An application of potential function in robot path planning and three optimized formulas for equivalent resistance
The study proposed an innovative path planning algorithm based on the potential function of a special case of the cobweb resistor network, addressing the path planning problem in globe environments with obstacles. For the non-regular $ m \times n $ cobweb resistor network with arbitrary longitude, w...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024315 |
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| _version_ | 1832590751304777728 |
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| author | Jianwei Dai Xiaoyu Jiang Yanpeng Zheng Xing Zhang Zhaolin Jiang |
| author_facet | Jianwei Dai Xiaoyu Jiang Yanpeng Zheng Xing Zhang Zhaolin Jiang |
| author_sort | Jianwei Dai |
| collection | DOAJ |
| description | The study proposed an innovative path planning algorithm based on the potential function of a special case of the cobweb resistor network, addressing the path planning problem in globe environments with obstacles. For the non-regular $ m \times n $ cobweb resistor network with arbitrary longitude, we found that by introducing Chebyshev polynomial of the second class, the precise equivalent resistance formulas could be optimized effectively. Compared with the original formula, optimized equivalent resistance formulas significantly reduced the time cost in large-scale data calculations. Furthermore, we have plotted 3D views of the equivalent resistance formulas for several special cases and conducted simulation experiments on the computational efficiency of the original and optimized formulas at different data scales, verifying the superiority of the optimized formulas. These findings provided new perspectives and tools for the computation of resistor networks and the design of path planning algorithms. |
| format | Article |
| id | doaj-art-7466585b5dc54b429f43174da79e90ee |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-7466585b5dc54b429f43174da79e90ee2025-01-23T07:53:06ZengAIMS PressElectronic Research Archive2688-15942024-12-0132126733676010.3934/era.2024315An application of potential function in robot path planning and three optimized formulas for equivalent resistanceJianwei Dai0Xiaoyu Jiang1Yanpeng Zheng2Xing Zhang3Zhaolin Jiang4School of Information Science and Engineering, Linyi University, Linyi 276000, ChinaSchool of Information Science and Engineering, Linyi University, Linyi 276000, ChinaSchool of Automation and Electrical Engineering, Linyi University, Linyi 276000, ChinaSchool of Information Science and Engineering, Linyi University, Linyi 276000, ChinaSchool of Mathematics and Statistics, Linyi University, Linyi 276000, ChinaThe study proposed an innovative path planning algorithm based on the potential function of a special case of the cobweb resistor network, addressing the path planning problem in globe environments with obstacles. For the non-regular $ m \times n $ cobweb resistor network with arbitrary longitude, we found that by introducing Chebyshev polynomial of the second class, the precise equivalent resistance formulas could be optimized effectively. Compared with the original formula, optimized equivalent resistance formulas significantly reduced the time cost in large-scale data calculations. Furthermore, we have plotted 3D views of the equivalent resistance formulas for several special cases and conducted simulation experiments on the computational efficiency of the original and optimized formulas at different data scales, verifying the superiority of the optimized formulas. These findings provided new perspectives and tools for the computation of resistor networks and the design of path planning algorithms.https://www.aimspress.com/article/doi/10.3934/era.2024315resistor networkpotential functionpath planningchebyshev polynomialequivalent resistance |
| spellingShingle | Jianwei Dai Xiaoyu Jiang Yanpeng Zheng Xing Zhang Zhaolin Jiang An application of potential function in robot path planning and three optimized formulas for equivalent resistance Electronic Research Archive resistor network potential function path planning chebyshev polynomial equivalent resistance |
| title | An application of potential function in robot path planning and three optimized formulas for equivalent resistance |
| title_full | An application of potential function in robot path planning and three optimized formulas for equivalent resistance |
| title_fullStr | An application of potential function in robot path planning and three optimized formulas for equivalent resistance |
| title_full_unstemmed | An application of potential function in robot path planning and three optimized formulas for equivalent resistance |
| title_short | An application of potential function in robot path planning and three optimized formulas for equivalent resistance |
| title_sort | application of potential function in robot path planning and three optimized formulas for equivalent resistance |
| topic | resistor network potential function path planning chebyshev polynomial equivalent resistance |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024315 |
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