Abstract
Multiple aircraft trajectory planning is a central problem in future air traffic management concepts where some part of the separation task, currently assumed by human controllers, will be delegated to on-board automated systems. Several approaches have been taken to address it and fall within two categories: meta-heuristic algorithms or deterministic methods. The framework proposed here models the planning problem as a optimization program in a space of functions with constraints obtained by semi-infinite programming.A specially designed innovative interior point algorithm is used to solve it.
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References
Arnol’d, V.: The cohomology ring of the colored braid group. Mathematical notes of the Academy of Sciences of the USSR 5(2), 138–140 (1969), http://dx.doi.org/10.1007/BF01098313 , doi:10.1007/BF01098313
Canny, J., Reif, J.: New lower bound techniques for robot motion planning problems. In: Proceedings of the 28th Annual Symposium on Foundations of Computer Science, SFCS 1987, pp. 49–60. IEEE Computer Society, Washington, DC (1987), http://dx.doi.org/10.1109/SFCS.1987.42 , doi:10.1109/SFCS.1987.42
Delahaye, D., Durand, N., Alliot, J.M., Schoenauer, M.: Genetic algorithms for air traffic control system. In: 14th IFORS Triennal Conference (1996)
Durand, N., Alliot, J.M.: Ant colony optimization for air traffic conflict resolution. In: 8th USA/Europe Air Traffic Management Research and Developpment Seminar (2009)
Latombe, J.C.: Robot Motion Planning: Edition en anglais. The International Series in Engineering and Computer Science. Springer (1991), http://books.google.com.au/books?id=Mbo_p4-46-cC
LaValle, S.: Planning Algorithms. Cambridge University Press (2006), http://books.google.com.au/books?id=-PwLBAAAQBAJ
Michor, P., Mumford, D.B.: Riemannian geometries on spaces of plane curves. Journal of the European Mathematical Society 8(1), 1–48 (2006), http://dx.doi.org/10.4171/JEMS/37 , doi:10.4171/JEMS/37
Motee, N., Jabdabaie, A., Pappas, G.: Path planing for multiple robots: an alternative duality approach. In: 2010 American Control Conference (2010)
Shapiro, A.: Semi-infinite progamming, duality, discretization and optimality conditions. Journal of Optimization 58(2), 133–161 (2009), doi:10.1080/023319309027300070
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Puechmorel, S., Delahaye, D. (2015). Functional Interior Point Programming Applied to the Aircraft Path Planning Problem. In: Bordeneuve-Guibé, J., Drouin, A., Roos, C. (eds) Advances in Aerospace Guidance, Navigation and Control. Springer, Cham. https://doi.org/10.1007/978-3-319-17518-8_30
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DOI: https://doi.org/10.1007/978-3-319-17518-8_30
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17517-1
Online ISBN: 978-3-319-17518-8
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