Set-Point Control of Elastic Joint Robots Using only Position Measurements

  • Son, Young-Ik (School of Electrical, Electronic & Computer Engineering, Dong-A University) ;
  • Hyungbo Shim (Division of Electrical and Computer Engineering, Hanyang University) ;
  • Seo, Jin-Heon (School of Electrical Engineering#23, Seoul National University)
  • Published : 2002.08.01

Abstract

Motivated by the dynamic output feedback passification results, point-to-point control laws for an elastic joint robot are presented when only the position measurements are available. The proposed method makes a parallel connection of the robot system and an input-dimensional linear system which obtains the effect of the desired differentiators. It is shown that the closed-loop nonlinear robot system can be rendered output strictly passive and the regulation of the system is achieved in the end. Robustness analysis is also given with regard to uncertainties on the robot parameters. Performance of the proposed control law is illustrated in the simulation studies of a manipulator with three revolute elastic joints.

Keywords

References

  1. Ailon, A. and Ortega, R. 1993, 'An Observer-Based Set-Point Controller for Robot Manipulators with Flexible Joints,' Systems & Control Letters 21, pp. 329-335 https://doi.org/10.1016/0167-6911(93)90076-I
  2. Bar-Kana, I., 1987, 'Parallel Feedforward and Simplified Adaptive Control,' Int. J. Adaptive Control and Signal Processing, 1 (2), pp. 95-109 https://doi.org/10.1002/acs.4480010202
  3. Bar-Kana, I. and Guez, A., 1990, 'Simple Adaptive Control for a Class of Non-Linear Systems with Application to Robotics,' Int. J. Control, 52(1), pp. 77-99
  4. Berghuis, B. and Nijmeijer, H., 1993, 'Global Regulation of Robots Using only Position Measurements,' Systems & Control Letters, 21, pp. 289-293 https://doi.org/10.1016/0167-6911(93)90071-D
  5. Byrnes, C. I., Isidori, A. and Willems, J. C, 1991, 'Passivity, Feedback Equivalence, and the Global Stabilization of Minimum Phase Nonlinear Systems,' IEEE Trans. Automat. Contr, 36(11), pp. 1228-1240 https://doi.org/10.1109/9.100932
  6. Edwards, C. and Spurgeon, S. K., 1998, Sliding Mode Control, Taylor & Francis
  7. Fradkov, A. L. and Hill, D. J. 1998, 'Exponential Feedback Passivity and Stabilizability of Nonlinear Systems,' Automatica, 34 (6), pp. 697-703 https://doi.org/10.1016/S0005-1098(97)00230-6
  8. Hill, D. J. and Moylan, P. J., 1977, 'Stability Results for Nonlinear Feedback Systems,' Automatica 13, pp. 377-382 https://doi.org/10.1016/0005-1098(77)90020-6
  9. Jiang, Z. P. and Hill, D. J., 1998, 'Passivity and Disturbance Attenuation via Output Feedback for Uncertain Nonlinear Systems,' IEEE Trans. Automat. Contr. 43(7), pp. 992-997 https://doi.org/10.1109/9.701109
  10. Kaufman, H., Bar-Kana, I. and Sobel, K., 1998. Direct Adaptive Control Algorithms, 2nd ed.. Springer-Verlag
  11. Kelly, R., Ortega, R., Ailon, A. and Loria, A., 1994, 'Global Regulation of Flexible Joint Robots Using Approximate Differentiation,' IEEE Trans. Automat. Contr. 39, pp. 1222-1224 https://doi.org/10.1109/9.293181
  12. Lanari, L. and Wen, J. T., 1992, 'Asymptotically Stable Set Point Control Laws for Flexible Robots,' Systems & Control Letters 19, pp. 119-129 https://doi.org/10.1016/0167-6911(92)90095-A
  13. Lin, W., 1995, 'Feedback Stabilization of General Nonlinear Control Systems: A Passive System Approach,' Systems & Control Letters 25, pp. 41-52. https://doi.org/10.1016/0167-6911(94)00056-2
  14. Nicosia, S. and Tomei, P., 1994, 'A Tracking Controller for Flexible Robots Using only Link Position Feedback,' In: Proc. of Conf. on Decision and Control, pp. 1817-1822
  15. Ortega, R., Lori, A., Nicklasson, P. J. and Sira-Ramirez, H., 1998, Passivity-Based Control of Euler-Lagrange Systems, Springer-Verlag
  16. Sepulchre, R., Jankovic, M. and Kokotovic, P. V., 1997, Constructive Nonlinear Control, Springer-Verlag
  17. Son, Young I., Shim Hyungbo and Seo JinH., 1999, 'Passification of Nonlinear Systems via Dynamic Output Feedback,' In : Proc. of Conf. on Decision and Control, pp. 4877-4878 https://doi.org/10.1109/CDC.1999.833316
  18. Son, Young I., Shim Hyungbo, Park, K. and Seo Jin H., 2000, 'Stabilization of Linear Systems via Low-Order Dynamic Output Feedback: A Passification Approach,' In : Proc. of American Control Conference https://doi.org/10.1109/ACC.2000.876937
  19. Spong, M. W. and Vidyasagar, M., 1989, Robot Dynamics and Control, John Wiley & Sons, Inc.
  20. Su, W. and Xie, L., 1996, 'Robust Control of Nonlinear Feedback Passive Systems,' Systems & Control Letters 28, pp. 85-93 https://doi.org/10.1016/0167-6911(96)00011-4
  21. Takegaki, M. and Arimoto, S., 1981, 'A New Feedback Method for Dynamic Control of Manipulators,' ASME J. Dynamic Systems, Measurement, and Control, 103, pp. 119-125
  22. Tomei, P., 1991a, 'Adaptive PD Controller for Robot Manipulators,' IEEE Trans. Robotics and Automation 7(4), pp. 565-570 https://doi.org/10.1109/70.86088
  23. Tomei, P., 1991b, 'A Simple PD Controller for Robots with Elastic Joints,' IEEE Trans. Automat. Contr, 36, pp. 1208-1213 https://doi.org/10.1109/9.90238