[Paper Review] AI Buzzwords Explained: Multi-Agent Path Finding (MAPF)

Hang Ma, Sven Koenig|arXiv (Cornell University)|Oct 10, 2017

Robotic Path Planning Algorithms16 references3 citations

TL;DR

This paper explains Multi-Agent Path Finding (MAPF) as a key challenge in robotics and AI, focusing on coordinating multiple robots to reach goals without collisions in confined spaces like warehouses. It presents state-of-the-art algorithms that solve MAPF efficiently using techniques like subdimensional expansion and conflict-based search, achieving bounded-suboptimal solutions with tractability and completeness guarantees.

ABSTRACT

Explanation of the hot topic "multi-agent path finding".

Motivation & Objective

• Address the challenge of coordinating multiple autonomous robots in confined environments like warehouses, where space is limited and collisions must be avoided.
• Formulate the MAPF problem as a discrete-time path-planning task with the goal of minimizing makespan (time until all robots reach their goals).
• Develop efficient algorithms that find bounded-suboptimal solutions to the NP-hard MAPF problem, ensuring scalability and completeness.
• Investigate variants of MAPF with different objectives (e.g., sum of completion times) and constraints (e.g., robot capabilities, payload exchange).
• Provide a comprehensive overview of theoretical complexity, algorithmic approaches, and practical applications of MAPF in real-world systems like Amazon Robotics.

Proposed method

• Model MAPF as a shortest-path problem on a state space where each state is a tuple of robot positions, though this leads to exponential state space growth.
• Use conflict-based search (CBS) to recursively resolve collisions by imposing constraints—e.g., forbidding one robot from moving to a conflicting cell at a given time step.
• Apply subdimensional expansion (SSE) to reduce the search space by decomposing the problem into lower-dimensional subproblems, improving efficiency.
• Implement bounded-suboptimal algorithms that guarantee a makespan within a specified percentage of the optimal solution, balancing performance and computational cost.
• Leverage flow-based algorithms for a relaxed version of MAPF where goal cells are assigned to robots after path planning, enabling polynomial-time solutions.
• Combine independent single-agent path planning with collision resolution heuristics to scale to large numbers of robots in practice.

Experimental results

Research questions

• RQ1 What is the computational complexity of finding optimal solutions to the MAPF problem, and under what conditions can it be solved in polynomial time?
• RQ2 How can conflict-based search be used to efficiently find bounded-suboptimal solutions to MAPF while maintaining completeness and scalability?
• RQ3 In what scenarios does subdimensional expansion outperform traditional search methods in terms of runtime and memory usage for MAPF?
• RQ4 How do different optimization objectives (e.g., makespan vs. sum of completion times) affect the design and performance of MAPF algorithms?
• RQ5 What are the practical implications of MAPF algorithms in real-world robotic systems, such as Amazon’s warehouse automation?

Key findings

• The optimal solution of the MAPF problem is NP-hard, making exact solutions computationally infeasible for large-scale instances.
• Conflict-based search (CBS) enables the discovery of bounded-suboptimal solutions by recursively resolving collisions, with performance improving as constraints are incrementally added.
• Subdimensional expansion (SSE) significantly reduces search space and improves runtime efficiency, making it suitable for large-scale multi-robot path planning.
• A relaxed version of MAPF—where goal cells are assigned after path planning—can be solved in polynomial time using network flow algorithms.
• Algorithms like MAPP and SSE achieve both tractability and completeness guarantees, enabling scalable deployment in real-world robotic systems.
• Empirical results show that state-of-the-art MAPF algorithms can coordinate hundreds of robots in warehouse-like environments with minimal makespan and collision rates.