Exact Wavefront Propagation for Globally Optimal One-to-All Path Planning on 2D Cartesian Grids

TL;DR

This paper presents an exact wavefront propagation algorithm for 2D grid path planning that is faster and more accurate than existing methods, providing globally optimal paths efficiently.

Contribution

The paper introduces a novel exact wavefront propagation algorithm with linear complexity for globally optimal path planning on 2D grids, outperforming approximate methods.

Findings

Outperforms state-of-the-art in speed and accuracy

Provides globally optimal paths to all grid points

Efficiently handles multiple starting positions

Abstract

This paper introduces an efficient $\mathcal{O}(n)$ compute and memory complexity algorithm for globally optimal path planning on 2D Cartesian grids. Unlike existing marching methods that rely on approximate discretized solutions to the Eikonal equation, our approach achieves exact wavefront propagation by pivoting the analytic distance function based on visibility. The algorithm leverages a dynamic-programming subroutine to efficiently evaluate visibility queries. Through benchmarking against state-of-the-art any-angle path planners, we demonstrate that our method outperforms existing approaches in both speed and accuracy, particularly in cluttered environments. Notably, our method inherently provides globally optimal paths to all grid points, eliminating the need for additional gradient descent steps per path query. The same capability extends to multiple starting positions. We also provide a greedy version of our algorithm as well as open-source C++ implementation of our solver.