Mathematical Models for Aircraft Trajectory Design: A Survey

Delahaye, Daniel; Puechmorel, Stéphane; Tsiotras, Panagiotis; Féron, Éric

doi:10.1007/978-4-431-54475-3_12

Cited by 66 publications

(62 citation statements)

References 77 publications

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“…With classical trajectory representation, as an ordered list of position vectors (samples) in 4D, brute force approach for detection of conflicting points implies a pairwise comparison of trajectory samples. This is, however, a time consuming process and not suitable for a problem that involves a large number of samples [27]. In this work, a grid-based scheme developed in [28] is used for position vector comparison.…”

Section: Robustness and Flight Interactionmentioning

confidence: 99%

Homotopy Route Generation Model for Robust Trajectory Planning

Vidosavljević

Delahaye

Tosic

2017

Lecture Notes in Electrical Engineering

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Although advance future avionics will enable full compliance with the given trajectory; there are many uncertainty sources that can deflect aircraft from their intended positions. In this article we investigate potential of robust trajectory planning, considered as an additional demand management action, as a mean to alleviate the en-route congestion in airspace. Robust trajectory planning (RTP) involves generation of congestion-free trajectories with minimum operating cost taking into account uncertainty of trajectory prediction and unforeseen event. The model decision variables include ground delay, change of horizontal route and vertical profile (flight level) to resolve congestion problem. The article introduces a novel approach for route generation (3D trajectory) based on homotopic feature of continuous functions. It is shown that this approach is capable of generating a large number of route shapes with a reasonable number of decision variables. RTP problem is modeled as a mixed-variable optimization problem and it is solved using stochastic optimization technique. The model is tested on a real-life example from the French airspace. The results indicate that, under certain conditions, with small increase of total planned costs, it is possible to increase robustness of the proposed solution providing a good alternative to the solutions given by existing conflict-free trajectory planning models.

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Section: Robustness and Flight Interactionmentioning

confidence: 99%

Homotopy Route Generation Model for Robust Trajectory Planning

Vidosavljević

Delahaye

Tosic

2017

Lecture Notes in Electrical Engineering

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“…In order to have smooth and realistic flight trajectories of the simulated intruder, they are generated using the basis spline model, a common method for aircraft trajectory modelling [19]. In particular we have implemented uniform splines of degree three.…”

Section: Trajectory Generationmentioning

confidence: 99%

SIGS: Synthetic Imagery Generating Software for the Development and Evaluation of Vision-based Sense-And-Avoid Systems

Carrio

Collumeau

et al. 2015

J Intell Robot Syst

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Unmanned Aerial Systems (UASs) have recently become a versatile platform for many civilian applications including inspection, surveillance and mapping. Sense-and-Avoid systems are essential for the autonomous safe operation of these systems in non-segregated airspaces. Vision-based Sense-andAvoid systems are preferred to other alternatives as their price, physical dimensions and weight are more suitable for small and medium-sized UASs, but obtaining real flight imagery of potential collision scenarios is hard and dangerous, which complicates the development of Vision-based detection and tracking algorithms. For this purpose, user-friendly software for synthetic imagery generation has been developed, allowing to blend user-defined flight imagery of a simulated aircraft with real flight scenario images to produce realistic images with ground truth annotations. These are extremely useful for the development and benchmarking of Vision-based detection and tracking algorithms at a much lower cost and risk. An image processing algorithm has also been developed for automatic detection of the occlusions caused by certain parts of the UAV which carries the camera. The detected occlusions can later be used by our software to simulate the occlusions due to the UAV that would appear in a real flight with the same camera setup. Additionally this algorithm could be used to mask out pixels which do not contain relevant information of the scene for the visual detection, making the image search process more efficient. Finally an application example of the imagery obtained with our software for the benchmarking of a state-of-art visual tracker is presented.

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“…A survey of mathematical models for aircraft trajectory design can be found in the work of Delahaye et al Planning several trajectories interacting with each other is a complex problem and different approaches can be considered to solve it. Among them, the simplest and most common one is the sequential approach .…”

Section: Introductionmentioning

confidence: 99%

“…On the opposite of direct approach or Pontryagin‐based optimization algorithms that rely on necessary conditions for optimality, HJB approach gives a global optimum avoiding initialization and convergence questions. For instance, according to, the optimal control formulation of a trajectory optimization problem using Pontryagin's Maximum Principle leads to a 2‐point Boundary Value Problem. Numerical techniques such as shooting methods can be applied to solve accurately this 2‐point Boundary Value Problem, but their convergence is very sensitive to the choice of an initial guess for the solution.…”

Section: Introductionmentioning

confidence: 99%

On a Hamilton‐Jacobi‐Bellman approach for coordinated optimal aircraft trajectories planning

Parzani

Puechmorel

2017

Optim Control Appl Methods

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Summary In the context of future air traffic management, an increasing importance is given to environmental considerations and especially fuel consumption. It is thus advisable to make an optimal use of external conditions knowledge, like wind or temperature, to reduce the total fuel needed to complete a flight. On the other hand, safety must be guaranteed all over the trajectory: encounters below the regulatory separation minima, termed as conflicts, must never occur. In this paper, we consider the problem of optimally planning conflict free aircraft trajectories, based on a minimal time criterion and taking into account an ambient wind field. Aircraft motions are restricted to the horizontal plane only to reduce the dimension of the problem and to avoid costly changes of flight level. Since global optimality for the whole set of aircraft is sought after, the admissible space is modeled after a Cartesian product of the individual, 2‐dimensional state spaces with forbidden configurations removed. A Hamilton‐Jacobi‐Bellman approach in the so‐called configuration space obtained that way is then applied to get a coordinated, conflict‐free optimal planning. One of the main advantages of this method is the insurance of getting a global optimum without having to rely on a complex initialization procedure. In this work, the Ultra‐Bee scheme is adapted to configuration spaces and solved in a 4‐dimensional plus time setting.

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Mathematical Models for Aircraft Trajectory Design: A Survey

Cited by 66 publications

References 77 publications

Homotopy Route Generation Model for Robust Trajectory Planning

Homotopy Route Generation Model for Robust Trajectory Planning

SIGS: Synthetic Imagery Generating Software for the Development and Evaluation of Vision-based Sense-And-Avoid Systems

On a Hamilton‐Jacobi‐Bellman approach for coordinated optimal aircraft trajectories planning

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