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Passivity and Absolute Stability Analysesof Trilateral Haptic Collaborative Systems

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Abstract

Trilateral haptic systems can be modeled as three-port networks. Analysis of coupled stability of a three-port network can be accomplished in either the passivity or the absolute stability frameworks assuming all three ports are connected to passive but otherwise unknown terminations. This paper first introduces our recent results in terms of extending Raisbecks passivity criterion and Llewellyns absolute stability criterion to general three-port networks – both criteria are founded on the properties of a positive-real Hermitian matrix. Next, we show that the absolute stability criterion is less conservative than the passivity criterion. Then, to show how the two criteria may be utilized at the system design stage, we apply them to the problem of designing controllers for a dual-user haptic teleoperation system and a triple-user collaborative haptic virtual environment. Using the two criteria, controllers are then designed and compared in terms of conservatism in simulations and experiments.

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Authors and Affiliations

  1. School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China

    Jian Li & Qi Huang

  2. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, T6G 2V4, Canada

    Jian Li, Mahdi Tavakoli & Victor Mendez

Authors
  1. Jian Li
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  2. Mahdi Tavakoli
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  3. Victor Mendez
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  4. Qi Huang
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Correspondence to Mahdi Tavakoli.

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Li, J., Tavakoli, M., Mendez, V. et al. Passivity and Absolute Stability Analysesof Trilateral Haptic Collaborative Systems. J Intell Robot Syst 78, 3–20 (2015). https://doi.org/10.1007/s10846-014-0049-2

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  • DOI: https://doi.org/10.1007/s10846-014-0049-2

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