V.I. Berdyshev. An object moving in $\mathbb R^2$ with a high-speed destructive miniobject and an unfriendly solid observer ... P. 76-82

We propose a model for the motion in a given corridor $Y\subset \mathbb R^2$ of an object $t$ equipped with a high-speed destructive miniobject in the presence of a solid unfriendly observer $f$. In $\mathbb R^2\backslash Y$ there is a subset $G$ that obstructs visibility and motion. For safety reasons, the observer sticks to neighborhoods of the angles and convex fragments of the boundary of $G$. The trajectory of $t$ is a curve $\cal T\subset Y$ with a given speed regime $v_t$ of the motion along it. The possibilities for the observer to track the object in a safe mode and for the object to avoid the observation depend on the positions of the observer and the object. We characterize the positions in which, for any $\cal T$, the object can choose a regime $v_t$ enabling the avoidance of observation and the positions guaranteeing that the observer can see a part of the trajectory.

Keywords: navigation, trajectory, observer, moving object

Received August 25, 2020

Revised October 23, 2020

Accepted October 26, 2020

Funding Agency: This study is a part of the research carried out at the Ural Mathematical Center.

Vitalii Ivanovich Berdyshev, RAS Academician, Krasovskii Institute of Mathematics and Mechanics 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. An object moving in $\mathbb R^2$ with a high-speed destructive miniobject and an unfriendly solid observer, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2020, vol. 26, no. 4, pp. 76–82.