Numerical study of optimal trajectories with singular arcs for space launcher problems

Pierre Martinon 1, 2 Frédéric Bonnans 1, 2 Julien Laurent-Varin 3 Emmanuel Trélat 4
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : The subject of this paper is the study of singular arcs (i.e. with a non maximal thrust) for a space launcher problem. We consider a flight to the GTO orbit for a heavy multi-stage launcher (Ariane 5 class), and use a realistic physical model for the drag force and rocket thrust. As a preliminary result, we first solve the complete flight with stage separations, at full thrust. Then we focus on the first atmospheric climbing phase, to investigate the possible existence of optimal trajectories with singular arcs. We primarily use an indirect shooting method (based on Pontryagin's Minimum Principle), coupled to a continuation (homotopy) approach. Some additional experiments are made with a basic direct method, and confirm the solutions obtained by the shooting. We study two slightly different launcher models, and observe that modifying parameters such as the aerodynamic reference area and specific impulsion can indeed lead to optimal trajectories with either full thrust or singular arcs.
Type de document :
[Research Report] RR-6460, INRIA. 2008, pp.26
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Soumis le : lundi 3 mars 2008 - 14:53:22
Dernière modification le : jeudi 10 mai 2018 - 02:04:11
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  • HAL Id : inria-00260180, version 2


Pierre Martinon, Frédéric Bonnans, Julien Laurent-Varin, Emmanuel Trélat. Numerical study of optimal trajectories with singular arcs for space launcher problems. [Research Report] RR-6460, INRIA. 2008, pp.26. 〈inria-00260180v2〉



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