mlsanityData to 14 Oct 2026

Coordinated Humanoid Robot Locomotion with Symmetry Equivariant Reinforcement Learning Policy

arXiv 2508.01247 ↗First posted 2 Aug 2025cs.ROcited by 2

On the map: Deep reinforcement learning methods → RL for robot locomotion and manipulation

Abstract (arXiv)

The human nervous system exhibits bilateral symmetry, enabling coordinated and balanced movements. However, existing Deep Reinforcement Learning (DRL) methods for humanoid robots neglect morphological symmetry of the robot, leading to uncoordinated and suboptimal behaviors. Inspired by human motor control, we propose Symmetry Equivariant Policy (SE-Policy), a new DRL framework that embeds strict symmetry equivariance in the actor and symmetry invariance in the critic without additional hyperparameters. SE-Policy enforces consistent behaviors across symmetric observations, producing temporally and spatially coordinated motions with higher task performance. Extensive experiments on velocity tracking tasks, conducted in both simulation and real-world deployment with the Unitree G1 humanoid robot, demonstrate that SE-Policy improves tracking accuracy by up to 40% compared to state-of-the-art baselines, while achieving superior spatial-temporal coordination. These results demonstrate the effectiveness of SE-Policy and its broad applicability to humanoid robots.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods. Builds on 26 of its 49 references that are in the map. First posted on arXiv 2 Aug 2025.

Builds on

26 of 49 references.

Closest ancestors · 3

Same direction, newest first

  1. 2024Reinforcement Learning with Euclidean Data Augmentation for State-Based Continuous Control16 Oct
  2. 2024Equivariant Ensembles and Regularization for Reinforcement Learning in Map-based Path Planning19 Mar
  3. 2024Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control30 Jan

Other references · 23

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2015High-Dimensional Continuous Control Using Generalized Advantage Estimationcited by 2,026
  3. 2021Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learningcited by 998
  4. 2020Learning Quadrupedal Locomotion over Challenging Terraincited by 604
  5. 2019Improving Sample Efficiency in Model-Free Reinforcement Learning from Imagescited by 274
  6. 2023Real-World Humanoid Locomotion with Reinforcement Learningcited by 187
  7. 2022Rapid Locomotion via Reinforcement Learningcited by 168
  8. 2020MDP Homomorphic Networks: Group Symmetries in Reinforcement Learningcited by 142
  9. 2019End-to-End Robotic Reinforcement Learning without Reward Engineeringcited by 122
  10. 2025HOMIE: Humanoid Loco-Manipulation with Isomorphic Exoskeleton Cockpitcited by 76
  11. 2024Humanoid-Gym: Reinforcement Learning for Humanoid Robot with Zero-Shot Sim2Real Transfercited by 53
  12. 2024Learning Humanoid Locomotion with Perceptive Internal Modelcited by 50
11 more
  1. 2022On-Robot Learning With Equivariant Modelscited by 42
  2. 2022CPG-RL: Learning Central Pattern Generators for Quadruped Locomotioncited by 34
  3. 2024Symmetry Considerations for Learning Task Symmetric Robot Policiescited by 28
  4. 2022Continuous MDP Homomorphisms and Homomorphic Policy Gradientcited by 27
  5. 2020Group Equivariant Deep Reinforcement Learningcited by 24
  6. 2024OrbitGrasp: SE(3)-Equivariant Grasp Learningcited by 16
  7. 2023Policy Gradient Methods in the Presence of Symmetries and State Abstractionscited by 9
  8. 2023Understanding when Dynamics-Invariant Data Augmentations Benefit Model-Free Reinforcement Learning Updatescited by 7
  9. 2025Natural Humanoid Robot Locomotion with Generative Motion Priorcited by 7
  10. 2023Addressing imperfect symmetry: A novel symmetry-learning actor-critic extensioncited by 5
  11. 2023Breaking Symmetries Leads to Diverse Quadrupedal Gaitscited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Beyond Topology: A Morphological Symmetry Graph Representation for Locomotion Policy Learningcited by 4
  2. 2026Constraint-Aware Diffusion Priors for High-Fidelity and Versatile Quadruped Locomotioncited by 1

Similar, not cited

Close in wording, no citation either way

  1. 2024Leveraging Symmetry in RL-based Legged Locomotion Control
  2. 2026EquiBim: Learning Symmetry-Equivariant Policy for Bimanual Manipulation
  3. 2025Time Reversal Symmetry for Efficient Robotic Manipulations in Deep Reinforcement Learning
  4. 2024Equivariant Reinforcement Learning under Partial Observability
  5. 2025SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey
  6. 2026Sample Complexity of Equivariant Reinforcement Learning
  7. 2025Symmetry-Guided Memory Augmentation for Efficient Locomotion Learning
  8. 2025Multi-Group Equivariant Augmentation for Reinforcement Learning in Robot Manipulation