Vol. 7, No. 2, 2019

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The object detection by autonomous apparatus as a solution of the Buffon needle problem

Mikhail A. Guzev, Gurami S. Tsitsiashvili and Marina A. Osipova

Vol. 7 (2019), No. 2, 189–201
Abstract

The problem of object detection by autonomous apparatus is considered. The probabilistic formulation of the problem is proposed by means of a reduction to the classical Buffon problem. The latter naturally arises when the problem is formulated in the coordinate system associated with the apparatus. The problem of detection is considered for devices moving in the open space along a circle around one body, for vehicles patrolling along the linear boundary protecting the bodies, and for devices protecting the system of bodies. The problem of object detection was shown to admit an analysis in the presence of an asymptotic parameter determined by the ratio of the local size of the apparatus scanning area to the global size of the problem under consideration. For all problems, the minimum number of apparatuses that could detect a penetrating object with probability one was calculated.

Keywords
extraneous mobile object, autonomous unmanned vehicle, detection probability
Mathematical Subject Classification 2010
Primary: 60D05
Secondary: 70Q05
Milestones
Received: 9 January 2019
Revised: 21 April 2019
Accepted: 27 June 2019
Published: 10 August 2019

Communicated by Francesco dell'Isola
Authors
Mikhail A. Guzev
Institute for Applied Mathematics
Far Eastern Branch
Russian Academy of Sciences
Vladivostok
Russia
Gurami S. Tsitsiashvili
Institute for Applied Mathematics
Far Eastern Branch
Russian Academy of Sciences
Vladivostok
Russia
Marina A. Osipova
Institute for Applied Mathematics
Far Eastern Branch
Russian Academy of Sciences
Vladivostok
Russia