Geodesic
A moving object and observers in $\mathbb R^2$ with piecewise smooth shading set
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 95-101 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the motion of an object $t$ in the space ${\mathbb R}^2$, where a bodily bounded bounded set $G$ with piecewise smooth boundary hinders the motion and visibility. In a neighborhood of convex parts of the boundary, there are observers, which can hide from $t$ in a shade set $s(t)\subset {\mathbb R}^2\setminus G$ in the case of danger from $t$. We find characteristic properties of the trajectory $\mathcal T$ of the object that maximizes the value $\min\{\rho(t,s(t)):\ t\in {\mathcal T}\}$.
Mots-clés : navigation, observer.
Keywords: escort problem, moving object 
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     author = {V. I. Berdyshev},
     title = {A moving object and observers in $\mathbb R^2$ with piecewise smooth shading set},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {95--101},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a8/}
}
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V. I. Berdyshev. A moving object and observers in $\mathbb R^2$ with piecewise smooth shading set. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 95-101. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a8/

[1] Berdyshev V.I., “K zadache soprovozhdeniya dvizhuschegosya ob'ekta nablyudatelyami”, Tr. In-ta matematiki i mekhaniki UrO RAN, 21:1 (2015), 46–55 | MR | Zbl

[2] Berdyshev V.I., “Pismo v redaktsiyu”, Tr. In-ta matematiki i mekhaniki UrO RAN, 21:4 (2015), 316