Augmented observer approach for high-impedance haptic system with time delay

Among others measures of performance, a haptic device may be characterized by its behavior in the implementation of a virtual wall in terms of the biggest value of the virtual stiffness leaving stable the device. This value depends on many factors including time delays and the virtual world implementation. The paper proposes a new architecture for this latter one based on the use of an augmented state observer which contributes to improve 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, a new LMI criterion for the stability of discrete-time systems with time-varying delay is given. Some numerical simulation results are included to prove the effectiveness of the proposed approach.