Trajectory Optimization for Launchers and Re-entry Vehicles
Launchers and reentry vehicles have in common the necessity to perform part of their trajectory along the planet atmosphere. While this has only negative effects for the launch vehicle, for the re-entry vehicle, the interaction with the atmosphere can be
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Trajectory Optimization for Launchers and Re-entry Vehicles Francesco Cremaschi
Abstract Launchers and reentry vehicles have in common the necessity to perform part of their trajectory along the planet atmosphere. While this has only negative effects for the launch vehicle, for the re-entry vehicle, the interaction with the atmosphere can be suitably exploited for the fulfillment of the mission. The launch and reentry trajectory is a complex scenario that should be modeled using simplified physics equations describing with sufficient accuracy the subsystems of the vehicle and the environment. In a second step, this simplified physical model, described by sets of differential equations, should be transcribed in a mathematical set of algebraic equations that can be solved by non-linear programming methods (NLP solvers). Upon further analysis of these direct transcription methods, two subclasses can be identified: shooting methods and collocation methods. The NLP solver can be a global optimizer, e.g., genetic algorithm, particle swarm, some other metaheuristics or sequential quadratic programming (SQP), in the case of differentiable functions. Several examples of launch and reentry vehicle problems are presented, with a strong emphasis on the advantages and disadvantages of the various transcription methods and solvers when applied to “real” world problems. Keywords Launcher • Re-entry vehicle • Trajectory • Gradient method • Multiple shooting • Collocation • Modeling
7.1
Introduction
The trajectory optimization for space applications comprises a wide spectrum of different scenarios: from powerful ascent of a multistage rocket to the gentle descent of a lunar lander, from the slow rendezvous and docking of an automatic
F. Cremaschi (*) Astos Solutions GmbH, Meitnerstrasse 8, Stuttgart, Germany e-mail: [email protected] G. Fasano and J.D. Pinte´r (eds.), Modeling and Optimization in Space Engineering, Springer Optimization and Its Applications 73, DOI 10.1007/978-1-4614-4469-5_7, # Springer Science+Business Media New York 2013
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cargo to the International Space Station (ISS,[1]) to the fast planet fly-by of an interplanetary probe. This chapter analyzes only the launchers and reentry vehicles, which have in common the necessity to perform part of their trajectory inside the planet atmosphere. In the case of a conventional launch vehicle, this thin layer counteracts the vehicle propulsion system reducing its performance; for the reentry vehicle, however, the interaction with the atmosphere can even be necessary for the fulfillment of the mission. The complexity of these scenarios requires an automatic optimization performed by a mathematical solver. Section 7.2 presents the modeling of satellite launchers, whereas Sect. 7.3 details the modeling of the re-entry vehicles. The most common simplified physical equations are listed in Sect. 7.4 whereas the transcription methods and the solvers are detailed in Sect. 7.5. The chapter is enriched with various examples taken from past and
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