Modeling of trajectory of the pursuer in space using the method of constant-bearing approach

Abstract

  This article examines the model of pursuit task, when the pursuer while moving in space, adheres to the strategy of constant-bearing approach. The velocity modules of the pursuer and target are constant. The object moves evenly and straightforwardly, for certainty of the model, since the test program is written based on the materials of the article. The velocity vectors of the target and the pursuer in the beginning of the pursuit are directed arbitrarily. The iterative process consists of the three parts. Calculation of trajectory of the pursuer in space, calculation of trajectory of the pursuer in a plane, calculation of the transition of trajectory from space to a plane are conducted. All parts of the iterative process have to meet the conditions specified in a task. An important condition is that the minimum radius of curvature of the trajectory should not exceed a certain set value. The scientific novelty of the geometric model consists in the possibility to regulate the time of reaching the target by changing the length of trajectory of the pursuer, as well as the orientation of a plane of pursuit. Calculation of the point of next position of the pursuer in space is the point of intersection of the sphere, cone and plane of constant-bearing approach. A plane of constant-bearing approach is perpendicular to a plane of pursuit. In the model under review, a plane of pursuit is determined by the target velocity vector and direct target that connects the pursuer and the target (sight line). The radius of the sphere is equal to the step of the pursuer for the time interval the time of the iterative process is divided into. The angle of solution of the cone is the angle by which the velocity vector of the pursuer can turn. The mathematical model presented in the article may be of interest to developers of unmanned aerial vehicles.