Conflict assessment and resolution of climate-optimal aircraft trajectories at network scale

Aviation contributes to anthropogenic climate change through carbon dioxide (CO2) and non-CO2 emissions. Due to dependency on atmospheric conditions, the non-CO2 climate impacts can be mitigated using aircraft trajectory optimization. However, adopting independently optimized trajectories may not be operationally feasible for the air traffic management system due to the associated impacts on the safety, demand, and complexity of air traffic. This study aims to explore the effects of employing climate-optimized trajectories on air traffic complexity in terms of the number of conflicts and propose a strategic resolution based on speed change to resolve the conflicts that arise. A scenario with 1005 flights is considered as the case study. The results indicate that the adoption of climate-optimal trajectories increases operational cost and the number of conflicts. Employing the proposed resolution algorithm, it is shown that the conflicts can be resolved by accepting slight increases in climate impact and cost

A survey on low-thrust trajectory optimization approaches

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

Robust Aircraft Trajectory Planning under Wind Uncertainty using Optimal Control

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 ut a l so r educed t hrough t he application of the proposed approach.This work has been partially supported by project TBO-MET project, which has receivedfunding from the SESAR JU under grant agreement No 699294 under the European Union’s Horizon 2020 research and innovation program. This work is also partially supported by the Spanish Government through Project entitled Analysis and optimisation of aircraft trajectories under the effects of meteorological uncertainty (TRA2014-58413-C2-2-R); this project has been funded under R&D&I actions of Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad (call 2014)

Fundamental framework to plan 4D robust descent trajectories for uncertainties in weather prediction

Aircraft trajectory planning is affected by various uncertainties. Among them, those in weather prediction have a large impact on the aircraft dynamics. Trajectory planning that assumes a deterministic weather scenario can cause significant performance degradation and constraint violation if the actual weather conditions are significantly different from the assumed ones. The present study proposes a fundamental framework to plan four-dimensional optimal descent trajectories that are robust against uncertainties in weather-prediction data. To model the nature of the uncertainties, we utilize the Global Ensemble Forecast System, which provides a set of weather scenarios, also referred to as members. A robust trajectory planning problem is constructed based on the robust optimal control theory, which simultaneously considers a set of trajectories for each of the weather scenarios while minimizing the expected value of the overall operational costs. We validate the proposed planning algorithm with a numerical simulation, assuming an arrival route to Leipzig/Halle Airport in Germany. Comparison between the robust and the inappropriately-controlled trajectories shows the proposed robust planning strategy can prevent deteriorated costs and infeasible trajectories that violate operational constraints. The simulation results also confirm that the planning can deal with a wide range of cost-index and required-time-of-arrival settings, which help the operators to determine the best values for these parameters. The framework we propose is in a generic form, and therefore it can be applied to a wide range of scenario settings

On maximizing safety in stochastic aircraft trajectory planning with uncertain thunderstorm development

Dealing with meteorological uncertainty poses a major challenge in air traffic management (ATM). Convective weather (commonly referred to as storms or thunderstorms) in particular represents a significant safety hazard that is responsible for one quarter of weather-related ATM delays in the US. With commercial air traffic on the rise and the risk of potentially critical capacity bottlenecks looming, it is vital that future trajectory planning tools are able to account for meteorological uncertainty. We propose an approach to model the uncertainty inherent to forecasts of convective weather regions using statistical analysis of state-of-the-art forecast data. The developed stochastic storm model is tailored for use in an optimal control algorithm that maximizes the probability of reaching a waypoint while avoiding hazardous storm regions. Both the aircraft and the thunderstorms are modeled stochastically. The performance of the approach is illustrated and validated through simulated case studies based on recent nowcast data and storm observations

Wind-Based Robust Trajectory Optimization using Meteorological Ensemble Probabilistic Forecasts

A major challenge for Trajectory-Based Operations is the existence of significant uncertainties in the models and systems required for trajectory prediction. In particular, weather uncertainty has been acknowledged as one of the most (if not the most) relevant ones. In the present paper we present preliminary results on robust trajectory planning at the pre-tactical level. The main goal is to plan trajectories that are efficient, yet predictable. State-of-the-art forecasts from Ensemble Prediction Systems are used as input data for the wind field, which we assume to be the unique source of uncertainty. We develop an ad-hoc optimal control methodology to solve trajectory planning problems considering uncertainty in wind fields. A set of Paretooptimal trajectories is obtained for different preferences between predictability and average efficiency; in particular, we present and discuss results for the minimum average fuel trajectory and the most predictable trajectory, including the trade-off between fuel consumption and time dispersion. We show how uncertainty can be quantified and reduced by proposing alternative trajectories.This work has been partially supported by project TBO-MET project (https://tbometh2020. com/), which has received funding from the SESAR JU under grant agreement No 699294 under European Union’s Horizon 2020 research and innovation programme. This work is also partially supported by the Spanish Government through Project entitled Analysis and optimisation of aircraft trajectories under the effects of meteorological uncertainty (TRA2014-58413-C2-2-R). The project has been funded under RD&I actions of Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad (call 2014).European Commissio

Optimal Aircraft Trajectory Planning in the Presence of Stochastic Convective Weather Cells

The Air Traffic Management system is heavily influenced by meteorological uncertainty, and convective weather cells represent one of the most relevant uncertain meteorological phenomena. They are weather hazards that must be avoided through tactical trajectory modifications. As a consequence of the existence in uncertainty in meteorological forecasts and nowcasts, it is important to consider the convective weather cells to be avoided as a stochastic, time-dependent process. In this paper we present a comparative analysis of two methodologies for handling stochastic storms in trajectory planning: one based on stochastic reachability and a second one, based on robust optimal control. In the former, the thunderstorm avoidance problem is modelled as a stochastic reach-avoid problem, considering the motion of the aircraft as a discrete-time stochastic system and the weather hazards as random set-valued obstacles. Dynamic programming is used to compute a Markov feedback policy that maximizes the probability of reaching the target before entering the unsafe set, i.e., the hazardous weather zones. For the latter, the stochastic dynamics of the storms are modeled in continuous time. We implement an optimal control formulation that allows different possible realizations of the stochastic process to be considered. The resulting problem is then transcribed to a nonlinear programming (NLP) problem through the use of direct numerical methods. A benchmark case study is presented, in which the effectiveness of the two proposed approaches are analyzed.This work has been partially supported by project TBO-MET project (https://tbomet-h2020.com/), which has received funding from the SESAR JU under grant agreement No 699294 under European Union’s Horizon 2020 research and innovation programme. This work is also partially supported by the Spanish Government through Project entitled Analysis and optimisation of aircraft trajectories under the effects of meteorological uncertainty (TRA2014-58413-C2-2-R). The project has been funded under RD&I actions of Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad (call 2014).European Commissio

Informed scenario-based RRT* for aircraft trajectory planning under ensemble forecasting of thunderstorms

Thunderstorms represent a major hazard for flights, as they compromise the safety of both the airframe and the passengers. To address trajectory planning under thunderstorms, three variants of the scenario-based rapidly exploring random trees (SB-RRTs) are proposed. During an iterative process, the so-called SB-RRT, the SB-RRT* and the Informed SB-RRT* find safe trajectories by meeting a user-defined safety threshold. Additionally, the last two techniques converge to solutions of minimum flight length. Through parallelization on graphical processing units the required computational times are reduced substantially to become compatible with near real-time operation. The proposed methods are tested considering a kinematic model of an aircraft flying between two waypoints at constant flight level and airspeed; the test scenario is based on a realistic weather forecast and assumed to be described by an ensemble of equally likely members. Lastly, the influence of the number of scenarios, safety margin and iterations on the results is analyzed. Results show that the SB-RRTs are able to find safe and, in two of the algorithms, closeto- optimum solutions.This work has received funding from (1) the Spanish Government (Project RTI2018-098471-B-C32) and (2) the SESAR Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 783287

Robust aircraft trajectory planning under uncertain convective environments with optimal control and rapidly developing thunderstorms

Convective weather, and thunderstorm development in particular, represents a major source of disruption, delays and safety hazards in the Air Traffic Management system. Thunderstorms are challenging to forecast and evolve on relatively rapid timescales; therefore, aircraft trajectory planning tools need to consider the uncertainty in the forecasted evolution of these convective phenomena. In this work, we use data from a satellite-based product, Rapidly Developing Thunderstorms, to estimate a model of the uncertain evolution of thunderstorms. We then introduce a methodology based on numerical optimal control to generate avoidance trajectories under uncertain convective weather evolution. We design a randomized procedure to initialize the optimal control problem, explore the different resulting local optima, and identify the best trajectory. Finally, we demonstrate the proposed methodology on a realistic test scenario, employing actual forecast data and an aircraft performance model.This work is supported by the Spanish Government through Project entitled Analysis and optimisation of aircraft trajectories under the effects of meteorological uncertainty (TRA2014-58413-C2-2-R)12; this project has been funded under R&D&I actions of Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad (call 2014).Publicad

Effects of Reducing Wind-Induced Trajectory Uncertainty on Sector Demand

In this paper, a first step to analyse the effects of reducing the uncertainty of aircraft trajectories on sector demand is presented. The source of uncertainty is wind, forecasted by Ensemble Prediction Systems, which are composed of different possible atmosphere realizations. A trajectory predictor determinesthe routes to be followed by the different flights to reduce the uncertainty of the arrival times. The sector demand is described in terms of entry count, that is, the number of flights entering the sector during a selected time period, which is uncertain because so are the the entry times to the sector. Results are presented for a realistic application, where the dispersion of the entry count isshown to be reduced when the dispersion of the arrival times is also reduced.This work is part of the project TBO-Met. This project has received funding from the SESAR Joint Undertaking under grant agreement No 699294 under European Union’s Horizon 2020 research and innovation programm