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Neural network two-dimensional routing of the aircraft's flight using the modified method of branches and borders


G.N. Lebedev – Dr.Sc. (Eng.), Professor, Department № 301, Moscow Aviation University (National Research University)
V.I. Goncharenko – Dr.Sc. (Eng.), Associate Professor, Head of Military Institute of the Moscow Aviation In-stitute
A.V. Roumakina – Assistant, Department № 301, Moscow Aviation University (National Research University)

To enhance the effectiveness of unmanned aerial vehicles, researchers pay more and more attention to their application in the group. In particular, group actions are the flights of the aircrafts in a number of airports during the day, and the task of monitor-ing multiple ground points with the help of several aircrafts. This requires a special way to plan the routes, the coordinated movement, also the additional loss of efficiency at their intersection is to be kept in mind. Therefore, the aim of the research is to develop a two-dimensional routing of the flight of unmanned aerial vehicles with maximum performance algorithm.
Numerical solution of the problem of two-dimensional routing the modified of branch and bound method was performed to achieve the objective of research. The paper proposed a neural network method for solving the коммивояжер problem in two-dimensional routing flight of unmanned aerial vehicles, characterized by the formation of two initial matrices of distances between points for two open routes, which are analyzed alternately with coordinated selection of the element of minimum length in each of them. The original condition of these matrices is equal to the state of total initial matrix, but a new column was added to each of them to specify the coordinates of the so-called "centers of gravity" of both generated routes. The term "centers of gravity" of routes is determined on the approximation of routes with a triangular model consisting of two rectangular segments emanating from the origin and the end of the routes to these centers. As a result, the dimensions of both matrices are reduced. The theoretical conclusions of the research are verified by a test example of the algorithm of coordinated planning of the two routes that are close to each other. It is confirmed that neural network algorithm for two-dimensional routing has a maximum speed.
To demonstrate the effect of ridding of the jumpers and use the triangular model of the trajectories of the test routes an example of a trajectory of the aircraft obtained in one-dimensional routing. Based on the results of research it is visible that in comparison with one-dimensional routing of neural network two-dimensional route planning allows to reduce the run time of the flight by 1.5 times.
For multi-dimensional routing of the flight of the aircraft group generalization of the proposed approach for multiple unmanned aircraft is suggested. The original distance matrix is replicated with several of the matrices and analyzed in turn in multidimensional routing. It is shown that reduction of the dimension of the analyzed matrices is inevitable, the centers of gravity of the flight trajectory will be uneven, enough to continue calculations.
A feed forward network with fourteen entrances, fourteen neurons was chosen as the structure of the neural network considered in the example with hyperbolic tangential activation function in the first layer, three neurons in the hidden layer and six neurons with relay activation function in the output layer. The program of formation, training and testing of the neural network was implemented using the software package “Matlab” To verify the developed neural network algorithm, an example of coordinated planning of two circular routes of two aircraft flights around Moscow for a given 30 points was considered.

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