Modeling of the Target’s Interception Delay in an ADT Game with One or Two Defenders

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This paper considers the Attacker–Defender–Target (ADT) problem with one or two defenders in a 2D statement. By assumption, the target and defenders move in a straight line with a constant velocity whereas the attacker moves along a catch-up trajectory with an unbounded radius of curvature. Compared to the target’s velocity, the defenders move slower whereas the attacker faster. The essence of using defenders is that the attacker first intercepts them and only then switches to pursuing the primary target. As a result, the time of intercepting the primary target increases, and the target may become unattainable for the attacker due to a limited fuel capacity. The angles and times of launching the defenders are optimized, including the case where both defenders are launched on the same side of the target. Different models of the homing system of an autonomous attacking vehicle are studied: moving to the center of mass of all pursued objects and moving to the nearest target by distance or by angular range. Numerical simulations are carried out, showing the importance of choosing the angle of launch of the defenders and the reasonability of using the second defender. Also, scenarios are obtained in which using defenders makes the primary target unattainable for the attacker.

About the authors

A. A Galyaev

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences

Email: galaev@ipu.ru
Moscow, Russia

A. S Samokhin

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences

Email: samokhin@ipu.ru
Moscow, Russia

M. A Samokhina

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences

Email: ph@ipu.ru
Moscow, Russia

References

  1. García, E., Casbeer, D., Pachter, M. The Complete Differential Game of Active Target Defense // Journal of Optimization Theory and Applications. – 2021. – Vol. 191. – P. 1–25. – doi: 10.1007/s10957-021-01816-z.
  2. Zhan, K., Yu, B., Wang, J. Simulations of the Anti-Torpedo Tactic of the Conventional Submarine Using Decoys and Jammers // Applied Mechanics and Materials. – 2011. – Vol. 65. – P. 165–168. – doi: 10.4028/ href='www.scientific.net/AMM.65.165' target='_blank'>www.scientific.net/AMM.65.165.
  3. Gong, X., Chen, W., Chen, Z. Intelligent Game Strategies in Target-Missile-Defender Engagement Using Curriculum-Based Deep Reinforcement Learning // Aerospace. – 2023. – Vol. 10, no. 2. – Art. no. 133. – doi: 10.3390/aerospace10020133.
  4. Jacob, T.E., Jay, P.W. Defender-Aware Attacking Guidance Policy for the Target–Attacker–Defender Differential Game // Journal of Aerospace Information Systems. – 2021. – Vol. 18, no. 6. – P. 366–376. – doi: 10.2514/1.I010877.
  5. Rubinovich, E.Ya. Missile-Target-Defender Problem with Incomplete a priori Information // Dynamic Games and Applications (Special Issue). – 2021. – Vol. 9, no. 17. – P. 851–857. – doi: 10.1007/s13235-019-00297-0.
  6. García, E., Casbeer, D. W., Pachter, M. Active Target Defense Differential Game with a Fast Defender // IET Control Theory and Applications. – 2017. – Vol. 17, no. 11. – P. 2985–2993. –doi: 10.1049/iet-cta.2017.0302.
  7. Alkaher, D., Moshaiov, A. Game-Based Safe Aircraft Navigation in the Presence of Energy-Bleeding Coasting Missile // Journal of Guidance, Control, and Dynamics. – 2016. – Vol. 39. – P. 1539–1550. – doi: 10.2514/1.G001676.
  8. Liu, F., Dong, X., Li, Q., Ren, Z. Cooperative differential games guidance laws for multiple attackers against an active defense target // Chinese Journal of Aeronautics. – 2022. – Vol. 35. – P. 374–389. – doi: 10.1016/j.cja.2021.07.033.
  9. Liang, H., Wang, J., Liu, J., Liu, P. Guidance strategies for interceptor against active defense spacecraft in two-on-two engagement // Aerospace Science and Technology. – 2020. – Vol. 96. – Art. no. 105529. – doi: 10.1016/j.ast.2019.105529.
  10. Zhou, Z., Zhang, W., Ding, J., et al. Cooperative pursuit with Voronoi partitions // Automatica. – 2016. – Vol. 72. – P. 64–72. – doi: 10.1016/j.automatica.2016.05.007.
  11. Chen, M., Zhou, Z., Tomlin, C.J. Multiplayer reach-avoid games via pairwise outcomes // IEEE Transactions on Automatic Control. – 2017. – Vol. 62, no. 3. – P. 1451–1457. – doi: 10.1109/TAC.2016.2577619.
  12. García, E., Casbeer, D., Pham, Kh., Pachter, M. Cooperative Aircraft Defense from an Attacking Missile using Proportional Navigation // AIAA Guidance, Navigation, and Control Conference. – Kissimmee, Florida, 2015. – P. 2926–2931. – doi: 10.2514/6.2015-0337.
  13. Girard, A., Kabamba P. Proportional Navigation: Optimal Homing and Optimal Evasion // SIAM Review. – 2015. – Vol. 57 – P. 611–624. – doi: 10.1137/130947301.
  14. Palumbo, N., Blauwkamp, R., Lloyd, J. Modern Homing Missile Guidance Theory and Techniques // Johns Hopkins APL Technical Digest. – 2010. – Vol. 29, no. 1. – P. 42–59.
  15. Хайрер Э., Нёрсетт С.П., Ваннер Г. Решение обыкновенных дифференциальных уравнений. – М.: Мир, 1989. – 512 С. [Hairer, E., Norsett, S.P., Wanner, G. Solving Ordinary Differential Equations. – Berlin: Springer-Verlag, 1987. – 480 p.]
  16. Самохин А.С., Самохина М.А. Решение задачи Коши многомерным методом Рунге-Кутты, основанным на расчётных формулах Дормана-Принса 8(7), с автоматическим выбором шага. Свидетельство о регистрации программы для ЭВМ № 2020611811 : заявл. 30.01.2020 : зарег. 11.02.2020. [Samokhin, A.S., Samokhina, M.A. Reshenie zadachi Koshi mnogomernym metodom Runge-Kutty, osnovannym na raschetnykh formulakh Dormana-Prinsa 8(7), s avtomaticheskim vyborom shaga. Svidetel'stvo o registratsii programmy dlya EVM no. 2020611811 : appl. 30.01.2020 : reg. 11.02.2020. (In Russian)]

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