Path Counting for Grid-Based Navigation

This paper solves the well-known problem of how to obtain straighter, more direct grid paths from traditional pathfinding methods like Dijkstra’s algorithm or A*. Our solution is a simple counting procedure inspired by Pascal’s triangle. The new method is currently being used to analyze architectural designs, though it could also be applied to pathfinding in video games or robotics.

Abstract

Path Counting for Grid-Based Navigation

Rhys Goldstein, Kean Walmsley, Jacobo Bibliowicz, Alexander Tessier, Simon Breslav, Azam Khan

Journal of Artificial Intelligence Research 2022

Counting the number of shortest paths on a grid is a simple procedure with close ties to Pascal’s triangle. We show how path counting can be used to select relatively direct grid paths for AI-related applications involving navigation through spatial environments. Typical implementations of Dijkstra’s algorithm and A* prioritize grid moves in an arbitrary manner, producing paths which stray conspicuously far from line-of-sight trajectories. We find that by counting the number of paths which traverse each vertex, then selecting the vertices with the highest counts, one obtains a path that is reasonably direct in practice and can be improved by refining the grid resolution. Central Dijkstra and Central A* are introduced as the basic methods for computing these central grid paths. Theoretical analysis reveals that the proposed grid-based navigation approach is related to an existing grid-based visibility approach, and establishes that central grid paths converge on clear sightlines as the grid spacing approaches zero. A more general property, that central paths converge on direct paths, is formulated as a conjecture.