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.

翻译：系统辨识的灰盒方法将深度学习与物理信息约束相结合，在捕捉复杂依赖关系的同时，提升了分布外泛化能力。尽管浮动基座系统（如仿人机器人和四足机器人）的重要性日益增长，现有的灰盒模型却忽略了其特定的物理约束。例如，惯性矩阵不仅是正定的，还表现出分支诱导的稀疏性和输入无关性。此外，浮动基座的6x6复合空间惯性继承了单刚体惯性矩阵的特性。正如我们所展示的，这包括复合旋转惯性特征值上的三角不等式。针对浮动基座系统深度学习模型中物理一致性的缺失，我们引入了一种满足所有这些约束的惯性矩阵参数化方法。受深度拉格朗日网络（DeLaN）的启发，我们训练神经网络来预测物理上合理的惯性矩阵，以最小化拉格朗日力学下的逆动力学误差。为进行评估，我们收集并发布了关于多种四足机器人和仿人机器人的数据集。在这些实验中，我们提出的浮动基座深度拉格朗日网络（FeLaN）在仿真和真实机器人上均实现了更优的整体性能，同时提供了更强的物理可解释性。