This program supports AI startups at any time of the year. Benefit from cutting-edge resources and tailored support to accelerate your technology's development.
Offered by Mila and the Public Policy Forum, this program is designed to equip policy and decision makers with the tools to navigate the opportunities and risks of AI. The next cohort will be held in French on September 1-2, 2026, at Mila.
Connect with a Mila academic advisor and current student-researchers to learn more about Mila's community and how to join us on August 19, 31 and September 11, 2026.
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Rendering haptic feedback with nonlinear virtual environments (VEs) is important in many applications that require highly accurate force fee… (see more)dback. 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.