Decentralised self-organisation of pivoting cube ensembles using geometric deep learning

We present a decentralized model for autonomous reconfiguration of homogeneous pivoting cube modular robots in two dimensions. Each cube in the ensemble is controlled by a neural network that only gains information from other cubes in its local neighborhood, trained using reinforcement learning. Furthermore, using geometric deep learning, we include the grid symmetries of the cube ensemble in the neural network architecture. We find that even the most localized versions succeed in reconfiguring to the target shape, although reconfiguration happens faster the more information about the whole ensemble is available to individual cubes. Near-optimal reconfiguration is achieved with only nearest neighbor interactions by using multiple information passing between cubes, allowing them to accumulate more global information about the ensemble. Compared to standard neural network architectures, using geometric deep learning approaches provided only minor benefits. Overall, we successfully demonstrate mostly local control of a modular self-assembling system, which is transferable to other space-relevant systems with different action spaces, such as sliding cube modular robots and CubeSat swarms.