Floating-Base Deep Lagrangian Networks

2025-10-20

AI Summary

Existing gray-box models for floating-base systems (e.g., humanoid and quadrupedal robots) neglect critical physical constraints. This work addresses this limitation by proposing a geometrically consistent parameterization of the inertia matrix—first explicitly encoding dynamical priors including branch-induced sparsity, input independence, and eigenvalue triangle inequalities of the composite spatial inertia matrix. Grounded in Lagrangian mechanics, we design a differentiable physics-informed neural network that jointly optimizes inverse dynamics error and physical constraint violations in an end-to-end manner. We validate the method across multiple simulation platforms and real-world robots, and publicly release the first multi-morphology robot identification dataset tailored to floating-base systems. Compared to baseline approaches, our method achieves significant improvements in out-of-distribution generalization, physical consistency, and interpretability.

Technology Category

• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Computer Vision: Low Level & Physics-based Vision

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Grey-box methods for system identification combine deep learning with physics-informed constraints, capturing complex dependencies while improving out-of-distribution generalization. Yet, 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 highly competitive performance on both simulated and real robots, while providing greater physical interpretability.

Problem

• Addressing physical inconsistency in floating-base system models
• Incorporating branch sparsity and eigenvalue constraints in inertia
• Improving generalization for humanoids and quadrupeds through physics-informed learning

Innovation

• Parameterizes inertia matrices satisfying physical constraints
• Trains networks to predict plausible inertia matrices
• Uses Lagrangian mechanics to minimize dynamics error