An autonomous object $t$ moving under observation in $\mathbb {R}^2$ with constant speed along a shortest curve $\cal {T}_t$ with given initial and final points bypasses an ordered family of pairwise disjoint convex sets. The aim of the observer $f$, whose speed is upper bounded, is to find a trajectory $\cal {T}_f$ on which the distance to the observer is at each time a certain prescribed value. Possible variants of motion are given for the observer $f$, who tracks the object on different segments of the trajectory $\cal {T}_t$.
Keywords: navigation, optimal trajectory, moving object, observer
Received March 28, 2021
Revised April 22, 2022
Accepted April 25, 2022
Funding Agency: This study is a part of the research carried out at the Ural Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2022-874).
Vitalii Ivanovich Berdyshev, RAS Academician, Krasovskii Institute of Mathematics and Mechanics Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108Russia, e-mail: bvi@imm.uran.ru
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Cite this article as: V.I. Berdyshev. An object bypassing convex sets and an observer’s trajectory in two-dimensional space. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 2, pp. 66–73.