# Reconfiguration of pivoting cube ensembles under local sensing constraints using geometric deep learning

arXiv: https://arxiv.org/abs/2509.03140 · HTML: https://mlsanity.com/paper/2509.03140/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 3 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Neural representation of a time optimal, constant acceleration rendezvous](https://mlsanity.com/paper/2203.15490/) (2022)
- [Neural Networks for Learning Counterfactual G-Invariances from Single Environments](https://mlsanity.com/paper/2104.10105/) (2021)
- [Guidance and Control Networks with Periodic Activation Functions](https://mlsanity.com/paper/2405.18084/) (2024)
- [ElectroVoxel: Electromagnetically Actuated Pivoting for Scalable Modular Self-Reconfigurable Robots](https://mlsanity.com/paper/2207.05732/) (2022)
- [Deep Q-Learning versus Proximal Policy Optimization: Performance Comparison in a Material Sorting Task](https://mlsanity.com/paper/2306.01451/) (2023)
- [Reconfiguration Algorithms for Cubic Modular Robots with Realistic Movement Constraints](https://mlsanity.com/paper/2405.15724/) (2024)

## Abstract (arXiv)

We demonstrate that local sensing is sufficient for effective global reconfiguration of homogeneous pivoting cube modular robots in two dimensions. While cube selection (i.e., which cube executes a movement) is assumed to be globally coordinated, each cube in the ensemble is controlled by a neural network that only gains information from other cubes in its local neighbourhood, trained using reinforcement learning. Furthermore, we study the effect of including grid symmetries of the cube ensemble (rotation and mirroring) in the neural network architecture. We find that even the most localised 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 neighbour interactions by using multiple information passing between cubes, allowing them to accumulate more global information about the ensemble. Compared to standard neural network architectures, including grid symmetries provides only minor benefits during training, but allows for reduced model sizes. The presented approach is transferable to other space-relevant systems with different action spaces, such as sliding cube modular robots and CubeSat swarms.