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Complex Number Formulation and Convex Relaxations for Aircraft Conflict Resolution [article]

David Rey, Hassan Hijazi
2017 arXiv   pre-print
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem.  ...  Our formulation features one binary variable per pair of aircraft, is free of trigonometric functions, and captures the non-convexity in a set of quadratic concave constraints.  ...  CONCLUSIONS AND FUTURE WORKS We have introduced a novel formulation for the aircraft conflict resolution problem based on a complex number representation of velocity (speed and heading) control.  ... 
arXiv:1703.06708v2 fatcat:xjkptovqorhbnorkmbu6nccaxi

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution [article]

Fernando H. C. Dias, Hassan Hijazi, David Rey
2020 arXiv   pre-print
We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions.  ...  The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic  ...  In this paper, we adopt and extend the complex number formulation for aircraft conflict resolution proposed by Rey and Hijazi (2017) to derive nonconvex mixed-integer programming (MIP) formulations for  ... 
arXiv:1911.12997v3 fatcat:b5kthfkgqveqfim7r7lc5mqbni

Resolution of Conflicts Involving Many Aircraft via Semidefinite Programming

E. Frazzoli, Z.-H. Mao, J.-H. Oh, E. Feron
2001 Journal of Guidance Control and Dynamics  
The resolution architecture relies on a combination of convex programming and randomized searches: It is shown that a v ersion of the planar, multi-aircraft con ict resolution problem that accounts for  ...  Aircraft con ict detection and resolution is currently attracting the interest of many air transportation service providers and is concerned with the following question: Given a set of airborne aircraft  ...  Marc Shewchun for his exploratory investigations. This work was supported by NASA Ames Research Center, under Grant NCC2-1044.  ... 
doi:10.2514/2.4678 fatcat:pxfygcbtfvanpltbzwjyarchvy

Hybridization of Nonlinear and Mixed-Integer Linear Programming for Aircraft Separation With Trajectory Recovery

Jeremy Omer, Jean-Loup Farges
2013 IEEE transactions on intelligent transportation systems (Print)  
The approach presented in this article aims at finding a solution to the problem of conflict-free motion planning for multiple aircraft on the same flight level with trajectory recovery.  ...  A new hybrid algorithm is thus developed in order to use the optimal solution of a mixed integer linear program as a starting point when solving a nonlinear formulation of the problem.  ...  For each scenario described above, four configurations were chosen with increasing numbers of aircraft and conflicts.  ... 
doi:10.1109/tits.2013.2257758 fatcat:wnoedfasw5adtbi6pvu2xqlfja

Joint Metering and Conflict Resolution in Air Traffic Control

Jerome Le Ny, George J. Pappas
2011 Journal of Guidance Control and Dynamics  
Moreover, the proposed methodology can account for some of the nonlinearities present in the formulations of conflict resolution problems, while incurring only a small penalty in computation time with  ...  Integer variables can be introduced to improve the quality of the solutions and to include combinatorial choices, for example, to optimize over aircraft sequences in merging streams.  ...  Simulation results show that complex problem instances involving many aircraft and metered boundaries can be solved very efficiently. II. Problem Formulation A.  ... 
doi:10.2514/1.53253 fatcat:e2rpb5225ragxkcazrvugbik2e

Aircraft Conflict Resolution with Trajectory Recovery Using Mixed-Integer Programming [article]

Fernando H. C. Dias, David Rey
2022 arXiv   pre-print
The avoidance stage extends existing mixed-integer programming formulations, and for the recovery stage, we propose a novel mixed-integer formulation.  ...  In this study, we address the aircraft conflict avoidance and trajectory recovery problem.  ...  The authors introduced a nonconvex formulation for the conflict resolution problem with speed and heading control and proposed a convex relaxation based on semi-definite programming and a heuristic algorithm  ... 
arXiv:2203.11990v1 fatcat:uxpyzajiyncnnjzzgjtceu4blq

Distributed hierarchical MPC for conflict resolution in air traffic control

G Chaloulos, P Hokayem, J Lygeros
2010 Proceedings of the 2010 American Control Conference  
The navigation function methodology is then used to generate conflict free trajectories for all aircraft.  ...  We present a decentralized Model Predictive Control scheme for hierarchical systems to tackle the collision avoidance problem for autonomous aircraft in an air traffic control setting.  ...  The authors would like to thank Giannis Roussos and Kostas Kyriakopoulos for their help and expertise on navigation functions methods.  ... 
doi:10.1109/acc.2010.5530640 fatcat:7nt6ajbumzeh7jy3welkm2riie

Human Control of Air Traffic Trajectory Optimizer

Oliver D. N. Turnbull, Arthur G. Richards
2018 IEEE transactions on intelligent transportation systems (Print)  
The latter include two lines for each aircraft: one in the range -1. The numbers identify the starting point of each flight and the squares mark the targets.  ...  The constraints allow the specification of the relative sense (ahead/behind/over/under) of conflict resolution between aircraft, or the class of the resolution (vertical/horizontal/temporal).  ... 
doi:10.1109/tits.2017.2712637 fatcat:7u4ciyu7gfbrdauajkj3teynty

Aircraft deconfliction with speed regulation: new models from mixed-integer optimization

Sonia Cafieri, Nicolas Durand
2013 Journal of Global Optimization  
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  ...  The problem being very difficult to solve, we also propose a heuristic procedure where the problem is decomposed and it is locally exactly solved.  ...  The solver of choice is COUENNE [3] , which implements a spatial Branch-and-Bound based on convex relaxations. Results are reported in Table 1 for the first proposed model.  ... 
doi:10.1007/s10898-013-0070-1 fatcat:oa6iqpfi6zao3cipjs5nbzzig4

An Airspace-Planning and Collaborative Decision-Making Model: Part II—Cost Model, Data Considerations, and Computations

Hanif D. Sherali, Raymond W. Staats, Antonio A. Trani
2006 Transportation Science  
parameter values for the overall model, and an investigation on incorporating a suitable set of valid inequalities in the model formulation.  ...  can be used by the FAA for both tactical and strategic applications.  ...  Acknowledgments This research has been supported by the National Science Foundation under Grant Number 0094462 and by a Federal Aviation Administration Grant under the National Center of Excellence for  ... 
doi:10.1287/trsc.1050.0141 fatcat:hmgpgwjwuzatxiwogukcsxjeju

Conflict avoidance: 0-1 linear models for conflict detection & resolution

A. Alonso-Ayuso, L. F. Escudero, P. Olaso, C. Pizarro
2011 TOP - An Official Journal of the Spanish Society of Statistics and Operations Research  
The Conflict Detection and Resolution Problem for Air Traffic Flow Management consists of deciding the best strategy for airborne aircraft so that there is guarantee that no conflict takes place, i.e.,  ...  Two integer linear optimization models for conflict avoidance between any number of aircraft in the airspace are proposed, the first being a pure 0-1 linear which avoids conflicts by means of altitude  ...  It has been partially supported by the Spanish Ministry of Science and Innovation through its agency CDTI and the i-Math Ingenio Mathematica project.  ... 
doi:10.1007/s11750-011-0224-6 fatcat:hxyl5zrqgvaszdsv42txl4lybq

An Airspace Planning Model for Selecting Flight-plans Under Workload, Safety, and Equity Considerations

Hanif D. Sherali, J. Cole Smith, Antonio A. Trani
2002 Transportation Science  
These requirements ensure that the workload for air-traffic controllers in each sector is held under a permissible limit, that any potential conflicts are routinely resolvable, and that the various airlines  ...  The model formulation seeks to minimize and delay fuel-cost-based objective function, subject to the constraints that each flight is assigned one of the designated flight-plans, and that the resulting  ...  Quan for his assistance with some of the computations and to two anonymous referees and an Associate Editor for their detailed and constructive comments.  ... 
doi:10.1287/trsc.36.4.378.546 fatcat:vtt2sg5qk5hxnnhmrdujcjhpfe

Graceful Degradation of Air Traffic Operations [article]

Maxime Gariel, Eric Feron
2008 arXiv   pre-print
To support our work, we also introduce a new conflict resolution algorithm, aimed at solving conflicts involving many aircraft when aircraft position information is in the process of degrading.  ...  and safe.  ...  The authors would like to thank John Hansman from MIT for useful discussions about parallel approaches.  ... 
arXiv:0801.4750v1 fatcat:zyi3r7jwjnehlaax5bebv27dkq

Homotopy Route Generation Model for Robust Trajectory Planning [chapter]

Andrija Vidosavljevic, Daniel Delahaye, Vojin Tosic
2017 Lecture Notes in Electrical Engineering  
It is shown that this approach is capable of generating a large number of route shapes with a reasonable number of decision variables.  ...  The article introduces a novel approach for route generation (3D trajectory) based on homotopic feature of continuous functions.  ...  data and specially Cyril Allignol for his assistance in CATS data manipulation.  ... 
doi:10.1007/978-4-431-56423-2_4 fatcat:vlpgl65gvnaczisnuvbusph4we

Conflict Resolution and Traffic Complexity of Multiple Intersecting Flows of Aircraft

K. Treleaven, Zhi-Hong Mao
2008 IEEE transactions on intelligent transportation systems (Print)  
However, if the constraint is relaxed to allow multiple, sequential maneuvers for individual aircraft to avoid conflicts, the analysis becomes simpler: The conflict resolution problem can be decomposed  ...  [17, 18, 19, 20] , and propose a general framework for the conflict resolution of multiple intersecting flows of aircraft.  ... 
doi:10.1109/tits.2008.2006771 fatcat:dxbakcv4gvgotc7moexkkumul4
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