Decentralized Multi-Agent Goal Assignment for Path Planning using Large Language Models

TL;DR

This work investigates decentralized goal assignment for multi-agent path planning in fully observable grid-worlds, formalizing the objective with $\text{Makespan} = \min_{\pi} \max_{i} C_i(\pi)$. It compares greedy, optimal centralized solvers, and LLM-based agents (e.g., GPT-4.1, LLaVA) using structured prompts, optional agent-goal distance tables, and a fixed conflict-resolution rule based on agent indices. Key findings show GPT-4.1 with distance information and re-ranking approaches achieves makespans within roughly two steps of the optimum (mean around $15.1$) across 100 scenarios, significantly outperforming greedy and random baselines; removing distance data degrades performance toward the greedy baseline, and LLaVA underperforms. The study underscores the crucial role of input structure and prompt design in enabling LLMs to approximate centralized efficiency in decentralized coordination and points to promising directions for integrating LLM reasoning into scalable multi-agent systems.

Abstract

Coordinating multiple autonomous agents in shared environments under decentralized conditions is a long-standing challenge in robotics and artificial intelligence. This work addresses the problem of decentralized goal assignment for multi-agent path planning, where agents independently generate ranked preferences over goals based on structured representations of the environment, including grid visualizations and scenario data. After this reasoning phase, agents exchange their goal rankings, and assignments are determined by a fixed, deterministic conflict-resolution rule (e.g., agent index ordering), without negotiation or iterative coordination. We systematically compare greedy heuristics, optimal assignment, and large language model (LLM)-based agents in fully observable grid-world settings. Our results show that LLM-based agents, when provided with well-designed prompts and relevant quantitative information, can achieve near-optimal makespans and consistently outperform traditional heuristics. These findings underscore the potential of language models for decentralized goal assignment in multi-agent path planning and highlight the importance of information structure in such systems.

Figures (3)

• Figure 1: Example 1 (Small World): A $5 \times 5$ grid with 3 agents, 3 goals (red color), and 2 obstacles (black color).
• Figure 2: Example 2 (Difficult World): A $20 \times 20$ grid with 3 agents, 3 goals, and multiple obstacles.
• Figure 3: Performance gap (mean steps above optimal) by number of agents for each method.