Complete follow-the-leader kinematics using concentric tube robots
File(s)
Published version
Author(s)
Garriga Casanovas, A
Rodriguez y Baena, F
Type
Journal Article
Abstract
Concentric tube robots offer the capability of follow-the-leader motion, which is desirable when navigating in cluttered environments, such as in minimally invasive surgery or in-situ inspections. The follow-the-leader capabilities identified in the existing literature, however, are limited to trajectories with piecewise constant-curvature segments or piecewise helical segments. A complete study of follow-the-leader kinematics is, therefore, relevant to determine the full potential of these robots, and clarify an open question. In this paper, a general analysis of follow-the-leader motion is presented, and a closed-form solution to the complete set of trajectories where follow-the-leader is possible under the assumption of no axial torsion of the tubes composing the robot is derived. For designs with constant-stiffness tubes, the precurvatures required are found to be either circumference arcs, helices, or deformed helices with exponentially varying curvature magnitude. The analysis developed also elucidates additional motions of interest, such as the combination of follow-the-leader motion in a robot segment with general maneuvers in another part. To determine the applicability of the assumption regarding the tubes’ torsion, the general equilibrium of the robot designs of interest is considered, and a closed-form solution to torsion in two-tube robots with helical precurvatures is derived. Criteria to select a desired torsional behavior are then extracted. This enables one to identify stable trajectories where follow-the-leader is possible, for potential application to minimally invasive surgery. An illustrative case study involving simulation and experiment is conceived using one of these trajectories, and the results are reported, showcasing the research.
Date Issued
2018-01-01
Date Acceptance
2017-11-14
Citation
International Journal of Robotics Research, 2018, 37 (1), pp.197-222
ISSN
0278-3649
Publisher
SAGE Publications
Start Page
197
End Page
222
Journal / Book Title
International Journal of Robotics Research
Volume
37
Issue
1
Copyright Statement
© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage).
License URL
Sponsor
Engineering & Physical Science Research Council (E
Identifier
https://journals.sagepub.com/doi/10.1177/0278364917746222
Grant Number
EP/K503733/1
Subjects
Science & Technology
Technology
Robotics
Concentric tube robots
kinematics
follow-the-leader
CONTINUUM ROBOTS
MODEL
0801 Artificial Intelligence and Image Processing
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status
Published
Date Publish Online
2017-12-28