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

González-Arribas, Daniel; Hentzen, Daniel; Sanjurjo-Rivo, Manuel; Soler, Manuel; Kamgarpour, Maryam

doi:10.2514/6.2017-3431

Cited by 3 publications

(4 citation statements)

References 16 publications

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“…Indirect methods are implemented to solve the multi-phase optimal control problem proposed in [16], whose results are compared with trajectories calculated by the FMS under various wind conditions [17]. Gonzalez-Arribas et al address in [46][47][48][49] a robust optimal trajectory planning problem under wind and convective weather uncertainties using stochastic optimal control. Direct collocation method is used in [19] to transform the optimal control formulation proposed for the optimization of the descent phase.…”

Section: Related Work and Contributionsmentioning

confidence: 99%

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Holistic Approach for Aircraft Trajectory Optimization Using Optimal Control

Kasmi¹,

Laporte²,

Mongeau³

et al. 2023

Journal of Aircraft

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This paper deals with an optimal control approach for commercial aircraft trajectory planning, focusing on the vertical path and the minimization of the fuel burned. The main contribution is the optimization of the whole trajectory, also called the mission, without prior separation into different flight phases (climb, cruise, and descent), contrary to traditional approaches that consider the flight phases sequentially. The proposed optimal control problem (OCP) is formulated and then solved using a direct collocation method. Initial results yield optimal trajectories with a gradual climb during the cruise (climb cruise), which correspond to theoretical trajectories that minimize fuel consumption. Furthermore, a penalization is introduced to ensure vertical profiles featuring horizontal cruise levels on so-called flight levels, compliant with current air traffic management regulations. The use of direct methods to address this OCP induces large nonlinear optimization problems that are solved using an interior point method. This methodology is likely to lead to poor local optima, but a simple multistart heuristic shows that the solutions found for standard problems appear to be globally optimal. Such an approach does not need to impose a priori the cruise flight levels and is suitable for commercial aircraft flight planning purposes. It leads to fuel saving and subsequently to important improvements against environmental impact by reducing [Formula: see text] emissions.

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Section: Related Work and Contributionsmentioning

confidence: 99%

“…Nevertheless, it is composed of simple and easily manageable equations that allow the representation of essential aircraft performance behavior. For these reasons, this model is commonly used by the research community, particularly in aircraft trajectory optimization [23,44,48].…”

Section: Performance Modelmentioning

confidence: 99%

Holistic Approach for Aircraft Trajectory Optimization Using Optimal Control

Kasmi¹,

Laporte²,

Mongeau³

et al. 2023

Journal of Aircraft

View full text Add to dashboard Cite

show abstract

“…In [203], a receding horizon optimization scheme is employed in order to compute avoidance trajectories. A different approach involves formulating a stochastic reach-avoid problem [6,10,204], which is then solved through dynamic programming techniques. Markov Decision Process techniques have also been employed in related works [205].…”

Section: Convective Environmentsmentioning

confidence: 99%

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

González-Arribas

Soler

Sanjurjo-Rivo

et al. 2019

Aerospace Science and Technology

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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...

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“…The problem was reformulated as a finite horizon stochastic optimal control problem and solved with Bellman's Dynamic Programming principle. We proposed this method as a feasible approach to aircraft trajectory planning in the presence of a single hypothetical thunderstorm, modeled by a stochastic ellipse Gonzalez-Arribas et al (2017). However, in this preliminary study, we assumed a priori knowledge of the stochastic unsafe-to-fly regions.…”

Section: Introductionmentioning

confidence: 99%

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

Hentzen

Kamgarpour

Soler

et al. 2018

Aerospace Science and Technology

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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.

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

Cited by 3 publications

References 16 publications

Holistic Approach for Aircraft Trajectory Optimization Using Optimal Control

Holistic Approach for Aircraft Trajectory Optimization Using Optimal Control

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

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

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