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Achievement of chaotic synchronization trajectories of master–slave manipulators with feedback control strategy

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Abstract

This paper addresses a master–slave synchronization strategy for complex dynamic systems based on feedback control. This strategy is applied to 3-DOF planar manipulators in order to obtain synchronization in such complicated as chaotic motions of end-effectors. A chaotic curve is selected from Duffing equation as the trajectory of master end-effector and a piecewise approximation method is proposed to accurately represent this chaotic trajectory of end-effectors. The dynamical equations of master–slave manipulators with synchronization controller are derived, and the Lyapunov stability theory is used to determine the stability of this controlled synchronization system. In numerical experiments, the synchronous motions of end-effectors as well as three joint angles and torques of master–slave manipulators are studied under the control of the proposed synchronization strategy. It is found that the positive gain matrix affects the implementation of synchronization control strategy. This synchronization control strategy proves the synchronization’s feasibility and controllability for complicated motions generated by master–slave manipulators.

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References

  1. Shaw S.W., Rand R.H.: The transition to chaos in a simple mechanical system. Int. J. Nonlinear Mech. 24(1), 41–56 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. Strogatz S.H.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Addison- Wesley, Reading (1994)

    Google Scholar 

  3. Moon F.: Chaotic Vibrations. Wiley, New York (1987)

    MATH  Google Scholar 

  4. Liu Y.Z., Chen L.Q.: Chaotic attitude motion of a magnetic rigid spacecraft in an elliptic orbit and its control. Acta Mech. Sin. 19(1), 71–78 (2003)

    Article  Google Scholar 

  5. Ravishankar A.S., Ghosal A.: Nonlinear dynamics and chaotic motions in feedback controlled two- and three-degree-of-freedom robots. Int. J. Robots Res. 18(1), 93–108 (1999)

    Google Scholar 

  6. Verduzco F., Alvarez J.: Bifurcation analysis of a 2-DOF robot manipulator driven by constant torques. Int. J. Bifurc. Chaos 9(4), 617–627 (1999)

    Article  MATH  Google Scholar 

  7. Daniel E., Buhler K.M.: Analysis of a simplified Hopping robot. J. Robots Res. 10(6), 606–628 (1991)

    Article  Google Scholar 

  8. Suzuki, T., Koimuma, M., Nakamura, Y.: Chaos and nonlinear control of a nonholonomic free-joint manipulator. In: Proceedings of the 1996 IEEE International Conference on Robotics and Automation, vol. 3, pp. 2668–2675 (1996)

  9. Koinuma, M., Nakamura, Y.: The nonlinearity of the multi-link system with free-joint. In: Proceedings of the 13th Annual Conference of the Robotics Society of Japan, pp. 210–212 (1995)

  10. Liu Z., Li L.: Chaotic self-motion of flexible redundant robots. China Mech. Eng. 15(13), 1186–1189 (2004)

    Google Scholar 

  11. Pikovsky A., Rosenblum M., Kurths J.: Synchronization, a Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  12. Blekhman I.I.: Synchronization in Science and Technology. ASME Press, New York (1988)

    Google Scholar 

  13. Wen B., Zhao C., Su D.: Vibration Synchronization and Controlled Synchronization. Science Press, Beijing (2003)

    Google Scholar 

  14. Rosenblum M., Pikovsky A.: Synchronization from pendulum clocks to chaotic lasers and chemical oscillators. Contemp. Phys. 44(5), 401–416 (2003)

    Article  Google Scholar 

  15. Rodriguez-Angeles, A.: Synchronization of mechanical systems. PhD dissertation, Technische Universiteit, Eindhoven (2002)

  16. Brunt, M.: Coordination of redundant systems. PhD dissertation, Technical University Delft, The Netherlands (1998)

  17. Ren L.: Adaptive synchronized control for a planar parallel manipulator: theory and experiments. Trans. ASME J. Dyn. Syst. Meas. Control 128(12), 976–979 (2006)

    Article  Google Scholar 

  18. Blekhman I.I. et al.: Self-synchronization and controlled synchronization: general definition and example design. Math. Comput. Simul. 58, 367–384 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Sun D., Mills J.K.: Adaptive synchronized control for coordination of multi-robot assembly tasks. IEEE Trans. Robot Autom. 18(4), 498–510 (2002)

    Article  Google Scholar 

  20. Chen H.H.: Adaptive synchronization of chaotic systems via linear balanced feedback control. J. Sound Vib. 306, 865–876 (2007)

    Article  Google Scholar 

  21. Han Q.K, Zhao X.Y., Wen B.C.: Synchronization motions of a two-link mechanism with an improved OPCL method. Appl. Math. Mech. 29(12), 1561–1568 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  22. Mahboobi S.H., Shahrokhi M., Pishkenari H.N.: Observer-based control design for three well-known chaotic systems. Chaos Solitons Fractals 29, 381–392 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  23. Gao T.G., Chen Z.Q., Yuan Z.Z.: Generalized reduced-order synchronization of chaotic system based on fast slide mode. Chin. Phys. 14, 2421–2427 (2005)

    Article  Google Scholar 

  24. Li G., Zhou S., Yang K.: Generalized projective synchronization between two different chaotic systems using active backstepping control. Phys. Lett. A 355(4–5), 326–330 (2006)

    Article  Google Scholar 

  25. Lei Y., Xu W., Zheng H.: Synchronization of two chaotic nonlinear gyros using active control. Phys. Lett. A 343, 153–158 (2005)

    Article  MATH  Google Scholar 

  26. Huang L., Feng R., Wang M.: Synchronization of chaotic systems via nonlinear control. Phys. Lett. A 320, 271–275 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  27. Rodriguez-Angeles A., Nijmeijer H.: Mutual synchronization of robots via estimated state feedback: a cooperative approach. IEEE Trans. Control Syst. Technol. 12(4), 542–554 (2004)

    Article  Google Scholar 

  28. Wu X., Cai J., Wang M.: Master-slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control. J. Sound Vib. 295, 378–387 (2006)

    Article  MathSciNet  Google Scholar 

  29. Paden B., Panja R.: Globally asymptotically stable ‘PD+’ controller for robot manipulators. Int. J. Control 47, 1697–1712 (1988)

    Article  MATH  Google Scholar 

  30. Zhang H., Li Z.: Research on nonlinear dynamics of two-degrees-of-freedom robot. Intell. Robot. Appl. 5314, 420–426 (2008)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, 110004, Shenyang, China

    Qingkai Han, Lina Hao, Hao Zhang & Bangchun Wen

Authors
  1. Qingkai Han
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  2. Lina Hao
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  3. Hao Zhang
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  4. Bangchun Wen
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Corresponding author

Correspondence to Qingkai Han.

Additional information

The project was supported by the Key Project of Chinese Ministry of Education (108037) and the National Natural Science Foundation of China (10402008 and 50535010).

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Han, Q., Hao, L., Zhang, H. et al. Achievement of chaotic synchronization trajectories of master–slave manipulators with feedback control strategy. Acta Mech Sin 26, 433–439 (2010). https://doi.org/10.1007/s10409-010-0340-9

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  • DOI: https://doi.org/10.1007/s10409-010-0340-9

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