(a) s i j = 0, 3D View. (b) (s i j ,t i j ) = (1, 0), 2D View. (c) (s i j ,t i j ) = (1, 1), 2D View. (d) (s i j, 3D, p.67 ,
European airspace concept handbook for PBN implementation, 2013. ,
Shortest Paths for Disc Obstacles, Proceedings of the International Conference on Computational Science and Its Applications, pp.62-70, 2004. ,
DOI : 10.1007/978-3-540-24767-8_7
Turn-constrained route planning for avoiding hazardous weather, Air Traffic Control Quarterly, vol.14, issue.2, pp.159-182, 2006. ,
Aircraft trajectory planning with dynamical obstacles by artificial evolution and convex hull generations, the 4th ENRI International Workshop on ATM/CNS (EIWAC2015), 2015. ,
DOI : 10.1007/978-4-431-56423-2_3
URL : https://hal.archives-ouvertes.fr/hal-01280638
Optimization of arrival and departure routes in terminal maneuvering area, the 6th International Conference on Research in Air Transportation (ICRAT2014), 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01002807
Allocating 3D-trajectories to air traffic flows using A* and genetic algorithms, Proceedings of the International Conference on Computational Intelligence for Modelling, Control, and Automation (CIMCA04), (Gold Coast, Australia), 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-01020102
LSZH (Zurich), 2007. ,
Current market outlook, 2016. ,
Optimizing the Design of a Route in Terminal Maneuvering Area Using Branch and Bound, the 4th ENRI International Workshop on ATM/CNS (EIWAC2015), 2015. ,
DOI : 10.1007/978-4-431-56423-2_9
URL : https://hal.archives-ouvertes.fr/hal-01503222
Optimizing the Design of a Route in Terminal Maneuvering Area Using Branch and Bound, Lecture Notes in Electrical Engineering, vol.41, pp.171-184, 2017. ,
DOI : 10.1007/978-4-431-56423-2_9
URL : https://hal.archives-ouvertes.fr/hal-01503222
Optimization-Based Design of Departure and Arrival Routes in Terminal Maneuvering Area, Journal of Guidance Control and Dynamics ,
URL : https://hal.archives-ouvertes.fr/hal-01512533
Optimal design of SIDs/STARs in TMA using simulated annealing, 2016 IEEE/AIAA 35th Digital Avionics Systems Conference (DASC), 2016. ,
DOI : 10.1109/DASC.2016.7778099
URL : https://hal.archives-ouvertes.fr/hal-01379998
A note on two problems in connexion with graphs, Numerische Mathematik, vol.4, issue.1, pp.269-271, 1959. ,
DOI : 10.1007/BF01386390
On a routing problem, Quarterly of Applied Mathematics, vol.16, issue.1, pp.87-90, 1958. ,
DOI : 10.1090/qam/102435
An Automatic Method of Solving Discrete Programming Problems, Econometrica, vol.28, issue.3, pp.497-520, 1960. ,
DOI : 10.2307/1910129
Branch-and-Bound Methods: A Survey, Operations Research, vol.14, issue.4, pp.699-719, 1966. ,
DOI : 10.1287/opre.14.4.699
Branch and Bound algorithms ? principles and examples, 1999. ,
Integer Programming by Implicit Enumeration and Balas??? Method, SIAM Review, vol.9, issue.2, pp.178-190, 1967. ,
DOI : 10.1137/1009031
URL : http://www.dtic.mil/get-tr-doc/pdf?AD=AD0628361
Discrete Programming by the Filter Method, Operations Research, vol.15, issue.5, pp.915-957, 1967. ,
DOI : 10.1287/opre.15.5.915
A Formal Basis for the Heuristic Determination of Minimum Cost Paths, IEEE Transactions on Systems Science and Cybernetics, vol.4, issue.2, pp.100-107, 1968. ,
DOI : 10.1109/TSSC.1968.300136
Metaheuristics for Hard Optimization, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-01341683
Particle swarm optimization, Proceedings of ICNN'95, International Conference on Neural Networks, pp.1942-1948, 1995. ,
DOI : 10.1109/ICNN.1995.488968
Ant Colony Optimization, 2004. ,
Genetic Algorithms in Search, Optimization and Machine Learning, 1989. ,
Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, 1992. ,
Genetic algorithms: An overview, Complexity, vol.1, issue.1, pp.31-39, 1995. ,
DOI : 10.1002/cplx.6130010108
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.117
Optimization by Simulated Annealing, Science, vol.220, issue.4598, pp.671-680, 1983. ,
DOI : 10.1126/science.220.4598.671
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.123.7607
Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm, Journal of Optimization Theory and Applications, vol.21, issue.1, pp.41-51, 1985. ,
DOI : 10.1007/BF00940812
A technique to analytically formulate and to solve the 2- dimensional constrained trajectory planning problem for a mobile robot, Journal of Intelligent and Robotic Systems, vol.27, issue.3, pp.237-262, 2000. ,
DOI : 10.1023/A:1008168615430
Path planning: A 2013 survey, Proceedings of 2013 International Conference on Industrial Engineering and Systems Management (IESM2013), pp.1-8, 2013. ,
Survey of robot 3d path planning algorithms, Journal of Control Science and Engineering, vol.2016, 2016. ,
Finding the k Shortest Paths, SIAM Journal on Computing, vol.28, issue.2, pp.652-673, 1999. ,
DOI : 10.1137/S0097539795290477
Shortest Loopless Paths in a Network, Management Science, vol.17, issue.11, pp.712-716, 1971. ,
DOI : 10.1287/mnsc.17.11.712
An algorithm for planning collision-free paths among polyhedral obstacles, Communications of the ACM, vol.22, issue.10, pp.560-570, 1979. ,
DOI : 10.1145/359156.359164
Shortest paths in the plane with convex polygonal obstacles, Information Processing Letters, vol.23, issue.2, pp.71-76, 1986. ,
DOI : 10.1016/0020-0190(86)90045-1
Shortest paths in the plane with polygonal obstacles, Journal of the ACM, vol.41, issue.5, pp.982-1012, 1994. ,
DOI : 10.1145/185675.185795
On shortest paths in polyhedral spaces, Proceedings of the 16th Annual ACM Symposium on Theory of Computing, pp.144-153, 1984. ,
Finding the 3D shortest path with visibility graph and minimum potential energy, Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93), pp.679-684, 1993. ,
DOI : 10.1109/IROS.1993.583190
3D Visibility Graph, the 12th CSI Computer Conference (CSICC2006), 2006. ,
New lower bound techniques for robot motion planning problems, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987), pp.49-60, 1987. ,
DOI : 10.1109/SFCS.1987.42
Path Planning Using a Tangent Graph for Mobile Robots Among Polygonal and Curved Obstacles: Communication, The International Journal of Robotics Research, vol.11, issue.4, pp.376-382, 1992. ,
DOI : 10.1177/027836499201100409
Minimal tangent visibility graphs, Computational Geometry, vol.6, issue.5, pp.303-314, 1996. ,
DOI : 10.1016/0925-7721(95)00016-X
URL : http://doi.org/10.1016/0925-7721(95)00016-x
Voronoi diagrams---a survey of a fundamental geometric data structure, ACM Computing Surveys, vol.23, issue.3, pp.345-405, 1991. ,
DOI : 10.1145/116873.116880
Sensor Based Motion Planning: The Hierarchical Generalized Voronoi Graph, 1996. ,
Visibility and intersection problems in plane geometry, Discrete & Computational Geometry, vol.10, issue.6, pp.551-581, 1989. ,
DOI : 10.1007/BF02187747
Exact cell decomposition of arrangements used for path planning in robotics, tech. rep, 1999. ,
Path planning using probabilistic cell decomposition, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004, pp.467-472, 2004. ,
DOI : 10.1109/ROBOT.2004.1307193
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.7019
Probabilistic roadmaps for path planning in high-dimensional configuration spaces, IEEE Transactions on Robotics and Automation, vol.12, issue.4, pp.566-580, 1996. ,
DOI : 10.1109/70.508439
Rapidly-exploring random trees: A new tool for path planning, tech. rep ,
Mathematical Models for Aircraft Trajectory Design: A Survey, Air Traffic Management and Systems: Selected Papers of the 3rd ENRI International Workshop on ATM/CNS (EIWAC2013), pp.205-247, 2014. ,
DOI : 10.1007/978-4-431-54475-3_12
URL : https://hal.archives-ouvertes.fr/hal-00913243
The Essentials of CAGD, 2000. ,
A Practical Guide to Splines, 1978. ,
DOI : 10.1007/978-1-4612-6333-3
Bézier and B-Spline Techniques, 2002. ,
On-line Path Generation for Small Unmanned Aerial Vehicles Using B-Spline Path Templates, AIAA Guidance, Navigation and Control Conference and Exhibit, 2008. ,
DOI : 10.2514/6.2008-7135
Optimizing B-splines using Genetic Algorithms Applied to Air-traffic Conflict Resolution, ICEC 2010, International Conference on Evolutionary Computation, pp.213-218, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00987459
On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents, American Journal of Mathematics, vol.79, issue.3, pp.497-516, 1957. ,
DOI : 10.2307/2372560
A polynomial-time algorithm for computing a shortest path of bounded curvature amidst moderate obstacles (extended abstract), Proceedings of the twelfth annual symposium on Computational geometry , SCG '96, pp.242-251, 1996. ,
DOI : 10.1145/237218.237393
Curvature-bounded traversals of narrow corridors, Proceedings of the twenty-first annual symposium on Computational geometry , SCG '05, pp.278-287, 2005. ,
DOI : 10.1145/1064092.1064135
Time-optimal paths for a Dubins airplane, 2007 46th IEEE Conference on Decision and Control, pp.2379-2384, 2007. ,
DOI : 10.1109/CDC.2007.4434966
Dubins path generation for a fixed wing UAV, 2014 International Conference on Unmanned Aircraft Systems (ICUAS), pp.339-346, 2014. ,
DOI : 10.1109/ICUAS.2014.6842272
Modeling and Optimization of Air Traffic, 2013. ,
DOI : 10.1002/9781118743805
URL : https://hal.archives-ouvertes.fr/hal-00924311
Path-Planning with Avoidance Using Nonlinear Branch-and-Bound Optimization, Journal of Guidance, Control, and Dynamics, vol.32, issue.2, pp.384-394, 2009. ,
DOI : 10.2514/1.40034
Generating Arrival Routes with Radius-to-Fix Functionalities, the 7th International Conference on Research in Air Transportation (ICRAT2016), (Philadelphia, United States), 2016. ,
Automatic Design of Aircraft Arrival Routes with Limited Turning Angle, the 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, pp.1-13, 2016. ,
Gurobi Optimizer Quick Start Guide, 2017. ,
Fast Marching Methods, SIAM Review, vol.41, issue.2, pp.199-235, 1998. ,
DOI : 10.1137/S0036144598347059
Weather avoidance optimal routing for extended terminal airspace in support of dynamic airspace configuration, the 31st IEEE/AIAA Digital Avionics Systems Conference (DASC2012), pp.3-4, 2012. ,
Integrated arrival and departure weather avoidance routing within extended terminal airspace, 2013 IEEE/AIAA 32nd Digital Avionics Systems Conference (DASC), pp.1-4, 2013. ,
DOI : 10.1109/DASC.2013.6712505
Separating air traffic flows by allocating 3D-trajectories, The 23rd Digital Avionics Systems Conference (IEEE Cat. No.04CH37576), pp.2-4, 2004. ,
DOI : 10.1109/DASC.2004.1391275
URL : https://hal.archives-ouvertes.fr/hal-00938063
Assessment of the 3D-separation of Air Traffic Flows, the 6th USA/ Europe Air Traffic Management Research and Development Seminar (ATM2005, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00938079
A review of conflict detection and resolution modeling methods, IEEE Transactions on Intelligent Transportation Systems, vol.1, issue.4, pp.179-189, 2000. ,
DOI : 10.1109/6979.898217
A Hybrid Metaheuristic Optimization Algorithm for Strategic Planning of 4D Aircraft Trajectories at the Continental Scale, IEEE Computational Intelligence Magazine, vol.9, issue.4, pp.46-61, 2014. ,
DOI : 10.1109/MCI.2014.2350951
Optimized vertical separation in europe, the 31st IEEE/AIAA Digital Avionics Systems Conference (DASC2012), pp.4-7, 2012. ,
4D-trajectory deconfliction through departure time adjustment, " in the 8th USA/Europe Air Traffic Management Research and Development Seminar, 2009. ,
Genetic Algorithms Applied to Air Traffic Management, Metaheuristics for Hard OptimizationMethods and Case Studies, pp.277-306, 2006. ,
DOI : 10.1007/3-540-30966-7_10
URL : https://hal.archives-ouvertes.fr/hal-01291429
North Atlantic Aircraft Trajectory Optimization, IEEE Transactions on Intelligent Transportation Systems, vol.15, issue.5, pp.2202-2212, 2014. ,
DOI : 10.1109/TITS.2014.2312315
URL : https://hal.archives-ouvertes.fr/hal-00981337
Aircraft deconfliction with speed regulation: new models from mixed-integer optimization, Journal of Global Optimization, vol.3, issue.1, pp.613-629, 2014. ,
DOI : 10.1007/s10898-013-0070-1
URL : https://hal.archives-ouvertes.fr/hal-00935215
Multi-agent systems for air traffic conflicts resolution by local speed regulation and departure delay, 2016 IEEE/AIAA 35th Digital Avionics Systems Conference (DASC), 2016. ,
DOI : 10.1109/DASC.2016.7778021
URL : https://hal.archives-ouvertes.fr/hal-01354259
Real-Time Obstacle Avoidance for Manipulators and Mobile Robots, The International Journal of Robotics Research, vol.5, issue.1, pp.90-98, 1986. ,
DOI : 10.1177/027836498600500106
Planning Algorithms, 2006. ,
DOI : 10.1017/CBO9780511546877
Planification de Trajectoires d'Avions sans Conflit : Fonctions Biharmoniques et Fonction de Navigation Harmonique, 2014. ,
URL : https://hal.archives-ouvertes.fr/tel-01084037
A light-propagation model for aircraft trajectory planning, Journal of Global Optimization, vol.7, issue.2, pp.873-895, 2013. ,
DOI : 10.1007/s10898-012-9896-1
URL : https://hal.archives-ouvertes.fr/hal-00935210
Survey of Numerical Methods for Trajectory Optimization, Journal of Guidance, Control, and Dynamics, vol.21, issue.2, pp.193-207, 1998. ,
DOI : 10.2514/2.4231
A study on trajectory optimization for the terminal area, the 6th International Conference on Research in Air Transportation (ICRAT2014), 2014. ,
Simultaneous Optimization Method for Trajectory and Sequence for Receding Horizon Guidance in Terminal Area, SICE Journal of Control, Measurement, and System Integration, vol.8, issue.2, pp.144-153, 2015. ,
DOI : 10.9746/jcmsi.8.144
Merging Optimization Method with Multiple Entry Points for Extended Terminal Maneuvering Area, the 4th ENRI International Workshop on ATM/CNS (EIWAC2015), 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01288387
Ordered upwind methods for static Hamilton-Jacobi equations, Proceedings of the National Academy of Sciences, pp.11069-11074, 2001. ,
DOI : 10.1190/1.1438187
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC58684
Generating optimal aircraft trajectories with respect to weather conditions, the 2nd International Conference on Interdisciplinary Science for Innovative Air Traffic Management (ISIATM2013), 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01511745
User Manual for the Base of Aircraft Data (BADA) Revision 3, 2011. ,
Garmin radius to fix leg project report, 2013. ,