On 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, since they do not exhibit spurious local minima. Harmonic functions are shown here to have a number of properties which 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. Journal of Robotic Systems, 10(7):931-946 y This work is supported in part by the National Science Foundation under grants CDA-8922572, IRI-9116297 and IRI-9208920. Contents 1 Introduction 3 2 Configuration Space 4 3 Harmonic functions 4 3.1 Numerical..