Компьютерное моделирование в задачах преследования

Abstract

Currently, computer simulation in virtual reality systems has a special status. In order for a computer model to meet the requirements of the tasks it models, it is necessary that the mathematical apparatus correctly describe the simulated phenomena. In this monograph, the simulation of pursuit problems is carried out. An adaptive modeling of the behavior of both pursuers and targets is carried out. An iterative calculation of the trajectories of the participants in the pursuit problem is carried out. The main attention is paid to the methods of pursuit and parallel rendezvous. These methods are taken as the basis of the study and are modified in the future. The scientific novelty of the study is the iterative calculation of the trajectories of the participants in the pursuit task when moving at a constant speed, while following the predicted trajectories. The predicted trajectories form a one-parameter network of continuous lines of the first order of smoothness. The predicted trajectories are calculated taking into account the restrictions on the curvature of the participant in the pursuit problem. The fact of restrictions on curvature can be interpreted as restrictions on the angular frequency of rotation of the object of the pursuit problem. Also, the novelty is the calculation of the iterative process of group pursuit of multiple targets, when targets are hit simultaneously or at specified intervals. The calculation of the parameters of the network of predicted trajectories is carried out with a curvature variation in order to achieve the desired temporal effect. The work also simulates the adaptive behavior of the pursuer and the target. The principle of behavior can be expressed on the example of a pursuer with a simple phrase: "You go to the left - I go to the left." This happens at each iteration step in terms of choosing the direction of rotation. For the purpose, the principle of adaptive behavior is expressed by the phrase: "You go to the left - I go to the right." The studies, algorithms and models presented in the monograph can be in demand in the design of autonomously controlled unmanned aerial vehicles with elements of artificial intelligence. The task models in the monograph are supplemented with many animated images, where you can see the research process. Also, the tasks have an implementation in a computer mathematics system and can be transferred to virtual reality systems if necessary.