Volume 17, Issue 10 (1-2018)                   Modares Mechanical Engineering 2018, 17(10): 367-374 | Back to browse issues page

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Mashayekhi A, Behbahani S, Ficuciello F, Siciliano B. A novel Lyapunov function for stability of haptic device in simulating virtual objects. Modares Mechanical Engineering. 2018; 17 (10) :367-374
URL: http://mme.modares.ac.ir/article-15-3853-en.html
1- Department of Mechanical Engineering, Isfahan, Iran
2- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan Iran.
3- Department of Electrical Engineering and Information Technology, University of Napoli Federico II, Naples, Italy
Abstract:   (2426 Views)
One of the main challenges of simulating virtual objects by haptic devices is instability, especially in simulating stiff objects. In this paper, a stability criterion for a haptic device is derived using Lyapunov approach. The haptic device is modeled as a mass and viscous friction, which has to simulate the touching a virtual environment (VE) with specified stiffness and damping. Dynamic equations and state-space equations are derived with assumption of small values of sampling time, time delay and virtual damping. A Lyapunov function is proposed, consisting of summation of kinetic and potential energy of the system, plus two unknown terms. Each one of these two unknown terms is a function of one system states (i.e. position and velocity). These two functions are determined so that, from one side the Lyapunov function be positive definite, and from the other side the stability criterion is reached with putting time derivation of the Lyapunov function negative. The stability condition determined by this method is a linear criterion between maximum permissible virtual stiffness, virtual damping of the VE, physical damping of the haptic device, sampling time and time delay, and is consistent with the results of previous researches with linear methods. The importance of the presented analysis in this paper is that this method can be extended by adding new terms to the Lyapunov function, to remove some limitations and to take into account nonlinear effects. Presented criterion and its results are verified by experiments on KUKA robot.
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Article Type: Research Article | Subject: Mechatronics
Received: 2017/08/19 | Accepted: 2017/09/24 | Published: 2017/10/27

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