Geodesic
Trajectory of an observer tracking the motion of an object around a convex set in $\mathbb{R}^3$
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 95-97.

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An object $t$ moving in $\mathbb{R}^3$ goes around a solid convex set along the shortest path $\mathscr{T}$ under observation. The task of an observer $f$ (moving at the same speed as the object) is to find a trajectory closest to $\mathscr{T}$ that satisfies the condition $\delta\le\|f-t\|\le K\cdot\delta$ for a given $\delta>0$. This condition makes it possible to track the object along the entire trajectory $\mathscr{T}$. A method is proposed for constructing an observer trajectory that ensures that the indicated inequality holds with a constant $K$ arbitrarily close to unity and the object can be observed on its trajectory $\mathscr{T}$, except for an arbitrarily small segment of $\mathscr{T}$.
Keywords: navigation, autonomous vehicle, trajectory, observer. 
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     author = {V. I. Berdyshev},
     title = {Trajectory of an observer tracking the motion of an object around a convex set in $\mathbb{R}^3$},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {95--97},
     publisher = {mathdoc},
     volume = {501},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_501_a17/}
}
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V. I. Berdyshev. Trajectory of an observer tracking the motion of an object around a convex set in $\mathbb{R}^3$. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 95-97. http://geodesic.mathdoc.fr/item/DANMA_2021_501_a17/

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