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Damping Design for Robot Manipulators

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Human-Friendly Robotics 2022 (HFR 2022)

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 26))

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Abstract

This paper studies the tuning process of controllers for fully actuated manipulators. To this end, we propose a methodology to design the desired damping matrix—alternatively, the derivative gain of a PD controller—of the closed-loop system such that n second-order systems can approximate its behavior with a prescribed damping coefficient, where n denotes the degrees of freedom of the system. The proposed approach is based on the linearization of the closed-loop system around the desired configuration and is suitable for different control approaches, such as PD control plus gravity compensation, impedance control, and passivity-based control. Furthermore, we extensively analyze simulations and experimental results in a cobot.

T. Coleman and G. Franzese: Equal contribution authorship.

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Notes

  1. 1.

    The matrix \(\phi _\texttt{n}\) can be obtained via Cholesky decomposition or singular value decomposition. For further details, we refer the reader to [5].

  2. 2.

    See https://github.com/marcocognetti/FrankaEmikaPandaDynModel.

  3. 3.

    Namely, \(K = \frac{1}{4}K_\texttt{d}\).

  4. 4.

    The code to implement the proposed controller in the Panda robot is available at https://github.com/franzesegiovanni/franka_damping_design.

  5. 5.

    See https://github.com/frankaemika/franka_ros.

References

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Acknowledgments

The authors thank Cosimo Della Santina for the fruitful discussions during the elaboration of this manuscript.

Tomás Coleman’s research is funded by the Netherlands Organization for Scientific Research project Cognitive Robots for Flexible Agro-Food Technology, grant P17-01.

Giovanni Franzese’s research is funded by the European Research Council Starting Grant Teaching Robots Interactively (TERI), project reference 804907.

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Authors and Affiliations

  1. Department of Cognitive Robotics, Delft University of Technology, Delft, The Netherlands

    Tomás Coleman, Giovanni Franzese & Pablo Borja

Authors
  1. Tomás Coleman
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  2. Giovanni Franzese
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  3. Pablo Borja
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Corresponding author

Correspondence to Pablo Borja .

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Editors and Affiliations

  1. Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands

    Pablo Borja

  2. Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands

    Cosimo Della Santina

  3. Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands

    Luka Peternel

  4. Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Elena Torta

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Coleman, T., Franzese, G., Borja, P. (2023). Damping Design for Robot Manipulators. In: Borja, P., Della Santina, C., Peternel, L., Torta, E. (eds) Human-Friendly Robotics 2022. HFR 2022. Springer Proceedings in Advanced Robotics, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-031-22731-8_6

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