Improvement of Mathematical Tools for Controlling the Group of Unmanned Aerial Vehicles

Abstract

The task of controlling unmanned aerial vehicles to solve the problems of territorial connectivity is updated. A complex of interrelated problems of organizing a joint flight of a group of aircrafts is formulated. A mathematical toolkit for calculating the control of an unmanned aerial vehicle that allows solving the problems of both the joint safe synchronous functioning of a group of aircrafts and their individual flight has been developed. To expand the intellectual capabilities of the designed technical system and to ensure human communication with it in natural language as well, it is proposed to use the apparatus of the theory of fuzzy sets that formalizes the operation with linguistic variables and fuzzy concepts. For immersion of flying objects into physical space the concepts of "friend", "foe" are introduced. Using the theory of pattern recognition, the mechanism of identification and operational response of aircrafts to various non-standard and force majeure situations is revealed. The concept of "traffic rules" for aircrafts is introduced and the meaning of their formation and use in airspace is revealed. The possibilities of using game theory for solving conflict situations are analyzed. The place of the catastrophe theory in mathematical description of the processes of aircrafts interaction with each other and with "nature" is indicated. The totality of flying vehicles is considered from the perspective of the theory of multi-agent systems and the theory of active systems that forms emergent (ant, swarm) intelligence in their environment.