Koopman Representation of Nonlinear Virtual Environments in Kinesthetic Haptic Systems
arXiv:2608.11461v1 Announce Type: new Abstract: 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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[Submitted on 11 Aug 2026]
Title:Koopman Representation of Nonlinear Virtual Environments in Kinesthetic Haptic Systems
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Abstract: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.
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2608.11461 [cs.RO]
(or arXiv:2608.11461v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2608.11461
arXiv-issued DOI via DataCite (pending registration)
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From: Yanting Zhou [view email] [v1] Tue, 11 Aug 2026 21:55:37 UTC (1,096 KB)
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