Abstract
Concentric tube robots are based on the deformation of elastic pre-curved tubes mounted in a telescopic manner. Their kinematic model consists in a boundary value problem which must be solved during analysis and design. When arbitrary properties and number of the tubes are considered, this model must be solved numerically. We consider in this paper the use of dynamic relaxation to perform this resolution. Its performances in terms of accuracy and computation time are assessed in a case study involving a two-tube CTR. Robustness of the method tuning to variations of CTR behaviour as encountered during a deployment is finally assessed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Baek, C., Yoon, K., Kim, D.-N.: Finite element modeling of concentric-tube continuum robots. Struct. Eng. Mech. 57(5), 809–821 (2016)
Barnes, M.R.: Form finding and analysis of tension structures by dynamic relaxation. Int. J. Space Struct. 14(2), 89–104 (1999)
Burgner-Kahrs, J., Rucker, D.C., Choset, H.: Continuum robots for medical applications: a survey. IEEE Trans. Robot. 31(6), 1261–1280 (2015)
Dupont, P.E., Lock, J., Itkowitz, B., Butler, E.: Design and control of concentric-tube robots. IEEE Trans. Robot. 26(2), 209–225 (2010)
Gilbert, H.B., Neimat, J., Webster, R.J.: Concentric tube robots as steerable needles: achieving follow-the-leader deployment. IEEE Trans. Robot. 31(2), 246–258 (2015)
Girerd, C., Rabenorosoa, K., Renaud, P.: Combining tube design and simple kinematic strategy for follow-the-leader deployment of concentric tube robots. In: Advances in Robot Kinematics 2016. Springer Proceedings in Advanced Robotics, pp. 23–31. Springer, Cham (2018)
Ha, J., Park, F.C., Dupont, P.E.: Elastic stability of concentric tube robots subject to external loads. IEEE Trans. Biomed. Eng. 63(6), 1116–1128 (2016)
Lewis, W.J., Jones, M.S., Rushton, K.R.: Dynamic relaxation analysis of the non-linear static response of pretensioned cable roofs. Comput. Struct. 18(6), 989–997 (1984)
Lock, J., Laing, G., Mahvash, M., Dupont, P.E.: Quasistatic modeling of concentric tube robots with external loads. In: 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2325–2332, October 2010
Rezaiee-Pajand, M., Alamatian, J.: The dynamic relaxation method using new formulation for fictitious mass and damping. Struct. Eng. Mech. 34(1), 109–133 (2010)
Rucker, D.C., Webster, R.J., Chirikjian, G.S., Cowan, N.J.: Equilibrium conformations of concentric-tube continuum robots. Int. J. Robot. Res. 29(10), 1263–1280 (2010)
Rushton, K.R.: Dynamic-relaxation solutions of elastic-plate problems. J. Strain Anal. 3(1), 23–32 (1968)
Zhang, L.C., Kadkhodayan, M., Mai, Y.W.: Development of the maDR method. Comput. Struct. 52(1), 1–8 (1994)
Acknowledgement
This work was supported by the French National Agency for Research within the Biomedical Innovation program (NEMRO ANR-14-CE17-0013), the Investissements d’Avenir (Robotex ANR-10-EQPX-44, Labex CAMI ANR-11-LABX-0004 and Labex ACTION ANR-11-LABX-0001-01) and Aviesan France Life Imaging infrastructure.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Peyron, Q., Rabenorosoa, K., Andreff, N., Renaud, P. (2019). Evaluation of Dynamic Relaxation to Solve Kinematics of Concentric Tube Robots. In: Lenarcic, J., Parenti-Castelli, V. (eds) Advances in Robot Kinematics 2018. ARK 2018. Springer Proceedings in Advanced Robotics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-93188-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-93188-3_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93187-6
Online ISBN: 978-3-319-93188-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)