A Variational Approach to Search and Path Planning Using Level Set Methods

Abstract

In this paper we propose a variational approach to a path planning problem in 2 dimensions using a level set framework. After defining an energy integral over the path, we use gradient flow on the defined energy and evolve the entire path until a locally optimal steady state is reached. Unlike typical level set implementations where the interface being tracked is a codimension-1 set, we allow for paths with positive, varying widths. Applications of this method extend to robotic motion, tool-path milling, and arial search patterns, for example. Numerical methods and algorithms are given, and examples are presented.