Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems
Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems
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DOI：
10.1109/tro.2021.3076581
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发表时间：
2021-12-01
影响因子：
7.8
通讯作者：
Murphey, Todd D.
中科院分区：
文献类型：
--
作者：
Mamakoukas, Giorgos;Castano, Maria L.;Murphey, Todd D.
本文提出了一种可推广的方法，用于数据驱动的非线性动态识别，该方法根据预测范围和系统状态导数的大小来限制模型误差。使用高阶导数的一般非线性动力学，不需要知道，我们构建了一个Koopman算子为基础的线性表示，并利用泰勒级数精度分析，推导出一个误差界。由此产生的误差公式用于选择基函数中的导数的阶数，并使用可以在真实的时间中计算的闭合形式的表达式来获得数据驱动的Koopman模型。使用倒立摆系统，我们说明了鲁棒性的误差界给定的噪声测量的未知动态，其中的衍生物的数值估计。当与控制相结合时，非线性系统的Koopman表示比竞争的非线性建模方法（如SINDy和NARX）具有更好的性能。此外，作为一个线性模型，Koopman方法本身很容易有效的控制设计工具，如线性二次调节器，而其他建模方法需要非线性控制方法。通过对尾部驱动机器鱼控制的仿真和实验结果进一步证明了该方法的有效性。实验结果表明，所提出的数据驱动控制方法优于一个调整的比例-积分-微分控制器和在线更新的数据驱动模型显着提高性能的存在未建模的流体扰动。这篇文章是补充与视频可在https://youtu.be/9_wx0tdDta0。
This article presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using higher order derivatives of general nonlinear dynamics that need not be known, we construct a Koopman-operator-based linear representation and utilize Taylor series accuracy analysis to derive an error bound. The resulting error formula is used to choose the order of derivatives in the basis functions and obtain a data-driven Koopman model using a closed-form expression that can be computed in real time. Using the inverted pendulum system, we illustrate the robustness of the error bounds given noisy measurements of unknown dynamics, where the derivatives are estimated numerically. When combined with control, the Koopman representation of the nonlinear system has marginally better performance than competing nonlinear modeling methods, such as SINDy and NARX. In addition, as a linear model, the Koopman approach lends itself readily to efficient control design tools, such as linear-quadratic regulator, whereas the other modeling approaches require nonlinear control methods. The efficacy of the approach is further demonstrated with simulation and experimental results on the control of a tail-actuated robotic fish. Experimental results show that the proposed data-driven control approach outperforms a tuned proportional-integral-derivative controller and that updating the data-driven model online significantly improves performance in the presence of unmodeled fluid disturbance. This article is complemented with a video available at https://youtu.be/9_wx0tdDta0.