Stability Analysis of Visual Servoing with Sliding-mode Estimation and Neural Compensation

  • Yu Wen (Departamento de Control Automatico)
  • Published : 2006.10.01

Abstract

In this paper, PD-like visual servoing is modified in two ways: a sliding-mode observer is applied to estimate the joint velocities, and a RBF neural network is used to compensate the unknown gravity and friction. Based on Lyapunov method and input--to-state stability theory, we prove that PD-like visual servoing with the sliding mode observer and the neuro compensator is robust stable when the gain of the PD controller is bigger than the upper bounds of the uncertainties. Several simulations are presented to support the theory results.

Keywords

References

  1. R. Kelly, 'Robust asymptotically stable visual servoing of planar robots,' IEEE Trans. on Robotics and Automation, vol. 12, no. 5, pp. 759-766, 1996 https://doi.org/10.1109/70.538980
  2. L. E. Weiss, A. C. Sanderson, and C. P. Neuman, 'Dynamic sensor-based control of robots with visual feedback,' IEEE Trans. on Robotics and Automation, vol. 3, no. 4, pp. 404-417, 1987 https://doi.org/10.1109/JRA.1987.1087115
  3. S. Hutchinson, G. D. Hager, and P. I. Corke, 'A tutorial on visual servo control,' IEEE Trans. Robotics and Automation, vol. 12, no. 5, pp. 651-670, 1996 https://doi.org/10.1109/70.538972
  4. F. Miyazaki and Y. Masutani, 'Robustness of sensory feedback control based on imperfect Jacobian,' Proc. of Robotics Research: 5th Int Symp., H. Miurna and S. Arimoto, Eds., Cambridge, MA, pp. 201-208, 1990
  5. N. P. Papanikolopoulos and P. K. Khosla, 'Adaptive robotic visual tracking: Theory and experiments,' IEEE Trans. on Automatic Control, vol. 38, no. 3, pp. 429-445, 1993 https://doi.org/10.1109/9.210141
  6. H. Hashimoto, T. Kubota, M. Sato, and F. Harashima, 'Visual control of robotic manipulator based on neural networks,' IEEE Trans. on Industrial Electronics, vol. 39, no. 6, pp. 490- 496, 1992 https://doi.org/10.1109/41.170967
  7. V. Santibanez and R. Kelly, 'Global asymptotic stability of the PD control with computed feedforward in closed loop with robot manipulators,' Proc. of the 14th IFAC World Congress, Beijing, pp. 197-203, 1999
  8. G. Loreto, W. Yu, and R. Garrido, 'Stable visual servoing with neural networks compensation,' Proc. of the IEEE International Symposium on Intelligent Control, Mexico City, Mexico, pp. 183-188, 2001
  9. B. Espiau, F. Chaumette, and O. Rives, 'A new approach to visual servoing in robotics,' IEEE Trans. on Robotics and Automation, vol. 8, no. 3, pp. 313-326, 1992 https://doi.org/10.1109/70.143350
  10. K. Hashimoto and H. Kimura, 'Visual servoing with nonlinear observer,' Proc. of IEEE Int. Conf. Robotics and Automation, pp. 484-498, 1995
  11. Y. H. Kim and F. L. Lewis, 'Neural network output feedback control of robot manipulators,' IEEE Trans. on Robotics and Automation, vol. 15, no. 2, pp. 301-309, 1999 https://doi.org/10.1109/70.760351
  12. R. Kelly, 'A tuning procedure for stable PID control of robot manipulators,' Robotica, vol. 13, no. 2, pp. 141-148, 1995 https://doi.org/10.1017/S0263574700017641
  13. K. Hashimoto and T. Noritsugu, 'Visual servoing with linearized observer,' Proc. of IEEE Int. Conf. Robotics and Automation, pp. 263-268, 1999
  14. B. K. Ghosh and E. P. Loucks, 'A realization theory for perspective systems with application to parametrer estimation problems in machine vision,' IEEE Trans. on Automatic Control, vol. 41, no. 12, pp. 1706-1722, 1996 https://doi.org/10.1109/9.545711
  15. M. Spong and M. Vidyasagar, Robot Dynamics and Control, New York, Wiley, 1989
  16. C. C. Cheah, K. Lee, S. Kawamura, and S. Arimoto, 'Asympototic stability of robot control with approximate Jacobian matrix and its application to visual servoing,' Proc. of the 40th Conference on Decision and Control, Orlando, USA, 2001
  17. M. Takegaki and S. Arimoto, 'A new feedback method for dynamic control of manipulator,' ASME Journal of Dynamic Systems, Measurement, and Control, vol. 103, pp. 119-125, 1981 https://doi.org/10.1115/1.3139651
  18. F. L. Lewis and T. Parisini, 'Neural network feedback control with guaranteed stability,' Int. J. Control, vol. 70, no. 3, pp. 337-339, 1998 https://doi.org/10.1080/002071798222262
  19. W. Yu and X. Li, 'Visual servoing with velocity observer and neural compensation,' Proc. of IEEE International Symposium on Intelligent Control, Taipei, Taiwan, pp. 454-459, 2004
  20. S. Haykin, Neural Networks: A Comprehensive Foundation, Macmillan College Publ. Co., New York, 1994
  21. W. Yu and X. Li, 'Some new results on system identification with dynamic neural networks,' IEEE Trans. on Neural Networks, vol. 12, no. 2, pp. 412-417, 2001 https://doi.org/10.1109/72.914535
  22. C. I. Byrnes, A. Isidori, and J. C. Willems, 'Passivity feedback equivalence and the global stabilization of minimum phase nonlinear systems,' IEEE Trans. on Automatic Control, vol. 36, no. 11, pp. 1228-1240, 1991 https://doi.org/10.1109/9.100932
  23. E. D. Sontag and Y. Wang, 'On characterization of the input-to-state stability property,' System & Control Letters, vol. 24, pp. 351-359, 1995 https://doi.org/10.1016/0167-6911(94)00050-6
  24. G. Cybenko, 'Approximation by superposition of sigmoidal activation function,' Math. Control, Sig Syst, vol. 2, pp. 303-314, 1989 https://doi.org/10.1007/BF02551274
  25. H. K. Khalil, Nonlinear Systems, 3rd Edition, Prentice-Hall, NJ, 1999