Journal of Intelligent & Robotic Systems

, Volume 71, Issue 1, pp 65–83 | Cite as

Design and Implementation of an Inverse Dynamics Controller for Uncertain Nonholonomic Robotic Systems

  • Khoshnam Shojaei
  • Alireza Mohammad Shahri
  • Behzad Tabibian
Article

Abstract

This paper addresses the trajectory tracking control problem of nonholonomic robotic systems in the presence of modeling uncertainties. A tracking controller is proposed such that it combines the inverse dynamics control technique and an adaptive robust PID control strategy to preserve robustness to both parametric and nonparametric uncertainties. A SPR-Lypunov stability analysis demonstrates that tracking errors are uniformly ultimately bounded (UUB) and exponentially converge to a small ball containing the origin. The proposed inverse dynamics tracking controller is successfully applied to a nonholonomic wheeled mobile robot (WMR) and experimental results are presented to validate the effectiveness of the proposed controller.

Keywords

Adaptive-robust Inverse dynamics control Nonholonomic systems Uncertainty Trajectory tracking 

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References

  1. 1.
    Brockett, R.W.: Asymptotic stability and fedback stabilization. In: Brockett, R.W., Milman, R.S., Sussman H.J. (eds.) Differential Geometric Control Theory, pp. 181–191. Boston (1983)Google Scholar
  2. 2.
    Sastry, S.S., Bodson, M.: Adaptive Control: Stability, Convergence and Robustness. Prentice-Hall, Englewood Cliffs, NJ (1989)MATHGoogle Scholar
  3. 3.
    Campion, G., d’Andrea-Novel, B., Bastin, G.: Modeling and State Feedback Control of Nonholonomic Mechanical Systems. In: Proceedings of the 30th Conference on Decision and Control, IEEE, pp. 1184–1189. England (1991)Google Scholar
  4. 4.
    Campion, G., d’Andrea-Novel, B., Bastin, G.: Controllability and state feedback stabilization of nonholonomic mechanical systems. In: de Wit, C.C. et al. (eds.) Lecture Notes in Control and Information Science, vol. 162, pp. 106–124. Springer, New York (1991)Google Scholar
  5. 5.
    Bloch, A.M., Reyhanoglu, M., McClamroch, N.H.: Control and stabiliztion of nonholonomic dynamic systems. IEEE Trans. Automat. Contr. 37(11), 1746–1757 (1992)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Yun, X., Kumar, V., Sarkar, N., Paljug, E.: Control of multiple arms with rolling constraints. In: Proceedings of the International Conference on Robotics and Automation, pp. 2193–2198 (1992)Google Scholar
  7. 7.
    Lewis, F.L., Abdallah, C.T., Dawson, D.M.: Contol of Robot Manipulators. MacMillan, New York (1993)Google Scholar
  8. 8.
    Sarkar, N., Yun, X., Kumar, V.: Control of mechanical systems with rolling constraint: application to dynamic control of mobile robots. Int. J. Rob. Res. 13(1), 55–69 (1994)CrossRefGoogle Scholar
  9. 9.
    Kolmanovsky, I., McClamroch, N.H.: Developments in nonholonomic control problems. IEEE Control Syst. Mag. 15(6), 20–36 (1995)CrossRefGoogle Scholar
  10. 10.
    Walsh, G., Bushnell, L.G.: Stabilization of multiple input chanied form control systems. Syst. Control Lett. 25, 227–234 (1995)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Qu, Z., Dawson, D.M.: Robust Tracking Control of Robot Manipulators. IEEE Press, Piscataway, NJ (1996)MATHGoogle Scholar
  12. 12.
    Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice-Hall, Englewood Cliffs, NJ (1996)MATHGoogle Scholar
  13. 13.
    Yun, X., Yamamoto, Y.: Stability analysis of the internal dynamics of a wheeled mobile robot. J. Robot. Syst. 14, 697–709 (1997)MATHCrossRefGoogle Scholar
  14. 14.
    Yun, X., Sarkar, N.: Unified formulation of robotic systems with holonomic and nonholonomic constraints. IEEE Trans. Robot. Autom. 14(4), 640–650 (1998)CrossRefGoogle Scholar
  15. 15.
    Kim, D.-H., Oh, J.-H.: Tracking Control of a two-wheeled mobile robot using input-output linearization. J. Control Eng. Pract. 7, 369–373 (1999)CrossRefGoogle Scholar
  16. 16.
    Dong, W., Xu, W.L., Huo, W.: Trajectory tracking control of dynamic non-holonomic systems with unknown dynamics. Int. J. Robust Nonlinear Control 9, 905–922 (1999)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Jiang, Z.-P., Nijmeijer, H.: A recursive technique for tracking control of dynamic nonholonomic systems in chained form. IEEE Trans. Automat. Contr. 34(32), 265–279 (1999)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Dixon, W.E., Dawson, D.M.: Tracking and regulation control of a mobile robot system with kinematic disturbances: a variable structure-like approach. Trans. ASME J. Dyn. Syst. Measure. Control 122, 616–623 (2000)CrossRefGoogle Scholar
  19. 19.
    Dong, W., Xu, W.L.: Adaptive tracking control of uncertain nonholonomic dynamic system. IEEE Trans. Automat. Contr. 46(3), 450–454 (2001)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Oriolo, G., De Luca, A., Vendittelli, M.: WMR control via dynamic feedback linearization: design, implementation, and experimental validation. IEEE Trans. Control Syst. Technol. 10(6), 835–852 (2002)CrossRefGoogle Scholar
  21. 21.
    Oya, M., Su, C.-Y., Katoh, R.: Robust adaptive motion/force tracking control of uncertain nonholonomic mechanical systems. IEEE Trans. Robot. Autom. 19(1), 175–181 (2003)CrossRefGoogle Scholar
  22. 22.
    Coelho, P., Nunes, U.: Lie algebra application to mobile robot control: a tutorial. Robotica 21(5), 483–493 (2003)CrossRefGoogle Scholar
  23. 23.
    De La Cruz, C., Carelli, R.: Dynamic modeling and centralized formation control of mobile robots. In: Proceedings of thirty-second annual conference of the IEEE industrial electronics society, pp. 3880–3885. IECON, Paris (2006)Google Scholar
  24. 24.
    Martins, F.N., Celeste, W.C., Carelli, R., Filho, M.S., Filho, T.F.B.: An adaptive dynamic controller for autonomous mobile robot trajectory tracking. J. Control Eng. Pract. 16, 1354–1363 (2008)CrossRefGoogle Scholar
  25. 25.
    Shojaei, K., Tarakameh, A., Mohammad Shahri, A.: Adaptive trajectory tracking of WMRs based on feedback linearization technique. In: Proceedings of the International Conference on Mechatronics and Automation, IEEE, pp. 729–734. Changchun, China (2009)Google Scholar
  26. 26.
    Shojaei, K., Mohammad Shahri, A., Tarakameh, A.: Adaptive feedback linearizing control of nonholonomic wheeled mobile robots in presence of parametric and nonparametric uncertainties. Robot. Comput.-Integr. Manuf. 27, 194–204 (2011)CrossRefGoogle Scholar
  27. 27.
    Shojaei, K., Mohammad Shahri, A., Tarakameh, A., Tabibian, B.: Adaptive trajectory tracking control of a differential drive wheeled mobile robot. Robotica 29, 391–402 (2010)CrossRefGoogle Scholar
  28. 28.
    Park, B.S., Yoo, S.J., Park, J.B., Choi, Y.H.: A simple adaptive control approach for trajectory tracking of electricaslly driven nonholonomic mobile robots. IEEE Trans. Control Syst. Technol. 18(5), 1199–1206 (2010)CrossRefGoogle Scholar
  29. 29.
    Chwa, D.: Tracking control of differential-drive wheeled mobile robots using a backstepping-like feedback linearization. IEEE Trans. Syst. Man Cybern. 40(6), 1285–1295 (2010)CrossRefGoogle Scholar
  30. 30.
    Das, T., Kar, I.N., Chaudhury, S.: Simple neuron-based adaptive controller for a nonholonomic mobile robot including actuator dynamics. J. Neurocomput. 69, 2140–2151 (2006)CrossRefGoogle Scholar
  31. 31.
    Park, B.S., Yoo, S.J., Park, J.B., Coi, Y.H.: Adaptive ouput-feedback control for trajectory tracking of eletcrically driven non-holonomic mobile robots. J. IET Control Theor. Appl. 5(6), 830–838 (2010)CrossRefGoogle Scholar
  32. 32.
    Shojaei, K., Shahri, A.M.: Output feedback tracking control of uncertain non-holonomic wheeled mobile robots: a dynamic surface control approach. J. IET Control Theor. Appl. 6(2), 216–228 (2012)Google Scholar
  33. 33.
    Moustris, G.P., Tzafestas, S.G.: Switching fuzzy tracking control for mobile robots under curvature constraints. J. Control Eng. Pract. 19(1), 45–53 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Khoshnam Shojaei
    • 1
  • Alireza Mohammad Shahri
    • 1
  • Behzad Tabibian
    • 2
  1. 1.Mechatronics and Robotics Research Laboratory, Electronic Research Center, Electrical Engineering DepartmentIran University of Science and TechnologyTehranIran
  2. 2.School of InformaticsUniversity of EdinburghEdinburghEngland

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