International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

Impedance Control of Flexible Base Mobile Manipulator Using Singular Perturbation Method and Sliding Mode Control Law

  • Salehi, Mahdi (Department of Mechanical Engineering, Sharif University of Technology) ;
  • Vossoughi, Gholamreza (Center of Excellence in Design, Robotics and Automation (CEDRA) and the Department of Mechanical, Sharif University of Technology)
  • Published : 2008.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the general problem of impedance control for a robotic manipulator with a moving flexible base is addressed. Impedance control imposes a relation between force and displacement at the contact point with the environment. The concept of impedance control of flexible base mobile manipulator is rather new and is being considered for first time using singular perturbation and new sliding mode control methods by authors. Initially slow and fast dynamics of robot are decoupled using singular perturbation method. Slow dynamics represents the dynamics of the manipulator with rigid base. Fast dynamics is the equivalent effect of the flexibility in the base. Then, using sliding mode control method, an impedance control law is derived for the slow dynamics. The asymptotic stability of the overall system is guaranteed using a combined control law comprising the impedance control law and a feedback control law for the fast dynamics. As first time, base flexibility was analyzed accurately in this paper for flexible base moving manipulator (FBMM). General dynamic decoupling, whole system stability guarantee and new composed robust control method were proposed. This proposed Sliding Mode Impedance Control Method (SMIC) was simulated for two FBMM models. First model is a simple FBMM composed of a 2 DOFs planar manipulator and a single DOF moving base with flexibility in between. Second FBMM model is a complete advanced 10 DOF FBMM composed of a 4 DOF manipulator and a 6 DOF moving base with flexibility. This controller provides desired position/force control accurately with satisfactory damped vibrations especially at the point of contact. This is the first time that SMIC was addressed for FBMM.

Keywords

References

  1. M. K. Khorasani and P. V. Kokotovic, "Feedback linearization of a flexible manipulator near its rigid body manifold," Systems & Control Letters, vol. 3, no. 6, pp. 187-192, 1985
  2. M. W. Spong, "Modeling and control of elastic joint robots," ASME Journal of Dynamic Systems, Measurement and Control, vol. 109, no. 4, pp. 310-319, 1987 https://doi.org/10.1115/1.3143860
  3. H. K. Khalil, Nonlinear Systems, 3rd edition, Chapter 11, Singular Perturbations, Pearson Education Int. Inc, New Jersey, USA, 1996
  4. J. Y. Lew and S. M. Moon, "A simple active damping controller compliant base manipulators," IEEE Trans. on Mechatornics, vol. 6, no. 3, pp. 305-310, 2001 https://doi.org/10.1109/3516.951368
  5. A. Ercodi-Finzi and P. Mantegazza, "Dynamic modeling and control strategies of space manipulators," Polytechnic of Milan, Italy, Part of Mechanic Pan-America, November 1993
  6. N. Hootsmans and S. Dubowsky, "Large motion control of an experimental mobile manipulator with limited sensing," Proc. of the 31st SICE Annual Conference, pp. 983-986, 1992
  7. M. A. Torres, S. Dubowsky, and A. Pisoni, "Path planning for elastically-mounted space manipulators," Proc. of IEEE Int. Conf. Robotics and Automation, San Diego, CA, May 1994
  8. C. Mavroidis, S. Dubowsky, and V. Raju, "End point control of long reach manipulator systems," The International Journal of Robotics, pp. 1836-1842, 1991
  9. J. Kenneth Salisbury, "Active stiffness control of a manipulator in Cartesian coordinates," Proc. of the IEEE Conference on Decision and Control, vol. 1, pp. 95-100, 1980
  10. N. Hogen, "Impedance control an approach to manipulation: Part I, Part II, Part III," ASME J. Dynamic Syst. Measurement. Contr., vol. 107, no. 3, pp. 1-24, 1987
  11. H. Kazerooni, T. B. Sheridan, and P. K. Houpt, "Robust compliant motion for manipulators, Part 1: fundamental concept of compliant motion, Part II: design method," IEEE. J. Robotics and Automation, vol. 2, no. 2, pp. 83-105, 1986 https://doi.org/10.1109/JRA.1986.1087045
  12. K. Inoue, T. Miyamoto, and Y. Okawa, "Impedance control of mobile manipulator with the stability to extended force," Proc. of IROS, Osaka University, pp. 721-728, 1996
  13. Ch. Lao and M. Donath, "Generalized impedance control of a redundant Manipulator for handling tasks with position uncertainty while avoiding obstacles," Proc. of the IEEE, Int Conf. on Robotics and Automation, New Mexico, pp. 575-579, 1997
  14. D. Yan and Y. Lin, "Modeling and impedance control of a two- manipulator system handling a flexible beam," Proc. of the IEEE Int. Conf. on Robotics and Automation, New Mexico, 1997
  15. S. A. A. Mossavian and E. Papadaouplos, "On the control of space free-flyers using multiple impedance control," Proc. of IEEE on Robotics and Automation, April 21-27, 1997
  16. S. Kang, K. Komoriya, K. Yokoi, K. Koutoku, and T. Tanie, "Reduced internal effect in damping-based posture control on mobile manipulator," Proc. of the IEEE/RSJ in Intelligent Robots and Systems, Hawaii, USA, 2001
  17. Y. Hu and G. Vukovich, "Position and force control of flexible joint robots with damping constrained motion tasks," Journal of Mechanism and Machine Theory, vol. 36, no. 7, pp. 853-871, 2001 https://doi.org/10.1016/S0094-114X(01)00021-0
  18. J. Roy and L. Whitcomb, "Adaptive force control of position/velocity controlled robots, theory and experiment," IEEE Trans. on Robotics and Automation, vol. 18, no. 2, pp. 121-137, 2002 https://doi.org/10.1109/TRA.2002.999642
  19. A. Schaffer, C. Ott, U. Frese, and G. Hirzinger, "Cartesian impedance control techniques for torque controlled light-weight robots," Proc. IEEE Int. Conf. on Robotics and Automation, pp. 657-663, 2002
  20. B. Subudhi and A. S. Morris, "Dynamic modeling, simulation and control of a manipulator with flexible link and joints," Journal of Robotics and Autonomous Systems, vol. 41, no. 4, pp. 257-270, 2002 https://doi.org/10.1016/S0921-8890(02)00295-6
  21. J. Tan, N. Xi, and Y. Wang, "Integrated task planning and control for mobile manipulator," Int. Journal of Robotics Research, vol. 22, no. 5, pp. 337-354, May 2003 https://doi.org/10.1177/0278364903022005004
  22. L. Hang, S. S. Ge, and T. H. Lee, "Fuzzy unidirectional force control of constrained robotic manipulators," Journal of Fuzzy Set and Systems, vol. 134, no. 1, pp. 135-146, 2003 https://doi.org/10.1016/S0165-0114(02)00234-8
  23. Ch. Ott, A. Shaffer, and A. Kugi, "Decoupling based cartesian impedance control of flexible joint robots," Proc. of IEEE Int. Conf. on Robotics and Automation, DLR, German Aerospace Center, pp. 2666-2672, 2003
  24. G. R.Vossoughi and A. Karimzadeh, "Impedance control of a two degree-of-freedom planar flexible link manipulator using singular perturbation theory," Robotica, Cambridge University Press, vol. 24, no. 2. pp. 221-228, 2006 https://doi.org/10.1017/S0263574705002055