DocumentCode :
1075281
Title :
Parsimonious Evaluation of Concentric-Tube Continuum Robot Equilibrium Conformation
Author :
Rucker, Daniel Caleb ; Webster, Robert J., III
Author_Institution :
Vanderbilt Univ., Nashville, TN, USA
Volume :
56
Issue :
9
fYear :
2009
Firstpage :
2308
Lastpage :
2311
Abstract :
Dexterous at small diameters, continuum robots consisting of precurved concentric tubes are well-suited for minimally invasive surgery. These active cannulas are actuated by relative translations and rotations applied at the tube bases, which create bending via elastic tube interaction. An accurate kinematic model of cannula shape is required for applications in surgical and other settings. Previous models are limited to circular tube precurvatures, and neglect torsional deformation in curved sections. Recent generalizations account for arbitrary tube preshaping and bending and torsion throughout the cannula, providing differential equations that define cannula shape. In this paper, we show how to simplify these equations using Frenet-Serret frames. An advantage of this approach is the interpretation of torsional components of the preset tube shapes as ldquoforcing functionsrdquo on the cannula´s differential equations. We also elucidate a process for numerically solving the differential equations, and use it to produce simulations illustrating the implications of torsional deformation and helical tube shapes.
Keywords :
biology computing; medical robotics; Frenet-Serret frames; cannula differential equations; concentric-tube continuum robot equilibrium conformation; forcing functions; helical tube shapes; parsimonious evaluation; torsional components; torsional deformation; Active shape model; Deformable models; Differential equations; Kinematics; Laser surgery; Medical robotics; Medical simulation; Minimally invasive surgery; Robotics and automation; Robots; Spine; Active cannula; continuum robot; medical robot; snake-like robot; Algorithms; Biomedical Engineering; Catheterization; Mechanical Phenomena; Models, Theoretical; Robotics; Surgical Procedures, Minimally Invasive;
fLanguage :
English
Journal_Title :
Biomedical Engineering, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9294
Type :
jour
DOI :
10.1109/TBME.2009.2025135
Filename :
5075590
Link To Document :
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