CONTROL PROCESSES

Trajectory of an observer tracking object motion around convex obstacles in $\mathbb{R}^2$ and $\mathbb{R}^3$

V. I. Berdyshev

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

Abstract: An autonomous object moves at a constant speed along the shortest path, while bypassing an ordered collection of pairwise disjoint convex sets. The object is tracked by an observer. The goal of the observer is to find a trajectory of motion along which the object can be tracked at each moment of time and can be followed at a given distance at possibly low speed. Options for the observer’s trajectories with an indication of the speed limit are proposed.

Keywords: navigation, autonomous vehicle, trajectory, observer.

UDC: 519.62

Received: 28.04.2022
Revised: 14.05.2022
Accepted: 28.05.2022

DOI: 10.31857/S268695432204004X

 English version: Doklady Mathematics, 2022, 106:1, 298–301

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