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State convergence theory applied to a nonlinear and delayed telerobotic system

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Abstract

State convergence is a control strategy that was proposed in the early 2000s to ensure stability and transparency in a teleoperation system under specific control gains values. This control strategy has been implemented for a linear system with or without time delay. This paper represents the first attempt at demonstrating, theoretically and experimentally, that this control strategy can also be applied to a nonlinear teleoperation system with \(n\) degrees of freedom and delay in the communication channel. It is assumed that the human operator applies a constant force on the local manipulator during the teleoperation. In addition, the interaction between the remote manipulator and the environment is considered passive. Communication between the local and remote sites is made by means of a communication channel with variable time delay. In this article the theory of Lyapunov–Krasovskii was used to demonstrate that the local–remote teleoperation system is asymptotically stable.

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Acknowledgments

The authors are grateful for the use of the facilities of the Robotics and Automatic Laboratory at the Universidad Politécnica de Madrid and the Laboratorio de Investigación en Biomecánica y Robótica Aplicada at the Pontificia Universidad Católica del Perú. The authors would also like to thank the Spanish government’s CICYT Project Ref. DPI2009-08778 and Comunidad de Madrid’s BOCITY2030-II Ref. P2009/DPI-1559 for their financial support.

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Authors and Affiliations

  1. Departamento de Ingeniería, Pontificia Universidad Católica del Perú, Lima 32, Lima, Peru

    Julio C. Tafur

  2. Centre for Automation and Robotics, Universidad Politécnica de Madrid, 28006, Madrid, Spain

    Cecilia García, Rafael Aracil & Roque Saltaren

  3. Escuela Técnica Superior de Ingeniería y Diseño Industrial, Universidad Politécnica de Madrid, Madrid, Spain

    Cecilia García

Authors
  1. Julio C. Tafur
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  2. Cecilia García
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  3. Rafael Aracil
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  4. Roque Saltaren
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Correspondence to Cecilia García.

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Tafur, J.C., García, C., Aracil, R. et al. State convergence theory applied to a nonlinear and delayed telerobotic system. J Eng Math 91, 193–210 (2015). https://doi.org/10.1007/s10665-014-9739-9

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  • DOI: https://doi.org/10.1007/s10665-014-9739-9

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