用物理约束提升软体机器人模拟精度，小数据下效果显著
Physics-informed Split Koopman Operators for Data-efficient Soft Robotic Simulation
- 结合连续与离散柯尔莫哥洛夫算子，利用轨迹和相空间数据
- 小样本下形状误差降低数个数量级，优于传统方法
- 适合有部分物理知识的系统，降低数据采集成本
柯尔莫哥洛夫算子理论提供了一种强大的数据驱动方法，可在线性框架中建模非线性动力系统，相比计算昂贵且高度非线性的物理仿真更具优势。然而，用于软体机器人的柯尔莫哥洛夫算子模型维度极高，需大量数据才能准确建模。受机器学习中物理信息方法启发，我们提出一种新型物理信息柯尔莫哥洛夫算子识别方法，在小样本条件下显著提升模拟精度。通过斯特朗分裂（Strang splitting），该方法同时利用连续与离散柯尔莫哥洛夫算子近似，从轨迹和相空间数据中提取信息。在腱驱动软体机械臂上验证，相较于标准方法，形状误差降低数个数量级。该方法有望大幅降低具有部分已知物理模型系统的柯尔莫哥洛夫算子数据需求，从而减少数据获取成本。
原文摘要 · Abstract (English)
Koopman operator theory provides a powerful data-driven technique for modeling nonlinear dynamical systems in a linear framework, in comparison to computationally expensive and highly nonlinear physics-based simulations. However, Koopman operator-based models for soft robots are very high dimensional and require considerable amounts of data to properly resolve. Inspired by physics-informed techniques from machine learning, we present a novel physics-informed Koopman operator identification method that improves simulation accuracy for small dataset sizes. Through Strang splitting, the method takes advantage of both continuous and discrete Koopman operator approximation to obtain information both from trajectory and phase space data. The method is validated on a tendon-driven soft robotic arm, showing orders of magnitude improvement over standard methods in terms of the shape error. We envision this method can significantly reduce the data requirement of Koopman operators for systems with partially known physical models, and thus reduce the cost of obtaining data.
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。