# Floating-Base Deep Lagrangian Networks

arXiv: https://arxiv.org/abs/2510.17270 · HTML: https://mlsanity.com/paper/2510.17270/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2025.

## Built on by (most cited first, 2 of 2)

- [Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurements](https://mlsanity.com/paper/2512.03035/) (2025)
- [STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matching](https://mlsanity.com/paper/2603.08478/) (2026)

## Abstract (arXiv)

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.