ISSN 0005-1179, Automation and Remote Control, 2017, Vol. 78, No. 8, pp. 1449–1459.
Pleiades Publishing, Ltd., 2017.
Original Russian Text
A.A. Galyaev, E.P. Maslov, V.P. Yakhno, T.G. Abramyants, 2017, published in Avtomatika i Telemekhanika, 2017, No. 8,
CONTROL IN TECHNICAL SYSTEMS
Evasion of a Moving Object
from Detection by a System of Observers:
Sensor–Maneuvering Search Means
A. A. Galyaev
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Received May 12, 2016
Abstract—Consideration was given to planning the optimal evasion trajectory of a moving
object from the system of observers consisting of a sensor and initial and terminal points of the
route. An optimization criterion was proposed. The optimal trajectory and the speed mode
of the moving object were determined for sector and ring—the two zones of search for the
maneuvering search means.
Keywords: conﬂict medium, planning of the optimal evasion trajectory, system of observers.
A class of control problems of moving objects in a conﬂict medium (according to A.N. Voronin )
was formed over the last ﬁfteen years. In literature such problems were named the “path planning
in the threat environment” [2, 3]. By the conﬂict medium is meant a collection of conﬂicting objects
to which approach is undesirable for a moving object (MO) executing its main task. The aim of
control of an object moving in the conﬂict medium lies in minimizing the negative eﬀect of the
conﬂicting objects on the controlled object by selecting its route, motion parameters and/or modes
of the hardware facilities. Depending on the gist of a particular task, the aims of the negative action
may be object detection, approach to a conﬂicting object at distances making defeat possible, and
so on. One of the ﬁrst publications  described a solution of the variational problem of constructing
on a plane the optimal MO evasion trajectory for detection by a single stationary observer (called
there the sensor) under constant MO speed.
The well-known publications on planning the moving object trajectories assume that the location
of the threat and its eﬀect are known in advance, which allows on to generate the risk functional
and seek a trajectory minimizing the given functional. For example, Ref.  considers ﬂight of
unmanned ﬂying vehicle under the dangerous conditions. The threats are deﬁned on the plane in
terms of a 2D relief, and an optimal 2D trajectory minimizing the risk under the restricted ﬂight
time and speed. In  the functional of detection is formed by a single observer moving along a
straight line. In  the trajectory is optimized under spatial and speed constraints imposed on the
In the present paper, the threats are arranged on the plane by a single stationary sensor and
the moving maneuvering facility. By solving the problem analytical representations for the optimal
speed modes of MO motion and its trajectory are determined.