Swarm-Inspired Generation of Collective Behaviors in Graph Dynamical Systems

Robot swarms utilize many independent limited-sensing agents to produce complex emergent behaviors without requiring centralized control. However, little research explores how agents can infer swarm-level behavior from purely local perception, a capability critical for detecting faults and behavior changes. In this paper, we introduce Synchronized Swarm Behavior Classification (SyncSBC), which combines improvements in machine learning and distributed consensus to classify collective swarm behavior and synchronize swarm decision-making in an entirely decentralized manner. We show that SyncSBC achieves high classification accuracy and low synchronization delay, making it suitable for real-world deployment. Finally, we use SyncSBC to demonstrate two promising swarm applications on real robots where we show that swarms utilizing SyncSBC can accurately identify anomalies in robot behavior and autonomously coordinate collective changes in swarm behavior. Videos, code and supplemental experiments are available at https://sites.google.com/view/sync-sbc/home.

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning stability landscapes, which provide deeper insights into synchronization behavior and from which many such scalar indices can be derived. Crucially, we pioneer a graph-to-image prediction paradigm: learning image-like landscapes as per-node targets directly from graph topology, a formulation we are not aware of having been established elsewhere in the literature. To support this task, we release two datasets of 10,000 graphs each at 20 and 100 nodes with per-node landscape labels, based on a conceptual oscillator model, capturing power grid synchronization behavior. A GNN encodes topology and a CNN decoder renders per-node images, learned end-to-end with good in-distribution accuracy, generalizing across graph sizes and to realistic power grid topologies. This demonstrates that stability landscapes, while beyond the reach of conventional network science, are learnable from topology and open new avenues for moving beyond scalar stability indices in biology, neuroscience, and power grids.

Modular miniature robots could provide scalable function in constrained environments, but coordinating many imperfect modules remains difficult when computation, communication and reliability are limited. A central robotics challenge is to coordinate many actuator-sensor modules without assigning a privileged leader, prescribing a fixed gait template, or relying on dense communication. Here we introduce a programmable synchronization-graph framework for modular miniature robots in which each actuator-sensor pair is represented as a network node and locomotor coordination is encoded through graph coupling. Fixed intra-subgraph links synchronize heterogeneous actuator groups, whereas a small number of signed inter-subgraph links program phase relationships between groups. In physical robot collectives with up to nine modules, graph coupling drives the emergence of synchronization, signed links tune the phase difference from in-phase to out-of-phase motion, and floor experiments produce gallop-like and trot-like contact patterns in a five-module robot assembly. Replacing dense all-to-all coupling with sparse d-regular topologies preserves synchronization while reducing the coupling burden. The same graph representation also captures fault tolerance: increasing graph degree increases the number of module deactivations tolerated before desynchronization. Finally, an upper-confidence-bound edge-selection algorithm learns inter-subgraph links that drive the system toward target phase states. In a separate deactivation benchmark, the graph-based controller avoids the leader-specific failure mode observed in centralized leader-follower control and reduces worst-case phase error by about threefold. These results establish programmable network topology as a compact control layer for gait phase programming, online adaptation and robustness to unit loss in modular miniature robots.