The concept of a fibrous material (hereinafter referred to as FM) as a soft structure formed by fiber elements surrounded by air and areas of fiber interaction on touch surfaces is proposed and substantiated. The fiber elements are in a deformed state. The deformation of the fibers is reversible, elastic-elastic. In the areas of interaction between the fibers, the forces of adhesion and dry friction act. The deformation of the fibers leads to the preservation of residual internal energy in the material. At low loads, the FM can change its state reversibly. At high loads, the structure of the interaction sites irreversibly changes. The processes of aging and degradation of FM are gradual irrevocable transitions from one group of states to others. The dynamics of these processes is statistical in nature. Therefore, a Markov model of state change has been developed in the form of several subsets of irrevocable subsets and one ergodic subset of states. At the qualitative level, the possibility of using the proposed model to describe the dynamics of FM aging processes and estimate the duration of this process, taking into account its probabilistic and statistical nature, is shown.

Keywords: fibrous material, aging, soft structure, elasto-elastic deformation, irreversible process, markov model, statistical dynamics

The article considers the process of relaxation of fibrous material after the action of the load on it is completed. A simple model of the relaxation process is constructed in the form of an exponential function, which describes this process quite accurately. It is determined that the relaxation time estimates are robust with respect to the parameter distributions. The constructed relaxation models make it possible to estimate the magnitude of the residual relative strain corresponding to the plastic strain of the material.

Keywords: relaxation, deformation, fibrous material, robustness, Monte Carlo method, exponential model, regression

In the automation of production, the use of robots is an important direction. When developing algorithms for controlling the movement of such a machine, multidirectional problems arise. In a critical situation, the robot must not harm workers or collide with its fellow robot. At the same time, the car must move along the optimal route. The article analyzes the methods of finding optimal paths on square navigation grids. The wave method on undirected planar graphs, the A* algorithm (an extension of Dijkstra's algorithm), and the D* Lite algorithm for graphs with non-constant or previously unknown structure were chosen for the analysis. A visualization and testing system in C#has been developed for the research and testing of algorithms. The system is implemented using the Microsoft Visual Studio 2019 IDE software tools and external GraphX and Emgu CV libraries. A unique feature of the system is the ability to directly read images of shop floor maps in widely used graphic formats and automatically convert them to a format that is understandable to the system. First, the user uploads the shop floor plan. For easier processing, the image is converted to two colors: black and white. Then the image is processed by the Emgu CV library, at the output we get all the contours of stationary obstacles. Then, depending on the size of the robot, an orthogonal navigation grid is superimposed. The analysis of the obtained results allows us to conclude that it is better to use a method (the D* Lite algorithm) that allows for a non-constant or unknown grid structure in advance.

Keywords: visualization, program, graphic format, work, shop, map, square, grid, cell, navigation, optimal route, planar graph