Abstract:
The paper is devoted to the problem of coordinated control for a flock of control systems moving jointly towards a target set with the requirement of noncollision of its elements. In the present paper, we consider its subproblem, which is formulated as follows. During the motion to the target, the members of the group must stay within a virtual ellipsoidal container, which forms a reference motion (“tube”). The container avoids obstacles, which are known in advance, by means of reconfigurations. In response, the flock must rearrange itself inside the container, avoiding collisions between its members. The present paper is concerned with the behavior of the flock inside the container, when the flock coordinates its motions according to the evolution of the container.
Citation:
A. B. Kurzhanskii, “Problem of collision avoidance for a group motion with obstacles”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 134–149; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 120–136
\Bibitem{Kur15}
\by A.~B.~Kurzhanskii
\paper Problem of collision avoidance for a group motion with obstacles
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 2
\pages 134--149
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 293
\issue , suppl. 1
\pages 120--136
\crossref{https://doi.org/10.1134/S0081543816050114}
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https://www.mathnet.ru/eng/timm1176
https://www.mathnet.ru/eng/timm/v21/i2/p134
This publication is cited in the following 8 articles:
Shujun Guo, Lujing Jing, Zhaopeng Dai, Yang Yu, Zhiqing Dang, Zhihang You, Ang Su, Hongwei Gao, Jinqiu Guan, Yujun Song, “Collision Avoidance Problem of Ellipsoid Motion”, Mathematics, 10:19 (2022), 3478
Abbas Ja'afaru Badakaya, Hassan Abdullahi, Mehdi Salimi, “A Pursuit Game in a Closed Convex Set on a Euclidean Space”, Differ Equ Dyn Syst, 2022
M. Ferrara, G. Ibragimov, I. A. Alias, M. Salimi, “Pursuit differential game of many pursuers with integral constraints on compact convex set”, Bull. Malays. Math. Sci. Soc., 43:4 (2020), 2929–2950
A. B. Kurzhanskii, “Hamiltonian formalism in team control problems”, Differ. Equ., 55:4 (2019), 532–540
Valerii Patsko, Sergey Kumkov, Varvara Turova, Handbook of Dynamic Game Theory, 2018, 1
Valerii Patsko, Sergey Kumkov, Varvara Turova, Handbook of Dynamic Game Theory, 2018, 951
S. S. Kumkov, S. Le Menec, V. S. Patsko, “Zero-sum pursuit-evasion differential games with many objects: survey of publications”, Dyn. Games Appl., 7:4, SI (2017), 609–633
Valerii Patsko, Sergey Kumkov, Varvara Turova, Handbook of Dynamic Game Theory, 2017, 1
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