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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The Air Traffic Management (ATM) system in the busiest airspaces in the world is currently being overhauled to deal with multiple capacity, socioeconomic, and environmental challenges. One major pillar of this process is the shift towards a concept of operations centered on aircraft trajectories (called Trajectory-Based Operations or TBO in Europe) instead of rigid airspace structures. However, its successful implementation (and, thus, the realization of the associated improvements in ATM performance) rests on appropriate understanding and management of uncertainty. Due to its complex socio-technical structure, the design and operations of the ATM system are heavily impacted by uncertainty, proceeding from multiple sources and propagating through the interconnections between its subsystems.One major source of ATM uncertainty is weather. Due to its nonlinear and chaotic nature, a number of meteorological phenomena of interest cannot be forecasted with complete accuracy at arbitrary lead times, which leads to uncertainty or disruption in individual air and ground operations that propagates to all ATM processes. Therefore, in order to achieve the goals of SESAR and similar programs, it is necessary to deal with meteorological uncertainty at multiple scales, from the trajectory prediction and planning processes to flow and traffic management operations. This thesis addresses the problem of single-aircraft flight planning considering two important sources of meteorological uncertainty: wind prediction error and convective activity. As the actual wind field deviates from its forecast, the actual trajectory will diverge in time from the planned trajectory, generating uncertainty in arrival times, sector entry and exit times, and fuel burn. Convective activity also impacts trajectory predictability, as it leads pilots to deviate from their planned route, creating challenging situations for controllers. In this work, we aim to develop algorithms and methods for aircraft trajectory optimization that are able to integrate information about the uncertainty in these meteorological phenomena into the flight planning process at both pre-tactical (before departure) and tactical horizons (while the aircraft is airborne), in order to generate more efficient and predictable trajectories.To that end, we frame flight planning as an optimal control problem, modeling the motion of the aircraft with a point-mass model and the BADA performance model. Optimal control methods represent a flexible and general approach that has a long history of success in the aerospace field. As a numerical scheme, we use direct methods, which can deal with nonlinear systems of moderate and high-dimensional state spaces in a computationally manageable way. Nevertheless, while this framework is well-developed in the context of deterministic problems, the techniques for the solution of practical ix x Abstract optimal control problems under uncertainty are not as mature, and the methods proposed in the literature are not applicable to the flight planning probl...

Abstract:One key issue in the simulation of bare electrodynamic tethers (EDTs) is the accurate and fast computation of the collected current, an ambient dependent operation necessary to determine the Lorentz force for each time step. This paper introduces a novel semianalytical solution that allows researchers to compute the current distribution along the tether efficient and effectively under orbital-motion-limited (OML) and beyond OML conditions, i.e., if tether radius is greater than a certain ambient dependent threshold. The method reduces the original boundary value problem to a couple of nonlinear equations. If certain dimensionless variables are used, the beyond OML effect just makes the tether characteristic length L* larger and it is decoupled from the current determination problem. A validation of the results and a comparison of the performance in terms of the time consumed is provided, with respect to a previous ad hoc solution and a conventional shooting method.

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