Generalizability of Graph Neural Networks for Decentralized Unlabeled Motion Planning

TL;DR

This work proposes a decentralized policy learned via a Graph Neural Network that enables robots to determine what information to communicate to neighbors and how to integrate received information with local observations for decision-making and lays the foundation for solving multi-robot coordination problems in settings where scalability is important.

Abstract

Unlabeled motion planning involves assigning a set of robots to target locations while ensuring collision avoidance, aiming to minimize the total distance traveled. The problem forms an essential building block for multi-robot systems in applications such as exploration, surveillance, and transportation. We address this problem in a decentralized setting where each robot knows only the positions of its $k$-nearest robots and $k$-nearest targets. This scenario combines elements of combinatorial assignment and continuous-space motion planning, posing significant scalability challenges for traditional centralized approaches. To overcome these challenges, we propose a decentralized policy learned via a Graph Neural Network (GNN). The GNN enables robots to determine (1) what information to communicate to neighbors and (2) how to integrate received information with local observations for decision-making. We train the GNN using imitation learning with the centralized Hungarian algorithm as the expert policy, and further fine-tune it using reinforcement learning to avoid collisions and enhance performance. Extensive empirical evaluations demonstrate the scalability and effectiveness of our approach. The GNN policy trained on 100 robots generalizes to scenarios with up to 500 robots, outperforming state-of-the-art solutions by 8.6\% on average and significantly surpassing greedy decentralized methods. This work lays the foundation for solving multi-robot coordination problems in settings where scalability is important.

Figures (6)

• Figure 1: Example for difference between assignment using sum of distances $\bfP_\text{LSAP}$ (solid lines) and sum of distances squared, $\bfP_\text{CAPT}$ (dashed lines). Agents are blue, and goals are red. $\bfP_\text{CAPT}$ prioritizes reducing the maximum distance traveled for each agent, which increases total distance.
• Figure 2: The average coverage $\sum_t^T c(t) / T$ and number of collisions per agent $\sum_t^T \sum_i^N p_i(t) / N T$ that the GNN achieves at each epoch. We run 10 simulations after each epoch and report the mean. The values are smoothed using a 9 epoch wide rolling window.
• Figure 3: The coverage $c(t)$ over time for the centralized, decentralized, and GNN policies. At each time and for each policy, we plot the mean coverage from 50 simulations. The bands represent the standard deviation.
• Figure 4: The coverage $c(t)$ over time for different numbers of agents, $N$. The density of agents is constant at $\rho = 1.0$.
• Figure 5: The coverage $c(t)$ over time for different agent densities, $\rho$. The number of agents is constant at $N = 100$.