Uncertainty in aircraft trajectory planning and prediction generates major challenges for the future Air Traffic Management system. Therefore, understanding and managing uncertainty will be necessary to realize improvements in air traffic capacity, safety, efficiency and environmental impact. Meteorology (and, in particular, winds) represents one of the most relevant sources of uncertainty. In the present work, a framework based on optimal control is introduced to address the problem of robust and efficient trajectory planning under wind forecast uncertainty, which is modeled with probabilistic forecasts generated by Ensemble Prediction Systems. The proposed methodology is applied to a flight p l anning s c enario u n der a f r ee-routing operational paradigm and employed to compute trajectories for different sets of user preferences, exploring the trade-off between average flight cost and p r edictability. Results show how the impact of wind forecast uncertainty in trajectory predictability at a pre-tactical planning horizon can be not only quantified, b u t a l so r e duced t h rough t h e application of the proposed approach.

In year 2000 a house-made orbital propagator was developed by the SDG-UPM (former Grupo de Dinámica de Tethers) based in a set of redundant variables including Euler parameters. This propagator was called DROMO * and it was mainly used in numerical simulations of electrodynamic tethers. It was presented for the first time in the international meeting V Jornadas de Trabajo en Mecánica Celeste, held in Albarracín, Spain, in 2002 (see reference 1). The special perturbation method associated with DROMO can be consulted in the paper. 2 In year 1975, Andre Deprit in reference 3 proposes a propagation scheme very similar to the one in which DROMO is based, by using the ideal frame concept of Hansen. The different approaches used in references 3 and 2 gave rise to a small controversy. In this paper we carried out a different deduction of the DROMO propagator, underlining its close relation with the Hansen ideal frame concept, and also the similarities and the differences with the theory carried out by Deprit in 3. Simultaneously we introduce some improvements in the formulation that leads to a more synthetic propagator.

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In this paper, we provide a survey on available numerical approaches for solving low-thrust trajectory optimization problems. First, a general mathematical framework based on hybrid optimal control will be presented. This formulation and their elements, namely objective function, continuous and discrete state and controls, and discrete and continuous dynamics, will serve as a basis for discussion throughout the whole manuscript. Thereafter, solution approaches for classical continuous optimal control problems will be briefly introduced and their application to low-thrust trajectory optimization will be discussed. A special emphasis will be placed on the extension of the classical techniques to solve hybrid optimal control problems. Finally, an extensive review of traditional and state-of-the art methodologies and tools will be presented. They will be categorized regarding their solution approach, the objective function, the state variables, the dynamical model, and their application to planetocentric or interplanetary transfers.

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