Applications of Harmonic Functions to Robotics

Harmonic functions are solutions to Laplace's Equation. As noted in a previous paper, they can be used to advantage for potential-field path planning, since they do not exhibit spurious local minima. In this paper, harmonic functions are shown to have a number of other properties (including completeness) which are essential to robotics applications. These properties strongly recommend harmonic functions as a mechanism for robot control. 1 Introduction Harmonic functions were proposed in Connolly et al. [1] as a means for generating paths in a robot configuration space. These functions are solutions to Laplace's Equation. One important feature of harmonic functions is that they can be used to generate smooth, collision-free paths without the threat of spurious local minima. In this paper, harmonic functions are shown to provide a global, complete path-planning scheme. As noted by Tarassenko and Blake [2], a resistive grid can compute such functions very quickly, further motivating thei..