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v1 (2008-03-03)

v2 (2008-03-03)

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

Pierre Martinon 1, 2, Frédéric J. Bonnans 1, 2, Julien Laurent-Varin 3, Emmanuel Trélat 4

(2008)

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.

1:	Commands (INRIA Futurs)
	INRIA – CNRS : UMR7641
2:	Centre de Mathématiques Appliquées (CMAP)
	CNRS : UMR7641 – Université de Versailles Saint-Quentin-en-Yvelines – Polytechnique - X
3:	Direction des lanceurs
	CNES
4:	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349

Domain

:

Mathematics/Optimization and Control

Keywords: optimal control – launcher problem – singular arcs – indirect shooting – continuation

inria-00260180, version 2

http://hal.inria.fr/inria-00260180

oai:hal.inria.fr:inria-00260180

From: Rapport De Recherche Inria <>

Submitted on: Monday, 3 March 2008 14:53:22

Updated on: Monday, 3 March 2008 14:56:15