Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Network for Robotic Dynamics Learning

Fengze Xie, Sizhe Wei, Yue Song, Yisong Yue, Lu Gan

TL;DR

The paper proposes Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Networks (MS-HGNN) to learn robotic dynamics by embedding both the kinematic morphology and symmetry priors directly into a graph neural framework. The approach constructs a morphology-aware HGNN and couples it with an encoder–decoder that enforces morphological symmetry equivariance, with theoretical guarantees of equivariance under the symmetry group $ ext{G}_m$. Empirical evaluations on quadruped platforms (Mini-Cheetah, A1, Solo) across contact-state classification, GRF regression, and centroidal momentum estimation demonstrate improved data efficiency, model efficiency, and generalization compared to state-of-the-art baselines. The results indicate that exploiting morphological priors yields better interpretability, robustness to unseen conditions, and substantial parameter savings, making MS-HGNN attractive for data-scarce robotic applications. The modular framework supports diverse morphologies and tasks, with future work aimed at incorporating temporary symmetries and real-world deployment.

Abstract

We present a morphological-symmetry-equivariant heterogeneous graph neural network, namely MS-HGNN, for robotic dynamics learning, that integrates robotic kinematic structures and morphological symmetries into a single graph network. These structural priors are embedded into the learning architecture as constraints, ensuring high generalizability, sample and model efficiency. The proposed MS-HGNN is a versatile and general architecture that is applicable to various multi-body dynamic systems and a wide range of dynamics learning problems. We formally prove the morphological-symmetry-equivariant property of our MS-HGNN and validate its effectiveness across multiple quadruped robot learning problems using both real-world and simulated data. Our code is made publicly available at https://github.com/lunarlab-gatech/MorphSym-HGNN/.

Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Network for Robotic Dynamics Learning

TL;DR

The paper proposes Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Networks (MS-HGNN) to learn robotic dynamics by embedding both the kinematic morphology and symmetry priors directly into a graph neural framework. The approach constructs a morphology-aware HGNN and couples it with an encoder–decoder that enforces morphological symmetry equivariance, with theoretical guarantees of equivariance under the symmetry group . Empirical evaluations on quadruped platforms (Mini-Cheetah, A1, Solo) across contact-state classification, GRF regression, and centroidal momentum estimation demonstrate improved data efficiency, model efficiency, and generalization compared to state-of-the-art baselines. The results indicate that exploiting morphological priors yields better interpretability, robustness to unseen conditions, and substantial parameter savings, making MS-HGNN attractive for data-scarce robotic applications. The modular framework supports diverse morphologies and tasks, with future work aimed at incorporating temporary symmetries and real-world deployment.

Abstract

We present a morphological-symmetry-equivariant heterogeneous graph neural network, namely MS-HGNN, for robotic dynamics learning, that integrates robotic kinematic structures and morphological symmetries into a single graph network. These structural priors are embedded into the learning architecture as constraints, ensuring high generalizability, sample and model efficiency. The proposed MS-HGNN is a versatile and general architecture that is applicable to various multi-body dynamic systems and a wide range of dynamics learning problems. We formally prove the morphological-symmetry-equivariant property of our MS-HGNN and validate its effectiveness across multiple quadruped robot learning problems using both real-world and simulated data. Our code is made publicly available at https://github.com/lunarlab-gatech/MorphSym-HGNN/.

Paper Structure

This paper contains 14 sections, 5 theorems, 19 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Morphology-Informed Heterogeneous Graph Neural Network
  5. Morphological Symmetries in Rigid Body Systems
  6. Methodology
  7. Experiments
  8. Contact State Detection for Mini-Cheetah Robot (Classification)
  9. Ground Reaction Force Estimation for A1 Robot (Regression)
  10. Centroidal Momentum Estimation for Solo Robot (Regression)
  11. Conclusions
  12. Morphological Symmetry of Kinematic Chains
  13. Proof Details
  14. Table For Results

Key Result

theorem 1

Assume our $\mathcal{G}$ with adjacency matrix $A_\mathcal{G}$ and node features $X_\mathcal{G}$, where different types of edges and nodes are represented by different integers. The mapping $\phi_{\rho_b}: \mathcal{G}\rightarrow\mathcal{G}$ is an automorphism if the edge and node features are preser

Figures (4)

  • Figure 1: Overview of the MS-HGNN framework for robots with symmetry type $\mathbb{G} := \textcolor{#6D016B}{\mathbb{K}_4}$. (a) The input space consists of the robot's current state observations, which are mapped to corresponding nodes in the HGNN. (b) and (d) The morphological symmetry encoder-decoder pair ensures that the learned representations respect the robot’s morphology. (c) The HGNN is automatically constructed to preserve geometric symmetry. (e) The output space consists of dynamics-relevant variables, obtained from their corresponding nodes in the HGNN.
  • Figure 2: (a) The visualization of the MS-HGNN architecture is shown for the morphological symmetry groups $\mathbb{G} := \textcolor{#6D016B}{\mathbb{K}_4}$ (left, Solo) and $\mathbb{G} := \textcolor{#8C96C6}{\mathbb{C}_2}$ (right, A1). Inputs and outputs of the MS-HGNN are distributed over graph nodes mapped to corresponding robot components (base, joint, foot). Variables representing the entire robot are placed on base nodes. Different node types represent distinct components of the robot’s kinematic structure, with contour colors indicating node types and filling colors denoting the group elements. The encoder and decoder types depend on the group elements, while edges between nodes are determined by node types and the robot’s symmetry. (b) Ground reaction force estimation test RMSE on simulated A1 dataset butterfield2024mihgnnmorphologyinformedheterogeneousgraph.
  • Figure 3: Contact state detection results on the real-world Mini-Cheetah dataset DBLP:conf/corl/LinZYG21. Left: F1 scores per leg, averaged F1 score, and 16-state accuracy (4-run average). Parameter counts are shown for each method. Right: Averaged F1 scores versus training set size. MS-HGNN ($\mathbb{C}_2$ & $\mathbb{K}_4$) achieve around 0.9 averaged F1-score with just 5$\%$ of training data.
  • Figure 4: Centroidal momentum estimation results on the synthetic Solo dataset DBLP:conf/rss/ApraezMAM23. Left: Test linear/angular cosine similarity and MSE of predictions, averaged over 4 runs. Right: Linear cosine similarity for models of varying sizes. Our MS-HGNN ($\mathbb{C}_2$ and $\mathbb{K}_4$) exhibit superior model efficiency without overfitting.

Theorems & Definitions (7)

  • theorem 1: Permutation Automorphism
  • lemma 1: Euclidean Group Equivariance
  • theorem 2: Morphological-Symmetry-Equivariant HGNN
  • theorem \ref{thm:permutation_auto}: Permutation Automorphism
  • proof
  • theorem \ref{theorem:msg-gnn}: Morphological-Symmetry-Equivariant HGNN
  • proof