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On-line Access: 2024-12-16

Received: 2024-07-21

Revision Accepted: 2024-10-10

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Citations:  Bibtex RefMan EndNote GB/T7714

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Frontiers of Information Technology & Electronic Engineering 

Accepted manuscript available online (unedited version)


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


Author(s):  Yu GUAN, Xiaoyu JIANG, Yanpeng ZHENG, Zhaolin JIANG

Affiliation(s):  School of Information Science and Engineering, Linyi University, Linyi 276000, China; more

Corresponding email(s):  jxy19890422@sina.com, zhengyanpeng0702@sina.com

Key Words:  Resistance network; Equivalent resistance; Potential function; Chebyshev polynomials; Path planning


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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 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 discussed the equivalent resistance formulas in several special cases and compared the computational efficiency of the equivalent resistance formulas before and after optimization. Finally, we made an innovative attempt of path planning through potential formulas and proposed a heuristic algorithm based on cobweb potential function for robot path planning in a cobweb environment with obstacles.

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