This article discusses the problem of building an optimal strategy for a drone in the task of chasing a target and avoiding obstacles. The paper analyzes a mathematical model of a game with incomplete information, in which players make decisions based on limited information about each other's condition. Theorems related to the existence of successful strategies for players in this task are presented. The study presents strategies for a drone in conditions of limited information and identifies optimal approaches to solving the problem of harassment. A strategy has been formulated for the drone in conditions of limited information and determine the optimal approaches to solving the task of pursuit. The results demonstrate in the MATLAB/SCRIPT application program the existence of an optimal strategy for unmanned aerial vehicles, which ensures effective overcoming of obstacles under various conditions and constraints. The results obtained can be applied to develop algorithms for controlling unmanned systems in pursuit scenarios.