Potential-based modeling of two dimensional workspace using several source distributions

One of the existing approaches to path planning problems uses a potential field function to represent the topological structure of the free space. The main advantages of this approach include the simplicity of the representation of free space and the guidance for obstacle avoidance available trough the variation in the potential field. Newtonian potential function can be used to represent polygonal objects and obstacles wherein their boundaries are assumed to be uniformly charged. In this paper, the idea is extended to more general cases where the source distributions can also be linear or quadratic. It is shown that the potential function for these distributions can also be derived in closed form. Possible applications of these analytic results include the modeling of free space of complex shape, and the representation for objects and obstacles having properties of interest which are not homogeneous along their boundaries