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From Differential Geometry of Curves to Helical Kinematics of Continuum Robots Using Exponential Mapping

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Advances in Robot Kinematics 2018 (ARK 2018)

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 8))

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Abstract

Kinematic modeling of continuum robots is challenging due to the large deflections that these systems usually undergone. In this paper, we derive the kinematics of a continuum robot from the evolution of a three-dimensional curve in space. We obtain the spatial configuration of a continuum robot in terms of exponential coordinates based on Lie group theory. This kinematic framework turns out to handle robotic helical shapes, i.e. spatial configurations with constant curvature and torsion of the arm.

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Acknowledgments

This work was partially supported by the FlexARM project, which has received funding from the European Commission’s Euratom Research and Training Programme 2014–2018 under the EUROfusion Engineering Grant EEG-2015/21 “Design of Control Systems for Remote Handling of Large Components” and partially by the RoDyMan project, which has received funding from the European Research Council under Advanced Grant 320992.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federico II, P.le Tecchio 80, 80125, Napoli, Italy

    Stanislao Grazioso & Giuseppe Di Gironimo

  2. Dipartimento di Ingegneria Elettrica e Tecnologie dell’Informazione, Università degli Studi di Napoli Federico II, Via Claudio 21, 80125, Napoli, Italy

    Bruno Siciliano

Authors
  1. Stanislao Grazioso
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  2. Giuseppe Di Gironimo
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  3. Bruno Siciliano
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Corresponding author

Correspondence to Stanislao Grazioso .

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Editors and Affiliations

  1. J. Stefan Institute, Ljubljana, Slovenia

    Jadran Lenarcic

  2. Department of Industrial Engineering, University of Bologna, Bologna, Italy

    Vincenzo Parenti-Castelli

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Grazioso, S., Di Gironimo, G., Siciliano, B. (2019). From Differential Geometry of Curves to Helical Kinematics of Continuum Robots Using Exponential Mapping. In: Lenarcic, J., Parenti-Castelli, V. (eds) Advances in Robot Kinematics 2018. ARK 2018. Springer Proceedings in Advanced Robotics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-93188-3_37

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