Development of a method for determining the area of operation of unmanned vehicles formation by using the graph theory - Zhuravska, Iryna; Kulakovska, Inessa; Musiyenko, Maksym (Eastern-European Journal of Enterprise Technologies, 2018)
The results of research into influence of modification of the topology of a heterogeneous formation of unmanned vehicles on the area, covered by this formation are presented. We proposed an approach, according to which the method for modeling the structure of complex technical systems is applied to describe the behavior of unmanned vehicles’ formation. The changes in topology and in the covered area as a result of unmanned vehicles’ rearrangement within a formation were considered. Based on the result of present study, a method for determining the area of unmanned vehicles’ formation operation involving the graph theory was proposed. Formation of the loaded directed graphs that correspond to the main (star, ring, bus) and mixed (hierarchical star with a bus, hierarchical star with a ring) formation topologies was considered in detail. The adjacency matrix and the loading matrix for the topology "hierarchical star" were analyzed. In addition, the study conducted allows us to conclude that to ensure a full coverage of a certain territory, the mathematical model of the structure of a dynamic system must be characterized by a random number of vertices that correspond to a variable number of unmanned vehicle in a formation. Various technical characteristics of unmanned vehicles, which belong to different classes by weight or control type, must be considered into account when constructing the matrix of graph loading. Calculation of the area, covered by an unmanned vehicles’ formation, is performed as calculation of the area of polygons, assigned by their vertices, using the interpolation concept to count the intermediate values of magnitudes by a discrete set of known coordinate values. Calculation of the formation area is based on the ranges, within which sustainable communication between the drones of different models is provided. Partition of the loading matrix into subordination units makes it possible to decrease computational complexity and thereby prolong operation of a formation. Application of this approach will allow us to plan more effectively the time and the number of drones in a formation, necessary for covering the territory of the specified size.