Trajectory Modeling in a Pursuit Problem with Curvature Restrictions

Abstract

The subject of research in our article is the modeling and calculation of the trajectory between the pursuing and the pursued object. A simulation method is proposed that allows solving practical research problems. The article describes the steps of modeling the trajectory of a moving body with a curvature restriction. It should be taken into account that a body moving along a given trajectory begins to move at an initial given angle and also completes it at a certain angle. Our task is of practical importance, since the approach to organizing the route of the aircraft in the vertical plane is considered in the presence of restrictions on state variables. The main results of the work, mathematical models of moving bodies are introduced, calculations for modeling their trajectories at each moment of time of motion are presented. The program code for mathematical modeling of the trajectory according to the task on the basis of the apparatus of analytical geometry is developed, the construction of the simulated trajectory is carried out in a certain class of functions. Based on this, a new path planning algorithm is described. This algorithm for solving the problem is relevant as the results of the work can be applied to solve applied problems of robotics, aircraft modeling, rocket modeling, etc. The solution to the problem, in the form of program code, was performed in the MathCAD programming environment. #CSOC1120.