Abstract
This article discusses models of the run method in the pursuit problem. The considered models are based on the correction of the direction vector. Let’s assume that the intended direction on ...a plane is the line of sight between the pursuer and the target. The direction correction consists in the rotation of the velocity vector until it coincides with the line of sight. When constructing trajectories on the surface, a line of sight is built on the horizontal projection plane. After calculating horizontal projections, all points are projected back onto the surface. On the basis of the research carried out proposed a mathematical model, proposed mathematical models of the method of pursuit on a plane and on a surface given in an explicit form. Mathematical models are the development of chase and parallel approach methods. A modification of these methods is that the speed of the pursuer and the target are directed at random. These models can be in demand by developers of autonomous unmanned vehicles equipped with artificial intelligence systems.
The article deals with the application of matrix modeling to the group pursuit of objects. The article applies matrix modeling to the group pursuit of objects based on models of actual objects' ...behavior and can be used in simulation modeling packages, virtual simulation of game processes, or transport logistics processes. The results of the article may be in demand in creating virtual reality models of delivery of postal goods by drones in creating an optimized hub - network. The author proposes to consider the model of group pursuit of multiple targets. Methods of pursuit by individual subjects are various modifications of methods of parallel approach, pursuit, and proportional approach. The author constructed a matrix reflecting the number of chasers and the number of targets. The conducted research contains a model of group pursuit of a set of targets. The model contains optimization based on the least time of simultaneous achievement of goals. These results are in the certificate of registration of programs for computers. Objectives assume that in the method of dynamic programming of matrices of distribution of pursuers, we will construct the matrix at each discrete moment, because the number of pursuers and objectives, and their strategies can change at any moment. The methods of forming matrices of distribution of pursuers and goals can be in demand in the design of virtual reality systems for game tasks. Such tasks simulate the process of group pursuit, running away, and evasion. The method of dynamic programming for the distribution matrix of pursuers on targets will allow us to move to an automated distribution process with optimization according to the specified parameters.
Abstract
In this article, the implementation of the method of parallel convergence in space in a computer mathematics system is considered and discussed. In this method, the pursuer’s velocity vector ...is directed arbitrarily. The pursuer’s trajectory gradually approaches movement in the plane formed by the line connecting the initial positions of the pursuer and the target, and the velocity vector. In this task, the target moves uniformly and rectilinearly. The pursuer moves evenly. The points of the pursuer’s trajectory are calculated sequentially. They are being the result of the intersection of the plane containing the line of sight, sphere and cone. As we approach the plane where the target is moving, the algorithm for calculating the trajectory points changes. Now the point of the pursuer’s trajectory is the result of the intersection of the sphere, the plane of movement of the target and the plane containing the line of sight.
Abstract
This article examines a kinematic model of a group pursuing several targets by the method of parallel approach. The model is based on the fact that pursuers try to adhere to pre-designed ...trajectories. The pursuers’ trajectories have curvature constraints. The initial directions of the pursuers’ velocities are arbitrary, which changes the well-known method of parallel approach. In our model, targets are chased 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 curvature in the initial segment of the trajectory.
Protein‐protein interactions play a central role in numerous processes in the cell and are one of the main fields of functional proteomics. This review highlights the methods of bioinformatics and ...functional proteomics of protein‐protein interaction investigation. The structures and properties of contact surfaces, forces involved in protein‐protein interactions, kinetic and thermodynamic parameters of these reactions were considered. The properties of protein contact surfaces depend on their functions. The contact surfaces of permanent complexes resemble domain contacts or the protein core and it is reasonable to consider such complex formation as a continuation of protein folding. Characteristics of contact surfaces of temporary protein complexes share some similarities with active sites of enzymes. The contact surfaces of the temporary protein complexes have unique structure and properties and they are more conservative in comparison with active site of enzymes. So they represent prospective targets for a new generation of drugs. During the last decade, numerous investigations were undertaken to find or design small molecules that block protein dimerization or protein(peptide)‐receptor interaction, or, on the contrary, to induce protein dimerization.
Abstract
The article considers the kinematic model of pursuit, transferred from plane to surface, by the method of parallel approach. Simulation of iterative pursuit processes is a topical ...continuation of autonomous unmanned vehicles. The aim of the article is to develop a model in which the trajectory of the pursuer is the result of following the predicted routes at each discrete moment in time. The research was carried out in the computer mathematics system Math CAD on a surface defined by a point basis. Situations with different initial states were simulated. Detailed results in the form of animated images based on materials, program codes can be found on the authors’ website and channel.
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.
This article considers a model of the pursuit problem using the parallel approach method. The purpose of this article is to modify the method of parallel approach in order to take into account the ...case when the pursuer's speed vector is not directed at the target at the pursuit beginning moment. In addition, in the model discussed in the article, the pursuer cannot instantly change the movement direction. That is, the condition is imposed that the pursuer's trajectory curvature radius cannot be less than a certain value. The proposed method is based on the fact that the pursuer, choosing a step at the iteration stage, will try to follow the predicted trajectories. Based on the materials of the article, we have written the test program that calculates the pursuer's trajectory, taking into account the conditions set out. The completed animated image visualizes the change in the coordinates of the pursuer, the target, and the predicted trajectories from time to time.
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