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Delay-Dependent Stability Analysis in Haptic Rendering

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Abstract

Nowadays haptic devices have lots of applications in virtual reality systems. While using a haptic device, one of the main requirements is the stable behavior of the system. An unstable behavior of a haptic device may damage itself and even may hurt its operator. Stability of haptic devices in the presence of inevitable time delay in addition to a suitable zero-order hold is studied in the presented paper, using two different methods. Both presented methods are based on Lyapunov-Krazuvskii functional. In the first method, a model transform is performed to determine the stability boundary, while the second approach is based on Free Weighing Matrices (FWMs). Delay-dependent stability criteria are determined by solving Linear Matrix Inequalities (LMIs). Results of these two methods are compared with each other and verified by simulations as well as experiments on a KUKA Light Weight Robot 4 (LWR4). It is concluded that using free weighing matrices leads to more unknown parameters and needs more calculation, but its results are less conservative.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

    Ahmad Mashayekhi & Saeed Behbahani

  2. CREATE Consortium, PRISMA Laboratory, Department of Electrical Engineering and Information Technology, University of Naples Federico II, 80125, Naples, Italy

    Fanny Ficuciello & Bruno Siciliano

Authors
  1. Ahmad Mashayekhi
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  2. Saeed Behbahani
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  3. Fanny Ficuciello
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  4. Bruno Siciliano
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Correspondence to Saeed Behbahani.

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Mashayekhi, A., Behbahani, S., Ficuciello, F. et al. Delay-Dependent Stability Analysis in Haptic Rendering. J Intell Robot Syst 97, 33–45 (2020). https://doi.org/10.1007/s10846-019-01017-x

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