A Discrete Harmonic Potential Field for Optimum Point-to-point Routing on a Weighted Graph

In this paper an attempt is made to adapt the harmonic potential field motion planning approach to operation in a discrete, sample-based mode. The strong relation between graph theory and electrical networks is utilized to suggest a discrete counterpart to the boundary value problem used to generate the continuous, harmonic, navigation potential. It is shown that a discrete potential field defined on each vertex of a weighted graph and made to satisfy the balance condition represented by Kirchhoff current law (KCL) is capable of generating a flow field that may be used to build algorithms for finding the minimum cost path between two vertices. Two algorithms of this type are suggested. Supporting definitions and propositions are also provided