A Compact Answer Set Programming Encoding of Multi-Agent Pathfinding

Rodrigo N Gomez,Carlos Hernandez,Jorge A Baier

doi:10.1109/access.2021.3053547

Rodrigo N Gomez, Carlos Hernandez + Show 1 more

Open Access

https://doi.org/10.1109/access.2021.3053547

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Journal: IEEE Access	Publication Date: Jan 1, 2021
Citations: 25	License type: CC BY 4.0

Affiliation: Pontificia Universidad Católica de Chile

Abstract

Multi-agent pathfinding (MAPF) is the problem of finding $k$ non-colliding paths connecting $k$ given initial positions with $k$ given goal positions on a given map. In its sum-of-costs variant, the total number of moves and wait actions performed by agents before they definitely reach the goal is minimized. Not surprisingly, since MAPF is combinatorial, a number of compilations to Boolean Satisfiability (SAT) and Answer Set Programming (ASP) exist. In this article, we describe in detail the first family of compilations to ASP that solve sum-of-costs MAPF over 4-connected grids. Compared to existing ASP compilations, a distinguishing feature of our compilation is that the number of total clauses (after grounding) grow linearly with the number of agents, while existing compilations grow quadratically. In addition, the optimization objective is such that its size after grounding does not depend on the size of the grid. In our experimental evaluation, we show that our approach outperforms search-based sum-of-costs MAPF solvers when grids are congested with agents. We also show that our approach is competitive with a SAT-based approach when follow conflicts are taken into account. We also explore the potential of our solver when finding makespan-optimal solutions, in which makespan is minimized first and then cost is minimized. Our results show that makespan-optimal solutions are slightly suboptimal in most benchmarks. Moreover, our MAPF solver, when run in that mode, is faster and scales better.

Highlights

Multi-agent pathfinding (MAPF) is the problem of finding k non-conflicting paths connecting k given initial positions with k given goal positions on a given map
We conclude in addition that finding makespan-optimal solutions allows Answer Set Programming (ASP)-based solvers to find solutions more quickly and to scale better, by sacrificing less than 1% average solution quality
MULTI-AGENT PATHFINDING A MAPF instance is defined by a tuple (G, A, init, goal), where G = (V, E) is a graph, A is the set of agents, and init : A → V and goal : A → V are functions used to denote the initial and goal vertex for each of the agents

Summary

INTRODUCTION

Multi-agent pathfinding (MAPF) is the problem of finding k non-conflicting paths connecting k given initial positions with k given goal positions on a given map. Gómez et al.: Compact ASP Encoding of MAPF (e.g., [5]), and considers a rather limited range of motion for agents This does not make this problem less relevant for the robotics community. We conclude in addition that finding makespan-optimal solutions allows ASP-based solvers to find solutions more quickly and to scale better, by sacrificing less than 1% average solution quality. This is important since it suggests that focusing on cost-optimal solutions instead of makespan-optimal solutions might not be a practical approach. The conclusions we draw from these experiments are important: a solver that is makespan-optimal scales better and finds solutions that are only slightly suboptimal in terms of cost.

BACKGROUND

ATOMS We use the following atoms:

INSTANCE SPECIFICATION

GOAL ACHIEVEMENT

A LINEAR ENCODING

Findings

USING SEARCH TO REDUCE THE ATOMS