Floating-Base Deep Lagrangian Networks
Lucas Schulze, Juliano Negri, Victor Barasuol, Vivian Suzano Medeiros, Marcelo Becker, Jan Peters, Oleg Arenz
AI summary
Problem
Current grey-box deep learning models for floating-base robots ignore critical physical constraints of their inertia matrices, such as branch-induced sparsity and the triangle inequality on composite spatial inertia, which limits generalization and interpretability.
Approach
The authors introduce FeLaN, which parameterizes the inertia matrix via a reordered Cholesky factorization to strictly enforce all physical constraints, then trains neural networks to predict these parameters by minimizing inverse dynamics error.
Key results
- Extended full physical consistency conditions to composite spatial inertia
- Proposed a novel inertia parametrization preserving branch-induced sparsity
- Developed FeLaN for physically consistent system identification
- Achieved superior accuracy and interpretability on simulated and real quadrupeds and humanoids
Why it matters
Provides a robust, physically grounded framework for learning robot dynamics, improving generalization and safety for complex legged systems.
Abstract
Grey-box methods for system identification com- bine deep learning with physics-informed constraints, captur- ing 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 6×6 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 plau- sible 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.