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 Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 2, Pages 134–149 (Mi timm1176)

Problem of collision avoidance for a group motion with obstacles

A. B. Kurzhanskii

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

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.

Keywords: group control, flock, target set, ellipsoidal trajectory, reference motion, noncollision, obstacles, coordination.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, 293, suppl. 1, 120–136

Bibliographic databases:

Document Type: Article
UDC: 519.857.3

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

Citation in format AMSBIB
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This publication is cited in the following articles:
1. 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
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