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Dynamic Modeling of a Class of Continuum Manipulators in Fixed Orientation

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Abstract

The current research topic on modeling continuum manipulators are shifting toward the development of accurate dynamic models by considering more specificities and mechanical properties. In this paper, we present a dynamic modeling of a class of continuum manipulators namely driving-cables robots based on the Euler-Lagrange method. The dynamic model is developed based on the kinematic equations of inextensible bending section with zero torsion and by using the constant curvature assumption. Taylor expansion has been applied to the geometric model in order to avoid singularities and reduce the complexity of the mathematical expressions. At the end, some simulation results are presented showing the static equilibrium as well as the dynamic behavior. In addition, a classic Proportional-Integrated-Derivative (PID) controller is proposed to ensure tracking trajectories using the point-to-point technique.

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References

  1. Robinson, G., Davies, J.B.C.: Continuum robots - A state of the art. In: Proceedings of IEEE International Conference on Robotics and Automation. Detroit, MI, USA (1999)

  2. Trivedi, D., Rahn, D.C., Kier, M.W., Walker, D.I.: Soft robotics: Biological inspiration, state of the art, and future research. Appl. Bionics Biomech. 5(3), 99–117 (2008)

    Article  Google Scholar 

  3. Webster III, 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)

    Article  Google Scholar 

  4. Renda, F., Giorelli, M., Calisti, M., Cianchetti, M., Laschi, C.: Dynamic model of a multibending soft robot arm driven by cables. IEEE Trans. Robot. 30(5), 1109–1122 (2014)

    Article  Google Scholar 

  5. Ataka, A., Qi, P., Liu, H., Althoefer, K.: Real-time planner for multi-segment continuum manipulator in dynamic environments. In: IEEE International Conference on Robotics and Automation Stockholm, Sweden (2016)

  6. Mahl, T., Hildebrandt, A., Sawodny, O.: Forward kinematics of a compliant pneumatically actuated redundant manipulator. In: IEEE Conference on Industrial Electronics and Applications, pp. 1267–1273 (2012)

  7. Laschi, C., Mazzolai, B., Mattoli, V., Cianchetti, M., Dario, P.: Design of a biomimetic robotic octopus arm. Bioinspir. Biomim. 4(1), 015006 (2009)

    Article  Google Scholar 

  8. McMahan, W.B., Jones, A., Walker, I.D.: Design and implementation of a multi-section continuum robot: Air-Octor, pp. 2578–2585 (2005)

  9. Davies, J.B.C., Lane, D.M., Robinson, G.C., O’Brien, D.J., Pickett, M., Sfakiotakis, M., Deacon, B.: Subsea applications of continuum robots. In: Proceedings of International Symposium on Underwater Technology. Tokyo, Japan (1998)

  10. Buckingham, R., Graham, A.: Nuclear snake-arm robots. Ind. Robot. Int. J. 39(1), 6–11 (2012)

    Article  Google Scholar 

  11. Burgner-Kahrs, J., Rucker, D.C., Choset, H.: Continuum robots for medical applications: a survey. IEEE Trans. Robot. 31(6), 1261–1280 (2015)

    Article  Google Scholar 

  12. Amouri, A., Mahfoudi, C., Zaatri, A., Lakhal, O., Merzouki, R.: A metaheuristic approach to solve inverse kinematics of continuum manipulators. J Syst. Control Eng. 231(5), 380–394 (2017)

    Google Scholar 

  13. Jones, B.A., Walker, I.D.: Kinematics for multi-section continuum robots. IEEE Trans. Robot. 22, 43–55 (2006)

    Article  Google Scholar 

  14. Iqbal, S., Mohammed, S., Amirat, Y.: A guaranteed approach for kinematic analysis of continuum robot based catheter. In: Proceedings of International Conference on Robotics and Biomimetics, pp. 1573–1578. Guilin, China (2009)

  15. Hannan, M.W., Walker, I.D.: Kinematics and the implementation of an elephant’s trunk manipulator and other continuum style robots. J. Robot. Syst. 20, 45–63 (2003)

    Article  MATH  Google Scholar 

  16. Godage, S., Medrano-Cerda, G.A., Branson, D.T., Guglielmino, E., Caldwell, D.G.: Modal kinematics for multi-section continuum arms. Bioinspir. Biomim. 10, 1–20 (2015)

    Article  Google Scholar 

  17. Mahl, T., Hildebrandt, A., Sawodny, O.: A variable curvature continuum kinematics for kinematic control of the bionic handling assistant. IEEE Trans. Robot. 30(4), 935–949 (2014)

    Article  Google Scholar 

  18. Lakhal, O., Melingui, A., Merzouki, R.: Hybrid approach for modeling and solving of kinematics of compact bionic handling assistant manipulator. IEEE/ASME Trans. Mechatron. 21(3), 1326–1335 (2016)

    Article  Google Scholar 

  19. Chirikjian, G.S.: Hyper-redundant manipulator dynamics: a continuum approximation. Adv. Robot. 9(3), 217–243 (1995)

    Article  Google Scholar 

  20. Mochiyama, H., Suzuki, T.: Kinematics and dynamics of a cable-like hyper-flexible manipulator. In: Proceedings of IEEE International Conference on Robotics and Automation, pp. 3672–3677. Taipei, Taiwan (2003)

  21. Tatlicioglu, E., Walker, I.D., Dawson, D.M.: New dynamic models for planar extensible continuum robot manipulators. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1485–1490. San Diego, USA (2007)

  22. Falkenhahn, V., Mahl, T., Hildebrandt, A., Neumann, R., Sawodny, O.: Dynamic modeling of bellows-actuated continuum robots using the Euler-Lagrange formalism. IEEE Trans. Robot. 31(6), 1–13 (2015)

    Article  Google Scholar 

  23. Godage, I.S., Medrano-Cerda, G.A., Branson, D.T., Guglielmino, E., Caldwell, D.G.: Dynamics for variable length multisection continuum arms. Int. J. Robot. Res. 35(6), 695–722 (2016)

    Article  Google Scholar 

  24. Rone, W.S., Ben-Tzvi, P.: Continuum robot dynamics utilizing the principle of virtual power. IEEE Trans. Robot. 30(1), 275–287 (2014)

    Article  Google Scholar 

  25. Rone, W.S., Ben-Tzvi, P.: Mechanics modeling of multi-segment rod-driven continuum robots. J. Mech. Robot. 6(4), 041006 (2014)

    Article  Google Scholar 

  26. He, B., Wang, Z., Li, Q., Xie, H., Shen, R.: An analytic method for the kinematics and dynamics of a multiple-backbone continuum robot. Int. J. Adv. Robot. Syst. 10, 1–13 (2013)

    Article  Google Scholar 

  27. Gravagne, I.A., Rahn, C.D., Walker, I.D.: Large deflection dynamics and control for planar continuum robots. IEEE/ASME Trans. Mechatron. 8(2), 299–307 (2003)

    Article  Google Scholar 

  28. Daachi, B., Madani, T., Benallegue, A.: Adaptive neural controller for redundant robot manipulators and collision avoidance with mobile obstacles. Neurocomputing 79, 50–60 (2012)

    Article  Google Scholar 

  29. Le, T.D., Kang, H.J.: An adaptive tracking controller for parallel robotic manipulators based on fully tuned radial basic function networks. Neurocomputing 137, 12–23 (2014)

    Article  Google Scholar 

  30. Xu, B., Yuan, Y.: Two performance enhanced control of flexible-link manipulator with system uncertainty and disturbances. Sci. China Inf. Sci. 60(5), 050202:1–050202:11 (2017)

    Article  Google Scholar 

  31. Xu, B.: Composite learning control of flexible-link manipulator using NN and DOB. IEEE Transactions on Systems, Man, and Cybernetics: Systems. https://doi.org/10.1109/TSMC.2017.2700433

  32. Xu, B., Zhang, P.: Composite learning sliding mode control of flexible-link manipulator. Complexity 2017 (9430259), 6 (2017). https://doi.org/10.1155/2017/9430259

    MathSciNet  MATH  Google Scholar 

  33. He, W., Chen, Y., Yin, Z.: Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Trans. Cybern. 46(3), 620–629 (2016)

    Article  Google Scholar 

  34. He, W., Dong, Y., Sun, C.: Adaptive neural impedance control of a robotic manipulator with input saturation. IEEE Trans. Syst. Man Cybern. Syst. 46(3), 334–344 (2016)

    Article  Google Scholar 

  35. He, W., Ouyang, Y., Hong, J.: Vibration control of a flexible robotic manipulator in the presence of input deadzone. IEEE Trans. Ind. Inf. 13(1), 48–59 (2017)

    Article  Google Scholar 

  36. Sun, C., He, W., Ge, W., Chang, C.: Adaptive neural network control of biped robots. IEEE Trans. Syst. Man Cybern. Syst. 47(2), 315–326 (2017)

    Google Scholar 

  37. Melingui, A., Lakhal, O., Daachi, B., Bosco Mbede, J., Merzouki, R.: Adaptive neural network control of a compact bionic handling arm. IEEE/ASME Trans. Mechatron. 2(6), 2862–2875 (2015)

    Article  Google Scholar 

  38. Braganza, D., Dawson, D.M., Walker, I.D., Nath, N.: A neural network controller for continuum robots. IEEE Trans. Robot. 23(6), 1270–1277 (2007)

    Article  Google Scholar 

  39. Antman, S.S.: Nonlinear problems of elasticity. 107. Springer-Verlag, New York (2005). https://doi.org/10.1007/0-387-27649-1

    MATH  Google Scholar 

  40. Nemat-Nasser, S., Guo, W.G.: Superelastic and cyclic response of NiTi SMA at various strain rates and temperatures. Mech. Mater. 38, 463–474 (2006)

    Article  Google Scholar 

  41. Fertis, D.G.: Advanced mechanics of structure. Marcel Dekker, Inc., New York City (1996)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering Sciences, University of Brothers Mentouri, Constantine, Algeria

    Ammar Amouri & Abdelouahab Zaatri

  2. Department of Mechanical Engineering, University Labri Ben M’Hidi Oum el Bouaghi, Oum El Bouaghi, Algeria

    Chawki Mahfoudi

Authors
  1. Ammar Amouri
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  2. Abdelouahab Zaatri
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  3. Chawki Mahfoudi
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Correspondence to Abdelouahab Zaatri.

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Amouri, A., Zaatri, A. & Mahfoudi, C. Dynamic Modeling of a Class of Continuum Manipulators in Fixed Orientation. J Intell Robot Syst 91, 413–424 (2018). https://doi.org/10.1007/s10846-017-0734-z

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  • DOI: https://doi.org/10.1007/s10846-017-0734-z

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