The problem of solving the equivalent resistance between two points for resistor networks has important significance in physics. This paper mainly changes and rewrites the formula for calculating the resistance between two points of an unconventional \(m\times n\) cylindrical resistor network with a zero resistor axis and any two left and right boundaries. To enhance the efficiency of calculating the equivalent resistance between two points, Chebyshev polynomials and hyperbolic cosine functions are employed to represent the new formula. And in the inference process, the famous discrete cosine transform of the third kind (DCT-III) is used to process the matrix. We give the equivalent resistance formula for several special cases, and display them by a three-dimensional graph. Subsequently, the calculation efficiency of the original formula and the rewritten formula are compared. At the end of the paper, a heuristic algorithm suitable for robot path planning on cylindrical environment is proposed.
