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

  • Stanislao GraziosoEmail author
  • Giuseppe Di Gironimo
  • Bruno Siciliano
Conference paper
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 8)


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.


Differential geometry Continuum robotics Kinematics 



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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Stanislao Grazioso
    • 1
    Email author
  • Giuseppe Di Gironimo
    • 1
  • Bruno Siciliano
    • 2
  1. 1.Dipartimento di Ingegneria IndustrialeUniversità degli Studi di Napoli Federico IINapoliItaly
  2. 2.Dipartimento di Ingegneria Elettrica e Tecnologie dell’InformazioneUniversità degli Studi di Napoli Federico IINapoliItaly

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