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 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.