The applications of harmonic functions to robotics

TLDR

Harmonic functions, solutions of Laplace's equation, provide potential‑field path planning without spurious local minima. The study demonstrates that harmonic functions possess properties essential for robotics, offering a complete path‑planning algorithm and a basis for reactive admittance control. Computing harmonic functions that adapt to sensed environmental changes enables control while the environment model is updated. Resulting paths are smooth, and the approach permits incremental updating of the environment model.

Abstract

Abstract Harmonic functions are solutions to Laplace's equation. Such functions can be used to advantage for potential‐field path planning because they do not exhibit spurious local minima. Harmonic functions are shown here to have a number of properties that are essential to robotics applications. Paths derived from harmonic functions are generally smooth. Harmonic functions also offer a complete path‐planning algorithm. We show how a harmonic function can be used as the basis for a reactive admittance control. Such schemes allow incremental updating of the environment model. Methods for computing harmonic functions respond well to sensed changes in the environment, and can be used for control while the environment model is being updated.