Delay-Dependent Stability Analysis in Haptic Rendering

Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality

“…Hence, the dynamic model of the haptic device can be linearized near its working point, and the device is considered to be a one degree of freedom (1-DOF) system with an equivalent mass of m with b as viscous friction. A structure diagram of a 1-DOF haptic device with an operator's hand is depicted in Figure 1 [4]. In this figure, F VE is the force of the virtual environment, and m, t d , K, B, c and b are mass, sampling time, time delay, virtual stiffness, virtual damping, coulomb friction and viscous friction of the haptic device, respectively.…”

“…Haptic devices are widely used in virtual reality systems, such as virtual prototyping [1], teleoperation [2] and human-robot interaction [3]. The haptic system utilizes communication networks to transmit information between the controller and the haptic device, inevitably including time delays [4,5]. These delays degrade the dynamic performance of haptic devices and can even hurt their operator.…”

“…In order to avoid calculating eigenvalue information, time-domain methods based on Lyapunov stability theory are introduced to study the stability of haptic systems. In [4], two methods were proposed to analyze the stability of the haptic system involving the time delay. In the first method of [4], model transform was used to determine the stability boundary, which brings conservatism in the process of defining cross terms, while the second was based on the free-weighing-matrix approach, which introduced free weighting matrices to reduce conservatism of calculation results of the time delay boundary, resulting in a large number of additional decision variables.…”

“…In [4], two methods were proposed to analyze the stability of the haptic system involving the time delay. In the first method of [4], model transform was used to determine the stability boundary, which brings conservatism in the process of defining cross terms, while the second was based on the free-weighing-matrix approach, which introduced free weighting matrices to reduce conservatism of calculation results of the time delay boundary, resulting in a large number of additional decision variables. Then, Mashayekhi et al extended the existing work of [4] by using state-space equations without parameter constraints [11].…”

“…Based on this promotion, any linear model of the operator's hand can be introduced into the stability analysis of haptic systems. The related stability criteria used in [4,11] are conservative, which reduces the accuracy of the stability analysis. Moreover, the above criteria with relatively low conservatism show high calculation complexity, which affects the efficiency of the stability analysis.…”