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