DocumentCode :
3675
Title :
Spatial Continuum Models of Rods Undergoing Large Deformation and Inflation
Author :
Tunay, I.
Author_Institution :
Stereotaxis, Inc., St. Louis, MO, USA
Volume :
29
Issue :
2
fYear :
2013
fDate :
Apr-13
Firstpage :
297
Lastpage :
307
Abstract :
Quaternions without unity constraint are used as configuration variables for rotational degrees of freedom of Cosserat rod models, thereby naturally incorporating inflation as well as bending, twisting, extension, and shear deformations of elongate robotic manipulators. The configuration space becomes isomorphic to a subspace of 7-D real-valued functions; thus, an unconstrained local minimizer of total potential energy is a static equilibrium. The ensuing calculus of variations is automated by computer algebra to derive weak-form integral equations that are easily translated to a finite-element package for efficient computation using internal forces. Discontinuities in strain variables are handled in a numerically reliable way. Inextensible, unshearable rod models are derived simply by taking limits of corresponding stiffness parameters. The same procedure facilitates unified software code for both flexible and rigid segments. Simulation experiments with an inflating tube, a helical coil, and a magnetic catheter produce good-quality results and indicate that the computational effort of the proposed method is about two orders of magnitude less than common 3-D finite-element models of large deformation nonlinear elasticity.
Keywords :
bending; coils; control engineering computing; elasticity; finite element analysis; force control; integral equations; manipulators; shear deformation; 3D finite-element model; 7D real-valued function; Cosserat rod model; bending; computer algebra; deformation nonlinear elasticity; elongate robotic manipulator; finite-element package; helical coil; inextensible rod model; inflating tube; inflation; internal force; isomorphic configuration space; magnetic catheter; rotational degrees of freedom; shear deformation; software code; spatial continuum model; static equilibrium; stiffness parameter; strain variable discontinuities; total potential energy; twisting; unconstrained local minimizer; unshearable rod model; weak-form integral equation; Computational modeling; Materials; Mathematical model; Quaternions; Robots; Strain; Vectors; Animation and simulation; Cosserat rods; continuum robots; finite deformation elasticity; flexible arms; medical robots and systems; soft robots;
fLanguage :
English
Journal_Title :
Robotics, IEEE Transactions on
Publisher :
ieee
ISSN :
1552-3098
Type :
jour
DOI :
10.1109/TRO.2012.2232532
Filename :
6407939
Link To Document :
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