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Certificate-Driven Closed-Loop Multi-Agent Path Finding with Inheritable Factorization

Jiarui Li, Runyu Zhang, Gioele Zardini

Abstract

Multi-agent coordination in automated warehouses and logistics is commonly modeled as the Multi-Agent Path Finding (MAPF) problem. Closed-loop MAPF algorithms improve scalability by planning only the next movement and replanning online, but this finite-horizon viewpoint can be shortsighted and makes it difficult to preserve global guarantees and exploit compositional structure. This issue is especially visible in Anytime Closed-Loop Conflict-Based Search (ACCBS), which applies Conflict-Based Search (CBS) over dynamically extended finite horizons but, under finite computational budgets, may terminate with short active prefixes in dense instances. We introduce certificate trajectories and their associated fleet budget as a general mechanism for filtering closed-loop updates. A certificate provides a conflict-free fallback plan and a monotone upper bound on the remaining cost; accepting only certificate-improving updates yields completeness. The same budget information induces a budget-limited factorization that enables global, inheritable decomposition across timesteps. Instantiating the framework on ACCBS yields Certificate-Driven Conflict-Based Search (CDCBS). Experiments on benchmark maps show that CDCBS achieves more consistent solution quality than ACCBS, particularly in dense settings, while the proposed factorization reduces effective group size.

Certificate-Driven Closed-Loop Multi-Agent Path Finding with Inheritable Factorization

Abstract

Multi-agent coordination in automated warehouses and logistics is commonly modeled as the Multi-Agent Path Finding (MAPF) problem. Closed-loop MAPF algorithms improve scalability by planning only the next movement and replanning online, but this finite-horizon viewpoint can be shortsighted and makes it difficult to preserve global guarantees and exploit compositional structure. This issue is especially visible in Anytime Closed-Loop Conflict-Based Search (ACCBS), which applies Conflict-Based Search (CBS) over dynamically extended finite horizons but, under finite computational budgets, may terminate with short active prefixes in dense instances. We introduce certificate trajectories and their associated fleet budget as a general mechanism for filtering closed-loop updates. A certificate provides a conflict-free fallback plan and a monotone upper bound on the remaining cost; accepting only certificate-improving updates yields completeness. The same budget information induces a budget-limited factorization that enables global, inheritable decomposition across timesteps. Instantiating the framework on ACCBS yields Certificate-Driven Conflict-Based Search (CDCBS). Experiments on benchmark maps show that CDCBS achieves more consistent solution quality than ACCBS, particularly in dense settings, while the proposed factorization reduces effective group size.

Paper Structure

This paper contains 15 sections, 5 theorems, 21 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Statement of Contribution
  3. Problem Definition and Preliminaries
  4. , finite-horizon , and
  5. Certificates and Valid Updates
  6. Certificate trajectories, fleet budget, and backup controller
  7. Certificate updates and completeness
  8. Budget-Limited Reachability and Inheritable Factorization
  9. Slackness and budget-limited reachable regions
  10. Factorization and inheritability
  11. Algorithm
  12. Details of the algorithm
  13. Theoretical analysis
  14. Experiments
  15. Conclusion and Future Work

Key Result

Lemma III.1

Suppose a closed-loop algorithm performs valid certificate updates at every timestep. If at least one agent has not yet reached its goal at time $t-1$, then $\mathcal{B}_t < \mathcal{B}_{t-1}$. Consequently, all agents reach their goals in finite time. $\blacktriangleleft$$\blacktriangleleft$

Figures (2)

  • Figure 1: With the certificates, the can achieve significantly better performance than , which does not have the certificate, especially in denser cases.
  • Figure 2: Across planning budgets, certificate-guided achieves lower average increment than , with advantages becoming most pronounced in denser instances.

Theorems & Definitions (31)

  • Definition II.1: instance
  • Definition II.2: Trajectories and conflicts
  • Definition II.3: system and the unified problem
  • Definition II.4: Running horizon and active prefix
  • Definition II.5: Node in the constraint tree
  • Definition II.6: Vertex constraints, edge constraints, and satisfaction
  • Definition II.7: Cost function
  • Definition III.1: Certificate trajectories and fleet budget
  • Remark III.1: Interpretation of certificates
  • Definition III.2: Backup controller
  • ...and 21 more