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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia // Archive

Dokl. RAN. Math. Inf. Proc. Upr., 2024 Volume 517, Pages 120–124 (Mi danma541)

This article is cited in 2 papers

MATHEMATICS

Methods for tracking an object moving in $\mathbb{R}^3$ under conditions of its counteraction

V. I. Berdyshev

N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russian Federation

Abstract: We propose ways of acting an observer $f$ when tracking an object $t$ moving in $\mathbb{R}^3$ along the shortest trajectory $\mathcal{T}$ bypassing a collection $\{G_i\}$ of convex sets. The object has high-speed miniobjects threatening the observer. The tracking methods depend on the geometric properties of $G_i$ and $\mathcal{T}$. The observer’s task is to track the motion of the object over as long a segment of $\mathcal{T}$ as possible.

Keywords: navigation, moving object, observer, locator, viewfinder, shortest trajectory.

UDC: 519.62

Received: 14.06.2024
Revised: 08.07.2024
Accepted: 08.07.2024

DOI: 10.31857/S2686954324030205


 English version:
Doklady Mathematics, 2024, 109:3, 291–294

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© Steklov Math. Inst. of RAS, 2026