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Multi-Agent Path Finding in Continuous Spaces with Projected Diffusion Models

Jinhao Liang, Jacob K. Christopher, Sven Koenig, Ferdinando Fioretto

TL;DR

This work tackles multi-agent path finding (MAPF) in continuous spaces by marrying diffusion-based trajectory generation with constraint-driven projection. It introduces Projected Diffusion Models (PDM) that couple the diffusion sampling process with a projection onto the MAPF feasibility set and employs an augmented Lagrangian method (ALM) to efficiently handle nonconvex collision constraints. The method directly generates collision-free trajectories for all agents, respecting start/goal, kinematic, and inter-agent/obstacle constraints, and scales to scenarios with many agents. Empirical results across narrow corridors, obstacle-dense, and agent-dense environments show zero constraint violations and shorter total path lengths compared to standard and guided diffusion baselines, highlighting the practical potential of integrating constrained optimization with diffusion models for complex, continuous-space MAPF problems.

Abstract

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics, requiring the computation of collision-free paths for multiple agents moving from their respective start to goal positions. Coordinating multiple agents in a shared environment poses significant challenges, especially in continuous spaces where traditional optimization algorithms struggle with scalability. Moreover, these algorithms often depend on discretized representations of the environment, which can be impractical in image-based or high-dimensional settings. Recently, diffusion models have shown promise in single-agent path planning, capturing complex trajectory distributions and generating smooth paths that navigate continuous, high-dimensional spaces. However, directly extending diffusion models to MAPF introduces new challenges since these models struggle to ensure constraint feasibility, such as inter-agent collision avoidance. To overcome this limitation, this work proposes a novel approach that integrates constrained optimization with diffusion models for MAPF in continuous spaces. This unique combination directly produces feasible multi-agent trajectories that respect collision avoidance and kinematic constraints. The effectiveness of our approach is demonstrated across various challenging simulated scenarios of varying dimensionality.

Multi-Agent Path Finding in Continuous Spaces with Projected Diffusion Models

TL;DR

This work tackles multi-agent path finding (MAPF) in continuous spaces by marrying diffusion-based trajectory generation with constraint-driven projection. It introduces Projected Diffusion Models (PDM) that couple the diffusion sampling process with a projection onto the MAPF feasibility set and employs an augmented Lagrangian method (ALM) to efficiently handle nonconvex collision constraints. The method directly generates collision-free trajectories for all agents, respecting start/goal, kinematic, and inter-agent/obstacle constraints, and scales to scenarios with many agents. Empirical results across narrow corridors, obstacle-dense, and agent-dense environments show zero constraint violations and shorter total path lengths compared to standard and guided diffusion baselines, highlighting the practical potential of integrating constrained optimization with diffusion models for complex, continuous-space MAPF problems.

Abstract

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics, requiring the computation of collision-free paths for multiple agents moving from their respective start to goal positions. Coordinating multiple agents in a shared environment poses significant challenges, especially in continuous spaces where traditional optimization algorithms struggle with scalability. Moreover, these algorithms often depend on discretized representations of the environment, which can be impractical in image-based or high-dimensional settings. Recently, diffusion models have shown promise in single-agent path planning, capturing complex trajectory distributions and generating smooth paths that navigate continuous, high-dimensional spaces. However, directly extending diffusion models to MAPF introduces new challenges since these models struggle to ensure constraint feasibility, such as inter-agent collision avoidance. To overcome this limitation, this work proposes a novel approach that integrates constrained optimization with diffusion models for MAPF in continuous spaces. This unique combination directly produces feasible multi-agent trajectories that respect collision avoidance and kinematic constraints. The effectiveness of our approach is demonstrated across various challenging simulated scenarios of varying dimensionality.

Paper Structure

This paper contains 21 sections, 20 equations, 2 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multi-Agent Path Finding.
  4. Path Finding with Generative Models.
  5. Preliminaries
  6. Diffusion Models.
  7. Multi-Agent Path Finding in Continuous Space
  8. Constrained Diffusion Models
  9. Recall The Sampling Process in DMs
  10. Projected Diffusion Models
  11. Efficient Projections for MAPFs
  12. Collision-free Trajectories Projection Mechanism
  13. Convex Constraints.
  14. Nonconvex Constraints.
  15. ALM for Efficient Projection
  16. ...and 6 more sections

Figures (2)

  • Figure 1: Collision-free trajectories generated by PDM in Narrow Corridor scenarios. Agents (solid circles) navigate to their goals (empty circles) by exchanging positions in confined spaces without collisions.
  • Figure 2: Collision-free trajectories generated by PDM in Obstacle-Dense scenarios. Agents successfully navigate through environments with numerous obstacles to reach their goals. The empty dashed circles denote starting points, and the solid circles represent the goals.