用柯尔莫哥洛夫算子表示非线性触觉环境，提升力反馈精度与系统稳定性。
Koopman Representation of Nonlinear Virtual Environments in Kinesthetic Haptic Systems
- 采用柯尔莫哥洛夫算子将非线性触觉环境升维为线性表示
- 在杜芬振子环境下实现更精确的力反馈，且稳定分析更宽松
- 适合对触觉系统建模精度和鲁棒性要求高的研究者
在需要高精度力反馈的应用中，渲染非线性虚拟环境（VE）的触觉反馈至关重要。本文提出利用柯尔莫哥洛夫算子来表征与触觉系统交互的非线性虚拟环境。仿真与实验结果表明，该方法能有效表示杜芬振子虚拟环境的非线性动力学特性。多用户研究进一步验证了这一结论。此外，基于柯尔莫哥洛夫表示的闭环（CL）稳定性分析，实现了比传统无源性方法更宽松的稳定性评估。由于使用所有升维状态的线性组合表示非线性，该方法对触觉装置建模不确定性也更具鲁棒性。
原文摘要 · Abstract (English)
Rendering haptic feedback with nonlinear virtual environments (VEs) is important in many applications that require highly accurate force feedback. This paper considers the use of the Koopman operator to represent a nonlinear VE interacting with a haptic system. Simulation and experimental results demonstrated that the proposed method provides an effective representation of the nonlinear dynamics of a Duffing-oscillator VE. A multi-user study further confirmed this conclusion. In addition, a closed-loop (CL) stability analysis is performed leveraging the Koopman representation of the nonlinear VE to access stability of the overall haptic system. This alternative way of representing nonlinear VEs enables a convenient CL stability analysis that is less conservative than traditional passivity-based methods. Since a linear combination of all lifted states is used to represent the nonlinearity, such representation is also more robust to uncertainties in the modeling of the haptic device than a traditional nonlinear model.
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