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

Abstract

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.

A Human Arm’s Mechanical Impedance Tuning Method for Improving the Stability of Haptic Rendering

“…There was an impedance-type force-feedback architecture using linear matrix inequality (LMI) to improve the stability of haptic systems. 19 Similarly, Liu et al 20 proposed a stability criterion based on LMI to obtain stable haptic systems. A local stiffness matrix is constructed to compute feedback force at a higher update rate for interaction with deformable objects, which removes the trade-off problem of conventional haptic rendering between the stability and performance.…”

Robust Stability Analysis Based on LMI for Haptic Interface Systems with Uncertain Delay

“…Although these passive conditions are almost accepted by many researchers, the passive design is only a very conservative design approach, and the range of stability is generally much larger than that of the passivity [11,12]. Thus, for a stable human-computer interaction, the condition for passivity is only a sufficient but not necessary condition, and seeking for a less conservative stability condition becomes a crucial issue to researchers [13][14][15][16].…”

“…It needs to be emphasized that for most of the control systems, especially for computer control systems, there are usually various time delays due to program calculation, data processing, and communication [15]. Similarly, there are also such delays in the haptic interface systems, which as a major source of instability may not be ignored.…”

“…This system is in fact a typical sampled-data control system with an uncertain time-varying delay; thus, most of the research on such system is based on the discrete time control theory. For instance, based on LMIs, Dang et al give the stability conditions of the haptic interface systems implemented by the virtual wall [2,13,15,17]. In literatures [13,15], observers are also used to directly obtain the states of the haptic device, but the state estimate errors are not included in the Lyapunov-Krasovskii functional and the observer gains cannot be directly obtained by solving the stability criterion in terms of LMIs (linear matrix inequality).…”

“…For instance, based on LMIs, Dang et al give the stability conditions of the haptic interface systems implemented by the virtual wall [2,13,15,17]. In literatures [13,15], observers are also used to directly obtain the states of the haptic device, but the state estimate errors are not included in the Lyapunov-Krasovskii functional and the observer gains cannot be directly obtained by solving the stability criterion in terms of LMIs (linear matrix inequality). Allowing this, a full-order state observer is used in this paper to estimate the states of the haptic device so as to calculate the force feedback [1,3,12].…”