Symplectic physics-embedded learning via Lie groups Hamiltonian formulation for serial manipulator dynamics prediction

Accurate dynamic modeling is critical for advanced robotic control, yet conventional methods struggle with manipulator nonlinear complexity. While Hamiltonian neural networks leveraging Lie group symmetries improve physical consistency of the network, existing methods overlook key limitations: unconstrained sparsity in mass, dissipation, and control matrices; redundancy in mass network outputs; and lack of validation on multi-rigid-body systems. This paper proposes a symplectic physics-embedded learning approach (SPEL) based on Lie group Hamiltonian formulations for enhanced dynamics modeling of serial manipulators. By systematically encoding physical priors such as Lie group symmetries and Hamiltonian dynamics into neural network design, SPEL enforces sparsity in mass, dissipation, and control input matrices via physics-driven constraints and replaces input-independent matrix elements with trainable parameters. These mechanisms structurally optimize the network topology, significantly reducing output dimensionality while preserving physical consistency of the network. Experimental validation on simulated two-link and revolute-prismatic-revolute (RPR) manipulators, as well as a real 6-DOF manipulator, demonstrates that SPEL reduces over 52% of the parameters, enhances computational efficiency by more than 75%, and achieves higher prediction accuracy. Additionally, Symplectic Physics-Embedded Learning Kolmogorov-Arnold Networks (SPEL-KAN) reduce over 63% of the parameters and improve computational efficiency by more than 39%. This approach embeds geometric-mechanical principles into architectures, balancing efficiency with interpretable predictions.