Informatics and Applications
2022, Volume 16, Issue 3, pp 103-109
KINEMATIC MODELS OF PURSUIT PROBLEMS ON THE PLANE BY THE METHODS OF PARALLEL APPROACH AND PURSUIT
- A. A. Dubanov
- V. A. Nefedova
Abstract
This article provides accurate pursuit models based on the parallel approach and chase methods. This article is a modification of the methods of parallel rapprochement and chasing what happens when the pursuit begins. It cannot instantly change the direction of movement. This should be a less affordable option. The proposed method is based on the fact that the pursuer chooses a step at the iteration stage and will try to follow the predicted trajectories. Based on the materials of the article, test programs have been written that calculate the trajectories of the pursuer taking into account the stated conditions. Execution of animated images visualizes the change in the coordinates of the pursuer, target, and predicted time trajectories.
[+] References (13)
- Petrosyan, L. A., andB. B. Rihsiev. 1961. Presledovaniena ploskosti [Flat pursuit]. Moscow: Nauka. 96 p.
- Petrosyan, L.A. 1995. Differentsial'nye igry presledovaniya [Differential pursuit games]. Sorosovskiy obrazovatel'nyy zh. [Soros Educational J.] 1:88-91.
- Metod parallel'nogo sblizheniya na ploskosti s ogranicheniyami na kriviznu [Method of parallel approach on a plane with restrictions on curvature]. Available at: https://www.youtube.com/watch?v=qNXdykK21Z8 (accessed May 25, 2022).
- Metod pogoni na ploskosti s ogranicheniyami na kriviznu [Plane chase method with curvature constraints]. Available at: https://www.youtube.com/watch?v=UQ5 bVKjVqZ4 (accessed May 25, 2022).
- Programmnyy kod v sisteme MathCAD [Program code in the MathCAD system]. Available at: http:// dubanov.exponenta.ru/books.htm (accessed May 25, 2022).
- Isaacs, R. 1965. Differential games: A mathematical theory with applications to warfare and pursuit, control and
optimization. Dover books on mathematics ser. Wiley 384 p.
- Ibragimov, G. A., and N. A. Hussin. 2010. Pursuit-evasion differential game with many pursuers and one evader. Malaysian J. Mathematical Sciences 4(2):183-194.
- Kuzmina, L. I., and Y. Y. Osipov. 2013. Raschet dliny traektorii dlya zadachi presledovaniya [Calculation ofthe path length in the pursuit problem]. Vestnik MGSU [Bulletin of MGSU] 12:20-26.
- Samatov, B.T. 2013. The pursuit-evasion problem under integral-geometric constraints on pursuer controls. Automat. Rem. Contr. 74:1072-1081.
- Ibragimov, G., A. R. Norshakila, A. Kuchkarov, and F Ismail. 2015. Multi pursuer differential game of optimal approach with integral constraints on controls of players. Taiwan. J. Math. 19 (3):963-976.
- Petrov, N. N., and N.A. Solov'eva. 2015. Group pursuit with phase constraints in recurrent Pontryagin's example. Int. J. Pure Applied Mathematics 100(2):263-278.
- Romannikov, D. O. 2018. Primer resheniya minimaksnoy zadachi presledovaniya s ispol'zovaniem neyronnykh setey [An example of solving a minimax pursuit problem using neural networks]. Sbornik nauchnykh trudov NGTU [Transactions of scientific papers of the Novosi
birsk State Technical University] 2(92):108-116. doi: 10.17212/2307-6879-2018-2-108-116.
- Ahmetzhanov, A. R. 2019. Dinamicheskie igry presledovaniya na poverkhnostyakh [Dynamic pursuit games on surfaces]. Moscow: MIPT. PhD Thesis. 28 p.
[+] About this article
Title
KINEMATIC MODELS OF PURSUIT PROBLEMS ON THE PLANE BY THE METHODS OF PARALLEL APPROACH AND PURSUIT
Journal
Informatics and Applications
2022, Volume 16, Issue 3, pp 103-109
Cover Date
2022-10-10
DOI
10.14357/19922264220314
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
target; pursuer; trajectory; convergence; modeling
Authors
A. A. Dubanov and V. A. Nefedova
Author Affiliations
Banzarov Buryat State University, 6a Ranzhurov Str., Ulan-Ude 670000, Russian Federation
|