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European Consortium for Mathematics in Industry

ECMI 2016: Progress in Industrial Mathematics at ECMI 2016 pp 705–711Cite as

Optimization and Sensitivity Analysis of Trajectories for Autonomous Small Celestial Body Operations

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Part of the book series: Mathematics in Industry ((TECMI,volume 26))

Abstract

Within this paper, a method for on-board trajectory calculation in the vicinity of a small celestial body is introduced. Therefore, high precision methods of nonlinear optimization and optimal control are used. Additionally, a parametric sensitivity analysis is implemented. This tool allows to approximate a perturbed optimal solution in case of model parameter deviations from nominal values without noticeable computational effort. Parametric sensitivity analysis is a recent research area of great interest. Parameter perturbations that occur in the dynamic of the system as well as in boundary conditions or in state and control constraints can be analyzed. Thus, additional stability information is provided. Furthermore, the fast and reliable approximation of perturbed controls can be used for real-time control in time critical navigation phases.

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References

  1. Betts, J.T.: Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, 2nd edn. SIAM, Philadelphia (2010)

    Book  MATH  Google Scholar 

  2. Broschart, S., Scheeres, D.: Control of hovering spacecraft near small bodies: application to asteroid 25143 Itokawa. J. Guid. Control. Dyn. 28(2), 343–354 (2005)

    Article  Google Scholar 

  3. Büskens, C., Maurer, H.: SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control. J. Comput. Appl. Math. 120(1), 85–108 (2000). doi:10.1016/S0377-0427(00)00305-8

    Article  MathSciNet  MATH  Google Scholar 

  4. Büskens, C., Wassel, D.: The ESA NLP solver WORHP. In: Fasano, G., Pintr, J.D. (eds.) Modeling and Optimization in Space Engineering. Springer Optimization and Its Applications, vol. 73, pp. 85–110. Springer, New York (2013). doi:10.1007/978-1-4614-4469-5_4

    Chapter  Google Scholar 

  5. Fiacco, A.V.: Introduction to sensitivity and stability analysis in nonlinear programming. In: Mathematics in Science and Engineering, vol. 165. Academic Press, New York (1983)

    Google Scholar 

  6. Hussmann, H., Oberst, J., Wickhusen, K., Shi, X., Damme, F., Lüdicke, F., Lupovka, V., Bauer, S.: Stability and evolution of orbits around the binary asteroid 175706 (1996 FG3): implications for the MarcoPolo-R mission. Planet. Space Sci. 70(1), 102–113 (2012)

    Article  Google Scholar 

  7. Knauer, M., Büskens, C.: From WORHP to TransWORHP. In: 5th International Conference on Astrodynamics Tools and Techniques (2012)

    Google Scholar 

  8. Probst, A., González Peytaví, G., Nakath, D., Schattel, A., Rachuy, C., Lange, P., Clemens, J., Echim, M., Schwarting, V., Srinivas, A., Gadzicki, K., Förstner, R., Eissfeller, B., Schill, K., Büskens, C., Zachmann, G.: KaNaRiA: identifying the challenges for cognitive autonomous navigation and guidance for missions to small planetary bodies. In: 66th International Astronautical Congress (IAC), pp. IAC-15-A3.IP.15-1–IAC-15-C3.IP.15-14. International Astronautical Federation (2015)

    Google Scholar 

  9. Schäfer, R.: Parametrische Sensitivitätsanalyse. Bachelor thesis, Center for Industrial Mathematics, University of Bremen, Germany (2012)

    Google Scholar 

  10. Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. In: Texts in Applied Mathematics, vol. 12, 3rd edn. Springer Science & Business Media, New York (2002)

    Google Scholar 

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Acknowledgements

This work was supported by the German Aerospace Center (DLR) with financial means of the German Federal Ministry for Economic Affairs and Energy (BMWi), project “KaNaRiA” (grant No. 50 NA 1318).

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Authors and Affiliations

  1. Center for Industrial Mathematics, University of Bremen, Bibliothekstr. 1, 28359, Bremen, Germany

    Anne Schattel, Andreas Cobus, Mitja Echim & Christof Büskens

Authors
  1. Anne Schattel
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  2. Andreas Cobus
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  3. Mitja Echim
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  4. Christof Büskens
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Corresponding author

Correspondence to Anne Schattel .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Peregrina Quintela

  2. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Patricia Barral

  3. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Dolores Gómez

  4. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Francisco J. Pena

  5. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Jerónimo Rodríguez

  6. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Pilar Salgado

  7. Department of Applied Mathematics, University of Santiago de Compostela, Lugo, Spain, Spain

    Miguel E. Vázquez-Méndez

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Schattel, A., Cobus, A., Echim, M., Büskens, C. (2017). Optimization and Sensitivity Analysis of Trajectories for Autonomous Small Celestial Body Operations. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_105

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