THE APPLICATIONS OF HARMONIC-FUNCTIONS TO ROBOTICS

Harmonic functions are solutions to Laplace's equation. Such functions can be used to advantage for potential-field path planning because th ey do not exhibit spurious local minima. Harmonic functions are shown here to have a number of properties that are essential to robotics app lications. 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 a dmittance control. Such schemes allow incremental updating of the envi ronment model. Methods for computing harmonic functions respond well t o sensed changes in the environment, and can be used for control while the environment model is being updated. (C) 1993 John Wiley & Sons, I nc.