A 3D conflict resolution and collision avoidance based on flight priority for multi-aircraft with game theory

Document Type : Research Paper

Authors

1 aerospace engineering, Faculty of New Science and Technology, Tehran university, Tehran, Iran

2 Associate Professor of Department of Aerospace Engineering/ Faculty of New Sciences and Technologies/ University of Tehran

3 Faculty of Iranian Space Research Center, Tehran, Iran

Abstract

The main goal of this research is the conflict resolution and collision avoidance between multi low altitude aircraft using differential game theory. The conflict resolution is investigated as a cooperative differential game using a non-inferior method. In this study, the problem is considered as a constrained nonlinear differential game and is transformed into a single objective function using the weighted combination of aircraft objective functions. The objective function obtained along with all functional and environmental constraints will be solved in nonlinear programming using the pseudo-spectral method. The three degrees of freedom with performance constraints are used to model the problem. Also for the validation, the problem of conflict resolution will be solved in four different examples using the performance characteristics of a real aircraft based on low altitude flight rules. In these examples, the impact of priority coefficients on the flight path, the impact of the presence and constraint of the flight space on two-dimensional and three-dimensional space will be examined. The results show that in order to resolution of conflict base on the flight priority, it affects the control effort and flight path of each of the conflicting aircraft. This flight priority can be based on the need for airlines, flight delay, number of passengers or etc.

Keywords

References

[1] C. Aviation and N. Zealand, Part 91, no. May, 2019.
[2] C. Aviation, The Rules of the Air Regulations, no. 734, 1996.
[3] 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.
[4] 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.
[5] 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.
[6] 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.
[7] 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.
[8] M. Zhang, J. Yu, Y. Zhang, S. Wang, and H. Yu, Flight conflict resolution during low-altitude rescue operation based on ensemble conflict models, Adv. Mech. Eng., vol. 9, no. 4, p. 168781401769665, 2017.
[9] 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.
[10] 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.
[11] S. R. Wolfe, P. A. Jarvis, F. Y. Enomoto, M. Sierhuis, and B.-J. Van Putten, A Multi-Agent Simulation of Collaborative Air Traffic Flow Management, Multi-Agent Syst. Traffic Transp. Eng., 2011.
[12] Z. H. Mao, D. Dugail, and E. Feron, Space partition for conflict resolution of intersecting flows of mobile agents, IEEE Trans. Intell. Transp. Syst., vol. 8, no. 3, pp. 512–527, 2007.
[13] Z.-H. Mao, E. Feron, and D. Dugail, Stability of intersecting aircraft flows under centralized and decentralized conflict avoidance rules, vol. 2, no. 2, pp. 101–109, 2013.
[14] S. Huang, E. Feron, G. Reed, and Z. H. Mao, Compact configuration of aircraft flows at intersections, IEEE Trans. Intell. Transp. Syst., vol. 15, no. 2, pp. 771–783, 2014.
[15] J. K. Kuchar and L. C. Yang, A review of conflict detection and resolution modeling methods, IEEE Trans. Intell. Transp. Syst., vol. 1, no. 4, pp. 179–189, 2000.
[16] 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.
[17] W. Lin, Distributed UAV formation control using differential game approach, Aerosp. Sci. Technol., vol. 35, no. 1, pp. 54–62, 2014.
[18] D. Gu, A differential game approach to formation control, IEEE Trans. Control Syst. Technol., vol. 16, no. 1, pp. 85–93, 2008.
[19] P. K. A. Menon, Optimal helicopter trajectory planning for terrain following flight, J. Heat Transfer, vol. 125, no. October, pp. 788–794, 1990.
[20] W. Lin, Differential Games for Multi-agent Systems under Distributed Information, 2013.
[21] 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.
[22] 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.
[23] M. Sassano, S. Member, and A. Astolfi, Dynamic Approximate Solutions of the HJ Inequality and of the HJB Equation for Input-Affine Nonlinear Systems, vol. 57, no. 10, pp. 2490–2503, 2012.
[24] P. A. Johnson, Numerical Solution Methods for Differential Game Problems, 2009.
[25] 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.
[26] C. R. HARGRAVES and S. W. PARIS, Direct trajectory optimization using nonlinear programming and collocation, J. Guid. Control. Dyn, vol. 10, no. 4, pp. 338–342, 2008.
[27] M. A. Patterson et al., an Overview of Three Pseudospectral Methods for the Numerical Solution of Optimal Control, Aas 09, pp. 1–17, 2009.
[28] 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.
[29] R. Dai, Three-dimensional aircraft path planning based on nonconvex quadratic optimization, Proc. Am. Control Conf., pp. 4561–4566, 2014.
[30] 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.
[31] 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.
[32] A. W. Starr and Y. C. Ho, Nonzero-Sum Differential Games 1, J. Optim. Theory Appl., vol. 3, no. 3, pp. 184–206, 1969.
[33] T. Başar, A. Haurie, and G. Zaccour, Nonzero-sum differential games, Handb. Dyn. Game Theory, vol. 3, no. 3, pp. 61–110, 2018.
[34] P. Method, Solving Nash Differential Game Based on Minimum Principle and Pseudo-spectral Method, no. 1, pp. 173–177, 2016.
[35] A. V Rao, C. L. Darby, and M. Patterson, User’s Manual for GPOPS Version 2. 3 : A MATLAB R Software for Solving Multiple-Phase Optimal Control Problems Using the Gauss Pseudospectral Method, no. August, 2009.
[36] J. Holden, N. Goel, and UBER, Fast-Forwarding to a Future of On-Demand Urban Air Transportation, VertiFlite, pp. 1–98, 2016.
[37] E. D’Amato, M. Mattei, and I. Notaro, Distributed Reactive Model Predictive Control for Collision Avoidance of Unmanned Aerial Vehicles in Civil Airspace, J. Intell. Robot. Syst., vol. 97, no. 1, pp. 185–203, 2020.
[38] R. K. Cecen and C. Cetek, Conflict-free en-route operations with horizontal resolution manoeuvers using a heuristic algorithm, Aeronaut. J., vol. 124, no. 1275, pp. 767–785, May 2020.
[39] D. P. Thipphavong et al., Urban Air Mobility Airspace Integration Concepts and Considerations, 2018.

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