Purpose of research. Among the many methods of surface shaping used in mechanical engineering, a significant part is occupied by the processes of processing parts by cutting, including turning. The process of cutting metals in most cases is accompanied by vibrations and oscillations of the tool, which destabilize the processing, reduce its quality, tool life and process productivity. It is possible to reduce the negative impact of vibration by using elements that absorb or reduce vibrations of the working part of the tool. There are known designs of cutters, called damping ones, that can reduce the negative impact of vibrations during turning. However, their main disadvantage is the rigid connection with the mounting and clamping elements of the machine, through which vibration is transmitted to the tool. This problem can be solved by improving the design of the tool in order to increase the stability of the cutting process. Designs of turning cutters that increase their durability, reduce vibrations that occur during the cutting process, and improve the quality of the machined surface are of practical and scientific interest. Purpose of research is to create innovative tool models, in particular turning cutters, that can improve the quality of the surface layer of the workpiece, its performance properties, as well as the durability of the cutting part of the tool.

Methods. Design and production of new cutters with a holder, which has elements that isolate the working part of the cutter from contact with the fastening part of the machine support, as well as various rigidities and sizes. Results. Increasing the efficiency of damping vibrations of the cutter, reducing its material consumption, because the dimensions of the elastic elements are less than half the length of the cutter holder, improving the quality of the surface layer of the workpiece, its operational properties, as well as the durability of the cutting part of the tool. The cutters can be used for turning various structural materials.

Conclusion. The proposed damping cutters meet the stated goals and objectives. Theoretical studies and industrial tests, simplicity of designs and manufacturing technologies of new damping cutters allow us to recommend them for implementation in production. The cutters can be used for turning various structural materials

Purpose of reseach. Improving the efficiency of the trajectory movement of three-wheeled robots by developing control system algorithms and selecting parameters based on mathematical modeling of robot movement along waypoints that characterize the required trajectory. Development of methods for planning the trajectories of a threewheeled mobile robot based on the Pure Pursuit algorithm. Development of a mathematical model of the device that allows to obtain a numerical solution for the controlled movement of the robot along the waypoints. Analysis of the simulation results in order to establish the applicability of the proposed solutions for the tasks of controlling a twosection wheeled robot for landscape work.

Methods. he Pure Pursuit algorithm is used as a basis for the development of a control system for the trajectory movement of the robot, which allows forming the trajectories of the robot along waypoints with specified motion parameters. Methods of theoretical mechanics, robot mechanics, numerical integration, control theory, electrical engineering and electromechanics were used in the development of the mathematical model. When creating software products, Matlab/Simulink mathematical packages were used.

Results. As a result of the conducted research, the main regularities of the influence of the Lookahead Distance parameter of the Pure Pursuit trajectory algorithm on the nature of the controlled robot movement were discovered and confirmed. It is shown that the choice of the value of this parameter should be justified by the control tasks and working conditions of the robot. The developed mathematical model made it possible to obtain time diagrams for the parameters of the robot's movement, to establish the accuracy of the proposed algorithms.

Conclusion. It is established in the work that the Pure Pursuit algorithm proposed in the work can be used to implement trajectory control of wheeled mobile robots. The method does not require high performance of the computing system and provides satisfactory qualitative and quantitative characteristics of motion control.

Purpose of research. The purpose of this work is to develop the technique for obtaining the membrane stress ratio in a fabric shell which consists of a number of arch-type sectors of given height at the center.

Methods. The iterative secant method is used for finding the membrane stress ratio. The height in the center of a sector is determined by means of the force density method at every iteration. The method includes applying a mesh on a shell surface and determining the nodal coordinates of the mesh via the solution of the set of equilibrium equations. The equations of the set are linearized by means of substitutions, which are the force to length ratios for the mesh elements.

Results. The iterative technique for obtaining the membrane stress ratio has been developed. The technique consists of the following stages: initial search range determination and discrepancy minimization between the required and calculated heights at the center of the shell sector. The quality of the algorithm is confirmed by numerical simulating of a number of sectors of an arch-type fabric roof on a rectangular plan. The discrepancy between the specified heights in the center of the sectors and the heights obtained by the specialized licensed software package does not exceed 1.0%.

Conclusion. The surface shape of fabric shells depends on the membrane stresses. The shape-finding problem is well elaborated theoretically by now. Judging by the literature survey, however, the inverse problem of finding the membrane stress ratio given the geometrical parameters of the shell has not been developed yet. The proposed technique will facilitate research and development of fabric building constructions. Further development of the technique is in the field of multi-section fabric structural analysis with supporting structure compliance considered.

Purpose of research. In the proposed publication, two main factors are selected as the purpose of the study, which include a comprehensive analysis of the functioning of a dependent heat supply system for buildings and structures and the synthesis of a control scheme for the distribution of resources of the specified system by applying mathematical methods and creating appropriate algorithms for regulating heat flows.

Methods. Methods of mathematical analysis and differential equations of thermal balance were used to form the optimal strategy. This approach made it possible to carry out a detailed description of the non-stationary mode of operation of the dependent heating system of buildings and structures, taking into account the temperature dynamics of the thermal load and the environment. Along the way, a study of the theoretical results obtained was conducted. Transients were taken into account when putting the projected control scheme into operation. The theory of similarity was widely used to form the output working formula for the organization of heat supply. The obtained ratio made it possible to form algorithms for managing the provision of heat to buildings and structures. This approach made it possible to synthesize heat flow control schemes based on the principles of resource allocation according to the smart home operation option for practical use.

Results. In the course of the study, a working formula was obtained for the control of the heat supply process of buildings and structures. On its basis, appropriate functional schemes were synthesized, taking into account the dynamics of changes in temperature conditions in the thermal load and the external environment.

Conclusion. The results obtained make it possible to apply the principles of smart home management in practice. At the end of the study, the results of the work will be summarized, as well as the main conclusions and recommendations for managing the heat supply system using mathematical analysis methods will be formulated. Also, in conclusion, an assessment of the effectiveness of the proposed solutions and their impact on the economy and the environment can be given.

Purpose of research. Development of a software implementation of a hierarchical approach to solving the inverse problem of the kinematics of a robot manipulator with an arbitrary number of joints. The developed library can be used both as part of mechanical engineering CAD systems with support for engineering analysis (CAE) functionality, and for the development of software for embedded control systems for multi-axis handling machines.

Methods. The idea of the approach is to iteratively approximate generalized coordinates in a sequence defined by the developer. The number of required iterations is determined by the required accuracy of the solution. As initial data for solving the inverse kinematics problem, a 4 × 4 “manipulator matrix” in symbolic form, initial values of generalized coordinates, and a 4 × 4 “manipulator matrix” describing the final position and orientation of the gripper are required. The ANSI C programming language was chosen for implementation because it provides sufficient portability and proximity to the hardware.

Results. The result of the work is a library of the C programming language for computers running operating systems of the Unix family (for example, GNU/Linux, freeBSD, openBSD, macOS, Solaris), which provides the functions necessary to solve the inverse problem of the kinematics of a robot manipulator.

Conclusion. The article shows an example of using this library for a three-link robotic manipulator, and also plots the trajectory of its movement along ten points. Using the libreRGM3 library proposed in the article can be an effective way to solve OZK when modeling robot movement in CAD (for example, OpenSCAD [8]), for educational or research purposes, when working with a computer without a graphical interface or with a programmable logic controller and microcontroller.

Purpose of research. Currently, interest in the use of drones in various fields is actively growing. The reasons are related to the continuous growth of technology, with the advent of fast microprocessors that provide autonomous control of multiple communication systems. Monitoring, construction, control and surveillance are just some of the areas in which the use of UAVs is becoming commonplace. The purpose of the work is to study the work of loaded information exchange protocols at various levels of interaction and to propose options for increasing the reliability of interaction based on hybrid technologies. The article provides details of the communication and data exchange protocols used in UAV systems, as well as their performance.

Methods. The article discusses the protocols involved in the operation of UAVs at different levels, their features, advantages and disadvantages, as well as their failures to restore communication. Using realistic technological features of unmanned aerial vehicles to test models and methods can be very relevant for practical purposes in various industries from civil to military.

Results.The objectives of the study are to detail the data exchange protocols in UAVs at various levels, taking into account the analysis of the structure of the transmitted information and the hybrid model.

Conclusion. To qualitatively assess the impact on information security, it is proposed to introduce hybrid models of components that dynamically adapt data exchange protocols based on real-time threat analysis and system capabilities. Efficient use of energy is critical to efficient and safe UAV operation. The issues of security of the transmission channel of the protocol load from the point of view of the cost of energy resources are touched upon and considered.

Purpose of reseach. Formalize an ontological model of the research subject area and develop, based on it, data models for an information system for extracting and processing expectations for the quality of corporate data storage.

Methods. In this study, an ontological approach and data modeling methods were used, and the task of implementing a data model was formalized using the conceptual apparatus and formal language of the relational data model and set theory. The Entity-Relationship model was used as a modeling approach.

Results. As a result of the research, conceptual, logical and physical models were developed for a relational database information system for retrieving and processing expectations for the quality of corporate data storage based on the ontology of the subject area under study. This allows us to expand the possibilities of using the information system developed in further research in industrial operation by organizations carrying out work on creating corporate data warehouses.

Conclusion. As a result, the results of the study showed that the transition to using a relational data model while preserving ontological semantics is possible and has been studied by a number of researchers: sets of classes, relationships between them and their attributes are defined in the ontological model, which makes it possible to develop data models for a relational database without providing for the need for ontology changes, and the relational database, in turn, can store instances of ontology classes in separate tables for each class, the fields of which will be the attributes of a particular class.

Purpose of research is to use non-binary staircase codes to correct errors that occur in the reading channels of external storage devices (ESD) of a computer.

Methods. Decoding of staircase codes is implemented by decoding words of component Reed-Solomon codes located in a pair of adjacent blocks in the decoding window. After decoding all the words of component codes, the data blocks in the window are shifted. Decoding of component code words in a window is performed in parallel, which reduces the delay of the staircase decoder. The procedure for decoding component Reed-Solomon codes involves the sequential execution of the following steps: 1) the syndrome polynomial is calculated; 2) polynomials of locators and error values are calculated (the key equation is solved); 3) the roots of the polynomial of error locators are sought; 4) error values are calculated; 5) erroneous symbols are corrected. To solve the key equation (step 2), it is proposed to use the ePIBMA (Enhanced Parallel Inversionless B-M Algorithm) algorithm.

Results. As a result of the study using computer simulation, the parameters of the staircase decoder were selected to optimize its operation: the number of half-iterations is 3; the decoding window size is 8 blocks; decoding delay is 6 blocks. For these parameters, the correction ability of the staircase decoder is close to maximum, with moderate complexity and latency. The effectiveness of staircase codes in the reading channels of the computer's ESD was studied using computer simulation. The percentage of blocks with uncorrectable errors was used as an indicator of efficiency. To take into account the grouping of errors symbols of ESD disk drives, a binary symmetric channel with memory (BSMC), which was described by a modified Bennett-Froelich model, was used as a channel model. The geometric distribution parameter g of this model was taken equal to 0.2, 0.5 and 0.9. A staircase code with component Reed-Solomon codes (224, 210, 15) defined over the GF(28) field was studied. Moreover, the speed of this staircase code is R = 0.87, which corresponds to the speed of the product of Reed-Solomon codes used in DVD optical discs. It is shown that when using code constructions with the same speed, the ratio of blocks with uncorrectable errors is smaller in the staircase code compared to the product of Reed-Solomon codes and that with increasing average error packet length this ratio decreases.

Conclusion. In the presented paper, it is proposed to use staircase codes with component Reed-Solomon codes to correct errors in the ESD of a computer with a sector organization. Decoding of these codes using the ePIBMA algorithm is considered. Using simulation, the parameters of the staircase code decoder were selected. The efficiency of error correction in channels with error grouping has been studied. The results of the study showed higher efficiency of staircase codes in channels with error grouping compared to a product of Reed-Solomon codes with the same redundancy

Purpose of research. Development of program code in the C# programming language that implements an algorithm for recognizing the shape of geometric objects in the input image while ensuring the reliability of this computational process is the main goal of the article.

Methods. The algorithm for recognizing the geometric shapes of objects is based on a combination of traditional image processing methods and intelligent rules that determine the type of geometric shape of an object depending on the characteristics of the contours, such as moments, the number of their sides, etc. To implement this method, the following sequence of mathematical operations which includes the following stages is proposed in the article. Firstly, this method includes the following operations: blur, convert the original image to grayscale, and invert. Detection of contours and determination of their characteristics, such as moments, perimeter, etc., is carried out at the second stage of the method. And at the final stage, the comparison of each found contour of a certain geometric figure is carried out depending on the number of sides included in the structure of the contour.

Results. An algorithm and instructions for creating program code have been developed for the software implementation of the process of recognizing the geometric shape of objects. It was determined that the proposed algorithm has a high reliability approximately equal 97%.

Conclusion. Traditional image processing methods such as blurring and grayscale conversion can be successfully combined with methods for identifying contours and determining their geometric characteristics. This synergy of image processing methods makes it possible to create an algorithm for recognizing geometric shapes. It is important to consider that the reliability and efficiency of such an algorithm depends on the settings of the threshold values used in the image processing functions and further study of their characteristics can lead to improved results of the algorithm presented in the article.

Purpose of research. The method proposed in this work is aimed at increasing the speed and accuracy of the computational process of training a fuzzy logic system. The developed parameterized membership functions were used as the subject of the study. The effectiveness indicator was the impact of changing the labels of input membership functions, created by the traditional method and using parameterized membership functions, on the output characteristic.

Methods. A method has been developed and implemented for constructing parametric membership functions that are used in the process of fuzzy logic inference fuzzification. In addition to fuzzification, the system implements fuzzy inference and defuzzification. Triangular membership functions were used in the fuzzification process. As a compositional rule, 6 activated degrees of membership were used, combined on the basis of Zadeh’s compositional rule into 5 conclusions of fuzzy logical inference. At the defuzzification stage, a simplified center of gravity method was used. The object of the study was fuzzy logical inference using traditional and parameterized membership functions synthesized at the fuzzification stage.

Results. A mathematical model of fuzzy inference with implemented parameterized membership functions at the fuzzification stage is obtained. Based on the experiment, it was concluded that the proposed model has a smoother resulting surface when one parameter of the input membership function changes. In this case, the condition for the division of unity is ensured.

Conclusion. A mathematical model of fuzzy inference with implemented parameterized membership functions at the fuzzification stage is obtained. Based on the experiment, it was concluded that the proposed model has a smoother resulting surface when one parameter of the input membership function changes. In this case, the condition for the division of unity is ensured.