Skip to main content
Log in

Optimal sliding mode control of a robot manipulator under uncertainty using PSO

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper presents a novel optimal control approach for robot manipulators using particle swarm optimization (PSO). Although the PSO algorithm can find an optimal solution for complex problems, there are some difficulties to apply the particle swarm optimization in real-time control. This paper deals with uncertainties in using the PSO for finding an optimal sliding mode control. Being a repetitive algorithm with an offline nature, the PSO is not as fast as sufficient to apply on a dynamical system. Moreover, the actual system is not repeatable in the presence of external disturbances. As a solution, this paper suggests that the PSO should be applied to the model of a system instead of an actual system. Then some modifications are given since the model differs from the actual system. According to a range of uncertainty, a few nominal models for the system are selected. Next, the optimal designs are obtained by the PSO in offline. In real time, the system is estimated to select a model and design the controller. Finally, the control design is applied to the system. Simulation results show the efficiency of the proposed control and its superiority over the sliding mode control.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Isodori, A.: Nonlinear Control Systems: An Introduction. Springer, Heidelberg (1989)

    Book  Google Scholar 

  2. Camacho, E.F., Alba, C.B.: Model Predictive Control. Springer, Heidelberg (2013)

    Google Scholar 

  3. Agrachev, A.A., Sachkov, Y.: Control Theory From the Geometric Viewpoint, vol. 2. Springer, Heidelberg (2004)

    Book  MATH  Google Scholar 

  4. Bertsekas, D.P.: Dynamic Programming and Optimal Control, vol. 1, 2nd edn. Athena Scientific, Belmont (1995)

  5. Slotine, J.J., Li, W.: Applied Nonlinear Control. Prentice Hall, Upper Saddle River (1991)

    MATH  Google Scholar 

  6. Wang, L.X.: A Course in Fuzzy Systems and Control. Prentice-Hall, Upper Saddle River (1997)

    MATH  Google Scholar 

  7. Tusset, A.M., Balthazar, J.M., Bassinello, D.G., Pontes Jr, B.R., Felix, J.L.P.: Statements on chaos control designs, including a fractional order dynamical system, applied to a “MEMS” comb-drive actuator. Nonlinear Dyn. 69(4), 1837–1857 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Khorashadizadeh, S., Fateh, M.M.: Robust control of electrically driven robots by adaptive fuzzy estimation of uncertainty. Nonlinear Dyn. 69, 1465–1477 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Khorashadizadeh, S., Fateh, M.M.: Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation. Nonlinear Dyn. 79(2), 1151–1161 (2014)

    Article  MathSciNet  Google Scholar 

  10. Khorashadizadeh, S., Fateh, M.M.: Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion. Robotica (2015, in press)

  11. Khorashadizadeh, S., Fateh, M.M.: Adaptive Fourier series control of electrically driven robot manipulators. 3rd International conference on Control, Instrumentation and Automation, (ICCIA), 213–218 (2013)

  12. Fard, M.B., Khorashadizadeh, S.: Model free robust impedance control of robot manipulators using Fourier series expansion. AI & Robotics (IRANOPEN), 1–7 (2015)

  13. Shabaninia, F., Khorshidi, R.: A control system for a single-spin LEO satellite employing supervisory control with fuzzy logic and adaptive control under uncertainty. J. Intell. Fuzzy Syst. 17(5), 533–540 (2005)

    MATH  Google Scholar 

  14. Lin, F., Brandt, R.D.: An optimal control approach to robust control of robot manipulators. IEEE Trans. Robot. Auto. 14(1), 69–77 (1998)

    Article  Google Scholar 

  15. Lin, F., Zhang, W., Brandt, R.D.: Robust hovering control of a PVTOL aircraft. IEEE Trans. Control Syst. Tech. 7(3), 343–351 (1999)

    Article  Google Scholar 

  16. Lu, Z., Shieh, L.S., Chen, G., Coleman, N.P.: Simplex sliding mode control for nonlinear uncertain systems via chaos optimization. Chaos Solitons Fractals 23(3), 747–755 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Serbencu, A.E., Serbencu, A., Cernega, D.C., Minzu, V.: Particle Swarm Optimization for the Sliding Mode controller parameters. 29th Chinese Control Conference (CCC), 1859–1864 (2010)

  18. Yuhu, X., Chongwei, Z., Wei, B., Lin, T.: Dynamic Sliding Mode Controller Based on Particle Swarm Optimization for Mobile Robot’s Path Following. International Forum on Information Technology and Applications, IFITA’ 09, 1, 257–260 (2009)

  19. Rafikov, M., Balthazar, J.M., Tusset, A.M.: An optimal linear control design for nonlinear systems. J. Brazil Soc. Mech. Sci. Eng. 30, 279–284 (2008)

    Article  Google Scholar 

  20. Balthazar, J.M., Tusset, A.M., De Souza, S.L.T., Bueno, A.M.: Microcantilever chaotic motion suppression in tapping mode atomic force microscope. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 227(8), 1730–1741 (2013)

    Article  Google Scholar 

  21. Balthazar, J.M., Tusset, A.M., Bueno, A.M.: TM-AFM nonlinear motion control with robustness analysis to parametric errors in the control signal determination. J. Theor. Appl. Mech. 52, 93–106 (2014)

    Google Scholar 

  22. Fateh, M.M., Azargoshasb, S., Khorashadizadeh, S.: Model-free discrete control for robot manipulators using a fuzzy estimator. Int. J. Comput. Math. Electr. Electron. Eng. 33(3), 1051–1067 (2014)

    Article  MathSciNet  Google Scholar 

  23. Fateh, M.M., Khorashadizadeh, S.: Optimal robust voltage control of electrically driven robot manipulators. Nonlinear Dyn. 70(2), 1445–1458 (2012)

    Article  MathSciNet  Google Scholar 

  24. Bingül, Z., Karahan, O.: A fuzzy logic controller tuned with PSO for 2 DOF robot trajectory control. Expert Syst. Appl. 38, 1017–1031 (2011)

    Article  Google Scholar 

  25. Wong, C.C., Wang, H.Y., Li, S.-A.: PSO-based motion fuzzy controller design for mobile robots. Int. J. Fuzzy Syst. 10(1), 284–292 (2008)

    MathSciNet  Google Scholar 

  26. Elkaranshway, H.A., Bayoumi, E.H.E., Soliman, H.M.: PSO-based robust PID control for flexible manipulator systems. Int. J. Model. Identif. Control 14(1–2), 1–12 (2011)

    Article  Google Scholar 

  27. Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  28. Kennedy, J., Eberhart, R.: Particle swarm optimization. Proceedings of IEEE international conference on neural networks, 1942–1948 (1995)

  29. Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern.-Part B 26(1), 29–41 (1996)

    Article  Google Scholar 

  30. Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modelling and Control. Wiley, Hoboken (2006)

    Google Scholar 

  31. Lee, C.S.George, Ziegler, M.: Geometric approach in solving inverse kinematics of PUMA robots. IEEE Trans. Aerosp. Electron. Syst. 6, 695–706 (1984)

    Article  Google Scholar 

  32. Eberhart, R.C., Shi, Y.: Comparison between genetic algorithms and particle swarm optimization. Evolut. Program. 7, 611–616 (1998)

    Google Scholar 

  33. Clerc, M.: Particle Swarm Optimization. Wiley, Hoboken (2006)

    Book  MATH  Google Scholar 

  34. Richards, M., Ventura, D.: Choosing a starting configuration for particle swarm optimization. Proceedings of the Joint Conference on Neural Networks, 2309–2312 (2004)

  35. Wong, T.T., Luk, W.S., Heng, P.A.: Sampling with Hammersley and Halton points. J. Gr. Tools 2(2), 9–24 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Seyed Mohammad Hashem Zadeh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hashem Zadeh, S.M., Khorashadizadeh, S., Fateh, M.M. et al. Optimal sliding mode control of a robot manipulator under uncertainty using PSO. Nonlinear Dyn 84, 2227–2239 (2016). https://doi.org/10.1007/s11071-016-2641-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2641-4

Keywords

Navigation