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Algorithmic Foundations of Robotics X pp 71–87Cite as

Equilibrium Configurations of a Kirchhoff Elastic Rod under Quasi-static Manipulation

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Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 86))

Abstract

Consider a thin, flexible wire of fixed length that is held at each end by a robotic gripper. The curve traced by this wire can be described as a local solution to a geometric optimal control problem, with boundary conditions that vary with the position and orientation of each gripper. The set of all local solutions to this problem is the configuration space of the wire under quasi-static manipulation. We will show that this configuration space is a smooth manifold of finite dimension that can be parameterized by a single chart. Working in this chart—rather than in the space of boundary conditions—makes the problem of manipulation planning very easy to solve. Examples in simulation illustrate our approach.

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Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Timothy Bretl

  2. Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Zoe McCarthy

Authors
  1. Timothy Bretl
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  2. Zoe McCarthy
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Corresponding author

Correspondence to Timothy Bretl .

Editor information

Editors and Affiliations

  1. Associate Professor of Aeronautics and, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Emilio Frazzoli

  2. MIT Comp. Sci. & Artificial Intel. Lab., Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Tomas Lozano-Perez

  3. Robust Robotics Group, Massachusetts Institute of Technology CSAIL, Cambridge, Massachusetts, USA

    Nicholas Roy

  4. Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Daniela Rus

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Bretl, T., McCarthy, Z. (2013). Equilibrium Configurations of a Kirchhoff Elastic Rod under Quasi-static Manipulation. In: Frazzoli, E., Lozano-Perez, T., Roy, N., Rus, D. (eds) Algorithmic Foundations of Robotics X. Springer Tracts in Advanced Robotics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36279-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-36279-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36278-1

  • Online ISBN: 978-3-642-36279-8

  • eBook Packages: EngineeringEngineering (R0)

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