Modeling of omnidirectional antenna space radiation shaped resistor networks and efficient path planning

This paper proposes an innovative omnidirectional antenna space radiation shaped resistor network model to analyze potential distribution characteristics in complex resistor networks and apply it to path planning. Through mathematical modeling based on Kirchhoff's laws and the recursive transformation method, combined with the discrete sine transform of the seventh kind and Chebyshev polynomials of the first kind, we derive precise formulas for node potentials and equivalent resistances. We further develop a novel path planning algorithm that leverages the natural decay properties of potentials, enhanced by directional deviation penalties and a backtracking mechanism. Comparative analyses with classical path planning algorithms demonstrate that the proposed method holds significant potential, particularly in dynamic environments. Finally, a fast algorithm for potential calculation is introduced, achieving a four- to five-fold improvement in computational efficiency over traditional approaches. These advances deepen research on resistor networks and provide strong support for applications in complex systems, autonomous driving, and wireless communications.