Research Papers

Kinematics Modeling of a Notched Continuum Manipulator

[+] Author and Article Information
Zhijiang Du

State Key Laboratory of Robotics and System,
Harbin Institute of Technology,
2 Yikuang Street,
Harbin 150080, China
e-mail: duzj01@hit.edu.cn

Wenlong Yang

State Key Laboratory of Robotics and System,
Harbin Institute of Technology,
2 Yikuang Street,
Harbin 150080, China
e-mail: yangwl@hit.edu.cn

Wei Dong

State Key Laboratory of Robotics and System,
Harbin Institute of Technology,
2 Yikuang Street,
Harbin 150080, China
e-mail: dongwei@hit.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 4, 2014; final manuscript received October 22, 2014; published online April 6, 2015. Assoc. Editor: Robert J. Wood.

J. Mechanisms Robotics 7(4), 041017 (Nov 01, 2015) (9 pages) Paper No: JMR-14-1125; doi: 10.1115/1.4028935 History: Received June 04, 2014; Revised October 22, 2014; Online April 06, 2015

In this paper, the kinematics modeling of a notched continuum manipulator is presented, which includes the mechanics-based forward kinematics and the curve-fitting-based inverse kinematics. In order to establish the forward kinematics model by using Denavit–Hartenberg (D–H) procedure, the compliant continuum manipulator featuring the hyper-redundant degrees of freedom (DOF) is simplified into finite discrete joints. Based on that hypothesis, the mapping from the discrete joints to the distal position of the continuum manipulator is built up via the mechanics model. On the other hand, to reduce the effect of the hyper-redundancy for the continuum manipulator's inverse kinematic model, the “curve-fitting” approach is utilized to map the end position to the deformation angle of the continuum manipulator. By the proposed strategy, the inverse kinematics of the hyper-redundant continuum manipulator can be solved by using the traditional geometric method. Finally, the proposed methodologies are validated experimentally on a triangular notched continuum manipulator which illustrates the capability and the effectiveness of our proposed kinematics for continuum manipulators and also can be used as a generic method for such notched continuum manipulators.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Robinson, G., and Davies, J. B. C., 1999, “Continuum Robots. A State of the Art,” IEEE International Conference on Robotics and Automation (ICRA'99), Detroit, MI, May 10–15, Vol. 4, pp. 2849–2854. [CrossRef]
Webster, III, R. J., and Jones, B. A., 2010, “Design and Kinematics Modeling of Constant Curvature Continuum Robots: A Review,” Int. J. Robot. Res., 29(13), pp. 1661–1683. [CrossRef]
Dogangil, G., Davies, B. L., and Rodriguez y Baena, F., 2010, “A Review of Medical Robotics for Minimally Invasive Soft Tissue Surgery,” Proc. Inst. Mech. Eng., Part H, 224(5), pp. 653–679. [CrossRef]
Dumpert, J., Lehman, A. C., Wood, N. A., Oleynikov, D., and Farritor, S. M., 2009, “Semi-Autonomous Surgical Tasks Using a Miniature In Vivo Surgical Robot,” 31st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2009), Minneapolis, MN, Sept. 3–6, pp. 266–269. [CrossRef]
Ding, J. N., Xu, K., Goldman, R., Allen, P., Fowler, D., and Simaan, N., 2010, “Design, Simulation and Evaluation of Kinematic Alternatives for Insertable Robotic Effectors Platforms in Single Port Access Surgery,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 1053–1058. [CrossRef]
Suzuki, N., Hattori, A., Tanoue, K., Ieiri, S., Konishi, K., Tomikawa, M., Kenmotsu, H., and Hashizume, M., 2010, “Scorpion Shaped Endoscopic Surgical Robot for NOTES and SPS With Augmented Reality Functions,” 5th International Workshop Medical Imaging and Augmented Reality (MIAR 2010), Beijing, China, Sept. 19–20, pp. 541–550. [CrossRef]
Rentschler, M. E., Dumpert, J., Platt, S. R., Farritor, S. M., and Oleynikov, D., 2002, “Natural Orifice Surgery With an Endoluminal Mobile Robot,” Surg. Endoscopy, 21(7), pp. 1212–1215. [CrossRef]
Buckingham, R., 1973, “Snake Arm Robots,” Industrial Robot, 29(3), pp. 242–245. [CrossRef]
Mochiyama, H., 2011, “Whole-Arm Impedance of a Serial-Chain Manipulator,” IEEE International Conference on Robotics and Automation (ICRA), Seoul, South Korea, May 21–26, pp. 2223–2228. [CrossRef]
Neppalli, S., Csencsits, M. A., Jones, B. A., and Walker, I. D., 2009, “Closed-Form Inverse Kinematics for Continuum Manipulators,” Adv. Rob., 23(15), pp. 2077–2091. [CrossRef]
Karpinska, J., and Tchon, K., 2012, “Performance-Oriented Design of Inverse Kinematics Algorithms: Extended Jacobian Approximation of the Jacobian Pseudo-Inverse,” ASME J. Mech. Rob., 4(2), p. 021008. [CrossRef]
Yahya, S., Moghawemi, M., and Mohamed, H. A. F., 2011, “Geometrical Approach of Planar Hyper-Redundant Manipulators: Inverse Kinematics, Path Planning, and Workspace,” Simul. Modell. Pract. Theory, 19(12), pp. 406–422. [CrossRef]
Perez, A., and McCarthy, J. M., 2005, “Sizing a Serial Chain to Fit a Task Trajectory Using Clifford Algebra Exponentials,” IEEE International Conference on Robotics and Automation (ICRA), Barcelona, Spain, April 18–22, pp. 4709–4715. [CrossRef]
Chirikjian, G. S., and Burdick, J. W., 1994, “A Modal Approach to Hyper-Redundant Manipulator Kinematics,” IEEE Trans. Rob. Autom., 10(3), pp. 343–354. [CrossRef]
Cheng, W.-B., Song, K.-Y., Di, Y.-Y., Zhang, E. M., Qian, Z.-Q., Kanagaratnam, S., Moser, M. A. J., Luo, W.-L., and Zhang, W.-J., 2012, “Kinematic Model of Colonoscope and Experimental Validation,” J. Med. Biol. Eng., 33(3), pp. 337–342. [CrossRef]
Xia, Y., and Wang, J., 2001, “A Dual Neural Network for Kinematics Control of Redundant Robot Manipulators,” IEEE Trans. Syst., Man, Cybernetics, Part B, 31(1), pp. 147–154. [CrossRef]
Köker, R., 2013, “A Genetic Algorithm Approach to a Neural-Network-Based Inverse Kinematics Solution of Robotic Manipulators Based on Error Minimization,” Inf. Sci., 222, pp. 528–543. [CrossRef]
Ozgoren, M. K., 2013, “Optimal Inverse Kinematic Solutions for Redundant Manipulators by Using Analytical Methods to Minimize Position and Velocity Measures,” ASME J. Mech. Rob., 5(3), p. 031009. [CrossRef]
Camarillo, D. B., Milne, C. F., Carlson, C. R., Zinn, M. R., and Salisbury, J. K., 2008, “Mechanics Modeling of Tendon-Driven Continuum Manipulators,” IEEE Trans. Rob., 24(6), pp. 1262–1273. [CrossRef]
Simaan, N., Taylor, R., and Flint, P., 2004, “A Dexterous System for Laryngeal Surgery,” IEEE International Conference Robotics and Automation (ICRA '04), New Orleans, LA, Apr. 26–May 1, pp. 351–357. [CrossRef]
Kutzer, M. D. M., Segreti, S. M., Brown, C. Y., Taylor, R. H., Mears, S. C., and Armand, M., 2011, “Design of a New Cable-Driven Manipulator With a Large Open Lumen: Preliminary Applications in the Minimally Invasive Removal of Osteolysis,” IEEE International Conference Robotics and Automation (ICRA), Shanghai, China, May 9–13, pp. 2913–2920. [CrossRef]
Murphy, R. J., Moses, M. S., Kutzer, M. D. M., Chirikjian, G. S., and Armand, M., 2013, “Constrained Workspace Generation for Snake-Like Manipulator With Applications to Minimally Invasive Surgery,” IEEE International Conference Robotics and Automation (ICRA), Karlsruhe, Germany, May 6–10, pp. 5321–5327. [CrossRef]
Hannan, M. A., and Walker, I. D., 2003, “Kinematics and the Implementation of an Elephant's Trunk Manipulator and Other Continuum Style Robots,” J. Rob. Syst., 20(2), pp. 45–63. [CrossRef]
Giorelli, M., Renda, F., Calisti, M., Arienti, A., Ferri, G., and Laschi, C., 2012, “A Two Dimensional Inverse Kinetics Model of a Cable Driven Manipulator Inspired by the Octopus Arm,” IEEE International Conference Robotics and Automation (ICRA), Saint Paul, MN, May 14–18, pp. 3819–3824. [CrossRef]
Godage, I. S., Branson, D. T., Guglielmino, E., Medrano-Cerda, G. A., and Caldwell, D. G., 2011, “Shape Function-Based Kinematics and Dynamics for Variable Length Continuum Robotic Arms,” IEEE International Conference Robotics and Automation (ICRA), Shanghai, China, May 9–13, pp. 452–457. [CrossRef]
Kang, R., Branson, D. T., Zheng, T., Guglielmino, E., and Caldwell, D. G., 2013, “Design, Modeling and Control of a Pneumatically Actuated Manipulator Inspired by Biological Continuum Structures,” Bioinspiration & Biomimetics, 8(3), p. 036008. [CrossRef]
Burgner, J., Rucker, D. C., Gilbert, H. B., Swaney, P. J., Russell, P. T., Weaver, K. D., and Webster, III, R. J., 2013, “A Telerobotic System for Transnasal Surgery,” IEEE/ASME Trans. Mechatronics, 19(3), pp. 996–1006. [CrossRef]
Lock, J., Laing, G., Mahvash, M., and Dupont, P. E., 2010, “Quasistatic Modeling of Concentric Tube Robots With External Loads,” IEEE/RSJ International Conference Intelligent Robots and Systems (IROS), Taipei, Taiwan, Oct. 18–22, pp. 2325–2332. [CrossRef]
Yang, W., Dong, W., and Du, Z., 2013, “Mechanics-Based Kinematics Modeling of a Continuum Manipulator,” IEEE/RSJ International Conference Intelligent Robots and Systems (IROS), Tokyo, Nov. 3–7, pp. 5052–5058. [CrossRef]
Han, S. M., Benaroya, H., and Wei, T., 1999, “Dynamics of Transversely Vibrating Beams Using Four Engineering Theories,” J. Sound Vib., 225(5), pp. 935–988 [CrossRef].
Luo, Y., 2008, “An Efficient 3D Timoshenko Beam Element With Consistent Shape Functions,” Adv. Theor. Appl. Mech., 1(3), pp. 95–106. http://www.m-hikari.com/atam/atam2008/atam1-4-2008/luoATAM1-4-2008-1
Cowper, G. R., 1966, “The Shear Coefficient in Timoshenko's Beam Theory,” ASME J. Appl. Mech., 33(2), pp. 335–340. [CrossRef]
Melosh, R. J., 1963, “Basis for Derivation of Matrices for the Direct Stiffness Method,” AIAA J., 1(7), pp. 1631–1637. [CrossRef]


Grahic Jump Location
Fig. 1

Prototype of the continuum manipulator featuring the triangular notches

Grahic Jump Location
Fig. 2

(a) CAD model and the anticipated bending on the bending plane. (b) Analysis of VSU and coordinate assignment.

Grahic Jump Location
Fig. 3

Force analysis of upper and lower beam segment's combinations

Grahic Jump Location
Fig. 4

A representation of beam index in the mechanics model and schematic drawing of the continuum manipulator and the bending arm kinematics

Grahic Jump Location
Fig. 5

The discretely date and fitting curve of mapping deformation angle and corresponding position

Grahic Jump Location
Fig. 6

(a) The setup for deformation angle test of the continuum manipulator prototype. (b) The setup for distal position test of the continuum manipulator prototype.

Grahic Jump Location
Fig. 7

The comparison of theoretical position value with experimental measured position

Grahic Jump Location
Fig. 8

The comparison of theoretical angle with experimental input value




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In