Goal-Directed Graph Neural Cellular Automata for Swarm Navigation

Cellular automata (CA) are a group of computational models in which each cell repeatedly updates its state through a local rule that depends on its own state and the states of its neighbors. After sufficient iterations, CA are able to exhibit emergent global complexity. Graph cellular automata (GCA) are a generalized version of CA that live and operate on an arbitrary graph rather than a lattice structure. The advantage of GCA is that they allow for dynamic edges between graph nodes instead of fixed distances between cells on a lattice, a feature with strong implications for control-oriented dynamical systems. Prior work used graph neural networks (GNNs) to learn the transition rules of graph cellular automata for flocking imitation. Our central contribution is to extend this framework beyond flocking to goal-directed swarm navigation in both two- and three-dimensional environments. First, we train GNNs to imitate an expert flocking controller that guides swarms from randomized initial configurations through a fixed sequence of waypoints. Then, we train GNNs to imitate the same controller under dynamically updated waypoints sampled throughout the spatial domain. We further evaluate robustness to the removal of up to half of the agents from the middle of the flock during execution, which changes both swarm size and graph topology on the fly. Together, these experiments broaden the role of learned GCA from reproducing dynamics to enabling task-directed collective behavior, highlighting their potential as learned policies for decentralized systems.