Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Finite element modeling of concentric-tube continuum robots

  • Baek, Changyeob (Department of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Yoon, Kyungho (Institute of Advanced Machines and Design, Seoul National University) ;
  • Kim, Do-Nyun (Department of Mechanical and Aerospace Engineering, Seoul National University)
  • Received : 2015.09.02
  • Accepted : 2015.12.14
  • Published : 2016.03.10
⟨ Previous Next ⟩

Abstract

Concentric-tube continuum robots have formed an active field of research in robotics because of their manipulative exquisiteness essential to facilitate delicate surgical procedures. A set of concentric tubes with designed initial curvatures comprises a robot whose workspace can be controlled by relative translations and rotations of the tubes. Kinematic models have been widely used to predict the movement of the robot, but they are incapable of describing its time-dependent hysteretic behaviors accurately particularly when snapping occurs. To overcome this limitation, here we present a finite element modeling approach to investigating the dynamics of concentric-tube continuum robots. In our model, each tube is discretized using MITC shell elements and its transient responses are computed implicitly using the Bathe time integration method. Inter-tube contacts, the key actuation mechanism of this robot, are modeled using the constraint function method with contact damping to capture the hysteresis in robot trajectories. Performance of the proposed method is demonstrated by analyzing three specifications of two-tube robots including the one exhibiting snapping phenomena while the method can be applied to multiple-tube robots as well.

Keywords

Acknowledgement

Supported by : Center for Advanced Meta-Materials (CAMM), National Research Foundation of Korea (NRF)

References

  1. ADINA R&D (2013), ADINA Theory and Modeling Guide, ADINA R&D, Watertown, MA.
  2. Auricchio, F. and Sacco, E. (1999), "A temperature-depedent beam for shape-memory alloys: constitutive modelling, finite-element implementation and numerical simulations", Comput. Struct., 174, 171-190.
  3. Bathe, K.J. and Bouzinov, P. (1997), "On the constraint function method for contact problems", Comput. Struct., 64, 1069-1085. https://doi.org/10.1016/S0045-7949(97)00036-9
  4. Bathe, K.J. and Baig, M.M.I. (2005), "On a composite implicit time integration procedure for nonlinear dynamics", Comput. Struct., 31-32, 2513-2524.
  5. Bathe, K.J. (2007), "Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme", Comput. Struct., 85, 437-445. https://doi.org/10.1016/j.compstruc.2006.09.004
  6. Bathe, K.J. and Noh, G. (2012), "Insight into an implicit time integration scheme for structural dynamics", Comput. Struct., 98-99, 1-6. https://doi.org/10.1016/j.compstruc.2012.01.009
  7. Burgner, J., Swaney, P.J., Rucker, D.C., Gilbert, H.B., Nill, S.T., Russell, P.T., Weaver, K.D. and Webster, R.J. (2011), "A bimanual teleoperated system for endonasal skull base surgery", Proc. IEEE/RSJ Int. Conf. Intell. Robot. Syst., 2517-2523.
  8. Burgner, J., Swaney, P.J., Lathrop, R.A., Weaver, K.D. and Webster, R.J. (2013), "Debulking from within a robotic steerable cannula for intracerebral hemorrhage evacuation", IEEE Tran. Biomed. Eng., 60, 2567-2575. https://doi.org/10.1109/TBME.2013.2260860
  9. Burgner, J., Rucker, D., Gilbert, H., Swaney, P., Russel, P., Weaver, K. and Webster, R. (2014), "A telerobotic system for transnasal surgery", IEEE/ASME Tran. Mech., 19, 996-1006. https://doi.org/10.1109/TMECH.2013.2265804
  10. Dupont, P.E., Lock, J. and Bulter, E. (2009), "Torsional kinematic model for concentric tube robots", Proc. IEEE Int. Conf. Robot. Autom., Kobe, Japan, 3851-3858.
  11. Dupont, P.E., Lock, J., Itkowitz, B. and Bulter, E. (2010), "Design and control of concentric tube robots", IEEE Tran. Robot., 26, 209-225. https://doi.org/10.1109/TRO.2009.2035740
  12. Gilardi, G. and Sharf, I. (2002), "Literature survey of contact dynamics modeling", J. Mech. Mach. Theory, 37, 1213-1239. https://doi.org/10.1016/S0094-114X(02)00045-9
  13. Kim, D.N. and Bathe, K.J. (2008), "A 4-node 3D-shell element to model shell surface tractions and incompressible behavior", Comput. Struct., 86, 2027-2041. https://doi.org/10.1016/j.compstruc.2008.04.019
  14. Kim, D.N. and Bathe, K.J. (2009), "A triangular six-node shell element", Comput. Struct., 87, 1451-1460. https://doi.org/10.1016/j.compstruc.2009.05.002
  15. Lock, J. and Dupont, P.E. (2011), "Friction modeling in concentric tube robots", Proc. IEEE Int. Conf. Robot. Autom., 1139-1146.
  16. Lee, P.S. and Bathe, K.J. (2004), "Development of MITC isotropic triangular shell finite elements", Comput. Struct., 82, 945-962. https://doi.org/10.1016/j.compstruc.2004.02.004
  17. Lee, Y.G., Yoon, K. and Lee, P.S. (2012), "Improving the MITC3 shell finite element by using the Hellinger-Reissner principle", Comput. Struct., 110-111, 93-106. https://doi.org/10.1016/j.compstruc.2012.07.004
  18. Noh, G., Ham, S. and Bathe, K.J. (2013), "Performance of an implicit time integration scheme in the analysis of wave propagations", Comput. Struct., 123, 93-105. https://doi.org/10.1016/j.compstruc.2013.02.006
  19. Rucker, D.C., Webster, R.J., Chirikjian, G.S. and Cowan, N.J. (2010), "Equilibrium conformations of concentric-tube continuum robots", Int. J. Robot. Res., 29, 1263-1280. https://doi.org/10.1177/0278364910367543
  20. Sears, P. and Dupont, P. (2006), "A steerable needle technology using curved concentric tubes", in Proc. IEEE/RSJ Int. Conf. Intell. Robot. Syst., 2850-2856.
  21. Webster, R.J., Okamura, A.M. and Cowan, N.J. (2006), "Toward active cannulas: Miniature snake-like surgical robots", Proc. IEEE/RSJ Int. Conf. Intell. Robot. Syst., 2857-2863.
  22. Webster, R.J., Romano, J.M. and Cowan, N.J. (2009), "Mechanics of precurved-tube continuum robots", IEEE Tran. Robot., 25, 67-78. https://doi.org/10.1109/TRO.2008.2006868