Elastic Stability of Concentric Tube Robots Subject to External Loads

Concentric tube robots, which are comprised of precurved elastic tubes that are concentrically arranged, are being developed for many medical interventions. The shape of the robot is determined by the rotation and translation of the tubes relative to each other, and also by any external forces appli...

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Bibliographic Details
Published inIEEE transactions on biomedical engineering Vol. 63; no. 6; pp. 1116 - 1128
Main Authors Ha, Junhyoung, Park, Frank C., Dupont, Pierre E.
Format Journal Article
LanguageEnglish
Published United States IEEE 01.06.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Bending
Biomechanical Phenomena
Concentric tube robot
continuum robot
Control theory
Dangerous
elastic stability
Elasticity
Electron tubes
Equipment Design
Kinematics
Loads (forces)
Optimal control
Potential energy
Robotic Surgical Procedures - instrumentation
Robots
Stability
Stability criteria
Translations
Tubes
Utilities
continuum robot
optimal control
elastic stability
Concentric tube robot
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Summary:Concentric tube robots, which are comprised of precurved elastic tubes that are concentrically arranged, are being developed for many medical interventions. The shape of the robot is determined by the rotation and translation of the tubes relative to each other, and also by any external forces applied by the environment. As the tubes rotate and translate relative to each other, elastic potential energy caused by tube bending and twisting can accumulate; if a configuration is not locally elastically stable, then a dangerous snapping motion may occur as energy is suddenly released. External loads on the robot also influence elastic stability. In this paper, we provide a second-order sufficient condition, and also a separate necessary condition, for elastic stability. Using methods of optimal control theory, we show that these conditions apply to general concentric tube robot designs subject to arbitrary conservative external loads. They can be used to assess the stability of candidate robot configurations. Our results are validated via comparison with other known stability criteria, and their utility is demonstrated by an application to stable path planning.
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P. E. Dupont with the Department of Cardiovascular Surgery, Boston Children’s Hospital, Harvard Medical School, Boston, Massachusetts, USA.
F.C. Park were supported in part by the SNU BMRR Center (DAPA-UD130070ID), SNU-IAMD, BK21+, and MI Technology Innovation Program (10048320) with the School of Mechanical Engineering, Seoul National University, Seoul, Korea
J. Ha supported in part by the SNU BMRR Center (DAPA-UD130070ID), SNU-IAMD, BK21+, and MI Technology Innovation Program (10048320) with the Department of Cardiovascular Surgery, Boston Children’s Hospital, Harvard Medical School, Boston, Massachusetts, USA
ISSN:0018-9294
1558-2531
1558-2531
DOI:10.1109/TBME.2015.2483560