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Decoupling Geometric Planning and Execution in Scalable Multi-Agent Path Finding

Fernando Salanova, Cristian Mahulea, Eduardo Montijano

Abstract

Multi-Agent Path Finding (MAPF) requires collision-free trajectories for multiple agents on a shared graph, often with the objective of minimizing the sum-of-costs (SOC). Many optimal and bounded-suboptimal solvers rely on time-expanded models and centralized conflict resolution, which limits scalability in large or dense instances. We propose a hybrid prioritized framework that separates geometric planning from execution-time conflict resolution. In the first stage, Geometric Conflict Preemption (GCP) plans agents sequentially with A* on the original graph while inflating costs for transitions entering vertices used by higher-priority paths, encouraging spatial detours without explicit time reasoning. In the second stage, a Decentralized Local Controller (DLC) executes the geometric paths using per-vertex FIFO authorization queues and inserts wait actions only when required to avoid vertex and edge-swap conflicts. Experiments on standard benchmark maps with up to 1000 agents show that the method scales with an empirically near-linear runtime trend and attains a 100% success rate on instances satisfying the geometric feasibility assumption. On bottleneck-heavy maps, GCP reduces synchronization-induced waiting and often improves SOC on bottleneck-heavy maps

Decoupling Geometric Planning and Execution in Scalable Multi-Agent Path Finding

Abstract

Multi-Agent Path Finding (MAPF) requires collision-free trajectories for multiple agents on a shared graph, often with the objective of minimizing the sum-of-costs (SOC). Many optimal and bounded-suboptimal solvers rely on time-expanded models and centralized conflict resolution, which limits scalability in large or dense instances. We propose a hybrid prioritized framework that separates geometric planning from execution-time conflict resolution. In the first stage, Geometric Conflict Preemption (GCP) plans agents sequentially with A* on the original graph while inflating costs for transitions entering vertices used by higher-priority paths, encouraging spatial detours without explicit time reasoning. In the second stage, a Decentralized Local Controller (DLC) executes the geometric paths using per-vertex FIFO authorization queues and inserts wait actions only when required to avoid vertex and edge-swap conflicts. Experiments on standard benchmark maps with up to 1000 agents show that the method scales with an empirically near-linear runtime trend and attains a 100% success rate on instances satisfying the geometric feasibility assumption. On bottleneck-heavy maps, GCP reduces synchronization-induced waiting and often improves SOC on bottleneck-heavy maps

Paper Structure

This paper contains 8 sections, 1 theorem, 6 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Definition
  4. Proposed Method
  5. Geometric Conflict Preemption (GCP)
  6. Decentralized Local Controller (DLC)
  7. Experimental Evaluation
  8. Conclusions

Key Result

Proposition 4.1

Under Assumption ass:residual_reach, the execution produced by the Decentralized Local Controller (DLC) is collision-free and complete. That is, (i) no vertex or edge-swap conflicts occur, and (ii) every agent reaches its goal in finite time and remains there thereafter.

Figures (3)

  • Figure 1: Success rate comparison (CA* values are consistently 100% and are covered by the red line of our method).
  • Figure 2: Runtime comparison (both axis in logarithmic scale). The red 'X' indicates that the algorithm failed to complete due to timeout.
  • Figure 3: Cost comparison for Room and Paris maps.

Theorems & Definitions (1)

  • Proposition 4.1: Correctness and Completeness of DLC Execution