[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Solving the Non-Linear Dynamic Equations of Motion of a Variable Curvature Continuum Robot Using Runge-Kutta Method and MATLAB Software

Journal of Applied Nonlinear Dynamics 13(1) (2024) 13--26 | DOI:10.5890/JAND.2024.03.002

Selman Djeffal, Chawki Mahfoudi, Abdelhamid Ghoul

Ecole Nationale de Polytechnique de Constantine (ENPC), Department of Mechanical Engineering, Algeria

Download Full Text PDF

 

Abstract

Continuum robots have remarkably exceeded rigid robots' abilities for specific tasks, such as the adaptation to twisted paths and their capacity to perform medical surgeries thanks to their flexible structure yet their dynamic modeling are complicated, in particular the highly non-linearity of their equation of motions. To this end, a simplified dynamic model for a variable curvature continuum robot is established and thoroughly developed based on Euler-Lagrange method, namely an approximate formula relating the robot's each unit is integrated in the dynamic model in order to reduce the number of the generated coordinates in the equation of motions. The equation of motions are figured out using Runge-Kutta method through MATLAB environment. To verify the effectiveness of the developed dynamic model, simulation examples through MATLAB are carried out. The first simulation is dedicated to a spatial single section variable curvature continuum robot, in which the robot is initially tilted from its equilibrium position then released and its behavior (oscillation) is graphically represented based on the equation of motions that are solved by Runge-Kutta method. While the second simulation example addresses the behavior of a variable curvature continuum robot when subjected to a force. It is found that the developed dynamic model properly simulates the behavior of variable curvature continuum robots and the Runge Kutta method can be considered as an effective numerical method to deal with the non-linearity of continuum robot's equation of motions.

References

  1. [1] McMahan, W., Chitrakaran, V., Csencsits, M., Dawson, D., Walker, I.D., Jones, B.A., Pritts, M., Dienno, D., Grissom, M., and Rahn, C.D. (2006), Field trials and testing of the OctArm continuum manipulator, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2336-2341.
  2. [2] Hirose, S. (1993), Biologically Inspired Robots, Snake-Like Locomotors and Manipulators, 62-282.
  3. [3] Cieslak, R. and Morecki, A. (1999), Elephant trunk type elastic manipulator-a tool for bulk and liquid materials transportation, Robotica, 17, 11-16.
  4. [4]  McMahan, W., Jones, B., Walker, I., Chitrakaran, V., Seshadri, A., and Dawson, D. (2004), Robotic manipulators inspired by cephalopod limbs, Proceedings of the Canadian Engineering Education Association (CEEA), 1-10.
  5. [5] Mahl, T., Hildebrandt, A., and Sawodny, O. (2014), A variable curvature continuum kinematics for kinematic control of the bionic handling assistant, IEEE Transactions on Robotics, 30(4), 935–949.
  6. [6] Webster III, R.J. and Jones, B.A. (2010), Design and kinematic modeling of constant curvature continuum robots: A review, The International Journal of Robotics Research, 29(13), 1661-1683.
  7. [7]  Khalil, W., Gallot, G., Ibrahim, O., and Boyer, F. (2005), Dynamic modeling of a 3-D serial eel-like robot, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 1270-1275.
  8. [8] Gonthina, P.S., Kapadia, A.D., and Godage, I.S. (2019), Modeling variable curvature parallel continuum robots using euler curves, International Conference on Robotics and Automation (ICRA), 1679-1685.
  9. [9]  Matsuno, F. and Sato, H. (2005), Trajectory tracking control of snake robots based on dynamic model, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 3029-3034.
  10. [10]  Yekutieli, Y., Sagiv-Zohar, R., Aharonov, R., Engel, Y., Hochner, B., and Flash, T. (2005), Dynamic model of the octopus arm. I, Biomechanics of the octopus reaching movement. Journal of Neurophysiology, 94(2), 1443-1458.
  11. [11]  Trivedi, D., Lotfi, A., and Rahn, C.D. (2007), Geometrically exact dynamic models for soft robotic manipulators, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, 1497-1502.
  12. [12]  Alqumsan, A.A., Khoo, S., and Norton, M. (2019), Robust control of continuum robots using Cosserat rod theory, Mechanism and Machine Theory, 131, 48-61.
  13. [13]  Mochiyama, H. and Suzuki, T. (2002), Dynamical modelling of a hyper-flexible manipulator, Proceedings of the 41st SICE Annual Conference SICE 2002, 3, 1505-1510.
  14. [14]  Bhattacherjee, S., Chattopadhayay, S., Rao, V., Seth, S., Mukherjee, S., Sengupta, A., and Bhaumik, S. (2018), Kinematics and teleoperation of tendon driven continuum robot, Procedia Computer Science, 133, 879-886.
  15. [15]  Li, M., Kang, R., Branson, D.T., and Dai, J.S. (2017), Model-free control for continuum robots based on an adaptive Kalman filter, IEEE/ASME Transactions on Mechatronics, 23(1), 286-297.
  16. [16]  Goharimanesh, M., Mehrkish, A., and Janabi-Sharifi, F. (2020), A fuzzy reinforcement learning approach for continuum robot control, Journal of Intelligent and Robotic Systems, 100(3), 809-826.
  17. [17]  Yekutieli, Y., Sagiv-Zohar, R., Aharonov, R., Engel, Y., Hochner, B., and Flash, T. (2005), Dynamic model of the octopus arm. I. Biomechanics of the octopus reaching movement, Journal of Neurophysiology, 94(2), 1443-1458.
  18. [18]  Amouri, A., Mahfoudi, C., and Zaatri, A. (2019), Dynamic modeling of a spatial cable-driven continuum robot using Euler-Lagrange method, International Journal of Engineering and Technology Innovation, 10(1), 60-74.
  19. [19]  Amouri, A., Zaatri, A., and Mahfoudi, C. (2018), Dynamic modeling of a class of continuum manipulators in fixed orientation, Journal of Intelligent and Robotic Systems, 91(3), 413-424.
  20. [20]  Trivedi, D., Lotfi, A., and Rahn, C.D. (2007), Geometrically exact dynamic models for soft robotic manipulators, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, 1497-1502.
  21. [21]  Liu, W. and Rahn, C.R. (2003), Fiber-reinforced membrane models of McKibben actuators, Journal of Applied Mechanics, 70(6), 853-859.
  22. [22]  Alqumsan, A.A., Khoo, S., and Norton, M. (2019), Robust control of continuum robots using Cosserat rod theory, Mechanism and Machine Theory, 131, 48-61.
  23. [23]  Mochiyama, H. and Suzuki, T. (2002), Dynamical modelling of a hyper-flexible manipulator, Proceedings of the 41st SICE Annual Conference. SICE 2002, 3, 1505-1510.
  24. [24]  Selman, D., Ammar, A., And Chawki, M. (2021), Kinematics modeling snd simulation analysis of variable curvature kinematics continuum robots, UPB Scientific Bulletin, Series D: Mechanical Engineering, 83(1), 28-42.
  25. [25]  Bin, H., Zhipeng, W., Qiang, L., Hong, X., and Runjie, S. (2013), An analytic method for the kinematics and dynamics of a multiple-backbone continuum robot, International Journal of Advanced Robotic Systems, 10(1), 1-13.
  26. [26]  Selman, D., Chawki, M., and Ammar, A. (2021), Comparison of three meta-heuristic algorithms for solving inverse kinematics problems of variable curvature continuum robots, 2021 European Conference on Mobile Robots (ECMR), IEEE, 1-6.
  27. [27]  Abdelhamid, G., Kamel, K., Mohamed, B., and Mohamed, H. (2022), Optimized nonlinear sliding mode control of a continuum robot manipulator, Journal of Control, Automation and Electrical Systems, 4, 1-9.

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates