# Symmetry-Aware Robot Design with Structured Subgroups

arXiv: https://arxiv.org/abs/2306.00036 · HTML: https://mlsanity.com/paper/2306.00036/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 54 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Embodied Intelligence via Learning and Evolution](https://mlsanity.com/paper/2102.02202/) (2021)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [One Policy to Control Them All: Shared Modular Policies for Agent-Agnostic Control](https://mlsanity.com/paper/2007.04976/) (2020)
- [MetaMorph: Learning Universal Controllers with Transformers](https://mlsanity.com/paper/2203.11931/) (2022)
- [RotoGrad: Gradient Homogenization in Multitask Learning](https://mlsanity.com/paper/2103.02631/) (2021)
- [Learning to Control Self-Assembling Morphologies: A Study of Generalization via Modularity](https://mlsanity.com/paper/1902.05546/) (2019)
- [My Body is a Cage: the Role of Morphology in Graph-Based Incompatible Control](https://mlsanity.com/paper/2010.01856/) (2020)
- [Reinforcement Learning for Improving Agent Design](https://mlsanity.com/paper/1810.03779/) (2018)
- [Policy Transfer with Strategy Optimization](https://mlsanity.com/paper/1810.05751/) (2018)
- [Scalable Co-Optimization of Morphology and Control in Embodied Machines](https://mlsanity.com/paper/1706.06133/) (2017)
- [Transform2Act: Learning a Transform-and-Control Policy for Efficient Agent Design](https://mlsanity.com/paper/2110.03659/) (2021)
- [Neural Graph Evolution: Towards Efficient Automatic Robot Design](https://mlsanity.com/paper/1906.05370/) (2019)
- [Contrasting Exploration in Parameter and Action Space: A Zeroth-Order Optimization Perspective](https://mlsanity.com/paper/1901.11503/) (2019)
- [Low-Rank Modular Reinforcement Learning via Muscle Synergy](https://mlsanity.com/paper/2210.15479/) (2022)

## Built on by (most cited first, 13 of 13)

- [VLMgineer: Vision Language Models as Robotic Toolsmiths](https://mlsanity.com/paper/2507.12644/) (2025)
- [Multi-Sender Persuasion: A Computational Perspective](https://mlsanity.com/paper/2402.04971/) (2024)
- [Towards Foundation-model-based Multiagent System to Accelerate AI for Social Impact](https://mlsanity.com/paper/2412.07880/) (2024)
- [BodyGen: Advancing Towards Efficient Embodiment Co-Design](https://mlsanity.com/paper/2503.00533/) (2025)
- [Roadmap on Incentive Compatibility for AI Alignment and Governance in Sociotechnical Systems](https://mlsanity.com/paper/2402.12907/) (2024)
- [Leveraging Hyperbolic Embeddings for Coarse-to-Fine Robot Design](https://mlsanity.com/paper/2311.00462/) (2023)
- [The Bandit Whisperer: Communication Learning for Restless Bandits](https://mlsanity.com/paper/2408.05686/) (2024)
- [House of Dextra: Cross-embodied Co-design for Dexterous Hands](https://mlsanity.com/paper/2512.03743/) (2025)
- [Embodied Co-Design for Rapidly Evolving Agents: Taxonomy, Frontiers, and Challenges](https://mlsanity.com/paper/2512.04770/) (2025)
- [Efficient Morphology-Control Co-Design via Stackelberg Proximal Policy Optimization](https://mlsanity.com/paper/2603.15388/) (2026)
- [Social Environment Design](https://mlsanity.com/paper/2402.14090/) (2024)
- [Shape Your Body: Value Gradients for Multi-Embodiment Robot Design](https://mlsanity.com/paper/2606.00702/) (2026)
- [Clutter Detection and Removal by Multi-Objective Analysis for Photographic Guidance](https://mlsanity.com/paper/2507.14553/) (2025)

## Abstract (arXiv)

Robot design aims at learning to create robots that can be easily controlled and perform tasks efficiently. Previous works on robot design have proven its ability to generate robots for various tasks. However, these works searched the robots directly from the vast design space and ignored common structures, resulting in abnormal robots and poor performance. To tackle this problem, we propose a Symmetry-Aware Robot Design (SARD) framework that exploits the structure of the design space by incorporating symmetry searching into the robot design process. Specifically, we represent symmetries with the subgroups of the dihedral group and search for the optimal symmetry in structured subgroups. Then robots are designed under the searched symmetry. In this way, SARD can design efficient symmetric robots while covering the original design space, which is theoretically analyzed. We further empirically evaluate SARD on various tasks, and the results show its superior efficiency and generalizability.