Generalized Momenta-Based Koopman Formalism for Robust Control of Euler-Lagrangian Systems

2025-09-21

AI Summary

To address the challenges of high parametric complexity, low data efficiency, and insufficient robustness in modeling and control of Euler–Lagrange systems, this paper proposes an implicit Koopman state representation framework grounded in generalized momentum. The key contribution is the first formulation of the Koopman latent state using generalized momentum, which decouples input channels from unactuated dynamics—enabling learning of only the control-free linear subsystem and drastically reducing model complexity and trainable parameters. The method integrates momentum-based Koopman operator modeling, a lightweight neural embedding architecture, and a linear generalized extended state observer (GESO) for real-time disturbance estimation and compensation. Extensive simulations and physical robot manipulator experiments demonstrate superior trajectory tracking accuracy, sample efficiency, and disturbance rejection robustness compared to state-of-the-art Koopman-based and neural dynamical approaches.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Learning to Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper presents a novel Koopman operator formulation for Euler Lagrangian dynamics that employs an implicit generalized momentum-based state space representation, which decouples a known linear actuation channel from state dependent dynamics and makes the system more amenable to linear Koopman modeling. By leveraging this structural separation, the proposed formulation only requires to learn the unactuated dynamics rather than the complete actuation dependent system, thereby significantly reducing the number of learnable parameters, improving data efficiency, and lowering overall model complexity. In contrast, conventional explicit formulations inherently couple inputs with the state dependent terms in a nonlinear manner, making them more suitable for bilinear Koopman models, which are more computationally expensive to train and deploy. Notably, the proposed scheme enables the formulation of linear models that achieve superior prediction performance compared to conventional bilinear models while remaining substantially more efficient. To realize this framework, we present two neural network architectures that construct Koopman embeddings from actuated or unactuated data, enabling flexible and efficient modeling across different tasks. Robustness is ensured through the integration of a linear Generalized Extended State Observer (GESO), which explicitly estimates disturbances and compensates for them in real time. The combined momentum-based Koopman and GESO framework is validated through comprehensive trajectory tracking simulations and experiments on robotic manipulators, demonstrating superior accuracy, robustness, and learning efficiency relative to state of the art alternatives.

Problem

• Develops momentum-based Koopman formulation for Euler-Lagrangian systems control
• Reduces model complexity by learning only unactuated dynamics parameters
• Ensures robustness through disturbance estimation and real-time compensation

Innovation

• Implicit momentum representation decouples linear actuation
• Learns only unactuated dynamics to reduce parameters
• Integrates linear observer for real-time disturbance compensation