# Sample Efficient Dynamics Learning for Symmetrical Legged Robots:Leveraging Physics Invariance and Geometric Symmetries

arXiv: https://arxiv.org/abs/2210.07329 · HTML: https://mlsanity.com/paper/2210.07329/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 20 of 20)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [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)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Deep Reinforcement Learning for Robotic Manipulation with Asynchronous Off-Policy Updates](https://mlsanity.com/paper/1610.00633/) (2016)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robots](https://mlsanity.com/paper/2103.14295/) (2021)
- [Learning Symmetric and Low-energy Locomotion](https://mlsanity.com/paper/1801.08093/) (2018)
- [The Sensory Neuron as a Transformer: Permutation-Invariant Neural Networks for Reinforcement Learning](https://mlsanity.com/paper/2109.02869/) (2021)
- [Learning Generalized Transformation Equivariant Representations via Autoencoding Transformations](https://mlsanity.com/paper/1906.08628/) (2019)
- [Learning Modular Robot Control Policies](https://mlsanity.com/paper/2105.10049/) (2021)
- [Structured Mechanical Models for Robot Learning and Control](https://mlsanity.com/paper/2004.10301/) (2020)
- [Dynamic Locomotion For Passive-Ankle Biped Robots And Humanoids Using Whole-Body Locomotion Control](https://mlsanity.com/paper/1901.08100/) (2019)
- [Nested Mixture of Experts: Cooperative and Competitive Learning of Hybrid Dynamical System](https://mlsanity.com/paper/2011.10605/) (2020)

## Built on by (most cited first, 1 of 1)

- [Symmetry-aware Reinforcement Learning for Robotic Assembly under Partial Observability with a Soft Wrist](https://mlsanity.com/paper/2402.18002/) (2024)

## Abstract (arXiv)

Model generalization of the underlying dynamics is critical for achieving data efficiency when learning for robot control. This paper proposes a novel approach for learning dynamics leveraging the symmetry in the underlying robotic system, which allows for robust extrapolation from fewer samples. Existing frameworks that represent all data in vector space fail to consider the structured information of the robot, such as leg symmetry, rotational symmetry, and physics invariance. As a result, these schemes require vast amounts of training data to learn the system's redundant elements because they are learned independently. Instead, we propose considering the geometric prior by representing the system in symmetrical object groups and designing neural network architecture to assess invariance and equivariance between the objects. Finally, we demonstrate the effectiveness of our approach by comparing the generalization to unseen data of the proposed model and the existing models. We also implement a controller of a climbing robot based on learned inverse dynamics models. The results show that our method generates accurate control inputs that help the robot reach the desired state while requiring less training data than existing methods.