In robotics, much emphasis is placed on mathematical modeling, as the creation, control, and optimization of robots for a wide field of work must be achieved precisely and adaptively. The aim of this paper is to present a systematic and structured approach to the literature review of mathematical models in robotics, critically considering mathematical frameworks that influence and shape robotics in light of current and prevailing trends. The paper underlines the complexities of maintaining accurate dynamic representations in robotic systems, revealing the challenges that arise from numerical simplifications. The study outlines the development of efficient remote-control systems that consider dynamic relationships among the components comprising the robot. The findings of the recent simulation prove that the developed mathematical model effectively supports designing an adaptive control system with artificial intelligence features, especially for autonomous mobile robotics with manipulators that are inherently complex and networked systems. If models are to accelerate robotics progress toward increasingly intelligent, adaptive, and efficient systems, they must learn to overcome some of the computational challenges while leveraging disciplinary synergies.

The authors of this article analyzed the problem of logistic robotics. This paper presents a method for robot navigation in a known environment. The method consists of two steps. The first step is to model the system, assign vector marks to the prominent edges of the virtual environment map, and direct the robot to reach these marks. The second step is to enable the robot to execute a specific task based on the given paths and deal with the local obstacles avoidance independently. The identification of the prominent point, the computation of the vector mark, and optimal path calculation are performed on the computer model using colored Petri nets in the software ‘Centaurus CPN’. The proposed approach was extended to simulate the work of a logistic robot, which has to take boxes and deliver them to certain places in storages. The experimental investigation has shown that the simulated mobile robots with the proposed navigation system were efficiently moving along the planned path. The analysis of the vector tree reveals that it takes 0.389 s to compute and graphically represent it. The occupation of certain places in storages is visualized and shown in experimental graphics.

In this paper a discrete-time PID controller is presented for a process with delay control. The discrete-time PID controller design in programmable logic controller has been researched. Finally, the complete algorithm is tested in the programmable logic controller, and the results of this test are explained.

The growing population and lack of change in resources of cultivated land have led to the search for more efficient farming solutions. The recovery of soil is facilitated by using chemicals designed for the enrichment of cultivated soil. Fertilisers are made of a combination of various substances that determine not only the chemical but also the shape characteristics of the fertiliser pellets. The effect of the quality of fertilisation on yield size is related to even distribution. Shape and size are closely related to the quality of the fertilisation process. The intense control of the production process would not be possible without automatised and quick measurements within the production line. Constant control is necessary to ensure that the products meet quality standards. The contactless assessment of pellet sizes allows a quick reaction to changes in production quality and reduces the costs arising from the reprocessing of defective pellets. The results of the assessment of pellet volume using their two-dimensional image are presented in this publication. Pellets must be analysed according to their most characteristic position, which can provide valuable information about their properties. The aim is to determine the placement positions of the equipment based on calculations and to compare the results with those of gold-standard equipment. Correctly calibrated equipment ensures that the measurement results match the results of the control equipment of fertiliser producers. Reliable non-contact measurements can reduce the reaction time to production changes.

Generative artificial intelligence tools are increasingly being used to support engineering tasks; however, their applicability to process identification, controller tuning, and control performance prediction remains insufficiently investigated. This article evaluates the capabilities of GenAI systems to identify dynamic process models, design PI and PID controllers, and predict closed-loop performance metrics. Five benchmark process models representing first-order, delayed, integrated, and second-order dynamics were considered. Open-loop and closed-loop datasets were provided to two AI systems, which were then requested to identify process models, propose controller parameters, and predict overshoot, settling time, integral of time-weighted absolute error, and disturbance rejection time. The generated controller settings were validated using MATLAB/Simulink simulations, and both absolute and relative prediction errors were calculated. The results show that both AI systems could generate feasible controller parameters that produced stable closed-loop responses for most of the processes investigated. However, significant discrepancies were observed between predicted and simulated performance indicators. The integrating process exhibited the highest prediction errors, indicating substantial difficulties in interpreting integrating dynamics. The results suggest that current GenAI systems can support preliminary controller design and process analysis but cannot yet replace simulation-based validation for accurate quantitative performance assessment.