Potential-Based Modeling of 2D Regions Using Non-uniform Source Distributions

One of existing approaches to path planning problems uses a potential function to represent the topological structure of the free space. Newtonian potential was used in [1] to represent object and obstacles in the two-dimensional (2-D) workspace wherein their boundaries are assumed to be uniformly charged. In this paper, more general, nonuniform distributions are considered. It is shown that for linear or quadratic source distributions, the repulsion between two polygonal objects can be evaluated analytically. Simulation results show that by properly adjusting the charge distribution along obstacle/object boundaries, path planning results can be improved in terms of collision avoidance, path length, etc.