Floating-Base Deep Lagrangian Networks

TL;DR

This paper introduces a physics-consistent neural network model for floating-base robotic systems, improving system identification by enforcing physical constraints on inertia matrices, leading to better performance and interpretability.

Contribution

We develop a parameterization of inertia matrices that ensures physical constraints are satisfied in deep learning models of floating-base systems, extending Deep Lagrangian Networks to these systems.

Findings

Achieved improved inverse dynamics prediction accuracy.

Demonstrated better generalization on real and simulated robots.

Provided a new dataset for quadrupeds and humanoids.

Abstract

Grey-box methods for system identification combine deep learning with physics-informed constraints, capturing complex dependencies while improving out-of-distribution generalization. Despite the growing importance of floating-base systems such as humanoids and quadrupeds, current grey-box models ignore their specific physical constraints. For instance, the inertia matrix is not only positive definite but also exhibits branch-induced sparsity and input independence. Moreover, the 6x6 composite spatial inertia of the floating base inherits properties of single-rigid-body inertia matrices. As we show, this includes the triangle inequality on the eigenvalues of the composite rotational inertia. To address the lack of physical consistency in deep learning models of floating-base systems, we introduce a parameterization of inertia matrices that satisfies all these constraints. Inspired by Deep Lagrangian Networks (DeLaN), we train neural networks to predict physically plausible inertia matrices that minimize inverse dynamics error under Lagrangian mechanics. For evaluation, we collected and released a dataset on multiple quadrupeds and humanoids. In these experiments, our Floating-Base Deep Lagrangian Networks (FeLaN) achieve better overall performance on both simulated and real robots, while providing greater physical interpretability.