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

Dokl. RAN. Math. Inf. Proc. Upr., 2025 Volume 525, Pages 144–148 (Mi danma724)

CONTROL PROCESSES

Observation of the flow of objects on a geodetic arc in $\mathbb{R}^3$ in conditions of counteraction

V. I. Berdyshev

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

Abstract: This paper proposes methods for an observer $f$ to track a flow of objects t$_i$ moving at constant velocity along a smooth geodesic trajectory $\mathcal{T}$, composed of a segment and an arc $\Lambda$. The observer detects pairs of objects at the moments they pass through predetermined fixed control points evenly distributed along $\mathcal{T}$. An unfriendly object, after being detected, may direct a dangerous mini-object toward the observer. The work presents algorithmic approaches for tracking objects moving along straight-line segments and smooth arcs.

Keywords: navigation, autonomous vehicle, trajectory, observer.

UDC: 519.62

Received: 21.07.2025
Revised: 20.08.2025
Accepted: 20.08.2025

DOI: 10.7868/S3034504925050199



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© Steklov Math. Inst. of RAS, 2026