Log-space harmonic function path planning

Abstract

We propose a log-space solution for robotic path planning with harmonic functions that solves the long-standing numerical precision problem. We prove that this algorithm: (1) performs the correct computations in log-space, (2) returns the true equivalent path using the log-space mapping, and (3) has a strong error bound given its convergence criterion. We evaluate the algorithm on 7 problem domains. A Graphics Processing Unit (GPU) implementation is also shown to greatly improve performance. We also provide an open source library entitled epic with extensive ROS support and demonstrate this method on a real humanoid robot: the uBot-6. Experiments demonstrate that the log-space solution rapidly produces smooth obstacle-avoiding trajectories, and supports planning in exponentially larger real-world robotic applications.