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<p>In recent years, the exploration and application of resistance networks have expanded significantly, and solving the equivalent resistance between two points of a resistance network has been an important topic. In this paper, we focus on optimizing the formula for calculating the two-point resistance of an <i>m</i> × <i>n</i> cobweb resistance network with 2<i>r</i> boundary conditions. To improve the computational efficiency of the equivalent resistance between two points, the formula is optimized by using the optimal approximation property of Chebyshev polynomials in combination with hyperbolic functions, and the derivation process is simplified. We discuss the equivalent resistance formulas in several special cases and compare the computational efficiency of the equivalent resistance formulas before and after optimization. Finally, we make an innovative attempt at path planning through potential formulas and propose a heuristic algorithm based on cobweb potential function for robot path planning in a cobweb environment with obstacles.</p>

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An optimized formula for the two-point resistance of a cobweb resistance network and its potential application

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Yu Guan,
  • Xiaoyu Jiang,
  • Yanpeng Zheng,
  • Zhaolin Jiang

摘要

In recent years, the exploration and application of resistance networks have expanded significantly, and solving the equivalent resistance between two points of a resistance network has been an important topic. In this paper, we focus on optimizing the formula for calculating the two-point resistance of an m × n cobweb resistance network with 2r boundary conditions. To improve the computational efficiency of the equivalent resistance between two points, the formula is optimized by using the optimal approximation property of Chebyshev polynomials in combination with hyperbolic functions, and the derivation process is simplified. We discuss the equivalent resistance formulas in several special cases and compare the computational efficiency of the equivalent resistance formulas before and after optimization. Finally, we make an innovative attempt at path planning through potential formulas and propose a heuristic algorithm based on cobweb potential function for robot path planning in a cobweb environment with obstacles.