Kinematic model of the pursuit problem on a plane by the chase method

Abstract

This article considers a kinematic, geometric model of the pursuit problem on a plane by the chase method, where the pursuer cannot instantly change the direction of movement, while moving at a constant modulo speed. The initial speed of the pursuer is not directed at the target when the pursuit begins. In order for the speed vector of the pursuer to be directed at the target after some time, we have developed a method that is based on following the trajectory that connects the pursuer and the target. This trajectory takes into account the inertia of the pursuer in the sense that the radius of curvature of the trajectory is not less than a certain threshold value. Based on the materials of this article, test programs were written and an animated image was made.