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MARPF: Multi-Agent and Multi-Rack Path Finding

Hiroya Makino, Yoshihiro Ohama, Seigo Ito

TL;DR

MARPF addresses multi-agent, multi-rack path finding in dense, passage-free environments by formulating the problem as a synchronized, time-expanded minimum-cost flow over two virtual AGV layers and separate rack networks. The method jointly relocates obstacle racks and conveys target racks to their goals, ensuring collision-free operation while minimizing makespan through an ILP formulation. To tackle computational complexity, the authors propose CA*-ILP, a hybrid global-local solver that uses CA* to place waypoints and ILP to optimize subpaths between them, with a cost structure that discourages rack interference. Experimental results on small grids demonstrate MARPF’s ability to resolve dense-rack scenarios that conventional MAPF-inspired methods struggle with, and show CA*-ILP significantly reduces computation time in challenging cases while maintaining solution quality.

Abstract

In environments where many automated guided vehicles (AGVs) operate, planning efficient, collision-free paths is essential. Related research has mainly focused on environments with pre-defined passages, resulting in space inefficiency. We attempt to relax this assumption. In this study, we define multi-agent and multi-rack path finding (MARPF) as the problem of planning paths for AGVs to convey target racks to their designated locations in environments without passages. In such environments, an AGV without a rack can pass under racks, whereas one with a rack cannot pass under racks to avoid collisions. MARPF entails conveying the target racks without collisions, while the obstacle racks are relocated to prevent any interference with the target racks. We formulated MARPF as an integer linear programming problem in a network flow. To distinguish situations in which an AGV is or is not loading a rack, the proposed method introduces two virtual layers into the network. We optimized the AGVs' movements to move obstacle racks and convey the target racks. The formulation and applicability of the algorithm were validated through numerical experiments. The results indicated that the proposed algorithm addressed issues in environments with dense racks.

MARPF: Multi-Agent and Multi-Rack Path Finding

TL;DR

MARPF addresses multi-agent, multi-rack path finding in dense, passage-free environments by formulating the problem as a synchronized, time-expanded minimum-cost flow over two virtual AGV layers and separate rack networks. The method jointly relocates obstacle racks and conveys target racks to their goals, ensuring collision-free operation while minimizing makespan through an ILP formulation. To tackle computational complexity, the authors propose CA*-ILP, a hybrid global-local solver that uses CA* to place waypoints and ILP to optimize subpaths between them, with a cost structure that discourages rack interference. Experimental results on small grids demonstrate MARPF’s ability to resolve dense-rack scenarios that conventional MAPF-inspired methods struggle with, and show CA*-ILP significantly reduces computation time in challenging cases while maintaining solution quality.

Abstract

In environments where many automated guided vehicles (AGVs) operate, planning efficient, collision-free paths is essential. Related research has mainly focused on environments with pre-defined passages, resulting in space inefficiency. We attempt to relax this assumption. In this study, we define multi-agent and multi-rack path finding (MARPF) as the problem of planning paths for AGVs to convey target racks to their designated locations in environments without passages. In such environments, an AGV without a rack can pass under racks, whereas one with a rack cannot pass under racks to avoid collisions. MARPF entails conveying the target racks without collisions, while the obstacle racks are relocated to prevent any interference with the target racks. We formulated MARPF as an integer linear programming problem in a network flow. To distinguish situations in which an AGV is or is not loading a rack, the proposed method introduces two virtual layers into the network. We optimized the AGVs' movements to move obstacle racks and convey the target racks. The formulation and applicability of the algorithm were validated through numerical experiments. The results indicated that the proposed algorithm addressed issues in environments with dense racks.
Paper Structure (15 sections, 6 equations, 12 figures, 2 tables, 2 algorithms)

This paper contains 15 sections, 6 equations, 12 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contribution
  3. Related Work
  4. MAPF
  5. Rearrangement-considering MAPD
  6. Problem Definition
  7. Proposed Method
  8. Definition of Networks
  9. Definition of Variables
  10. Minimum Cost Flow Problem
  11. Applications for Real-Time Solving
  12. Experiments
  13. Experiment 1: Comparative Evaluation of the Proposed Method against Existing Methods
  14. Experiment 2: Evaluation of the Effectiveness of CA*-ILP
  15. Conclusion

Figures (12)

  • Figure 1: Environments of MAPF and MARPF. MAPF needs passages, whereas MARPF does not.
  • Figure 2: Two layers to express AGVs’ movements. The movements between these layers correspond to whether they are conveying a rack or not. When an AGV loads a rack, it virtually transitions from the "w/o rack" layer to the "w/rack" layer; unloading a rack reverses this transition.
  • Figure 3: Unsolvable example by MAPD.
  • Figure 4: Type of conflicts.
  • Figure 5: Problem example.
  • ...and 7 more figures