aiqbench analysis
This research advances AI-driven robotics by integrating structure-preserving neural architectures with Koopman operator theory to ensure physical stability in nonlinear systems. By explicitly enforcing energy conservation and passivity constraints during the learning process, the method eliminates artificial energy growth common in data-only models. The approach offers a rigorous framework for deploying reliable predictive control in high-dimensional mechanical applications without relying on post-hoc corrections.
Port-Hamiltonian Koopman Operator Synthesis for Mechanical Systems
arXiv:2609.17249v1 Announce Type: new Abstract: Finite-dimensional Koopman models enable efficient linear prediction and control of nonlinear robotic systems. However, models learned purely from trajectory data may violate the energetic structure of the underlying mechanics, producing predictions that exhibit artificial energy growth and diverge under recursive propagation. This work presents a structure-preserving Koopman framework for Euler-Lagrange systems built on generalized-momentum coordinates. The momentum transformation exposes the mechanical actuation as a known, state-independent port, which is preserved explicitly in the lifted dynamics. A structure-constrained neural architecture is developed to jointly learn the lifting functions and a port-Hamiltonian Koopman generator, rendering the learned dynamics passive by construction rather than through penalty terms or post-hoc projection. A Cayley-midpoint discretization further preserves the corresponding storage-dissipation balance exactly in discrete time. These properties are established analytically by deriving the discrete storage balance and associated stability guarantees of the learned predictor. Simulation and experimental studies demonstrate improved prediction accuracy, data efficiency, and closed-loop tracking over Koopman baselines, with increasing gains for higher-dimensional systems.
Abstract:Finite-dimensional Koopman models enable efficient linear prediction and control of nonlinear robotic systems. However, models learned purely from trajectory data may violate the energetic structure of the underlying mechanics, producing predictions that exhibit artificial energy growth and diverge under recursive propagation. This work presents a structure-preserving Koopman framework for Euler-Lagrange systems built on generalized-momentum coordinates. The momentum transformation exposes the mechanical actuation as a known, state-independent port, which is preserved explicitly in the lifted dynamics. A structure-constrained neural architecture is developed to jointly learn the lifting functions and a port-Hamiltonian Koopman generator, rendering the learned dynamics passive by construction rather than through penalty terms or post-hoc projection. A Cayley-midpoint discretization further preserves the corresponding storage-dissipation balance exactly in discrete time. These properties are established analytically by deriving the discrete storage balance and associated stability guarantees of the learned predictor. Simulation and experimental studies demonstrate improved prediction accuracy, data efficiency, and closed-loop tracking over Koopman baselines, with increasing gains for higher-dimensional systems.
Robotics (cs.RO); Systems and Control (eess.SY)
arXiv:2609.17249 [cs.RO]
(or arXiv:2609.17249v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2609.17249 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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