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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 $\mathscr{T}$.
Mots-clés : navigation, observer.
Keywords: autonomous vehicle, trajectory 
@article{DANMA_2021_501_a17,
     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},
     year = {2021},
     volume = {501},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_501_a17/}
}
TY  - JOUR
AU  - V. I. Berdyshev
TI  - Trajectory of an observer tracking the motion of an object around a convex set in $\mathbb{R}^3$
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 95
EP  - 97
VL  - 501
UR  - http://geodesic.mathdoc.fr/item/DANMA_2021_501_a17/
LA  - ru
ID  - DANMA_2021_501_a17
ER  - 
%0 Journal Article
%A V. I. Berdyshev
%T Trajectory of an observer tracking the motion of an object around a convex set in $\mathbb{R}^3$
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2021
%P 95-97
%V 501
%U http://geodesic.mathdoc.fr/item/DANMA_2021_501_a17/
%G ru
%F DANMA_2021_501_a17
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/

[1] Pogorelov A.V., Differentsialnaya geometriya, Nauka, M., 1969, 176 pp.

[2] Milka A.D., “Kratchaishie linii na vypuklykh poverkhnostyakh”, DAN SSSR, 248:1 (1979), 34–36 | Zbl