Mathematical models of coordinated group pursuit with autonomous defenders’ control

Abstract

This paper considers a computer model of a quasi-discrete group pursuit game. In which there are pursuers, targets, and defenders. In the models of the paper, the goal of the pursuers is to reach static goals. It is possible for more than one pursuer to reach a goal at different times. The goal of the defenders is to defeat the pursuers. A victory for the defenders is the defeat of all targets. For the defenders, the number of pursuers is uncertain. In the paper model, a uniform detection environment of pursuers is formed. The uniform detection environment is the result of set-theoretic operations on points in space. In the paper models, the uniform detection environment is a single connected numerous. A pursuer is considered detected if it enters the given area. As a variant of the optimization factor, the defender for a pursuer can be selected based on the minimum distance to the pursuer. The paper also considers variants of defender localization at a single point. Additional algorithms of the above models are developed that take into account the constraints of defenders at a single location. The difference of algorithms in case of presence or absence of information for defenders about the number of pursuers, their targets, etc. is considered. The results obtained in the paper can be demanded by the developers of robot complexes with autonomous control. Under the coordinated behavior of pursuers in the paper we consider following projected curvilinear trajectories from the locations of pursuers with timed launch to solve the following objectives: the task of simultaneously reaching static targets, the task of simultaneously entering the detection area. The paper does not consider the problems of automatic evasion of pursuers from defenders and from collisions with other pursuers.