Skip to main content
SpringerLink
Log in

Multiple Space Debris Collecting Mission: Optimal Mission Planning

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Successive missions must be planned to clean the near-Earth space from the heaviest debris. The problem mixes combinatorial optimization to select and order the debris, and continuous optimization to define the orbital maneuvers. In order to reduce the costs all missions have to be achieved by identical expendable vehicles with a minimum fuel requirement. The solution method proposed consists in three stages. Firstly the orbital transfer problem is solved for all pairs of debris and for discretized dates, considering a generic transfer strategy suited either to a high-thrust or to a low-thrust vehicle. The results are stored in cost matrices defining a response surface. Secondly a simulated annealing algorithm is applied to find the optimal mission planning. The cost is assessed by interpolation on the response surface. The convergence is quite fast, yielding an optimal mission planning. Thirdly the successive missions are re-optimized in terms of transfer maneuvers without changing the debris order. These continuous problems yield a refined performance requirement for designing the removal vehicle. The solution method is illustrated on a representative application case.

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

Similar content being viewed by others

Abbreviations

LEO:

Low earth orbit

SSO:

Sun-synchronous orbit

RAAN:

Right ascension of ascending node

SDC:

Space debris collecting

TSP:

Travelling salesman problem

RSM:

Response surface modeling

SA:

Simulated annealing

NLP:

Nonlinear programming

References

  1. Position paper on space debris mitigation. International Academy of Astronautics (2005)

  2. Klinkrad, K. (s.d.): Space debris models and risks analysis. ISBN:3-540-25448-X

  3. Liou, J.: An assessment of the current LEO debris environment and what needs to be done to preserve it for future generations (2008)

  4. Walker R., Martin C.E., Stokes P.H., Wilkinson J.E. : Studies of space debris mitigation options using the debris environment long term analysis (DELTA) model. In: 51st International Astronautical Congress, Brazil, pp. IAA-00_IAA.6.6.07. Rio de Janeiro (2000)

  5. Nemhauser, G.L., Rinnooy Kan, A.H.G., Todd, M.J.: Optimization. In: Handbooks in Operations Research and Management Science, vol. 1. Elsevier, Amsterdam (1989)

  6. Dréo J., Pétrowski A., Siarry P., Taillard E.: Métaheuristiques Pour l’optimisation Difficile. Eyrolles, Paris (2003)

  7. Schneider, J.J., Kirkpatrick, S.: Stochastic Optimization. Springer, Berlin (2006)

    MATH  Google Scholar 

  8. Cerf, M.: Multiple space debris collecting mission, debris selection and trajectory optimization. J. Optim. Theory Appl. 156, 761–796 (2013). doi:10.1007/s10957-012-0130-6

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

    Article  Google Scholar 

  10. Barbee, B.W., Alfano, S., Piñon, E., Gold, K., Gaylor, D.: Design of spacecraft missions to remove multiple orbital debris objects. AAS 12-017. In: 35th Annual AAS Guidance and Control Conference (2012)

  11. Zuiani, F., Vasile, M.: Preliminary design of debris removal missions by means of simplified models for low-thrust many revolution transfers. Int. J. Aerosp. Eng. 836250 (2012)

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

    Article  Google Scholar 

  13. Stuart, J., Howell, K., Wilson, R.: Application of multi-agent coordination methods to the design of space debris mitigation tours. In: 24th International Symposium on Space Flight Dynamics (2014)

  14. Chobotov, V.: Orbital Mechanics, 3rd edn. AIAA Education Series (2002)

  15. Vallado, D.A.: Fundamentals of Astrodynamics and Applications, 3rd edn. Space Technology Library (2007)

  16. Leitmann, G.: Theory of maxima and minima. In: Optimization Technique with Applications to Aerospace System. Academic Press, New York (1962)

  17. Conway, B.A.: Spacecraft Trajectory Optimization. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  18. NORAD Two Line Elements. http://www.celestrak.com/NORAD/elements/

Download references

Acknowledgments

This work was carried out at Airbus Defence and Space in 2013–2014 in the frame of the internal R&D. I would like to thank the R&D team project for having supported this work.

Author information

Authors and Affiliations

  1. AIRBUS Defence and Space, Les Mureaux, France

    Max Cerf

Authors
  1. Max Cerf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Max Cerf.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cerf, M. Multiple Space Debris Collecting Mission: Optimal Mission Planning. J Optim Theory Appl 167, 195–218 (2015). https://doi.org/10.1007/s10957-015-0705-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-015-0705-0

Keywords

Mathematics Subject Classification

Search

Navigation