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

Area of Science:

• Robotics
• Machine Learning
• Control Theory

Background:

• Accurate dynamic modeling is crucial for advanced robotic control.
• Conventional methods face challenges with manipulator nonlinear complexity.
• Existing Hamiltonian neural networks have limitations in matrix constraints and validation.

Purpose of the Study:

• To propose a Symplectic Physics-Embedded Learning (SPEL) approach for enhanced dynamics modeling of serial manipulators.
• To address limitations of existing methods by encoding physical priors into neural network design.
• To improve physical consistency, reduce network parameters, and enhance computational efficiency.

Main Methods:

• Developed SPEL based on Lie group Hamiltonian formulations.
• Systematically encoded Lie group symmetries and Hamiltonian dynamics into neural network architecture.
• Enforced sparsity in mass, dissipation, and control input matrices via physics-driven constraints.
• Replaced input-independent matrix elements with trainable parameters to optimize network topology.

Main Results:

• SPEL reduced over 52% of parameters and enhanced computational efficiency by more than 75% on manipulators.
• Symplectic Physics-Embedded Learning Kolmogorov-Arnold Networks (SPEL-KAN) reduced over 63% of parameters and improved efficiency by over 39%.
• Achieved higher prediction accuracy and preserved physical consistency.
• Validated on simulated and real-world robotic systems (2-link, RPR, 6-DOF).

Conclusions:

• SPEL offers a physics-informed approach for efficient and accurate robot dynamics modeling.
• Embedding geometric-mechanical principles into neural networks balances efficiency with interpretable predictions.
• The method significantly optimizes network topology and reduces computational load.