Spatial continuum models of rods undergoing large deformation and inflation

IEEE Transactions on Robotics

Volumn 29, Issue 2, 2013, Pages 297-307

  Tunay, Ilker ^a  

^a Stereotaxis Inc   (United States)

Author keywords

Animation and simulation; continuum robots; Cosserat rods; finite deformation elasticity; flexible arms; medical robots and systems; soft robots

Indexed keywords

ANIMATION AND SIMULATIONS; CONTINUUM ROBOT; COSSERAT ROD; FINITE DEFORMATION ELASTICITY; FLEXIBLE ARM; MEDICAL ROBOTS AND SYSTEMS; SOFT ROBOT;

ANIMATION; COMPUTER SIMULATION; CONTINUUM MECHANICS; DEFORMATION; ELASTICITY; FLEXIBLE MANIPULATORS; ROBOTS; THREE DIMENSIONAL COMPUTER GRAPHICS;

FINITE ELEMENT METHOD;

EID: 84876138713     PISSN: 15523098     EISSN: None     Source Type: Journal    
DOI: 10.1109/TRO.2012.2232532     Document Type: Article

References (33)

1. S. Antman, Nonlinear Problems of Elasticity, 2nd ed. New York: Springer-Verlag, 2005.
2. N.Auciello andM.DeRosa, "Free vibrations of circular arches:Areview," J. Sound Vibration, vol. 176, no. 4, pp. 433-458, 1994.
3. J. Simo, "A finite strain beam formulation. The three dimensional dynamic problem-Part I," Comput. Meths. Appl. Mech. Eng., vol. 49, pp. 55-70, 1985. (Pubitemid 15514250)
4. W. Lawton, R. Raghavan, S. Ranjan, and R. Viswanathan, "Ribbons and groups: A thin rod theory for catheters and filaments," J. Phys. A, vol. 32, pp. 1709-1735, 1999.
5. S. Kehrbaum and J. Maddocks, "Elastic rods, rigid bodies, quaternions and the last quadrature," Philosoph. Trans. Royal Soc. London, Ser. A (Math. Phys. Eng. Sci.), vol. 355, pp. 2117-2136, 1997.
6. E. Celledoni and N. Safstrom, "A Hamiltonian and multi-Hamiltonian formulation of a rod model using quaternions," Comput. Meth. Appl. Mech. Eng., vol. 199, pp. 2813-2819, 2010.
7. P. Dupont, J. Lock, B. Itkowitz, and E. Butler, "Design and control of concentric-tube robots," IEEE Trans. Robot., vol. 26, no. 2, pp. 209-25, Apr. 2010.
8. D. Rucker, B. Jones, and R. J.Webster, "A geometrically exact model for externally loaded concentric-tube continuum robots," IEEE Trans. Robot., vol. 26, no. 5, pp. 769-780, Oct. 2010.
9. D. C. Rucker and R. J. Webster, "Statics and dynamics of continuum robots with general tendon routing and external loading," IEEE Trans. Robot., vol. 27, no. 6, pp. 1033-1044, Dec. 2011.
10. D. Trivedi, A. Lotfi, and C. Rahn, "Geometrically exact models for soft robotic manipulators," IEEE Trans. Robot., vol. 24, no. 4, pp. 773-780, Aug. 2008.
11. M. Mahvash and P. Dupont, "Stiffness control of surgical continuum manipulators," IEEE Trans. Robot., vol. 27, no. 2, pp. 334-345, Apr. 2011.
12. I. Tunay, "Distributed parameter statics of magnetic catheters," in Proc. 33rd Annu. Int. Conf. IEEE Eng. Med. Biol. Soc., Boston, MA, Sep. 2011, pp. 8344-8347.
13. J. Spillmann and M. Teschner, "CORDE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects," presented at the Symp. Comput. Animat., San Diego, CA, Aug. 2007.
14. H. Lang, J. Linn, and M. Arnold, "Multibody dynamics simulation of geometrically exact Cosserat rods," presented at the Multibody Dynam., Warsaw, Poland, Jun. 2009.
15. K. Chandrasekhar, S. Mukherjee, J. Paci, and G. Schatz, "An atomisticcontinuum Cosserat rod model of carbon nanotubes," J. Mech. Phys. Solids, vol. 57, pp. 932-958, 2009.
16. B. Jones, R. Gray, and K. Turlapati, "Three dimensional statics for continuum robotics," presented at the Int. Conf. Intell. Robot. Syst., St. Louis, MO, Oct. 2009, pp. 2659-2664.
17. T. Healey and P. Mehta, "Straightforward computation of spatial equilibria of geometrically exact Cosserat rods," Int. J. Bifurc. Chaos, vol. 15, no. 3, pp. 949-965, Mar. 2005. (Pubitemid 40878392)
18. I. Romero and F. Armero, "An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics," Int. J. Numer. Meth. Eng., vol. 54, pp. 1683-1716, 2002. (Pubitemid 34850642)
19. W. Lawton, R. Raghavan, S. Ranjan, and R. Viswanathan, "Tubes in tubes: Catheter navigation in blood vessels and its applications," Int. J. Solids Struct., vol. 37, pp. 3031-3054, 2000. (Pubitemid 30557513)
20. I. Tunay, S.-Y.Yoon, K.Woerner, and R.Viswanathan, "Vibration analysis and control ofmagnet positioner using curved-beam models," IEEE Trans. Control Syst. Technol., vol. 17, no. 6, pp. 1415-1423, Nov. 2009.
21. J. Park and W.-K. Chung, "Geometric integration on Euclidean group with application to articulated multibody systems," IEEE Trans. Robot., vol. 21, no. 5, pp. 850-863, Oct. 2005. (Pubitemid 41489337)
22. J. Simo and L. Vu-Quoc, "A three dimensional finite-strain rod model-Part II," Comput. Meths. Appl. Mech. Eng., vol. 58, pp. 79-116, 1986. (Pubitemid 17461054)
23. T. Healey, "Material symmetry and chirality in nonlinearly elastic rods," Math. Mech. Solids, vol. 7, pp. 405-420, 2002.
24. T. Lauderdale and O. O'Reilly, "On transverse and rotational symmetries in elastic rods," J. Elastic., vol. 82, no. 1, pp. 31-47, Jan. 2006.
25. J. Kuipers, Quaternions and Rotation Sequences: A Primer With Applications To Orbits, Aerospace, and Virtual Reality. Princeton, NJ: Princeton Univ. Press, 1999.
26. S. P. Bhat and D. S. Bernstein, "A topological obstruction to continuous global stabilization of rotationalmotion and the unwinding phenomenon," Syst. Control Lett., vol. 39, pp. 63-70, 2000.
27. L. Meunier, G. Chagnon, D. Favier, L. Orǵeas, and P. Vacher, "Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber," Polymer Test., vol. 27, pp. 765-777, 2008.
28. D. G. Luenberger, Optimization by Vector Space Methods. NewYork: Wiley, 1969.
29. T. M. Apostol, Mathematical Analysis, 2nd ed. Reading, MA: Addison-Wesley, 1974.
30. COMSOL solid mechanics module. (2011). [Online]. Available: http://www.comsol.com/products/structural-mechanics
31. E. Oberg, F. Jones, H. Horton, and H. Ryffel, Machinery's Handbook, 23rd ed. New York: Industrial Press, 1990.
32. I. Tunay, "Position control of catheters using magnetic fields," presented at the IEEE Int. Conf.Mechatron., Istanbul, Turkey, Jun. 2004, pp. 392-397. (Pubitemid 40266808)
33. I. Tunay, "Modeling magnetic catheters in external fields," presented at the 26th Annu. Int. Conf. IEEE Eng. Med. Biol. Soc., San Francisco, CA, Sep. 2004, vol. 3, pp. 2006-2009. (Pubitemid 40035807)