Research Papers

An Efficient Static Analysis of Continuum Robots

[+] Author and Article Information
Shahir Hasanzadeh

Department of Mechanical
and Industrial Engineering,
Ryerson University,
Toronto, ON M5B 2K3, Canada
e-mail: shahir.hasanzadeh@ryerson.ca

Farrokh Janabi-Sharifi

Department of Mechanical
and Industrial Engineering,
Ryerson University,
Toronto, ON M5B 2K3, Canada
e-mail: fsharifi@ryerson.ca

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 25, 2013; final manuscript received March 17, 2014; published online April 25, 2014. Assoc. Editor: Philippe Wenger.

J. Mechanisms Robotics 6(3), 031011 (Apr 25, 2014) (5 pages) Paper No: JMR-13-1139; doi: 10.1115/1.4027305 History: Received July 25, 2013; Revised March 17, 2014

An efficient yet accurate model of the continuum robot is the main component for its real-time control, simulation as well as localization. Previous models of the continuum robot, based on rod theory, suffer from high computational burden. The models also require a priori knowledge of the robot environment. This paper presents an efficient static model for the planar continuum robot that experiences external forces at the tip as a result of contact with its surroundings (measured by the built-in force sensors), thus no a priori information about the environment is required. The typical example of such robots is steerable catheters used in medical operations. The proposed approach involves discretizing the robot backbone curve to elastic arc elements. After deriving the equilibrium equations for the infinitesimal elements, a recursive algorithm with the time complexity of O(n) is proposed for realizing the shape of the robot as a result of the external force. Accuracy of the proposed method is evaluated both theoretically and experimentally for a case study, i.e., an intracardiac ablation catheter. Results validate the accuracy and time-efficiency of the proposed approach for real-time applications.

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Sears, P., and Dupont, P., 2006, “A Steerable Needle Technology Using Curved Concentric Tubes,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, October 9–15, pp. 2850–2856. [CrossRef]
Webster, R., Okamura, A. M., and Cowan, N. J., 2006, “Toward Active Cannulas: Miniature Snake-Like Surgical Robots,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, October 9–15, pp. 2857–2863. [CrossRef]
Bailly, Y., and Amirat, Y., 2005, “Modeling and Control of a Hybrid Continuum Active Catheter for Aortic Aneurysm Treatment,” IEEE International Conference on Robotics and Automation (ICRA 2005), Barcelona, Spain, April 18–22, pp. 924–929. [CrossRef]
Chen, G., Pham, M. T., and Redarce, T., 2009, “Sensor-Based Guidance Control of a Continuum Robot for a Semi-Autonomous Colonoscopy,” Rob. Autom. Syst., 57(6), pp. 712–722. [CrossRef]
Ganji, Y., and Janabi-Sharifi, F., 2009, “Catheter Kinematics for Intracardiac Navigation,” IEEE Trans. Biomed. Eng., 56(3), pp. 621–632. [CrossRef] [PubMed]
Dore, A., Smoljkic, G., Poorten, E. V., Sette, M., Sloten, J. V., and Yang, G.-Z., 2012, “Catheter Navigation Based on Probabilistic Fusion of Electromagnetic Tracking and Physically-Based Simulation,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Villamoura, Portugal, October 7–12, pp. 3806–3811. [CrossRef]
Webster, R. J., and Jones, B. A., 2010, “Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review,” Int. J. Robot. Res., 29(13), pp. 1661–1683. [CrossRef]
Rucker, D., and Webster, R., 2011, “Statics and Dynamics of Continuum Robots With General Tendon Routing and External Loading,” IEEE Trans. Rob., 27(6), pp. 1033–1044. [CrossRef]
Jones, B. A., Gray, R. L., and Turlapati, K., 2009, “Three Dimensional Statics for Continuum Robotics,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2009), St. Louis, MO, October 10–15, pp. 2659–2664. [CrossRef]
Rucker, D., Jones, B. A., and Webster, R. J., 2010, “A Geometrically Exact Model for Externally Loaded Concentric-Tube Continuum Robots,” IEEE Trans. Rob., 26(5), pp. 769–780. [CrossRef]
Trivedi, D., Lotfi, A., and Rahn, C. D., 2008, “Geometrically Exact Models for Soft Robotic Manipulators,” IEEE Trans. Rob., 24(4), pp. 773–780. [CrossRef]
Mochiyama, H., and Suzuki, T., 2002, “Dynamical Modelling of a Hyper-Flexible Manipulator,” 41st SICE Annual Conference (SICE 2002), Osaka, Japan, August 5–7, pp. 1505–1510. [CrossRef]
Tatlicioglu, E., Walker, I. D., and Dawson, D. M., 2007, “Dynamic Modelling for Planar Extensible Continuum Robot Manipulators,” IEEE International Conference on Robots and Automation, Rome, Italy, April 10–14, pp. 1357–1362. [CrossRef]
Gravagne, I. A., Rahn, C. D., and Walker, I. D., 2003, “Large Deflection Dynamics and Control for Planar Continuum Robots,” IEEE/ASME Trans. Mechatron., 8(2), pp. 299–307. [CrossRef]
Luboz, V., Lai, J., Blazewski, R., Gould, D., and Bello, F., 2008, “A Virtual Environment for Core Skills Training in Vascular Interventional Radiology,” 4th International Symposium on Biomedical Simulation (ISBMS 2008), London, UK, July 7–8, pp. 215–220. [CrossRef]
Alderliesten, T., Bosman, P. A., and Niessen, W. J., 2007, “Towards a Real-Time Minimally-Invasive Vascular Intervention Simulation System,” IEEE Trans. Med. Imaging, 26(1), pp. 128–132. [CrossRef] [PubMed]
Anjyo, K.-I., Usami, Y., and Kurihara, T., 1992, “A Simple Method for Extracting the Natural Beauty of Hair,” 19th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '92), Chicago, IL, July 27–31, pp. 111–120. [CrossRef]
Moll, M., and Kavraki, L. E., 2006, “Path Planning for Deformable Linear Objects,” IEEE Trans. Rob., 22(4), pp. 625–636. [CrossRef]
Lenoir, J., Meseure, P., Grisoni, L., and Chaillou, C., 2002, “Surgical Thread Simulation,” Modelling & Simulation for Computer-Aided Medicine and Surgery (MS4CMS'02), Rocquencourt, France, November 12–15, pp. 102–107. [CrossRef]
Theetten, A., Grisoni, L., Duriez, C., and Merlhiot, X., 2007, “Quasi-Dynamic Splines,” ACM Symposium on Solid and Physical Modeling (SPM'07), Beijing, China, June 4–6, pp. 409–414. [CrossRef]
Wakamatsu, H., and Hirai, S., 2004, “Static Modeling of Linear Object Deformation Based on Differential Geometry,” Int. J. Rob. Res., 23(3), pp. 293–311. [CrossRef]
Li, S., Qin, J., Gao, J., Chui, Y.-P., and Heng, P.-A., 2011, “A Novel FEM-Based Numerical Solver for Interactive Catheter Simulation in Virtual Catheterization,” J. Biomed. Imaging, 2011, p. 815246. [CrossRef]
Yokoyama, K., Nakagawa, H., Shah, D. C., LambertH., Leo, G., Aeby, N., Ikeda, A., Pitha, J. V., Sharma, T., Lazzara, R., and Jackman, W. M., 2008, “Novel Contact Force Sensor Incorporated in Irrigated Radiofrequency Ablation Catheter Predicts Lesion Size and Incidence of Steam Pop and Thrombus: Clinical Perspective,” Circ.: Arrhythmia Electrophysiol., 1(5), pp. 354–362. [CrossRef]
Featherstone, R., 1984, “Robot Dynamics Algorithms,” Ph.D. thesis, Department of Artificial Intelligence, University of Edinburgh, Edinburgh, UK.
Antman, S., 2005, Nonlinear Problems of Elasticity, Vol. 107, Springer, New York.
Perna, F., Heist, E. K., Danik, S. B., Barrett, C. D., Ruskin, J. N., and Mansour, M., 2011, “Assessment of Catheter Tip Contact Force Resulting in Cardiac Perforation in Swine Atria Using Force Sensing Technology: Clinical Perspective,” Circ.: Arrhythmia Electrophysiol., 4(2), pp. 218–224. [CrossRef]
Santangeli, P., di Baise, L., Burkhardt, D. J., Horton, R., Sanchez, J., Bai, R., Pump, A., Perez, M., Paul, J. W., Natale, A., and Al-Ahmad, A., 2008, “Relationship Between Catheter Forces, Lesion Characteristics, Popping, and Char Formation: Experience With Robotic Navigation System,” J. Cardiovasc. Electrophysiol., 20(4), pp. 436–440. [CrossRef] [PubMed]
Lagarias, J. C., Reeds, J. A., Wright, M. H., and Wright, P. E., 1998, “Convergence Properties of the Nelder–Mead Simplex Method in Low Dimensions,” SIAM J. Optim., 9(1), pp. 112–147. [CrossRef]


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Fig. 1

Schematic view of the continuum robot with the applied loads (a). Infinitesimal elastic arc element (b).

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Fig. 6

Shape of the catheter obtained by experiment versus model

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Fig. 5

Experimental setup

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Fig. 2

Schematic view of a steerable catheter (a). Actuation mechanism of distal shaft of a bidirectional catheter. The torque equal to T = FTd is applied at the tip of the catheter as a result of tendon tension (b).

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Fig. 3

Shape of the catheter obtained by elastica and the proposed approach with 50 sections

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Fig. 4

Tip distance error for the proposed approach for different number of sections



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