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This paper explores the application of the Koopman operator to effectively represent nonlinear virtual environments (VEs) in kinesthetic haptic systems, addressing the challenge of rendering accurate force feedback. Through simulations and experiments, the authors demonstrate that their method not only captures the dynamics of a Duffing-oscillator VE but also allows for a less conservative closed-loop stability analysis compared to traditional passivity-based approaches. The findings indicate that this representation is more robust to modeling uncertainties, enhancing the reliability of haptic feedback systems in complex environments.
Leveraging the Koopman operator could revolutionize haptic feedback by enabling more accurate and stable interactions in nonlinear virtual environments.
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.
