Multi-Agent Path Finding with Delay Probabilities

TL;DR

This paper introduces a new MAPF problem model accounting for delay probabilities, proposes robust execution policies, and develops a two-level solver to generate plans that minimize expected delays and prevent collisions.

Contribution

It formalizes MAPF with delay probabilities, defines valid plans, and presents a two-level solver with decentralized robust policies for imperfect plan execution.

Findings

Proposes the formal MAPF-DP problem with delay considerations.

Introduces decentralized robust plan-execution policies.

Develops a two-level solver for MAPF-DP plans.

Abstract

Several recently developed Multi-Agent Path Finding (MAPF) solvers scale to large MAPF instances by searching for MAPF plans on 2 levels: The high-level search resolves collisions between agents, and the low-level search plans paths for single agents under the constraints imposed by the high-level search. We make the following contributions to solve the MAPF problem with imperfect plan execution with small average makespans: First, we formalize the MAPF Problem with Delay Probabilities (MAPF-DP), define valid MAPF-DP plans and propose the use of robust plan-execution policies for valid MAPF-DP plans to control how each agent proceeds along its path. Second, we discuss 2 classes of decentralized robust plan-execution policies (called Fully Synchronized Policies and Minimal Communication Policies) that prevent collisions during plan execution for valid MAPF-DP plans. Third, we present a 2-level MAPF-DP solver (called Approximate Minimization in Expectation) that generates valid MAPF-DP plans.