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Investigation of Error Propagation in Multi-backbone Continuum Robots

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Advances in Robot Kinematics

Abstract

Snake-like robots using multiple backbones have gained increased use in surgical robotics. These robots are essentially parallel robots with constrained flexible legs. Change in the equilibrium configuration of these robots is obtained by pushing/pulling on the robots’ legs. This chapter presents an investigation of the effects of assembly and home position errors on the accuracy of these robots. The assembly errors considered in this chapter include twisting about the backbone curve and deviation of the equilibrium shapes from assumed circular shapes. A modeling framework for the inverse and direct kinematics is presented while taking into account twisting and shape deviation. The configuration space and the identification Jacobian matrices are derived and then used to investigate the effects of the assembly/modeling errors on inducing errors in configuration and task space.

This work was supported by NSF Career grant No. IIS-1063750.

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References

  1. Chirikjian, G., Burdick, J.: A modal approach to hyper-redundant manipulator kinematics. IEEE Trans. Robot. Autom. 10(3), 343–354 (1994). doi:10.1109/70.294209

    Article  Google Scholar 

  2. Ding, J., Goldman, R.E., Xu, K., Allen, P.K., Fowler, D.L., Simaan, N.: Design and coordination kinematics of an insertable robotic effectors platform for single-port access surgery. IEEE/ASME Trans. Mechatron. 18, 1612–1624 (2013). doi:10.1109/TMECH.2012.2209671

    Article  Google Scholar 

  3. Goldman, R.E., Bajo, A., MacLachlan, L.S., Pickens, R., Herrell, S.D., Simaan, N.: Design and performance evaluation of a minimally invasive telerobotic platform for transurethral surveillance and intervention. IEEE Trans. Biomed. Eng. 60(4), 918–925 (2013). doi:10.1109/TBME.2012.2226031

    Article  Google Scholar 

  4. Gravagne, I., Walker, I.: On the kinematics of remotely-actuated continuum robots. In: Proceedings of IEEE International Conference on Robotics and Automation, vol. 3, pp. 2544–2550. (2000). doi:10.1109/ROBOT.2000.846411

  5. Hirose, S., Kado, T., Umetani, Y.: Tensor actutated elastic manipulator. In: Proceedings of the Sixth World Congress on Theory of Machines and Mechanisms, pp. 978–981 (1983)

    Google Scholar 

  6. Nahvi, A., Hollerbach, J.: The noise amplification index for optimal pose selection in robot calibration. In: Proceedings of IEEE International Conference on Robotics and Automation, vol. 1, pp. 647–654. (1996). doi:10.1109/ROBOT.1996.503848

  7. Robinson, G., Davies, J.: Continuum robots—a state of the art. In: Proceedings of IEEE International Conference on Robotics and Automation, vol. 4, pp. 2849–2854. (1999). doi:10.1109/ROBOT.1999.774029

  8. Rone, W.S., Ben-Tzvi, P.: Continuum manipulator statics based on the principle of virtual work. In: Volume 4: Dynamics, Control and Uncertainty, Parts A and B, p. 321. ASME, New York (2012). doi:10.1115/IMECE2012-87675

  9. Rucker, D.C., Webster III, R.J.: Statics and dynamics of continuum robots with general tendon routing and external loading. IEEE Trans. Robot. 27(6), 1033–1044 (2011). doi:10.1109/TRO.2011.2160469

    Article  Google Scholar 

  10. Simaan, N.: Snake-like units using flexible backbones and actuation redundancy for enhanced miniaturization. In: Proceedings IEEE International Conference on Robotics and Automation, pp. 3012–3017. IEEE, Barcelona (2005). doi:10.1109/ROBOT.2005.1570572

  11. Simaan, N., Taylor, R., Flint, P.: A dexterous system for laryngeal surgery. In: Proceedings of IEEE International Conference on Robotics and Automation, pp. 351–357 vol. 1. IEEE, New Orleans (2004). doi:10.1109/ROBOT.2004.1307175

  12. Simaan, N., Xu, K., Wei, W., Kapoor, A., Kazanzides, P., Flint, P., Taylor, R.: Design and integration of a telerobotic system for minimally invasive surgery of the throat. Int. J. Robot. Res. 28(9), 1134–1153 (2009). doi:10.1177/0278364908104278

    Article  Google Scholar 

  13. Tatlicioglu, E., Walker, I.D., Dawson, D.M.: Dynamic modelling for planar extensible continuum robot manipulators. In: Proceedings of IEEE International Conference on Robotics and Automation, pp. 1357–1362. IEEE (2007). doi:10.1109/ROBOT.2007.363173

  14. Wang, Y., Chirikjian, G.S.: Nonparametric second-order theory of error propagation on motion groups. Int. J. Robot. Res. 27(11–12), 1258–1273 (2008). doi:

    Article  Google Scholar 

  15. Webster, R.J., Jones, B.A.: Design and kinematic modeling of constant curvature continuum robots: a review. Int. J. Robot. Res. 29(13), 1661–1683 (2010). doi:10.1177/0278364910368147

    Article  Google Scholar 

  16. Xu, K., Simaan, N.: An investigation of the intrinsic force sensing capabilities of continuum robots. IEEE Trans. Robot. 24(3), 576–587 (2008). doi:10.1109/TRO.2008.924266

    Article  Google Scholar 

  17. Xu, K., Simaan, N.: Analytic formulation for kinematics, statics and shape restoration of multibackbone continuum robots via elliptic integrals. ASME J. Mech. Robot. 2, 11006–11013 (2010) doi:10.1115/1.4000519

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Authors and Affiliations

  1. Department of Mechanical Engineering, Vanderbilt University, Nashville, TN, 37212, USA

    Long Wang & Nabil Simaan

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  1. Long Wang
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  2. Nabil Simaan
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Correspondence to Long Wang .

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Editors and Affiliations

  1. J. Stefan Institute, Ljubljana-Vic-Rudnik, Slovenia

    Jadran Lenarčič

  2. Department of Computer Science Artificial Intelligence Laboratory, Stanford University, Stanford, California, USA

    Oussama Khatib

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Wang, L., Simaan, N. (2014). Investigation of Error Propagation in Multi-backbone Continuum Robots. In: Lenarčič, J., Khatib, O. (eds) Advances in Robot Kinematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06698-1_40

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  • DOI: https://doi.org/10.1007/978-3-319-06698-1_40

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06697-4

  • Online ISBN: 978-3-319-06698-1

  • eBook Packages: EngineeringEngineering (R0)

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