• Denys Vasyliev Ukrainian State Air Traffic Services Enterprise (UkSATSE), Airport, , Boryspil



aircraft, air traffic control, conflict resolution, dynamic programming, flight safety, multi-aircraft conflict, multi-objective optimization


Purpose: The risk of critical proximities of several aircraft and appearance of multi-aircraft conflicts increases under current conditions of high dynamics and density of air traffic. The actual problem is a development of methods for optimal multi-aircraft conflicts resolution that should provide the synthesis of conflict-free trajectories in three-dimensional space. Methods: The method for optimal resolution of multi-aircraft conflicts using heading, speed and altitude change maneuvers has been developed. Optimality criteria are flight regularity, flight economy and the complexity of maneuvering. Method provides the sequential synthesis of the Pareto-optimal set of combinations of conflict-free flight trajectories using multi-objective dynamic programming and selection of optimal combination using the convolution of optimality criteria. Within described method the following are defined: the procedure for determination of combinations of aircraft conflict-free states that define the combinations of Pareto-optimal trajectories; the limitations on discretization of conflict resolution process for ensuring the absence of unobservable separation violations. Results: The analysis of the proposed method is performed using computer simulation which results show that synthesized combination of conflict-free trajectories ensures the multi-aircraft conflict avoidance and complies with defined optimality criteria. Discussion: Proposed method can be used for development of new automated air traffic control systems, airborne collision avoidance systems, intelligent air traffic control simulators and for research activities.

Author Biography

Denys Vasyliev, Ukrainian State Air Traffic Services Enterprise (UkSATSE), Airport, , Boryspil

PhD in Engineering.

Instructor of Training and Certification Centre of Ukrainian State Air Traffic Services Enterprise (UkSATSE), Boryspil, Ukraine

Associate Professor of Air Navigation Systems Department of National Aviation University, Kyiv, Ukraine.

PhD in Engineering on specialty “Navigation and Traffic Control” (2014)

Education: National Aviation University, Kyiv, Ukraine (2010).

Research area: situation analysis and decision-making in air traffic management.


Eby M.S. A Self-Organizational Approach for Resolving Air Traffic Conflicts. The Lincoln Laboratory Journal, 1994, vol. 7, no. 2, pp. 239-254.

Eby M.S., Kelly W.E. Free Flight Separation Assurance Using Distributed Algorithms. Proceedings of 1999 IEEE Aerospace Conference, 1999, vol. 2, pp. 429-441. doi: 10.1109/AERO.1999.793186

Kosecka J., Tomlin C., Pappas G., Sastry S. Generation of Conflict Resolution Maneuvers for Air Traffic Management. Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems, 1997, vol. 3, pp. 1598-1603. doi: 10.1109/IROS.1997.656571

Zeghal K. A Review of Different Approaches Based on Force Fields for Airborne Conflict Resolution. Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, Boston, 1998, pp. 818-827. doi: 10.2514/6.1998-4240

Chepizhenko V.I. Energetiko-potentcialnyi metod garantirovannogo razresheniia polikonfliktov stolknoveniia dinamicheskikh obektov [Energy-Potential Method of the Guaranteed Collision Polyconflicts Resolution of Dynamic Objects]. Kibernetika i vychislitelnaia tekhnika, 2012, issue 168, pp. 54–61. (in Russian)

Chepizhenko V.I., Pavlov V.V., Pavlova S.V. Virtualnye Einshteinovskie silovye polia v sinergii navigatcionnogo prostranstva slozhnykh ergaticheskikh sistem [Virtual Einsteinian Force Fields in the Synergy of Navigating Space of Difficult Ergatic Systems]. Proceedings of the National Aviation University, 2012, vol. 52, no. 3, pp. 15–27. doi: 10.18372/2306-1472.52.2343 (in Russian)

Zakora S.A. Poslidovne rozviazannia konfliktnykh sytuatsii dlia sukupnosti litakiv za rakhunok vidkhylennia za kursovym kutom [Sequential Resolution of Multi-Aircraft Conflicts Using Deviations of Heading Angle]. Proceedings of the National Aviation University, 2006, vol. 27, no. 1, pp. 57-63. doi: 10.18372/2306-1472.27.1265 (in Ukrainian)

Zakora S.A. Urakhuvannia nevyznachenosti prohnozovanoho polozhennia litakiv pry poslidovnomu rozviazanni konfliktnykh sytuatsii [Considering the Uncertainty of Aircraft Predicted Position at Sequential Conflicts Resolution]. Proceedings of the National Aviation University, 2006, vol. 28, no. 2, pp. 51-56. doi: 10.18372/2306-1472.28.1319 (in Ukrainian)

Zakora S.A. Poshuk optymalnoi poslidovnosti rozv’iazannia konfliktnykh sytuatsii dlia sukupnosti povitrianykh suden [Search of Optimal Sequence for Multi-Aircraft Conflict Resolution]. Visnyk Zhytomyrskoho derzhavnoho tekhnolohichnoho universytetu, 2006, vol. 37, no. 2, pp. 126-131. (in Ukrainian)

Bicchi A., Pallottino L. On Optimal Cooperative Conflict Resolution for Air Traffic Management Systems. IEEE Transactions on Intelligent Transportation Systems, 2000, vol. 1, no. 4, pp. 221-231. doi: 10.1109/6979.898228

Frazzoli E., Mao Z.-H., Oh J.-H., Feron E. Resolution of Conflicts Involving Many Aircraft Via Semidefinite Programming. Journal of Guidance, Control, and Dynamics, 2001, vol. 24, no. 1, pp. 79-86. doi: 10.2514/2.4678

Hu. J., Prandini M., Sastry S. Optimal Maneuver for Multiple Aircraft Conflict Resolution: A Braid Point of View. Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, 2000, vol. 4, pp. 4164-4169. doi: 10.1109/CDC.2000.912369

Hu J., Prandini M, Sastry S. Optimal Coordinated Maneuvers for Three Dimensional Aircraft Conflict Resolution. Journal of Guidance, Control, and Dynamics, 2002, vol. 25, no. 5, pp. 888-900. doi: 10.2514/2.4982

Cafieri S., Durand N. Aircraft Deconfliction with Speed Regulation: New Models from Mixed-Integer Optimization. Journal of Global Optimization, 2014, vol. 58, issue 4, pp. 613-629. doi: 10.1007/s10898-013-0070-1

Vasyliev D. Method of Multi-Objective Resolution of Two-Aircraft Conflict in Three-Dimensional Space Based on Dynamic Programming. Proceedings of the National Aviation University, 2016, vol. 68, no. 3, pp. 35-45. doi: 10.18372/2306-1472.68.10907

Vasyliev D.V. Bahatokryterialnyi syntez bezkonfliktnykh traiektorii polotu povitrianykh korabliv [Multi-Objective Synthesis of Conflict-Free Aircraft Trajectories]. Naukoiemni tekhnolohii, 2014, vol. 21, no. 1, pp. 37-40. doi: 10.18372/2310-5461.21.6051 (in Ukrainian)

Vasyliev D.V. An Approach to Optimal Avoidance of Multiple UAV Conflict. Actual Problems of Unmanned Aerial Vehicles Developments, IEEE 3rd International Conference, Kyiv, 2015, pp. 99-101. doi: 10.1109/APUAVD.2015.7346571

Bellman R. Dynamic Programming. Princeton, New Jersey, Princeton University Press, Six Printing, 1972, 366 p.

Vasyliev D.V. Matematychna model kerovanoho rukhu litaka dlia doslidzhennia protsesiv aeronavihatsiinoho obsluhovuvannia polotiv [Mathematical Model of Controlled Aircraft Motion for Analysis of Air Navigation Service Processes]. Systemy ozbroiennia i viiskova tekhnika, 2013, vol. 34, no. 2, pp. 63-67. (in Ukrainian)

Vasyliev D.V. Model bahatokryterialnoho vyboru traiektorii manevruvannia pry rozv’iazanni konfliktnykh sytuatsii mizh litakamy [Model of Multi-Objective Selection of Trajectories for Aircraft Conflicts Resolution]. Systemy obrobky informatsii, 2013, vol. 111, issue 4, pp. 85-88. (in Ukrainian)



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