Mathematical Models of Mobile Robots in The Digital Twin Concept: Comparative Analysis and Research of Usage Trends

Abstract

The article explores mathematical models of mobile robots in the Digital Twin concept, taking into account current trends in the development of robotic systems and Industry 5.0. The purpose of the study is to conduct a comprehensive qualitative, numerical, and comparative analysis of kinematic models of mobile robots and determine the patterns of their use in digital twins and scientific publications. The object of research is the process of functioning of mobile robots in a dynamic environment in conditions of digital representation of their behavior. The subject of research is mathematical models of motion, in particular Unicycle, Differential Drive, Bicycle, Omni-directional and Ackermann, as well as methods of their application in navigation and control systems. The scientific novelty of the work lies in the systematization of approaches to modeling the motion of mobile robots in the SE(2) state space, conducting a comprehensive comparative analysis of their characteristics, and conducting the first-ever study of trends in the use of these models based on data from the international scientometric database Scopus for 2022–2025. The results obtained showed that the Differential Drive model occupies a dominant position among the studied models, demonstrating the highest dynamics of the growth of the number of publications, which is due to its optimal combination of computational simplicity and physical adequacy to real robotic platforms, while other models have a narrower specialization or increased complexity of implementation. The analysis confirmed that the choice of a mathematical model for a digital twin is determined by a compromise between the accuracy of reproduction, the complexity of calculations and the requirements for control and navigation systems. The results obtained can be used in the development of digital twins of mobile robots, autonomous navigation systems, multi-robot systems and intelligent manufacturing platforms.