Problems of search and pursuit of unmanned aerial vehicles using the game-theoretic approach

Currently, the application of mathematical modeling theory is widely used in various fields and, among other things, can be used to prevent illegal actions. This study examines scenarios involving a single pursuer tracking a single evader, as well as situations involving multiple pursuers pursuing multiple evaders. The authors formulate this problem as a search and pursuit problem for four-rotor unmanned aerial vehicles (UAVs) or quadcopters. The solution to the problem is based on game theory, as it provides a mathematical framework for modeling and studying strategic interactions involving multiple decision makers. The authors consider a game where the set of strategies of the runner is the set of possible combinations of speeds and directions of his movement, and the set of strategies of the pursuer is the set of all possible permutations of the elements of his speeds. The matrix of the resulting game consists of elements that are the time of capture. A mathematical problem on the optimal assignments of searching and pursuing unmanned aerial vehicles is formulated and solved. Purpose: optimizing the effectiveness of strategies for detecting and capturing four-rotor unmanned aerial vehicles (quadcopters). Methods: methods of mathematical modeling, game theory apparatus, Hungarian method of solving the problem of assignments, decision theory, the principle of dynamic programming, the Maple package for solving examples were used. Results: In order to fulfill the conditions for solving the problem of optimal assignments, it is necessary and sufficient that it is balanced. This assignment problem can be balanced by entering the required number of fictitious boats or escaping boats. After that, it is possible to formulate and solve the dual problem of optimal appointments. The resulting game can be solved by any method of solving matrix games. In this way, it is possible to determine the policy of harassment and search between drones. Practical importance: All escaped quadcopter UAVs can be chased and successfully intercepted using the developed models. Examples of the study of mathematical models using the Maple software package are given.