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Symbolic Planning and Multi-Agent Path Finding in Extremely Dense Environments with Unassigned Agents

Bo Fu, Zhe Chen, Rahul Chandan, Alex Barbosa, Michael Caldara, Joey Durham, Federico Pecora

TL;DR

The Block Rearrangement Problem (BRaP) formalizes rearranging assigned blocks in extremely dense warehouse grids as a graph search with conflict constraints and time-stamped actions.The authors present five algorithms spanning configuration-space search, PDDL-based planning, priority-based planning, BR-LaCAM, and a heuristic method, combining symbolic planning and MAPF ideas to address BRaP’s complexity.Extensive experiments on 13,860 test cases up to $80\times80$ grids show BR-LaCAM and a heuristic approach offering the best balance of solution quality and speed, solving large instances that other methods struggle with.The work provides strong baselines for BRaP, highlights the practical viability of dense-grid planning in warehouses, and suggests avenues for future variants, objectives, and goal-selection improvements.

Abstract

We introduce the Block Rearrangement Problem (BRaP), a challenging component of large warehouse management which involves rearranging storage blocks within dense grids to achieve a goal state. We formally define the BRaP as a graph search problem. Building on intuitions from sliding puzzle problems, we propose five search-based solution algorithms, leveraging joint configuration space search, classical planning, multi-agent pathfinding, and expert heuristics. We evaluate the five approaches empirically for plan quality and scalability. Despite the exponential relation between search space size and block number, our methods demonstrate efficiency in creating rearrangement plans for deeply buried blocks in up to 80x80 grids.

Symbolic Planning and Multi-Agent Path Finding in Extremely Dense Environments with Unassigned Agents

TL;DR

The Block Rearrangement Problem (BRaP) formalizes rearranging assigned blocks in extremely dense warehouse grids as a graph search with conflict constraints and time-stamped actions.The authors present five algorithms spanning configuration-space search, PDDL-based planning, priority-based planning, BR-LaCAM, and a heuristic method, combining symbolic planning and MAPF ideas to address BRaP’s complexity.Extensive experiments on 13,860 test cases up to $80\times80$ grids show BR-LaCAM and a heuristic approach offering the best balance of solution quality and speed, solving large instances that other methods struggle with.The work provides strong baselines for BRaP, highlights the practical viability of dense-grid planning in warehouses, and suggests avenues for future variants, objectives, and goal-selection improvements.

Abstract

We introduce the Block Rearrangement Problem (BRaP), a challenging component of large warehouse management which involves rearranging storage blocks within dense grids to achieve a goal state. We formally define the BRaP as a graph search problem. Building on intuitions from sliding puzzle problems, we propose five search-based solution algorithms, leveraging joint configuration space search, classical planning, multi-agent pathfinding, and expert heuristics. We evaluate the five approaches empirically for plan quality and scalability. Despite the exponential relation between search space size and block number, our methods demonstrate efficiency in creating rearrangement plans for deeply buried blocks in up to 80x80 grids.

Paper Structure

This paper contains 21 sections, 2 equations, 9 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Description
  3. Actions
  4. Terminal State
  5. Objectives and Metrics
  6. Variants of the Problem
  7. Related Work
  8. Symbolic Planning and PDDL
  9. Multi-Agent Path Finding
  10. Applicable Methodologies
  11. Configuration Space Search
  12. PDDL-based Configuration Space Search
  13. Priority-based Configuration Space Search
  14. Heuristic Approach: Moving Along the Least Blocking Path
  15. LaCAM-based Multi-Agent Path Finding
  16. ...and 6 more sections

Figures (9)

  • Figure 1: Fulfillment center with blocks in storage grids separated by travel lanes. Assigned blocks marked in orange.
  • Figure 2: Block Rearrangement Problem definition.
  • Figure 3: Three types of conflicts mapf.
  • Figure 4: A graph of configuration states and actions.
  • Figure 5: Move assigned blocks along the least blocking path.
  • ...and 4 more figures

Theorems & Definitions (2)

  • proof
  • proof