Robot navigation using a pressure generated mechanical stress field: "the biharmonic potential approach"

Abstract

This paper suggests a new approach for navigation in a known environment. The approach is based on the biharmonic potential fields which govern mechanical stress fields in homogeneous solids. It is observed that a path generated by such a technique is free of sharp turns that may appear in its counterpart that is generated from an underlying harmonic potential. This in turns makes a path from the former more dynamically suitable for traversal. Also, the navigation field is extracted from the biharmonic potential in a manner that bypass the rapidly vanishing field problem which is encountered in the harmonic potential approach. Development of the biharmonic approach, simulation results, as well as comparison with the Neumann and Dirichlet setting of the harmonic approach are provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>