Modeling and controlling complex robotic systems require capturing both the structural heterogeneity of the robots and their underlying physical dynamics. Traditional Graph Neural Networks (GNNs) often assume homogeneous structures and full equivariance under group transformations, which limits their effectiveness in heterogeneous robotic systems. To address this limitation, we propose a novel framework called Subequivariant Heterogeneous Graph Network (SHGN). SHGN models robots by representing their limbs as graph nodes and their joints as graph edges, using a heterogeneous graph representation and incorporating Kane’s equations as an inductive bias. For reinforcement learningbased robot control, our approach leverages Transformers with heterogeneous edge encoding while relaxing strict equivariance constraints. This design allows the policy to generalize across all directions, thereby enhancing exploration efficiency. Experimental results demonstrate that SHGN effectively captures fine-grained dynamic properties of robotic systems, achieving superior performance in modeling and control tasks. Furthermore, evaluations in various robotic environments reveal that SHGN significantly outperforms existing GNN-based methods, highlighting the importance of considering structural heterogeneity and subequivariance in physical dynamics modeling.

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Subequivariant Heterogeneous Graph Network for Physical Dynamics: Modeling and Control

  • Bingwei Huang,
  • Chenxi Zhang,
  • Fengge Wu,
  • Junsuo Zhao

摘要

Modeling and controlling complex robotic systems require capturing both the structural heterogeneity of the robots and their underlying physical dynamics. Traditional Graph Neural Networks (GNNs) often assume homogeneous structures and full equivariance under group transformations, which limits their effectiveness in heterogeneous robotic systems. To address this limitation, we propose a novel framework called Subequivariant Heterogeneous Graph Network (SHGN). SHGN models robots by representing their limbs as graph nodes and their joints as graph edges, using a heterogeneous graph representation and incorporating Kane’s equations as an inductive bias. For reinforcement learningbased robot control, our approach leverages Transformers with heterogeneous edge encoding while relaxing strict equivariance constraints. This design allows the policy to generalize across all directions, thereby enhancing exploration efficiency. Experimental results demonstrate that SHGN effectively captures fine-grained dynamic properties of robotic systems, achieving superior performance in modeling and control tasks. Furthermore, evaluations in various robotic environments reveal that SHGN significantly outperforms existing GNN-based methods, highlighting the importance of considering structural heterogeneity and subequivariance in physical dynamics modeling.