Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurements

TL;DR

This paper introduces a novel learning algorithm for Lagrangian systems that enhances physical consistency without requiring acceleration data, improving model-based control applications on real systems.

Contribution

It proposes an original loss function for learning physically consistent Lagrangian models without acceleration measurements, validated through simulations and experiments.

Findings

Significant improvement in physical consistency of learned models

Enhanced performance of control techniques using the proposed models

Successful application on both simulated and real experimental systems

Abstract

This article investigates the modeling and control of Lagrangian systems involving non-conservative forces using a hybrid method that does not require acceleration calculations. It focuses in particular on the derivation and identification of physically consistent models, which are essential for model-based control synthesis. Lagrangian or Hamiltonian neural networks provide useful structural guarantees but the learning of such models often leads to inconsistent models, especially on real physical systems where training data are limited, partial and noisy. Motivated by this observation and the objective to exploit these models for model-based nonlinear control, a learning algorithm relying on an original loss function is proposed to improve the physical consistency of Lagrangian systems. A comparative analysis of different learning-based modeling approaches with the proposed solution shows significant improvements in terms of physical consistency of the learned models, on both simulated and experimental systems. The model's consistency is then exploited to demonstrate, on an experimental benchmark, the practical relevance of the proposed methodology for feedback linearization and energy-based control techniques.