An Analysis of Constraint-Based Multi-Agent Pathfinding Algorithms

TL;DR

The paper analyzes how constraint formulations—conservative (motion constraints) versus aggressive (priority constraints)—impact constraint-based MAPF solvers (CBS and CBSw/P) across a hybrid grid-roadmap representation that models MRMP challenges. By systematically varying representation topology and resolution on 27 maps with 15-minute limits and 25 scenarios per map, it derives a flowchart to guide constraint choice and provides insights for applying MAPF techniques to MRMP domains. The key finding is that high-coordination environments favor conservative constraints for completeness and coordination, while open or low-coordination settings benefit from aggressive constraints for scalability and faster solution discovery, albeit with potential completeness trade-offs. The work offers practical guidance for solver design and MRMP adaptation, highlighting representation topology as a critical factor and providing a public GitHub resource with raw data for replication and further study.

Abstract

This study informs the design of future multi-agent pathfinding (MAPF) and multi-robot motion planning (MRMP) algorithms by guiding choices based on constraint classification for constraint-based search algorithms. We categorize constraints as conservative or aggressive and provide insights into their search behavior, focusing specifically on vanilla Conflict-Based Search (CBS) and Conflict-Based Search with Priorities (CBSw/P). Under a hybrid grid-roadmap representation with varying resolution, we observe that aggressive (priority constraint) formulations tend to solve more instances as agent count or resolution increases, whereas conservative (motion constraint) formulations yield stronger solution quality when both succeed. Findings are synthesized in a decision flowchart, aiding users in selecting suitable constraints. Recommendations extend to Multi-Robot Motion Planning (MRMP), emphasizing the importance of considering topological features alongside problem, solution, and representation features. A comprehensive exploration of the study, including raw data and map performance, is available in our public GitHub Repository: https://GitHub.com/hannahjmlee/constraint-mapf-analysis

Figures (12)

• Figure 1: A flowchart summarizing our findings and providing a general set of guidelines in determining when to use aggressive vs. conservative constraints given our heuristics derived from comparing vanilla CBS and CBSw/P. These decision points may shift with other search strategies or under different settings.
• Figure 2: Comparison of Grid, Grid Roadmap, and Roadmap Representations for a 2D square robot with 2 DoF. The orange position $R$ represents the robot across all three representations. In the grid representation, states are mapped to discrete cells. The grid roadmap uses a uniform grid-sampler to map states to configurations, while the roadmap representation employs a random sampler to map states to the configuration space. For the roadmap, obstacles (gray) are inflated by the robot’s radius (orange) to define the obstacle space. The top row depicts an environment without narrow passages, where random sampling inadvertently creates one. In contrast, the bottom row shows a narrow passage environment that the roadmap fails to capture, resulting in a representation that overlooks the passage.
• Figure 3: Shown are samples of true grid and grid roadmap representations at resolutions 1, 2, and 4. This highlights cell-based planning in true grids and vertex-based planning in grid roadmaps. In grid roadmaps, resolution 1 grids equate to 4 vertices, while resolution 2 and 4 grids scale to 9 and 25 vertices, respectively. Sample paths are depicted for each resolution, showcasing increased vertex count with higher resolutions. When projecting a resolution 1 path into higher resolutions, the number of states in the path increases, akin to increasing edge discretization in a MRMP roadmap representation.
• Figure 4: The grid roadmap representation graph for two sample environments is shown with varying resolutions of 1, 2, and 4.
• Figure 5: Betweenness Centrality visualizations for six environments. Blue indicates low betweenness centrality and red indicates high betweenness centrality. Note that the betweenness centrality is not effective for environments devoid of obstacles.