Kinematic model of group pursuit for multiple targets using the method of parallel convergence

In this paper, a kinematic model of group pursuit for multiple targets using the method of parallel convergence is considered. The model is based on the fact that the pursuers try to adhere to pre-designed trajectories. The main difference of the proposed model is that the curvature of the trajectories of the pursuers is imposed with restrictions, which is typical for objects not having the ability to change the direction of speed instantly. The initial directions of the pursuers' speeds are arbitrary, what introduces changes to the well-known method of parallel convergence. In the considered geometric model, the targets are reached by the pursuers simultaneously. This is due to the change in the lengths of the predicted trajectories in such a way as to synchronize the time to reach the target. The change in the lengths of the predicted trajectories occurs due to an increase in the radius of the curvature in the initial segment of the trajectory. A program, in which two pursuers with initial arbitrary directions of speeds begin to pursue a target moving in a straight line at a constant speed, and also a program, where a group of three pursuers pursuit a group of two targets, have been developed. The targets are reached simultaneously. An important issue in the presented model is the distribution of pursuers as per targets. In the test program, the distribution was done manually.