运动觉力反馈系统中非线性虚拟环境的库普曼表示
Koopman Representation of Nonlinear Virtual Environments in Kinesthetic Haptic Systems
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中文总结 AI 辅助
该研究将库普曼算子用于表示与力反馈系统交互的非线性虚拟环境，通过仿真、实验及多用户研究验证其有效性，且该方法的闭环稳定性分析保守性更低、鲁棒性更强。
中文摘要 AI 辅助
在许多需要高精度力反馈的应用中，用非线性虚拟环境（VE）渲染力反馈至关重要。本文研究采用库普曼（Koopman）算子表示与力反馈系统交互的非线性虚拟环境。仿真和实验结果表明，所提方法能有效表示杜芬振子（Duffing-oscillator）型虚拟环境的非线性动力学。多用户研究进一步证实了该结论。此外，利用非线性虚拟环境的库普曼表示开展闭环（CL）稳定性分析，以评估整个力反馈系统的稳定性。这种非线性虚拟环境的表示方式可实现便捷的闭环稳定性分析，其保守性低于传统基于无源性的方法。由于采用所有提升状态的线性组合表示非线性，该表示方式相比传统非线性模型，对力反馈设备建模中的不确定性具有更强的鲁棒性。
英文摘要
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.
