Skip to main content
×
Home
    • Aa
    • Aa

Control and disturbances compensation in underactuated robotic systems using the derivative-free nonlinear Kalman filter

  • Gerasimos G. Rigatos (a1)
Summary
SUMMARY

The Derivative-free nonlinear Kalman Filter is used for developing a robust controller which can be applied to underactuated MIMO robotic systems. The control problem for underactuated robots is non-trivial and becomes further complicated if the robot is subjected to model uncertainties and external disturbances. Using differential flatness theory it is shown that the model of a closed-chain 2-DOF robotic manipulator can be transformed to linear canonical form. For the linearized equivalent of the robotic system it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system cannot be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is shown that one can estimate simultaneously external disturbance terms that affect the robotic model or disturbance terms which are associated with parametric uncertainty. The efficiency of the proposed Kalman Filter-based control scheme is tested in the case of a 2-DOF planar robotic manipulator that has the structure of a closed-chain mechanism.

Copyright
Corresponding author
*Corresponding author. E-mail: grigat@ieee.org
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1. J. Franch , S. K. Agrawal and V. Sangwan , “Differential flatness of a class of -DOF planar manipulators driven by 1 or 2 actuators,” IEEE Trans. Autom. Control 55 (2), 548554 (2010).

2. C. Zhang , J. Franch and S. K. Agrawal , “Differentially flat design of a closed-chain planar underactuated 2-DOF system,” IEEE Trans. Robot. 29 (1), 277282 (2013).

3. X. Xin , S. Tanaka , J. She and T. Yamasaki , “New analytical results of energy-based swing-up control for the Pendubot,” Int. J. Non-Linear Mech., 52, 110118 (2013).

4. X.-Z. Lai , C.-Z. Pan , M. Wu and S. X. Yang , “Unified control of n-link underactuated manipulator with single passive joint: A reduced order approach,” Mech. Mach. Theory, Elsevier 56, 170185 (2012).

7. A. D. Mahindrakar , S. Rao and R. N. Banavar , “Point-to-point control of a 2R planar horizontal underactuated manipulator,” Mech. Mach. Theory, Elsevier 41, 838844 (2006).

8. K. S. Hong , “An open-loop control for underactuated manipulators using oscillatory inputs: Steering capability of an unactuated joint,” IEEE Trans. Control Syst. Technol. 10 (3), 469479 (2002).

10. H. Gao , X. Song , L. Ding , K. Xia and N. Li , “Adaptive motion control of wheeled mobile robot with unknown slippage,” Int. J. Control 87 (8), 15131522 (2014).

11. C. Torres , J. J. Rubio , C. Aguilar-Ibañez and J. H. Perez-Cruz , “Stable optimal control applied to a cylindrical robotic arm,” Neural Comput. Appl. 24 (3–4), 937944 (2014).

12. Y. Zhang , X. Yu , Y. Yin , C. Peng and Z. Fan , “Singularity-conquering ZG controllers of z2g1 type for tracking control of the IPC systems,” Int. J. Control 87 (9), 17291746 (2014).

13. J. J. Rubio , Z. Zamudio , J. Pacheco and D. Mujica-Vargas , “Proportional derivative control with inverse dead-zone for pendulum systems,” Math. Problems Eng. 2013, 19 (2013).

14. S. H. Ri , J. Huang , Y. Wang , M. H. Kim and S. An , “Terminal sliding mode control of mobile wheeled inverted pendulum system with nonlinear disturbance observer,” Math. Problems Eng. 2014, 18 (2014).

15. S. K. Agrawal and V. Sangwan , “Differentially flat designs of underactuated open-chain planar robots,” IEEE Trans. Robot. 24 (6), 14451451 (2008).

19. G. G. Rigatos , Modelling and Control for Intelligent Industrial Systems: Adaptive Algorithms in Robotcs and Industrial Engineering (Springer, 2011).

20. J. Lévine , “On necessary and sufficient conditions for differential flatness,” Appl. Algebra Eng. Commun. Comput., Springer 22 (1), 4790 (2011).

22. J. Villagra , B. d'Andrea-Novel , H. Mounier and M. Pengov , “Flatness-based vehicle steering control strategy with SDRE feedback gains tuned via a sensitivity approach,” IEEE Trans. Control Syst. Technol. 15, 554565 (2007).

25. S. Bououden , D. Boutat , G. Zheng , J. P. Barbot and F. Kratz , “A triangular canonical form for a class of 0-flat nonlinear systems,” Int. J. Control, Taylor and Francis 84 (2), 261269 (2011).

27. G. G. Rigatos , “A derivative-free Kalman Filtering approach to state estimation-based control of nonlinear dynamical systems,” IEEE Trans. Ind. Electron. 59 (10), 39873997 (2012).

28. G. G. Rigatos , “Nonlinear Kalman filters and particle filters for integrated navigation of unmanned aerial vehicles,” Robot. Auton. Syst. Elsevier, 2012.

29. W. H. Chen , D. J. Ballance , P. J. Gawthrop and J. O. Reilly , “A nonlinear disturbance observer for robotic manipulators,” IEEE Trans. Ind. Electron. 47 (4), 932938 (2000).

30. R. Cortesao , J. Park and O. Khatib , “Real-time adaptive control for haptic telemanipulation with Kalman Active Observers,” IEEE Trans. Robot. 22 (5), 987999 (2005).

31. R. Cortesao , “On Kalman active observers,” J. Intell. Robot. Syst., Springer 48 (2), 131155 (2006).

32. A. Gupta and M. K. O. Malley , “Disturbance-observer-based force estimation for haptic feedback,” ASME J. Dyn. Syst. Meas. Control 133 (1), article no, 014505 (2011).

35. G. Rigatos , Nonlinear Control and Filtering using Differential Flatness Approaches: Applications to Electromechanical Systems (Springer, 2015).

37. C. Harris , X. Hong and Q. Gan , Adaptive Modelling, Estimation and Fusion From Data (Springer, 2002).

40. E. W. Kamen and J. K. Su , Introduction to Optimal Estimation (Springer, 1999).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Robotica
  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 33 *
Loading metrics...

Abstract views

Total abstract views: 169 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd September 2017. This data will be updated every 24 hours.