# Priority Inheritance with Backtracking for Iterative Multi-agent Path Finding

## TL;DR

This paper introduces PIBT, a scalable sub-optimal algorithm for iterative multi-agent pathfinding that guarantees agent delivery in certain graph environments and performs well in large, real-world scenarios.

## Contribution

PIBT is a novel priority inheritance with backtracking algorithm that efficiently solves large-scale, iterative MAPF problems with guaranteed agent delivery in specific graph conditions.

## Key findings

- PIBT guarantees all agents reach their destinations in finite time on certain graphs.
- PIBT performs efficiently with hundreds of agents, providing acceptable solutions rapidly.
- PIBT outperforms existing methods in runtime and solution quality in warehouse package conveyance scenarios.

## Abstract

In the Multi-Agent Path Finding (MAPF) problem, a set of agents moving on a graph must reach their own respective destinations without inter-agent collisions. In practical MAPF applications such as navigation in automated warehouses, where occasionally there are hundreds or more agents, MAPF must be solved iteratively online on a lifelong basis. Such scenarios rule out simple adaptations of offline compute-intensive optimal approaches; and scalable sub-optimal algorithms are hence appealing for such settings. Ideal algorithms are scalable, applicable to iterative scenarios, and output plausible solutions in predictable computation time. For the aforementioned purpose, this study presents Priority Inheritance with Backtracking (PIBT), a novel sub-optimal algorithm to solve MAPF iteratively. PIBT relies on an adaptive prioritization scheme to focus on the adjacent movements of multiple agents; hence it can be applied to several domains. We prove that, regardless of their number, all agents are guaranteed to reach their destination within finite time when the environment is a graph such that all pairs of adjacent nodes belong to a simple cycle (e.g., biconnected). Experimental results covering various scenarios, including a demonstration with real robots, reveal the benefits of the proposed method. Even with hundreds of agents, PIBT yields acceptable solutions almost immediately and can solve large instances that other established MAPF methods cannot. In addition, PIBT outperforms an existing approach on an iterative scenario of conveying packages in an automated warehouse in both runtime and solution quality.