Abstract

International audience Air traffic management (ATM) represents a domain of emerging and challenging applications of mixed-integer nonlinear programming (MINLP). A number of problems arising in ATM lead naturally to optimization problems whose efficient and reliable solution constitutes a key ingredient of air traffic safety [576]. The air traffic level currently attained in Europe is on the order of tens of thousands of flights per day, and it is expected to grow further on the world scale during the next 20 years. Increasing levels of traffic raise the problem of increasing the capacity of air sectors by better managing the air traffic. This requires increasing the level of automation in ATM, as pointed out in the context of the major projects Single European Sky ATM Research (SESAR) [1667] in Europe and Next Generation Air Transportation System (NextGen) [906] in the United States, which are aimed at designing future ATM systems. Aircraft conflict detection and resolution in en route flights, and the related problem of conflict-free aircraft trajectory planning, are prominent examples of problems that urgently need to be addressed to ensure a higher level of automation in ATM, and consequently more efficiency and safety in air traffic. These problems still deserve investigation of both the identification of suitable mathematical models and the development of efficient and reliable solution methods and algorithms. Mixed-integer nonlinear optimization formulations appear particularly suitable, as they allow us to simultaneously consider continuous as well as discrete decision-making variables and model the complex nonlinear processes characterizing ATM systems. Document type: Part of book or chapter of book

Abstract

International audience; Automatic conflict solving is an old standing problem within the field of ATM. Proposed algorithms fall into two categories : - Deterministic ones that have a provable property of collision avoidance. For all known algorithms, trajectories produced are generally not flyable because no bounds on speed and curvature can be imposed. - Stochastic methods that select an optimal sequence of manoeuvres. By design, trajectories are flyable, but no guarantee can be given on the fact that a collision-free planning can be found in finite time. It is highly desirable for a wide social acceptance of automated trajectory planning, even at a strategical level, that the algorithms in use have by-design the collision avoidance property and, at the same time, a mean of keeping the speed within a given interval. Navigation functions are common in the field of robotics but do not have the last property. We present a new approach based on biharmonic functions yielding a navigation field with constant speed. Such functions have been considered previously, but proof of collision avoidance is lacking: we address this problem in this work as summarized below. Navigation functions produce a speed field by taking the gradient of a potential function: if the obstacles to be avoided are at a higher potential than inner points of the domain (including destination), collision avoidance is guaranteed. If the potential has the Morse property (no critical point is degenerated) then there exists a descent direction at every point of the admissible domain, making the destination reachable. In the framework of biharmonic functions, a tensor field is produced instead of a vector one ; the Morse property is no longer relevant. We show here that all benefits of navigation functions can be recovered through the use of the bienergy density, with the ability to get constant speed fields. Document type: Conference object

Abstract

ft conflict avoidance is a crucial issue arising in air traffic management. The problem is to keep a given separation distance for aircraft along their trajectories. We focus on an optimal control model based on speed regulation to achieve aircraft separation. We propose a solution strategy based on the decomposition of the problem and on the hybridization of a direct and an indirect method applied on the obtained subproblems. Numerical results show that the proposed approach is promising in terms of reduction of computing time for conflict avoidance.

Abstract

Detecting and solving aircraft conflicts, which occur when aircraft sharing the same airspace are too close to each other according to their predicted trajectories, is a crucial problem in Air Traffic Management. We focus on mixed-integer optimization models based on speed regulation. We first solve the problem to global optimality by means of an exact solver. The problem being very difficult to solve, we also propose a heuristic procedure where the problem is decomposed and it is locally solved by an exact solver. Computational results show that the proposed approach provides satisfactory results in reasonable time.

Abstract

International audience; In this paper a numerical study is provided to solve the aircraft conflict avoidance problem through velocity regulation maneuvers. Starting from optimal controlbased model and approaches in which aircraft accelerations are the controls, and by applying the direct shooting technique, we propose to study two different largescale nonlinear optimization problems. In order to compare different possibilities of implementation, two environments (AMPL and MATLAB) and deterministic local optimization solvers are used. Numerical results are discussed. They show that the considered problem is really difficult to solve to global optimality, as different local minima are found using different methods.