In this study, we demonstrate application of Levant's differentiator for velocity estimation from optical encoder readings. Levant's differentiator is a sliding mode control theory-based real-time differentiation algorithm. The application of the technique allows stable implementation of higher stiffness virtual walls as compared to using the common finite difference method (FDM) cascaded with low-pass filters for velocity estimation. A single degree-of-freedom(DOF) linear haptic device is used as a test bed and an automatedvirtual wall hitting task is implemented to experimentally demonstrate that it is possible to extend the impedance-width (or Z-width) of a haptic interface via Levant's differentiator.

Levant's differentiator is a viable alternative to FDM, and exhibits increased accuracy in velocity estimation at high sample rates compared to FDM. However, the passivity of this nonlinear velocity estimation technique cannot be shown using conventional methods. We employ a time domain passivity framework to analyze and enforce passive behavior of Levant's differentiator for haptic displays in discrete time. The performance of this approach is explored both in simulation and experimentally on a custom made one degree-of-freedom haptic interface. Results demonstrate the effectiveness of the time domain passivity approach for compensating the active behavior observed with use of Levant's differentiator for velocity estimation.