Geometric deep learning lets pivoting cube robots reconfigure with local sensing

Modular robots — homogeneous cubes that pivot around each other — have traditionally needed global sensing or centralized control to reconfigure into a target shape. In a new paper published in Astrodynamics (Springer Nature, 2026), researchers including ESA's Dario Izzo and collaborators demonstrate that local sensing is sufficient for effective global reconfiguration in two dimensions. Each cube is controlled by a neural network that only receives information from cubes in its immediate neighborhood, trained end-to-end using reinforcement learning. Cube selection (which cube moves) remains globally coordinated, but the actual movement decisions are decentralized and only rely on local observations.

The team tested several architectures, including versions that encode grid symmetries (rotation and mirroring) directly into the network. They found that even the most localized variants succeed in reconfiguring to target shapes, but reconfiguration happens faster when individual cubes have more global information. Crucially, near-optimal performance can be achieved with only nearest-neighbor interactions by using multiple rounds of information passing between cubes, effectively letting local signals accumulate into global awareness. Including grid symmetries provided only minor training benefits but significantly reduced model sizes. The method is claimed to transfer to other space-relevant systems with different action spaces, such as sliding cube robots and CubeSat swarms, suggesting a path toward simpler, more robust autonomous assembly in orbit.