A course of action is proposed for an observer $f$ tracking an object $t$ that moves along a shortest trajectory $\cal T$ enveloping a family $\{G_i\}$ of convex sets. The object can send a dangerous high-speed mini-object in the direction of the observer. Observation methods depend on the geometric properties of the trajectory $\cal T$, i.e., on the location of the segments and convex arcs that constitute it. The aim of the observer is to track the motion of the object along the largest possible part of the trajectory $\cal T$.
Keywords: navigation, optimal trajectory, moving object, observer, video sensor, video finder
Received February 6, 2024
Revised March 1, 2024
Accepted March 4, 2024
Vitalii Ivanovich Berdyshev, RAS Academician, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: bvi@imm.uran.ru
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Cite this article as: V.I. Berdyshev. Observation of an object opposed to the observer in the space $\mathbb R^2$. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 3, pp. 45–52.
