基于李群的力学系统动力学学习，仅用位置数据实现精准建模
Learning Forced Multibody Dynamics on Lie Groups
- 在李群上构建离散受力欧拉-拉格朗日方程，保留系统几何结构
- 仅依赖位置数据，对速度噪声或缺失具有鲁棒性
- 适用于多体系统和外部控制，真实与合成数据表现优异
我们提出一种基于李群上离散受力欧拉-拉格朗日方程的动力学学习架构，仅使用位置数据即可建模机械系统。通过在流形值配置空间中直接表述动力学，该方法自然尊重系统的几何结构，保持几何不变量与守恒律。由于仅依赖位置测量，该框架适用于速度数据不可用或噪声较大的场景。方法可自然扩展至多体系统，支持外部控制输入，并在合成与真实世界数据集上均表现出色。
原文摘要 · Abstract (English)
We propose an architecture for learning the dynamics of mechanical systems based on discrete forced Euler-Lagrange equations on Lie groups using only position data. By formulating the dynamics directly on manifold-valued configuration spaces, the method naturally respects the geometric structure of the systems and preserves geometric invariants and conservation laws. The reliance on position measurements alone makes the framework applicable in settings where velocity data are unavailable or noisy. The approach extends naturally to multibody systems, accommodates external control inputs, and demonstrates strong performance on both synthetic and real-world datasets.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。