Koopman Representation of Nonlinear Virtual Environments in Kinesthetic Haptic Systems
Yanting Zhou, Jozsef Kovecses, James Richard Forbes
AI summary
Problem
Accurately simulating nonlinear virtual environments is essential for realistic haptic feedback but complicates system stability analysis and slows computation. Traditional passivity-based stability criteria are overly conservative and sacrifice transparency.
Approach
The authors apply the Koopman operator framework to lift the nonlinear dynamics of a virtual environment into a higher-dimensional linear space, allowing the use of established linear system tools for both rendering and stability analysis.
Key results
- Accurate simulation and experimental reproduction of nonlinear Duffing-oscillator dynamics
- Multi-user study confirms highly similar perceived force feedback to baseline nonlinear models
- Closed-loop stability analysis via eigenvalue checking proves less conservative than passivity-based methods
- Enhanced robustness to haptic device modeling uncertainties compared to traditional nonlinear representations
Why it matters
This method enables safer, more transparent, and computationally efficient haptic rendering for high-fidelity applications like surgical simulation and rehabilitation.
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 experimen- tal 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.