А. К планированию маршрутов в 3D-среде с многовариантной моделью. Аннотация. В данной статье излагаются результаты исследований по планированию маршрутов автономных подвижных объектов на априорно сформированной многовариантной модели маршрута (МММ) как множестве альтернативных путей из начальной точки в целевую. Построение МММ основывается на компьютерном методе функционально-воксельного моделирования, сочетающем аналитическую форму описания 3D-сцены с воксельным представлением ее локальных геометрических характеристик. Синтез управления движением и стабилизация траектории движения обеспечиваются представлением объекта управления в форме многорежимной модели и применением к ней метода редукции. Ключевые слова: Многовариантная модель маршрута, R-функциональное моделирова-ние, функционально-воксельное моделирование, метод редукции.
Vassilyev S.N., Loktev M.A., Tolok A.V., Tolok N.B., Ulyanov S.A. Route Planning in 3dEnvironment with Multivariant Model. Abstract. We present results of the research on the planning of routes of unmanned vehicles (autonomous moving objects). The routing is based on the multivariant route model (MRM) formed a priori as a set of alternative paths from an initial point to the target. The MRM construction is done using the computer method of functional voxel modeling, combining the analytical form of describing a 3D-environment with the voxel representation of its local geometrical characteristics. Synthesis of the motion control and stabilization of the path trajectory are done by representing the control object as a multimode model and applying the reduction method to it.
The article discusses some methods for obtaining the analytical expression of a Bezier curve and approaches to constructing analytically defined spline curves. A solution to the problem of constructing a functional region of a Bezier curve as its locally analytical description is proposed. The proposed solution is implemented through R-functional modeling (Rvachev function) and functional-voxel approach.
The paper proposes a method of functional voxel modeling (FVM) of stresses arising under the influence of a force or heat load in an isotropic body. We consider the principles of modeling the unit stress in a volume vector a geometric object, set by analogy with the normal vector with two parameters: the function of the value and the function of the angle of direction.The principles of constructing a functional-voxel model are demonstrated that allows a computer to graphically represent a three-dimensional vector as a set of M-images displaying local geometric characteristics of the obtained functional area.The possibilities of constructing stress fields from distributed loads by means of sequential addition of a single stress distributed in space are considered. The principles of constructing a single thermal stress and constructing distributed fields based on it are considered separately. Existing approaches are used to model the shape of thermal expansion of the body. The obtained visual images of stresses and strains are compared with the simulated results in the existing computational modules based on FEM. The advantages of visualizing the results obtained from the standpoint of accuracy and clarity of representation are demonstrated. The prospects of such an approach to modeling visual physical quantities in relation to the visual diagnostics of the part geometry are considered.
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