The object of the study is the process of constructing and analyzing the trajectories of the gripping device of a collaborative robot-manipulator under spatial constraints and the presence of obstacles in a dynamic environment. The subject of the study is mathematical models, algorithmic and software for modeling the optimal motion of the manipulator end effector taking into account kinematic, dynamic and energy constraints. The aim of the research is to construct trajectories of the collaborative robot's gripping device, taking into account constraints and optimal control actions in continuous time, which ensure the construction of trajectories with minimal energy consumption, compliance with given spatial constraints, and avoidance of collisions with obstacles. The research methodology is based on the application of the Pontryagin maximum principle to form the conditions for optimal control and the construction of a system of differential equations with boundary conditions. A special cost functional has been developed to quantify energy consumption and take into account penalties for approaching prohibited zones. The numerical solution of the problem was implemented using the Euler method, and the optimization of the trajectory parameters with fixed final effector coordinates was implemented using the least squares method with constraints. The Python programming language and the Matplotlib library were used to visualize the results. As a result of the study, optimal trajectories of the gripping device were obtained, which ensure collision avoidance, compliance with spatial constraints, and reduced energy consumption when reaching the specified final effector positions. The simulation confirmed the effectiveness of the developed method and its resistance to changes in environmental parameters. The conclusions of the study indicate that the proposed approach allows for a comprehensive solution to the problem of planning the movement of collaborative robots in the optimal control mode taking into account constraints. The results obtained can be applied in Industry 5.0 production systems, robotic service complexes, automated warehouse systems, and robots that interact with humans in a limited space.

This paper addresses the decision-making problem for trajectory planning of a collaborative mobile robot operating in an uncertain dynamic environment. A risk-aware trajectory planning method based on model predictive control is proposed, which integrates probabilistic state estimation of the robot and its environment with the prediction of dynamic obstacle motion and safety constraints. The method relies on the fusion of data from a camera, an inertial measurement unit, and an ultrasonic sensor, enabling increased robustness and adaptability of trajectory planning under sensor noise and incomplete information. Numerical simulation results confirm the effectiveness of the proposed approach in terms of maintaining safety margins, control stability, and goal reachability in complex navigation scenarios.

This article examines the problem of synchronizing the operation of a group of collaborative robots in a shared workspace with humans, in light of modern requirements for human-centered manufacturing and the Industry 5.0 concept. The relevance of the research stems from the need to ensure coordinated movement of multiple robots while adhering to strict safety constraints in HRC scenarios, where traditional centralized approaches do not guarantee sufficient reliability and scalability. The objective of this work is to develop a mathematical model for the synchronized control of collaborative manipulators, taking into account mutual coordination, tracking of a shared trajectory, and active avoidance of dangerous proximity to humans and between robots. The subject of the study is decentralized synchronization laws in the problem space with projection into joint space and the use of potential safety fields. The work uses methods of mathematical modeling of manipulator dynamics based on Euler–Lagrange equations, consensus control methods, pseudo-inversion of the Jacobian matrix, fourth-order Runge–Kutta numerical integration methods, and methods for analyzing safety metrics. The objectives of the study are to formalize the laws of consensus control in the problem space, integrate safety potential fields, and perform numerical validation of the model for a group of manipulators in a shared workspace. Modeling results for a group of three two-link planar manipulators showed the formation of coordinated trajectories with a reduction in characteristic oscillations and stabilization of dynamics; however, the average tracking error of the common trajectory remains at 0.38–0.40 m. An analysis of minimum robot-to-robot and robot-to-human distances confirmed the effectiveness of potential barriers in steady-state operation, but revealed dangerous gaps in transitional sections. It is concluded that the proposed model ensures stable synchronization and a basic level of safety, but to guarantee compliance with safety margins throughout the entire time interval, it is advisable to switch to rigid barrier constraints such as CBF and task-priority control schemes.

Технологія цифрових двійників передбачає створення віртуальної моделі фізичного об’єкта, процесу або системи, яка може бути використана для моделювання, моніторингу, тестування та прогнозування можливого розвитку подій на основі інформації від розподіленої мережі сенсорів технологічного обладнання. Упровадження цифрових двійників у систему автоматизованого управління технологічними процесами дасть змогу підвищити ефективність виробничих процесів на інтелектуальних виробництвах. Предметом дослідження є архітектура автоматизованої системи управління технологічними процесами (АСУ ТП) на інтелектуальному заводі з інтеграцією технології промислового Інтернету речей та цифрового двійника виробничого процесу. Мета роботи – вдосконалення методів децентралізованого управління ТП для підвищення ефективності виробничого процесу на інтелектуальному виробництві за допомогою інтеграції цифрових двійників в АСУ. Завдання: розробити архітектуру розподіленої АСУ ТП на інтелектуальному заводі з інтеграцією технології промислового Інтернету речей та цифрового двійника виробничого процесу; проаналізувати поняття "цифровий двійник" у контексті поєднання цієї технології з процесами сталого розвитку й трансформації виробничої галузі; дослідити запропонований метод інтеграції цифрового двійника в задачу управління ТП. У процесі досліджень упроваджено такі методи: комп’ютерне моделювання, теорія автоматичного управління, аналіз і синтез децентралізованих виробничих систем. Досягнуто таких результатів: розроблено архітектуру автоматизованої системи з використанням цифрового двійника як еталона, що описує ідеальний розвиток процесу керування об’єктом автоматизації із застосуванням цифрового ПІД-регулятора. Результати моделювання продемонстрували, що фізичний макет досить точно відтворює поведінку математичної моделі ПІД-регулятора із заданими параметрами. Висновки. Результати експериментального дослідження показали, що інтеграція цифрових двійників в АСУ дає змогу вдосконалити методи децентралізованого управління ТП та підвищити ефективність виробничого процесу на інтелектуальному виробництві. Успішне впровадження технології цифрових двійників у інтелектуальне виробництво в поєднанні з хмарними обчисленнями та машинним навчанням спрямоване на досягнення цілей сталого розвитку.

Our article is devoted to the development of a small robot prototype using 3D printing technology. Particular attention is paid to its use in conditions associated with the destruction of reinforced concrete panel buildings, which becomes especially relevant in connection with man-made destruction as a result of military operations in Ukraine. The robot is an innovative technology solution designed to improve rescue, recovery and safety operations in environments where traditional methods may not be effective. In this article, we will look at the development process and functional features of this mobile robot, and also discuss the prospects for its use in complex and emergency situations.

In the current conditions of transition to the Industry 5.0 paradigm, the key task is to ensure effective and safe interaction between humans and robots in a shared production environment. Mobile manipulator robots perform complex operations in a dynamically changing environment where numerous factors influence the control system's decisions: people's movement trajectories, the presence of obstacles, changes in the location of objects, etc. Traditional control systems based solely on sensor data or machine vision have limitations in response speed and recognition accuracy. The use of a hybrid control system that combines machine vision and sensor networks makes it possible to improve the accuracy of situation assessment, decision-making speed, and the safety of interaction with the operator.

У контексті розвитку концепції Індустрія 5.0, яка передбачає тісну взаємодію між людиною та інтелектуальними автоматизованими системами, особливого значення набуває дослідження механізмів гнучкого й безпечного управління колаборативними роботами-маніпуляторами. Дослідження спрямовано на побудову математичної моделі ієрархічного високорівневого керування для триланкового колаборативного робота, що дає змогу адаптувати поведінку маніпулятора до динамічних змін у виробничому середовищі та наявності людини в робочій зоні. Мета статті – розроблення математичної моделі, що поєднує класичний підхід моделювання динаміки з такими методами: рівняння Ейлера – Лагранжа та сучасні адаптивні алгоритми регулювання, реалізовані за допомогою нечіткої логіки, що дає змогу оптимізувати швидкість і траєкторію руху виконавчих органів в умовах змінного навантаження та часткової невизначеності середовища. Запропонована модель реалізує багаторівневу архітектуру управління, що бере до уваги не лише фізичні параметри маніпулятора, а й когнітивні аспекти взаємодії з оператором та оточенням, шляхом побудови контролера на базі Fuzzy Rule. У статті запропоновано формалізацію математичних виразів, описано всі рівні системи керування, їх призначення та взаємозв’язок, а також проведено чисельне моделювання за допомогою Python і PyCharm. Результати моделювання підтвердили ефективність запропонованої системи в умовах присутності людини, забезпечення безпечної відстані, адаптацію до навантаження та відповідність до заданих виробничих параметрів. Висновки. Запропонована модель здатна суттєво покращити якість управління маніпулятором в умовах Індустрії 5.0, особливо під час роботи в гібридних середовищах. Модель можна адаптувати до різних типів колаборативних роботів, що відкриває перспективи для її подальшого вдосконалення, зокрема завдяки інтеграції з нейромережевими підходами, глибоким навчанням та мультиагентними системами в межах розподіленого інтелектуального виробництва.

This study’s object is those factors that affect the defects of photopolymer 3D models. The task addressed relates to identifying the factors that cause the appearance of surface defects and deviations in geometric dimensions in photopolymer 3D models. The influence of the photopolymer resin temperature on the surface defects appearance and deviations in geometric dimensions, as well as the layers exposure parameters influence on the photopolymer resin temperature, has been revealed. At the final stage of the study, it was found that the exposure parameters of the photopolymer model layers affect the photopolymer resin temperature, which, in turn, increases the likelihood of defects and geometric deviations in the finished model. Provided that the photopolymer resin temperature is kept within the range of 18–26°C, the model dimensions geometric deviation decreases by 0.054 mm along the XY axis and by 0.006 mm along the Z axis. A linear dependence of the size deviations on the exposure parameters and the photopolymer resin temperature has been established. The process of heat transfer from a UV radiation source to a photopolymer resin has been described. A thermodynamic scheme for controlling the resin temperature based on modeling the heat transfer between the exposed layers and the resin volume, considering the exposure time and UV radiation intensity, has been devised, which makes it possible to predict a critical temperature increase and minimize defects. While devising a method for controlling products during photopolymer 3D printing, the photopolymer temperature parameter was considered as one of the factors affecting the quality of parts and the level of rejects. Thus, the proposed method for controlling products during photopolymer 3D printing could be used to improve the technological process of manufacturing parts by reducing the number of defects and improving the finished products quality

The relevance of this study is due to the growing demands for intelligent robotic systems capable of safe interaction with humans in a collaborative work environment. It is especially important to provide adaptive control of grippers, which allows manipulators to accurately and delicately grasp objects of various shapes, masses, and stiffness. The subject of the research is the process of controlling a gripper as part of a collaborative robot manipulator, and the topic is the development of effective mathematical software for adapting control parameters in real time. The aim of the work is to improve the accuracy, reliability, and flexibility of the intelligent gripper by integrating Sensor Fusion and Neuro-PID control methods. In the course of the study, methods of mathematical modeling, sensor information processing, and numerical error analysis based on experimental data were used. The developed model takes into account the symmetry of the applied forces and ensures stable control of the gripping force, as evidenced by the results of experiments on controlling the asymmetric error and the control signal. The analysis showed that the deviations of the gripping error remain within ±0.2 N, and the control signal has smoothed dynamics without sharp impulses, which provides an adaptive response to external changes. The conclusions confirm the feasibility of the proposed approach to improve the control efficiency of robotic grippers. The scope of the results includes industrial collaborative robots, automated warehousing systems, manipulation of delicate objects, and biomedical robotic systems where high accuracy and adaptability of interaction is required.

The article presents an improved encoding information method for QR-codes, designed to increase the efficiency of robotic conveyor lines for sorting pharmaceutical products. The proposed solution is based on the use of the redundancy operator and random permutation algorithms, which allows reducing the number of errors during reading, increasing the resistance of QR codes to mechanical damage and reducing processing time. The conducted studies demonstrate an increase in sorting accuracy by 35% and a decrease in the frequency of failures by 25%, which provides significant optimization of production processes and improved reliability of automated systems.

The technology of digital twins involves the creation of a virtual model of a physical object, process, or system that can be used for modeling, monitoring, testing, and predicting possible future developments based on information from a distributed network of sensors of technological equipment. The implementation of digital twins in the system of automated control of technological processes will allow increasing the efficiency of production processes in intelligent manufacturing. The subject of the research is the architecture of an automated process control system of technology process (ACS TP) in an intelligent factory with the integration of the Industrial Internet of Things technology and a digital twin of the production process. The aim of the research is to improve decentralized control methods for technological processes to enhance the efficiency of production processes in intelligent manufacturing by integrating digital twins into automated control systems. Task: to develop the architecture of a distributed ACS TP in an intelligent factory with the integration of the Industrial Internet of Things technology and a digital twin of the production process. To review the concept of "Digital Twin" in the context of combining this technology with the processes of sustainable development and transformation of the manufacturing industry. To conduct research on the proposed method of integrating a digital twin into the TP management task. In the research, the following methods were used: computer modeling, methods of automatic control theory, methods of analysis, and synthesis of decentralized production systems. The following results were obtained: an architecture of an automated system was developed using a digital twin as a reference model, which describes the ideal development of the control process of the automation object using a digital PID controller. The simulation results showed that the physical model quite accurately reproduces the behavior of the mathematical model of the PID controller with the given parameters. Conclusions: the results of the experimental research showed that the integration of digital twins into automated control systems improves decentralized control methods for technological processes and enhances the efficiency of production processes in intelligent manufacturing. The successful implementation of digital twin technology in intelligent manufacturing, in combination with cloud computing and machine learning, is aimed at achieving sustainable development goals, specifically addressing task 9.5.

У даній статті розглянуто актуальну проблему алокації завдань між людьми та колаборативними роботами в умовах Індустрії 5.0 з використанням блочного процесного планування. Основна увага приділяється аналізу взаємодії між операторами та автоматизованими системами, що працюють у спільному виробничому середовищі. Основною метою є забезпечення гармонійної співпраці між людьми та роботами шляхом оптимізації розподілу завдань з урахуванням низки важливих факторів, таких як часові та ресурсні обмеження, складність виконуваних операцій, рівень автономності роботизованих систем, а також пріоритетність виконання різних етапів виробництва. У рамках дослідження запропоновано математичну модель, яка включає функції вартості та вигідності, що дозволяють оцінити ефективність планування. Модель також містить численні обмеження на час і ресурси, що є критично важливими для підтримки продуктивності, безпеки та гнучкості сучасних виробничих систем. Для перевірки її працездатності було розроблено програмне забезпечення на мові Python, яке дозволяє не лише автоматично здійснювати процес планування, але й оцінювати загальну ефективність запропонованих стратегій розподілу завдань. Проведені експериментальні дослідження продемонстрували, що успішність планування значною мірою залежить від збалансованості часових і ресурсних параметрів. Проведені експерименти показали, що успішність планування залежить від збалансованості часових і ресурсних параметрів: при значеннях Tmax ≥ 5 і Rmax ≥ 7 всі обмеження виконуються, а функція вартості коливається в межах 30–80. Натомість у разі недостатності ресурсів система виявляє підвищену чутливість, що робить виконання деяких завдань неможливим або неефективним. Отримані результати підтверджують, що розроблена модель є стійкою до змін параметрів і забезпечує оптимальний розподіл завдань у більшості виробничих сценаріїв. Перспективи подальших досліджень включають розширення моделі для динамічних середовищ, інтеграцію алгоритмів машинного навчання для прогнозування та вдосконалення процесу адаптивного планування.

The subject matter is a method for determining the robot trajectory with four steering wheels to reach a given point on a terrain map. The research goal is to develop a method for determining the orientation of the wheels depending on the trajectory of the mobile platform to increase the maneuverability of an autonomous robotic vehicle in a limited production space. Tasks to be solved: to analyze similar solutions, describe the proposed design of the steering unit mechanism for a mobile robotic cart, describe the kinematics of a mobile robot with four steerable wheels, develop an algorithm for the steering unit control module, propose a method for controlling a mobile platform with four steerable wheels, and perform experimental studies on the application of the proposed method. Scientific novelty: a method for determining the orientation of the wheels to reach a given point on the terrain plan has been proposed. An algorithm for performing calculations using a software tool has been developed. A mathematical justification for the method of controlling individual wheel blocks of a mobile platform has been provided. Methods of the study: modeling methods and automatic control theory, methods for describing linear dynamic systems, analytical modeling methods, computer modeling in the Matlab/Simulink environment. Results and conclusions: The mobile platform movement principle using four independent steering wheels is considered. A method for determining the orientation of the steering wheels depending on the trajectory of movement is proposed, which is based on the geometric analysis of the position of the platform and the target point, which allows calculating the angle of rotation of each wheel in such a way as to ensure movement to a given point without lateral slippage. A mathematical model of the control system is built, a structural and functional diagram is developed, an algorithm for processing commands, calculating the angles of rotation is described, and a three-level control system is implemented: linear speed, wheel orientation angle and angular speed of the entire platform. The developed mock-up sample of the mechatronic steering wheel assembly is described. The simulation conducted in the Simulink environment confirmed the operability of the proposed system.

Modern mobile robots are actively being introduced in industry, logistics, the service sector, and autonomous transport, which requires them to be able to effectively navigate dynamic and unpredictable environments [1,2]. Building safe and optimal trajectories in real time is becoming a key challenge, as traditional planning methods do not provide sufficient flexibility and speed

Currently, the areas of use of robots in general and zoomorphic ones in particular are very diverse. They are used in various fields: from research to social support for elderly and sick people. When creating such robots, scientists face a number of problems. This paper considers the problem of maintaining balance in a four-legged, Spot type robot. A block diagram for balancing a zoomorphic mobile robot of the Spot type has been developed. We have created a balancing system and carried out studies, which show promising results and a quick response to disturbances. As a result, the robot restores balance after all applied disturbances.

In automated process control systems, automation equipment (sensors, converters, amplifiers, etc.) with technical defects arising during their manufacture, which are one of the main causes of failures, is widely used. The paper establishes the possibility of using the laws of nonequilibrium thermodynamics as the basis for determining the relationship between the controlled parameters of automation equipment and the parameters of the displayed medium, which made it possible to build a deterministic model of the development of production defects and, ultimately, determine the directions for changing and adjusting the technological processes of production of automation equipment. A method has been developed for implementing a guaranteed forecast of changes in the parameters of automation equipment based on solving the evolution equation using optimal filtering algorithms, which is the subject of research. The purpose of the work is to improve the quality and reliability of automation equipment by improving the monitoring of defects arising in the production of instruments, functional units and sensors of automation equipment. The article solves the following problems: analysis of existing approaches to the problem of manufacturing defects and methods for their detection and setting a research task; modeling of the process of development of production defects causing changes in the technical condition of automation equipment; development of a decision-making method based on guaranteed prediction of the technical state of automation equipment. The methodology of work is based on the methods of thermodynamic description of the kinetics of processes (when developing a model of the process of development of production defects that cause a change in technical condition) and methods of assessment and forecasting based on optimal filtering algorithms (when developing a decision-making method based on guaranteed foresight of technical condition). The results of the work include a model of the process of development of manufacturing defects that cause a change in the technical condition of automation equipment, and a decision-making method based on a guaranteed forecast of the technical condition of automation equipment. Conclusions. The paper establishes the possibility of using the laws of nonequilibrium thermodynamics to determine the relationship between the controlled parameters of automation equipment and the displayed medium, and to build a deterministic thermodynamic model of the development of production defects. Disclosed is an equation of evolution of technical state of automation equipment based on a deterministic kinetic model of processes occurring in a multicomponent medium, and an observation model which takes into account errors caused by instability of external effects and measurement errors. Disclosed is a method of implementing a guaranteed forecast of change in parameters of automation equipment based on solving the evolution equation using optimal filtering algorithms, which are used to solve estimation and prediction problems.

Formalized universal approaches, which can be suitable for industrial products digitalization implementations providing the real time continuous technical diagnostics of electromechanical systems are developed. These approaches are based on the parametric identification of electromechanical systems by means the least square method with digitalization of real time measurements data. Increasing of the diagnostics accuracy with decreasing of the time discretization step of measured data digitalization shown through computer simulations proves correctness of the developed generalized approaches and it gives the ways of the further researches.

a Bayesian model is proposed for determining the optimal variant of the MEMS component manufacturing technological process A software tool has been developed to automate this process Calculations are performed using the proposed models and software.

The article presents the results of work aimed at research of electric-physical properties of carbon-carbon composite material (CCCM) under conditions of heat exchange by radiation in vacuum and creation of a thermalresistive heat radiation converter for measuring temperatures up to 2500 °C.