|
Abstract
A model for path planning based upon a natural phenomenon is presented.
An electrostatic field is shown to have a similarity to path planning in
generating multiple, alternative solution paths. Analysis of the electrostatic
model results in a partial differential equation for the potential field
and its boundary conditions which correspond to the path planning problem
requirements. A finite difference approximation for computing the numerical
solution to the partial differential equation is also derived. This finite
difference approximation is the basis for a neural network architecture
designed to compute the numerical solution of the potential field. Gradient
descent over the potential field produces the multiple path solutions. |