通过Lie组进行简单的物理嵌入式学习,用于串行操纵器动态预测的哈密尔顿公式
Fei Wang1, Liping Chen2, Jianwan Ding1
1School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China.
Scientific reports
|September 26, 2025
概括
本研究引入了Symplectic Physics-Embedded Learning (SPEL) 方法用于机器人动态建模,显著减少参数并提高效率. 通过将物理原理集成到神经网络中,SPEL提高了准确性和可解释性.
科学领域:
- 机器人技术 机器人技术 机器人技术
- 机器学习 机器学习
- 控制理论 控制理论
背景情况:
- 精确的动态建模对于先进的机器人控制至关重要.
- 传统方法面临的挑战是操纵非线性复杂性.
- 现有的哈密尔顿神经网络在矩阵约束和验证方面存在局限性.
研究的目的:
- 提出一种Symplectic Physics-Embedded Learning (SPEL) 方法,用于增强串行操纵器的动态建模.
- 通过将物理先验编码到神经网络设计中来解决现有方法的局限性.
- 为了提高物理一致性,减少网络参数,提高计算效率.
主要方法:
- 基于李群哈密尔顿公式开发了SPEL.
- 在神经网络架构中系统地编码了李群对称性和哈密尔顿动态.
- 通过物理驱动的约束,强制减少质量,消散和控制输入矩阵.
- 用可训练参数取代输入独立的矩阵元素以优化网络拓.
主要成果:
- 在操纵器上,SPEL减少了超过52%的参数,并提高了超过75%的计算效率.
- 综合物理嵌入式学习科尔莫戈罗夫-阿诺德网络 (SPEL-KAN) 减少了超过63%的参数,效率提高了39%以上.
- 实现了更高的预测准确度,并保持了物理一致性.
- 在模拟和真实世界机器人系统 (2链,RPR,6-DOF) 上验证.
结论:
- SPEL提供了一种基于物理的方法,用于高效和准确的机器人动态建模.
- 将几何机械原理嵌入到神经网络中,以可解释的预测平衡效率.
- 该方法显著优化了网络拓,并减少了计算负载.
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