Abstract
The article discusses the procedure for correcting the trajectory of a robotic platform (RTP) on a plane in order to reduce the probability of its defeat/detection in the field of a finite number of repeller sources. Each of these sources is described by a mathematical model of some factor of counteraction to the RTP. This procedure is based, on the one hand, on the concept of a characteristic probability function of a system of repeller sources, which allows us to assess the degree of influence of these sources on the moving RTP. From this concept follows the probability of its successful completion used here as a criterion for optimizing the target trajectory. On the other hand, this procedure is based on solving local optimization problems that allow you to correct individual sections of the initial trajectory, taking into account the location of specific repeller sources with specified parameters in their vicinity. Each of these sources is characterized by the potential, frequency of impact, radius of action, and parameters of the field decay. The trajectory is adjusted iteratively and takes into account the target value of the probability of passing. The main restriction on the variation of the original trajectory is the maximum allowable deviation of the changed trajectory from the original one. If there is no such restriction, then the task may lose its meaning, because then you can select an area that covers all obstacles and sources, and bypass it around the perimeter. Therefore, we search for a local extremum that corresponds to an acceptable curve in the sense of the specified restriction. The iterative procedure proposed in this paper allows us to search for the corresponding local maxima of the probability of RTP passage in the field of several randomly located and oriented sources, in some neighborhood of the initial trajectory. First, the problem of trajectory optimization is set and solved under the condition of movement in the field of single source with the scope in the form of a circular sector, then the result is extended to the case of several similar sources. The main problem of the study is the choice of the General form of the functional at each point of the initial curve, as well as its adjustment coefficients. It is shown that the selection of these coefficients is an adaptive procedure, the input variables of which are characteristic geometric values describing the current trajectory in the source field. Standard median smoothing procedures are used to eliminate oscillations that occur as a result of the locality of the proposed procedure. The simulation results show the high efficiency of the proposed procedure for correcting the previously planned trajectory.
Highlights
Вначале происходит увеличение вероятности прохождения до u=10, затем робототехнической платформы (РТП) попадает в зону влияния одного из источников, заходя в неё с тыльной стороны, поэтому qSu далее начинает уменьшаться вплоть до u=20, однако уже ранее 30-й итерации возобновляется рост qS,u, в результате которого эта функция начинает превышать целевое значение вероятности q=0.9 при u=130
The article discusses the procedure for correcting the trajectory of a robotic platform (RTP) on a plane in order to reduce the probability of its defeat/detection in the field of a finite number of repeller sources
Each of these sources is described by a mathematical model of some factor of counteraction to the RTP
Summary
2. Если точка образа, находясь во втором/третьем квадранте, претерпевает смещение к отрицательной полуоси OX- так, что угол между этой полуосью и радиус-вектором точки становится меньше, то точка прообраза смещается так, что угол между радиус-вектором прообраза и левой/правой границей сектора становится меньше. 3. Если точка образа, находясь во втором/ третьем квадранте, претерпевает смещение к положительной полуоси OY+/ отрицательной полуоси OY- так, что угол между этой полуосью и радиус-вектором точки становится меньше, то соответствующая точка прообраза смещается в такое положение, что угол между её радиус-вектором и средней линией сектора источника становится меньше. ( ) где ρ= S,Tr, M – неотрицательный параметр преобразования, имеющий размерность длины и являющийся пока не определенной функцией от параметров источника S, исходной траектории Tr и точки M (xM, yM); 1,2 = 1,2 (S,Tr, M ) – пока не определенные функции взвешенных факторов удаления от центра и приближения к боковой границе, зависящие от S,Tr, M , причем 0≤δ1,2≤1, δ1+δ1≤1. Стационарные точки P′st функционалов (22) и (23) имеют следующие координаты: для случая 1 x x P',st
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