ACD-EDMD: Analytical Construction for Dictionaries of Lifting Functions in Koopman Operator-Based Nonlinear Robotic Systems
ACD-EDMD: Analytical Construction for Dictionaries of Lifting Functions in Koopman Operator-Based Nonlinear Robotic Systems
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DOI：
10.1109/lra.2021.3133001
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发表时间：
2021-11
影响因子：
5.2
通讯作者：
Lu Shi;Konstantinos Karydis
中科院分区：
文献类型：
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作者：
Lu Shi;Konstantinos Karydis
Koopman算子理论在数据驱动的机器人系统的模型提取、规划和控制方面获得了越来越多的发展。Koopman算子从数据中提取动力学的能力在很大程度上取决于提升函数的适当字典的选择。在这封信中，我们提出了ACD-EDMD，一种新的方法，用于分析构建一系列数据驱动的基于Koopman算子的非线性机器人系统的适当提升函数的字典。这项工作的关键见解是，非线性系统的基本拓扑空间（如其配置空间和工作空间）的信息可以被利用来引导基于Hermite多项式的提升函数的构造。我们表明，所提出的方法导致字典是简单的实现，同时享受可证明的完整性和收敛保证时，观测值加权有界。我们评估ACD-EDMD使用一系列不同的非线性机器人系统在模拟和物理硬件实验（轮式移动的机器人，两个旋转关节的机器人手臂，和软机器人腿）。结果表明，我们的方法导致字典，使高精度的预测，并可以推广到不同的验证集。我们算法的相关GitHub存储库可以在https://github.com/UCR-Robotics/ACD-EDMD上访问。
Koopman operator theory has been gaining momentum for model extraction, planning, and control of data-driven robotic systems. The Koopman operator’s ability to extract dynamics from data depends heavily on the selection of an appropriate dictionary of lifting functions. In this letter, we propose ACD-EDMD, a new method for Analytical Construction of Dictionaries of appropriate lifting functions for a range of data-driven Koopman operator based nonlinear robotic systems. The key insight of this work is that information about fundamental topological spaces of the nonlinear system (such as its configuration space and workspace) can be exploited to steer the construction of Hermite polynomial-based lifting functions. We show that the proposed method leads to dictionaries that are simple to implement while enjoying provable completeness and convergence guarantees when observables are weighted bounded. We evaluate ACD-EDMD using a range of diverse nonlinear robotic systems in both simulated and physical hardware experimentation (a wheeled mobile robot, a two-revolute-joint robotic arm, and a soft robotic leg). Results reveal that our method leads to dictionaries that enable high-accuracy prediction and that can generalize to diverse validation sets. The associated GitHub repository of our algorithm can be accessed at https://github.com/UCR-Robotics/ACD-EDMD.