“In the field of resistance networks, this paper optimizes the formula for calculating two-point resistance in an m × n cobweb resistance network with 2r boundary conditions. By using Chebyshev polynomials and hyperbolic functions, the computational efficiency of equivalent resistance is improved, and the derivation process is simplified. The paper also discusses equivalent resistance formulas in special cases and compares computational efficiency before and after optimization. An innovative attempt at path planning through potential formulas is made, proposing a heuristic algorithm based on cobweb potential function for robot path planning in a cobweb environment with obstacles.”