Geometric quasi-discrete model of group pursuit of a single target

This article describes a geometric model of the process of pursuing a single target by a group of pursuers. The quasi-discrete model of group pursuit of a target is based on the fact that the pursuers, at the estimated time corresponding to their steps, design the predicted trajectory of movement, according to their targets and strategy. The movement occurs on a plane, but if necessary, this model can be transferred to the explicitly defined surface. The speed of movement of all participants, both pursuers and targets, is constant in magnitude. The targets and strategies of the pursuers, despite the difference in trajectories, are united by one criterion: they strive to approach the point in space associated with the pursued object, under a given direction, observing the restrictions on the curvature of the trajectory. The target and strategy of the object of pursuit is determined by the behavior of the pursuer who, having reached a certain distance to the target, switches to moving with the speed of the latter (“pursuit strategy”). The other two pursuers are aimed at points moving parallel to the target's course. Having reached the target points, the pursuers move to a course parallel to the target's course, at a speed equal to the target's movement speed. Another pursuer has a point located in front of the target as a target. These pursuers seek to approach a given point at a right angle to the target's trajectory.