Geodesic
An object bypassing convex sets and an observer's trajectory in two-dimensional space
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 2, pp. 66-73
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An autonomous object $t$ moving under observation in $\mathbb{R}^2$ with constant speed along a shortest curve $\mathcal{T}_t$ with given initial and final points bypasses an ordered family of pairwise disjoint convex sets. The aim of the observer $f$, whose speed is upper bounded, is to find a trajectory $\mathcal{T}_f$ on which the distance to the observer is at each time a certain prescribed value. Possible variants of motion are given for the observer $f$, who tracks the object on different segments of the trajectory $\mathcal{T}_t$.
Mots-clés : navigation, observer.
Keywords: optimal trajectory, moving object 
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     title = {An object bypassing convex sets and an observer's trajectory in two-dimensional space},
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     pages = {66--73},
     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a4/}
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V. I. Berdyshev. An object bypassing convex sets and an observer's trajectory in two-dimensional space. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 2, pp. 66-73. http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a4/

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