基于李群的随机神经网络，精准建模水下车辆运动规律。
Stochastic Physics-Informed Neural Networks on Lie Groups for Learning Underwater Vehicle Dynamics
- 结合李群几何与随机积分，构建物理一致的神经网络架构。
- 在港口浮标环境中实现高精度动态建模，控制更安全可靠。
- 适合水下机器人、海洋智能控制等研究者参考使用。
准确的水下车辆运动模型对于自主执行海底设施巡检和科学采样等任务至关重要。然而，传统基于物理的方法难以刻画此类运动。本文提出一种新颖的数据驱动框架，用于学习具有随机性的水下车辆动力学。利用欧拉-泊松动力学与李群几何，构建了满足物理与几何约束的随机物理信息神经网络。方法采用保结构的随机积分，并基于矩匹配与有限维匹配，确保训练过程的几何一致性。我们在仿真环境及一艘实际航行于港口浮标间的水下车辆上进行了评估。结果表明，该方法能学习到准确且鲁棒的动力学模型，支持复杂海洋环境下的安全模型预测控制。
原文摘要 · Abstract (English)
Accurate models of underwater vehicle motion are needed for autonomous execution of marine tasks like infrastructure inspection and scientific sampling. However, such motion is challenging to characterize using traditional physics-based methods. This paper presents a novel data-driven framework for learning stochastic underwater vehicle dynamics. Using Euler-Poincaré dynamics and the geometry of Lie groups, we develop a stochastic physics-informed neural network architecture that respects the physical and geometric constraints of underwater vehicles. Our approach leverages structure-preserving stochastic integration and builds upon moment matching and finite dimensional matching to ensure geometrically-consistent training. We evaluate our approach in simulation and on an underwater vehicle navigating dock pylons in a harbor environment. The results demonstrate that our method learns accurate and robust dynamics models, enabling safe model-based control in challenging marine environments.
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