Application of Levant´s differentiator for velocity estimation and increased Z-width in haptic interfaces

In this paper, we present results from implementation 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 proposed as a velocity estimator. 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 automated virtual 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.