DOI
10.34229/KCA2522-9664.26.1.6
UDC 517.977
A.A. Chikrii
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine,
g.chikrii@gmail.com
I.S. Rappoport
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine, jeffrappoport@gmail.com
GAME PROBLEMS OF APPROACHING IN NON-FIXED TIME
FOR A GROUP OF RAY-CONTROLLED OBJECTS
Abstract. For conflict-controlled processes of non-fixed duration, the problems of group approaching along a ray and by motion masking are considered. Two modifications of the method of resolving functions are proposed, where the resolving functions do not depend on the moment of approach. A strategy of the group quasi-parallel approach, based on the first modification, is defined. It ensures the approach by a fixed moment of time and in the test examples coincides with the well-known rule of parallel motion. A group approach strategy is formulated that justifies the well-known law of ray pursuit. The second modification of the method of resolving functions justifies the group approach along a ray and the motion masking by a fixed moment oftime. The theoretical results of the work are illustrated on a test example.
Keywords: conflict-controlled processes of non-fixed duration, group parallel pursuit strategy, group motion masking strategy, pursuit along a ray.
full text
REFERENCES
- 1. Qu X., Linghui Z., Shihang Q., Feifei Long, Rubo Zhang. An overview of recent advances in pursuit–evasion games with unmanned surface vehicles. Journal of Marine Science and Engineering. 2025. Vol. 13, N 3. P. 458–469. https://doi.org/10.3390/jmse13030458.
- 2. Fang X., Wang C., Xie L., Chen J. Cooperative pursuit with multi-pursuer and one faster free-moving evader. IEEE Transactions on Cybernetics. 2022. Vol. 52, N 3. P. 1405–1414. https://doi.org/10.1109/TCYB.2019.2958548.
- 3. Yuchen H., Hongjian W., Yudan Y., Wangzhao W. Research on multi-UUV pursuit-evasion games strategies under the condition of strongly manoeuvrable evader. 40th chinese control conference (CCC). Shanghai, China, 2021. P. 5504–5511. https://doi.org/10.23919/CCC52363.2021.9550358.
- 4. Lee Y., Bakolas E. Relay pursuit of an evader by a heterogeneous group of pursuers using potential games. American Control Conference (ACC). New Orleans, LA, USA, 2021. P. 3182–3187. https://doi.org/10.23919/ACC50511.2021.9482912.
- 5. Silveira J., Cabral K., Rabbath C.-A., Givigi S. Deep reinforcement learning solution of reach-avoid games with superior evader in the context of unmanned aerial systems. International Conference on Unmanned Aircraft Systems (ICUAS). Warsaw, Poland, 2023. P. 911–918. https://doi.org/10.1109/ICUAS57906.2023.10156154.
- 6. Luo Y., Jiang X., Zhong S., Ji Y., Sun G. A multi-satellite swarm pursuit-evasion game based on contract network protocol and optimal Lambert method. Yan L., Duan H., Deng Y. (eds.). Advances in Guidance. Navigation and Control. ICGNC 2022. Lecture Notes in Electrical Engineering. Singapore, Springer. 2022. Vol. 845. https://doi.org/10.1007/978-981-19-6613-2_222.
- 7. Lee Y., Bakolas E., Akella M.R. Feedback strategies for hypersonic pursuit of a ground evader. IEEE Aerospace Conference (AERO). Big Sky, MT, USA, 2022. P. 1–7. https://doi.org/10.1109/AERO53065.2022.9843434.
- 8. Xiao Liang, Boran Zhou, Linping Jiang, Guanglei Meng, Yiwei Xiu. Collaborative pursuit-evasion game of multi-UAVs based on Apollonius circle in the environment with obstacle. Connection Science. 2023. Vol. 35, N 1. https://doi.org/10.1080/09540091.2023.2168253.
- 9. Tan M., Shen H. The differential game cooperative guidance law for the single target. Yan L., Duan H., Deng Y. (eds.). Advances in Guidance. Navigation and Control. ICGNC 2022. Lecture Notes in Electrical Engineering. 2022. Vol. 845. Springer, Singapore. https://doi.org/10.1007/978-981-19-6613-2_188.
- 10. Rappoport I.S. Group approach strategies in the method of resolving functions for quasilinear conflict-controlled processes. Kibernetika i sistemnyj analiz. 2019. Vol. 55, No. 1. P. 149–163. https://doi.org/10.1007/s10559-019-00118-7.
- 11. Chikrii A.A., Rappoport I.S. Guaranteed result in game problems of group approach of controlled objects. Problems of Control and Informatics. 2021. No. 5. pp. 57–71.
- 12. Chikrii A.A. Conflict controlled processes. Boston; London; Dordrecht: Springer Science and Business Media, 2013. 424 p.
- 13. Locke A.S. Projectile Control. Moscow: State Publishing House of Technical and Theoretical Literature, 1957, 766 p.
- 14. Siouris G.M. Missile guidance and control systems. New York: Springer, 2004. 666 p.
- 15. Matichin I.I., Chikrii A.A. Motion masking in differential pursuit games. Problems of Control and Information Science. 2005. No. 2. pp. 5–10.
- 16. Matychyn I. Pursuit strategy of motion camouflage in dynamic games. Dynamic Games and Applications. 2020. Vol. 10. P. 145–156. https://doi.org/10.1007/s13235-019-00316-0.
- 17. Mizutani A., Chahl J., Srinivasan M. Insect behaviour: motion camouflage in dragonflies. Nature. 2003. Vol. 423. P. 604.
- 18. Anderson A.J., McOwan P.W. Model of a predatory steals behavior camouflaging motion. Royal Society London. Biology letters. 2003. Vol. 270. P. 189–195.
- 19. Anderson A., McOwan P. Humans deceived by predatory stealth strategy camouflaging motion. Royal Society London. Biology letters. 2003. Vol. 270. P. 25–31.
- 20. Glendinning P. The mathematics of motion camouflage. Royal Society London. Biology letters. 2004. Vol. 271. P. 477–481.
- 21. Nikolsky M.S. The first direct method of L.S. Pontryagin in differential games. Moscow: Moscow State University Press, 1984. 65 p.
- 22. Hajek O. Pursuit games. Vol. 12. New York: Acad. Press, 1975. 266 p.
- 23. Chikrii A.A., Rappoport I.S. Method of resolving functions in the theory of conflict-controlled processes. Kibernetika i sistemnyj analiz. 2012. Vol. 48, No. 4. P. 40–64.
- 24. Aubin J.-P., Frankowska H. Set-valued analysis. Boston; Basel; Berlin: Birkhauser, 1990. 461 p.
