用神经网络建模非完整约束机械系统，保持能量守恒且约束更准确。
Lagrangian neural networks for nonholonomic mechanics
- 将拉格朗日神经网络改造用于处理非完整约束系统
- 轨迹预测精度提升，能量守恒性优于无约束模型
- 适合需要精确物理约束的机器人与动力学仿真场景
拉格朗日神经网络（LNN）是一种强大的物理系统建模工具，尤其适用于受守恒律支配的系统。通过参数化系统的拉格朗日量，LNN 能够预测具有近似守恒能量的轨迹，在无约束及完整约束系统中均表现良好。本文将 LNN 方法拓展至含非完整约束的机械系统。我们在多个经典非完整约束案例上验证该方法，结果表明，将约束信息融入神经网络学习过程，不仅提升了轨迹估计精度，还确保了约束满足性，并展现出优于无约束模型的能量行为。
原文摘要 · Abstract (English)
Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy. These techniques have proven effective in unconstrained systems as well as those with holonomic constraints. In this work, we adapt LNN techniques to mechanical systems with nonholonomic constraints. We test our approach on some well-known examples with nonholonomic constraints, showing that incorporating these restrictions into the neural network's learning improves not only trajectory estimation accuracy but also ensures adherence to constraints and exhibits better energy behavior compared to the unconstrained counterpart.
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