar approach directions respectively in the situations with and without one collocated satellite. Safety performance and velocity increments of the scenarios are compared and a conclusion is reached that the collocated satellite has a significant influence on the scenario design.

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

References

  1. [1]

    Li, H. N. Geostationary Satellites Collocation. New York: Springer, 2014.

    Book  Google Scholar 

  2. [2]

    Smith, D. A., Martin, C., Kassebom, M., Petersen, H., Shaw, A., Skidmore, B., Smith, D., Stokes, H., Willig, A. A mission to preserve the geostationary region. Advances in Space Research, 2004, 34(5): 1214–1218.

    Article  Google Scholar 

  3. [3]

    Anderson, P. V., Schaub, H. Local orbital debris flux study in the geostationary ring. Advances in Space Research, 2006, 51(12): 2195–2206.

    Article  Google Scholar 

  4. [4]

    Xu, W. F., Liang, B., Li, B., Xu, Y. A universal on-orbit servicing system used in the geostationary orbit. Advances in Space Research, 2011, 48(1): 95–119.

    Article  Google Scholar 

  5. [5]

    Fehse, W. Automated Rendezvous and Docking of Spacecraft. London: Cambridge University Press, 2003.

    Book  Google Scholar 

  6. [6]

    Luo, Y., Zhang, J., Tang, G. Survey of orbital dynamics and control of space rendezvous. Chinese Journal of Aeronautics, 2014, 27(1): 1–11.

    Article  Google Scholar 

  7. [7]

    Barbee, B. W., Carpenter, J. R., Heatwole, S., Markley, F. L., Moreau, M., Naasz, B. J., van Eepoel, J. A guidance and navigation strategy for rendezvous and proximity operations with a noncooperative spacecraft in geosynchronous orbit. The Journal of the Astronautical Sciences, 2011, 58(3): 389–408.

    Article  Google Scholar 

  8. [8]

    Li, Y. H., Yang, K. Z., Shan, C. S., Luo, D., Guan, H., Zheng, J., Cheng, H., Man, L. A preliminary study on dead geostationary satellite removal. Science China Technological Sciences, 2010, 53(12): 3389–3396.

    Article  MATH  Google Scholar 

  9. [9]

    Tarabini, L., Gil, J., Gandia, F., Molina, M. Á., Cural, J. M. D., Ortega, G. Ground guided CX-OLEV rendezvous with uncooperative geostationary satellite. Acta Astronautica, 2007, 61(1-6): 312–325.

    Article  Google Scholar 

  10. [10]

    Eckstein, M. C., Rajasingh, C. K., Blumer, P. Colocation strategy and collision avoidance for the geostationary satellites at 19 degrees west. In: Proceedings of the International Symposium on Space Flight Dynamics, 1989.

    Google Scholar 

  11. [11]

    Li, H. N., Gao, Z. Z., Li, J. S., Li, Q. J., Xue, D., Li, D. L. Mathematical prototypes for collocating geostationary satellites. Science China Technological Sciences, 2013, 56(5): 1086–1092.

    Article  Google Scholar 

  12. [12]

    Beigelman, I., Gurfil, P. Optimal geostationary satellite collocation using relative orbital element corrections. Journal of Spacecraft and Rockets, 2009, 46(1): 141–150.

    Article  Google Scholar 

  13. [13]

    Luo, Y.-Z., Lei, Y.-J., Tang, G.-J. Optimal multi-objective nonlinear impulsive rendezvous. Journal of Guidance, Control, and Dynamics, 2007, 30(4): 994–1002.

    Article  Google Scholar 

  14. [14]

    Breger, L., How, J. P. Safe trajectories for autonomous rendezvous of spacecraft. Journal of Guidance, Control, and Dynamics, 2008, 31(5): 1478–1489.

    Article  Google Scholar 

  15. [15]

    Ma, L., Meng, X., Liu, Z., Du, L. Suboptimal power-limited rendezvous with fixed docking direction and collision avoidance. Journal of Guidance, Control, and Dynamics, 2013, 36(1): 229–239.

    Article  Google Scholar 

  16. [16]

    Jones, B. A., Doostan, A. Satellite collision probability estimation using polynomial chaos expansions. Advances in Space Research, 2013, 52(11): 1860–1875.

    Article  Google Scholar 

  17. [17]

    Patera, R. P. Satellite collision probability for nonlinear relative motion. Journal of Guidance, Control, and Dynamics, 2003, 26(5): 728–733.

    Article  Google Scholar 

  18. [18]

    Luo, Y.-Z., Liang, L.-B., Wang, H., Tang, G.-J. Quantitative performance for spacecraft rendezvous trajectory safety. Journal of Guidance, Control, and Dynamics, 2011, 34(4): 1264–1269.

    Article  Google Scholar 

  19. [19]

    Sun, Z. J., Luo, Y. Z., Niu, Z. Y. Spacecraft rendezvous trajectory safety quantitative performance index eliminating probability dilution. Science China Technological Sciences, 2014, 57(6): 1219–1228.

    Article  Google Scholar 

  20. [20]

    Goodman, J. L. History of space shuttle rendezvous and proximity operations. Journal of Spacecraft and Rockets, 2006, 43(5): 944–959.

    MathSciNet  Article  Google Scholar 

  21. [21]

    Mulder, T. A. Orbital express autonomous rendezvous and capture flight operations, Part 2 of 2: AR&C exercise 4,5, and end-of-life. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Guidance, Navigation, and Control and Co-located Conferences, 2008: AIAA 2008–6768.

    Google Scholar 

  22. [22]

    Clohessy, W. H., Wiltshire, R. S. Terminal guidance system for satellite rendezvous. Journal of the Aerospace Sciences, 1960, 27(9): 653–658, 674.

    Article  MATH  Google Scholar 

  23. [23]

    Niu, Z. Y. Safety assessment method and design optimization of rendezvous trajectory in view of early warning threshold. Master Thesis. Changsha, China: National University of Defense Technology, 2012. (in Chinese)

    Google Scholar 

  24. [24]

    Sellmaier, F., Boge, T., Spurmann, J., Gully, S., Rupp, T., Huber, F. On-orbit servicing missions: Challenges and solutions for spacecraft operations. In: Proceedings of the SpaceOps 2010 Conference, 2010: AIAA 2010–2159.

    Google Scholar 

  25. [25]

    Luo, Y.-Z., Liang, L.-B., Niu, Z.-Y., Tang, G.-J. Safety-optimal linearized impulsive rendezvous with trajectory uncertainties. Journal of Aerospace Engineering, 2014, 27(6): 04014038.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11572345 and 11402257) and the National Basic Research Program of China (973 Program, Grant No. 2013CB733100).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ya-Zhong Luo.

Additional information

Ya-Zhong Luo received his B.S., M.S., and Ph.D. degrees in aerospace engineering from National University of Defense Technology (NUDT), Hunan, China, in 2001, 2003, and 2007, respectively. Since December 2013, he has been a professor in the College of Aerospace Science and Engineering, NUDT. His current research interests include manned spaceflight mission planning, spacecraft dynamics and control, and evolutionary computation. He was the recipient of the 2010 National Top 100 Doctoral Dissertation Award, the 2012 National Excellent Young Scholars Science Foundation, and the 2014-2016 Most Cited Chinese Researchers (Elsevier).

Zhen-Jiang Sun received his B.S. and M.S. degrees in aerospace engineering from National University of Defense Technology (NUDT), Hunan, China, in 2012 and 2014, respectively. He is now pursuing his Ph.D. degree in aerospace engineering under the supervision of Prof. Ya-Zhong Luo. His current research interests include spacecraft dynamics and control, collision probability, and trajectory optimization.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Luo, YZ., Sun, ZJ. Safe rendezvous scenario design for geostationary satellites with collocation constraints. Astrodyn 1, 71–83 (2017). https://doi.org/10.1007/s42064-017-0006-5

Download citation

Keywords

  • geostationary orbit (GEO)
  • rendezvous and docking (RVD)
  • safety performance
  • satellite collocation