Applications of harmonic functions to robotics

Abstract

Motivation for using harmonic functions as solutions to Laplace's equation arose from the resulting prevention of spurious local minima. Harmonic functions are shown to have several more useful properties that make them well suited for robotics applications such as fast surface normal computation, completeness, ability to exhibit different modes of behavior, and robust control in the presence of unanticipated obstacles and errors. A system that demonstrates this usefulness for control of a revolute robot arm is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>