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

Yu GUAN; Xiaoyu JIANG; Yanpeng ZHENG; Zhaolin JIANG

doi:10.1631/FITEE.2400613

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

Regular Papers | Updated：2025-07-02

- An optimized formula for the two-point resistance of a cobweb resistance network and its potential application
  Enhanced Publication
- 蛛网电阻网络两点电阻的优化公式及其势的应用
- Frontiers of Information Technology & Electronic Engineering Vol. 26, Issue 6, Pages: 946-958(2025)
- Affiliations：
  
  1.School of Information Science and Engineering, Linyi University, Linyi 276000, China
  2.School of Automation and Electrical Engineering, Linyi University, Linyi 276000, China
  3.School of Mathematics and Statistics, Linyi University, Linyi 276000, China
- Author bio：
  
  ‡ Corresponding authors
- Funds：
- DOI：10.1631/FITEE.2400613
  CLC： TM13;O441.1
- Received：21 July 2024，
  
  Revised：10 October 2024，
  
  Published：2025-06
- Accepted：
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Yu GUAN, Xiaoyu JIANG, Yanpeng ZHENG, et al. An optimized formula for the two-point resistance of a cobweb resistance network and its potential application[J]. Frontiers of information technology & electronic engineering, 2025, 26(6): 946-958.
DOI：

Yu GUAN, Xiaoyu JIANG, Yanpeng ZHENG, et al. An optimized formula for the two-point resistance of a cobweb resistance network and its potential application[J]. Frontiers of information technology & electronic engineering, 2025, 26(6): 946-958. DOI： 10.1631/FITEE.2400613.

摘要

近年来，电阻网络的探索和应用范围显著扩大，求解电阻网络两点间的等效电阻一直是一个重要课题。本文重点优化了具有2

边界条件的

蛛网电阻网络的两点电阻计算公式。为提高两点间等效电阻的计算效率，利用切比雪夫多项式的最优逼近特性，结合双曲函数对公式进行优化，并简化推导过程。讨论了几种特殊情况下的等效电阻公式，并比较了优化前后等效电阻公式的计算效率。最后，通过势公式进行路径规划的创新尝试，提出一种基于蛛网势函数的启发式算法，用于机器人在有障碍物的蛛网环境中的路径规划。

Abstract

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

cobweb resistance network with 2

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.

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Keywords

references

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