On the performance of passivity-based control of haptic displays employing levant´s differentiator for velocity estimation

In impedance-type haptic interfaces, encoders are typically employed to provide high resolution position measurements from which velocity is estimated, most commonly via the finite difference method (FDM). This velocity estimation technique performs reliably, unless very fast sampling is required, in which case noise or delay due to filtering of the position signals reduces accuracy in the estimate. Despite this limitation, FDM is attractive because it is a passive process, and therefore the passivity of the overall system can be guaranteed. 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. In this paper, 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.