# Solving Multi-Entity Robotic Problems Using Permutation Invariant Neural Networks

arXiv: https://arxiv.org/abs/2402.18345 · HTML: https://mlsanity.com/paper/2402.18345/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2024.

## Built on by (most cited first, 2 of 2)

- [Learning Multi-Agent Loco-Manipulation for Long-Horizon Quadrupedal Pushing](https://mlsanity.com/paper/2411.07104/) (2024)
- [Human2LocoMan: Learning Versatile Quadrupedal Manipulation with Human Pretraining](https://mlsanity.com/paper/2506.16475/) (2025)

## Abstract (arXiv)

Challenges in real-world robotic applications often stem from managing multiple, dynamically varying entities such as neighboring robots, manipulable objects, and navigation goals. Existing multi-agent control strategies face scalability limitations, struggling to handle arbitrary numbers of entities. Additionally, they often rely on engineered heuristics for assigning entities among agents. We propose a data driven approach to address these limitations by introducing a decentralized control system using neural network policies trained in simulation. Leveraging permutation invariant neural network architectures and model-free reinforcement learning, our approach allows control agents to autonomously determine the relative importance of different entities without being biased by ordering or limited by a fixed capacity. We validate our approach through both simulations and real-world experiments involving multiple wheeled-legged quadrupedal robots, demonstrating their collaborative control capabilities. We prove the effectiveness of our architectural choice through experiments with three exemplary multi-entity problems. Our analysis underscores the pivotal role of the end-to-end trained permutation invariant encoders in achieving scalability and improving the task performance in multi-object manipulation or multi-goal navigation problems. The adaptability of our policy is further evidenced by its ability to manage varying numbers of entities in a zero-shot manner, showcasing near-optimal autonomous task distribution and collision avoidance behaviors.