Investigating cooperative and non-cooperative interference elimination between aircraft using game theory

Kosari, Amir Reza; Mirzaei Tashenizi, Masoud

doi:10.22034/jast.2021.127948

Document Type : Original Article

Authors

¹ Department of New Sciences and Technologies ,Tehran university, Tehran, Iran

² Faculty of New Sciences and Technologies, University of Tehran

https://doi.org/10.22034/jast.2021.127948

Abstract

This article is aimed to investigate the interference elimination between multiple aircraft using game theory. A differential game is used to eliminate the interference if all the interfering aircraft cooperate to eliminate the interference or if each makes a rational decision based on their own interests. All interfering aircraft calculate the interference elimination route in cooperative mode by defining the flight priority. In the non-cooperative state, the problem of eliminating the interference is investigated using the Nash equilibrium, and then the new path is calculated. A point mass model has been used to implement this problem, which is converted into a linear model by changing the control variable. The above problem is solved using the quasi-spectral numerical solution method. In order to validate the presented method, the problem of eliminating the interference between several aircraft in two-dimensional space has been studied, and the results show the appropriate performance of the presented method.

Keywords

20.1001.1.17352134.2020.13.2.12.8

Main Subjects

Flight Mechanics Stability & Contorl

Article Title [Persian]

Investigating cooperative and non-cooperative interference elimination between aircraft using game theory

Authors [Persian]

Amir reza Kosari ¹
Masoud Mirzaei Tashenizi ²

¹ Department of New Sciences and Technologies ,Tehran university, Tehran, Iran

² Faculty of New Sciences and Technologies, University of Tehran

Abstract [Persian]

Keywords [Persian]

Interference Elimination
Differential Game

References

[1] P. K. Menon, G. D. Sweriduk, and B. Sridhar, “Optimal Strategies for Free-Flight Air Traffic Conflict Resolution,” J. Guid. Control. Dyn., vol. 22, pp. 202–211, 1999.

[2] A. L. Visintini, W. Glover, J. Lygeros, and J. Maciejowski, “Monte {Carlo} {Optimization} for {Conflict} {Resolution} in {Air} {Traffic} {Control},” IEEE Trans. Intell. Transp. Syst., vol. 7, no. 4, pp. 470–482, 2006.

[3] A. U. Raghunathan, V. Gopal, D. Subramanian, L. T. Biegler, and T. Samad, “Dynamic Optimization Strategies for Three-Dimensional Conflict Resolution of Multiple Aircraft,” J. Guid. Control. Dyn., vol. 27, no. 4, pp. 586–594, 2008.

[4] S. Cafieri and D. Rey, “Maximizing the number of conflict-free aircraft using mixed-integer nonlinear programming,” Comput. Oper. Res., vol. 80, pp. 147–158, 2017.

[5] Y. Lu, B. Zhang, and X. Zhang, “Air conflict resolution algorithm based on optimal control,” Proc. 33rd Chinese Control Conf. CCC 2014, no. c, pp. 8919–8923, 2014.

[6] Malaek, Seyed & Golchoubian, Mahsa. (2020). Enhanced Conflict Resolution Maneuvers for Dense Airspaces. IEEE Transactions on Aerospace and Electronic Systems. PP. 1-1. 10.1109/TAES.2020.2972422..

[7] E. Calvo-Fernández, L. Perez-Sanz, J. M. Cordero-García, and R. M. Arnaldo-Valdés, “Conflict-Free Trajectory Planning Based on a Data-Driven Conflict-Resolution Model,” J. Guid. Control. Dyn., vol. 40, no. 3, pp. 615–627, 2016.

[8] W. Chen, J. Chen, Z. Shao, and L. T. Biegler, “Three-Dimensional Aircraft Conflict Resolution Based on Smoothing Methods,” J. Guid. Control. Dyn., vol. 39, no. 7, pp. 1481–1490, 2016.

[9] T. Mylvaganam and M. Sassano, “Autonomous collision avoidance for wheeled mobile robots using a differential game approach,” Eur. J. Control, vol. 40, pp. 53–61, 2018.

[10] W. Lin, “Distributed UAV formation control using differential game approach,” Aerosp. Sci. Technol., vol. 35, no. 1, pp. 54–62, 2014.

[11] D. Gu, “A differential game approach to formation control,” IEEE Trans. Control Syst. Technol., vol. 16, no. 1, pp. 85–93, 2008.

[12] P. K. A. Menon, “Optimal helicopter trajectory planning for terrain following flight,” J. Heat Transfer, vol. 125, no. October, pp. 788–794, 1990.

[13] W. Lin, “Differential Games for Multi-agent Systems under Distributed Information,” 2013.

[14] T. Mylvaganam, M. Sassano, and A. Astolfi, “A Differential Game Approach to Multi-agent Collision Avoidance,” IEEE Trans. Automat. Contr., vol. 62, no. 8, pp. 4229–4235, 2017.

[15] T. Mylvaganam, M. Sassano, and A. Astolfi, “A Differential Game Approach to Multi-agent Collision Avoidance,” IEEE Trans. Automat. Contr., vol. 62, no. 8, pp. 4229–4235, 2017.

[16] M. A. Patterson et al., “an Overview of Three Pseudospectral Methods for the Numerical Solution of Optimal Control,” Aas 09, pp. 1–17, 2009.

[17] T. Guo, J. Li, H. Baoyin, and F. Jiang, “Pseudospectral methods for trajectory optimization with interior point constraints: Verification and applications,” IEEE Trans. Aerosp. Electron. Syst., vol. 49, no. 3, pp. 2005–2017, 2013.

[18] R. Dai, “Three-dimensional aircraft path planning based on nonconvex quadratic optimization,” Proc. Am. Control Conf., pp. 4561–4566, 2014.

[19] N. E. Smith, R. Cobb, S. J. Pierce, and V. Raska, “Optimal Collision Avoidance Trajectories via Direct Orthogonal Collocation for Unmanned/Remotely Piloted Aircraft Sense and Avoid Operations,” no. January, 2014.

[20] P. Bonami, A. Olivares, M. Soler, and E. Staffetti, “Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization,” J. Guid. Control. Dyn., vol. 36, no. 5, pp. 1267–1277, 2013.

[21] C. Aviation, “The Rules of the Air Regulations,” no. 734, 1996.

[22] A. W. Starr and Y. C. Ho, “Nonzero-Sum Differential Games 1,” J. Optim. Theory Appl., vol. 3, no. 3, pp. 184–206, 1969.

[23] T. Başar, A. Haurie, and G. Zaccour, “Nonzero-sum differential games,” Handb. Dyn. Game Theory, vol. 3, no. 3, pp. 61–110, 2018

[24] Z. Nikooeinejad, A. Delavarkhalafi, and M. Heydari, “A numerical solution of open-loop Nash equilibrium in nonlinear differential games based on Chebyshev pseudospectral method,” J. Comput. Appl. Math., vol. 300, pp. 369–384, 2016.

[25] P. Method, “Solving Nash Differential Game Based on Minimum Principle and Pseudo-spectral Method,” no. 1, pp. 173–177, 2016.

[26] J. Holden, N. Goel, and UBER, “Fast-Forwarding to a Future of On-Demand Urban Air Transportation,” VertiFlite, pp. 1–98, 2016.

Journal of Aerospace Science and Technology

Investigating cooperative and non-cooperative interference elimination between aircraft using game theory

References

References

Volume 13, Issue 2
October 2020
Pages 103-113

Investigating cooperative and non-cooperative interference elimination between aircraft using game theory

References

References

Volume 13, Issue 2October 2020Pages 103-113

Volume 13, Issue 2
October 2020
Pages 103-113