An optimized potential formula of the $m\times n$ apple surface network and its application of potential in path planning

An optimized potential formula for the $m\times n$ apple surface network has been introduced in this paper. Compared with the original potential formula, this method significantly enhances the efficiency required for rapid and large-scale numerical simulations. Based on the optimized potential function, we proposed a metaheuristic algorithm suitable for apple surface environment path planning. Chebyshev polynomials of the first class were employed to represent the potential function. Subsequently, a fast algorithm for calculating the potential utilizing the first kind of discrete sine transform (DST-I) was devised. We proposed potential formulas for several cases to visually present the distribution of the potential and illustrated them using three-dimensional graphs. We also conducted simulation experiments on the computational efficiency of the original and optimized formulas at different data scales, verifying the superiority of the optimized formulas. These findings provided new perspectives and tools for the computation of resistor networks and the design of path planning algorithms. Experiments were conducted to analyze the efficiency and availability of various techniques for computing potential.