Experimental study on the stability of an impedance-type force-feedback architecture based on an augmented-state observer for a haptic system under time delay using a LMI approach

One of the most important performance measures of a haptic interface may be characterized by its behaviour in the implementation of a virtual wall in terms of the biggest value of the virtual stiffness that still leaves the device stable. This value depends on many factors including time delays and the virtual world implementation. In this paper we propose a new architecture for this latter factor based on the use of an augmented-state observer which contributes to improving, without additional costs, the performance of a haptic device with respect to the standard implementation based on the use of the backward finite-difference method. In order to compute the stability boundaries of the device in terms of virtual wall parameters, some conditions expressed in terms of LMI (linear matrix inequality) for the stability of discrete-time haptic systems under constant or variable time delay are given. An implementation of a force-feedback haptic test bench is presented. The obtained experimental results confirm the efficiency of the proposed force-feedback architecture with respect to the traditional backward finite-difference method in enlarging the choice for the parameters of the virtual environment for which the haptic system is stable.