Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function
The rapid advancement of robotic technologies has demonstrated the significant potential of Multi-Robot Systems (MRS) for application across various fields, particularly in automation, manufacturing, and rescue operations. However, enhancing the reliability of Multi-Robot Systems, particularly in cr...
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MDPI AG
2025-02-01
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| author | Xing Qiao Dan Ma Shuang Guo |
| author_facet | Xing Qiao Dan Ma Shuang Guo |
| author_sort | Xing Qiao |
| collection | DOAJ |
| description | The rapid advancement of robotic technologies has demonstrated the significant potential of Multi-Robot Systems (MRS) for application across various fields, particularly in automation, manufacturing, and rescue operations. However, enhancing the reliability of Multi-Robot Systems, particularly in critical applications, has emerged as a primary focus of research. A mathematical model of a five-robot system, equipped with early warning capabilities, is developed using Markov process theory and the supplementary variable method in this paper. A model of an abstract Cauchy problem system is developed, employing semigroup theory to investigate the well-posedness of solutions for this five-robot system. The stability of the system is verified using analytical methods, confinal correlation theory, and modern functional analysis techniques. Several key reliability indicators are presented using the eigenvector method. Numerical simulations and comparative methods effectively demonstrate the efficacy of the proposed eigenvector method. Firstly, the innovation of this paper lies in the combination of qualitative and quantitative analyses to improve and enrich the theory and methods of repairable systems. Secondly, mathematical analysis methods and the mathematical software are employed to provide both analytical and numerical solutions for the system. |
| format | Article |
| id | doaj-art-db5adcd0d433421ca09e4acc2b9750c0 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-db5adcd0d433421ca09e4acc2b9750c02025-08-20T02:44:34ZengMDPI AGAxioms2075-16802025-02-0114211310.3390/axioms14020113Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning FunctionXing Qiao0Dan Ma1Shuang Guo2School of Mathematical Science, Daqing Normal University, Daqing 163712, ChinaSchool of Mathematical Science, Daqing Normal University, Daqing 163712, ChinaSchool of Mathematical Science, Daqing Normal University, Daqing 163712, ChinaThe rapid advancement of robotic technologies has demonstrated the significant potential of Multi-Robot Systems (MRS) for application across various fields, particularly in automation, manufacturing, and rescue operations. However, enhancing the reliability of Multi-Robot Systems, particularly in critical applications, has emerged as a primary focus of research. A mathematical model of a five-robot system, equipped with early warning capabilities, is developed using Markov process theory and the supplementary variable method in this paper. A model of an abstract Cauchy problem system is developed, employing semigroup theory to investigate the well-posedness of solutions for this five-robot system. The stability of the system is verified using analytical methods, confinal correlation theory, and modern functional analysis techniques. Several key reliability indicators are presented using the eigenvector method. Numerical simulations and comparative methods effectively demonstrate the efficacy of the proposed eigenvector method. Firstly, the innovation of this paper lies in the combination of qualitative and quantitative analyses to improve and enrich the theory and methods of repairable systems. Secondly, mathematical analysis methods and the mathematical software are employed to provide both analytical and numerical solutions for the system.https://www.mdpi.com/2075-1680/14/2/113reliabilitythe five-robot systemearly warning functionstability |
| spellingShingle | Xing Qiao Dan Ma Shuang Guo Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function Axioms reliability the five-robot system early warning function stability |
| title | Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function |
| title_full | Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function |
| title_fullStr | Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function |
| title_full_unstemmed | Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function |
| title_short | Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function |
| title_sort | reliability analysis and numerical simulation of the five robot system with early warning function |
| topic | reliability the five-robot system early warning function stability |
| url | https://www.mdpi.com/2075-1680/14/2/113 |
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