Advertisement

Sādhanā

, 44:109 | Cite as

Simultaneous estimation of parameter uncertainties and disturbance trajectory for robotic manipulator

  • VIJYANT AGARWALEmail author
  • HARISH PARTHASARATHY
Article
  • 12 Downloads

Abstract

In this work, a systematic approach is proposed to estimate the disturbance trajectory using a new generalized Lyapunov matrix valued function of the joint angle variables and the robot’s physical parameters using the maximum likelihood estimate (MLE). It is also proved that the estimated disturbance error remains bounded over the infinite time interval. Here, the manipulator is excited with a periodic torque and by the position and velocity data collected at discrete time points construct an ML estimator of the parameters at time \( t + dt \). This process is carried over hand in hand in a recursive manner, thus resulting in a novel unified disturbance rejection and parameter estimation in a general frame work. These parameter estimates are then analyzed for mean and covariance and compared with the Cramer Rao Lower Bound (CRLB) for the parametric statistical model. Using the Lyapunov method, convergence of the “disturbance estimation error” to zero is established. We assume that a Lyapunov matrix dependent on the link angle and form the energy corresponding to this matrix as a quadratic function of the disturbance estimate error. Using the dynamics of the disturbance observer, the rate of change of the Lyapunov energy is evaluated as a quadratic form in the disturbance error. This quadratic form is negative definite for the angular velocity in a certain range and for a certain structured form of the Lyapunov energy matrix. The most general form of the Lyapunov matrix is obtained that guarantees negative rate of increase of the energy and a better bound on the disturbance estimation error convergence rate to zero. This is possible only because we have used the most general form of the Lyapunov energy matrix.

Keywords

Nonlinear disturbance observer (NDO) parameter estimation maximum likelihood estimation (MLE) Cramer Rao lower bond (CRLB) Lyapunov energy function stochastic process 

Notes

Acknowledgements

This work was supported by grant (SR/CSI/24/2011(C and G)) from the Department of Science and Technology, Government of India.

References

  1. 1.
    Mohammadi A, Tavakoli M, Marquez H J and Hashemzadeh F 2013 Nonlinear disturbance observer design for robotic manipulators. Control Engineering Practice 21: 253–267CrossRefGoogle Scholar
  2. 2.
    Wen-Hua Chen, Ballance D J, Gawthrop P J and O’ Reilly J 2000 A nonlinear disturbance observer for robotic manipulators. IEEE Transactions on Industrial Electronics 47: 932–938CrossRefGoogle Scholar
  3. 3.
    Nikoobin A and Haghighi R 2009 Lyapunov-based nonlinear disturbance observer for serial n-link manipulators. Journal of Intelligent and Robotic Systems 55: 135–153CrossRefGoogle Scholar
  4. 4.
    Seok Jinwook, Woojong Yoo and Sangchul Won 2012 Inertia-related Coupling Torque Compensator for Disturbance Observer based Position Control of Robotic Manipulator. International Journal of Control, Automation, and Systems 10(4): 753–760CrossRefGoogle Scholar
  5. 5.
    Kong Kyoungchul and Tomizuka Masayoshi 2013 Nominal Model Manipulation for Enhancement of Stability Robustness for Disturbance Observer-Based Control Systems. International Journal of Control, Automation and Systems 11(1): 12–20CrossRefGoogle Scholar
  6. 6.
    Kobayashi Hideyuki Kobayashi, Seiichiro Katsura and Kouhei Ohnishi 2007 An analysis of parameter variations of disturbance observer for motion control. IEEE Transactions on Industrial Electronics 54(6): 3413–3421CrossRefGoogle Scholar
  7. 7.
    Shim H and Jo N H 2009 An almost necessary and sufficient condition for robust stability of closed loop systems with disturbance observer. Automatica 45(1): 296–299MathSciNetCrossRefGoogle Scholar
  8. 8.
    Emre and Ohnishi Kouhei 2015 Stability and Robustness of Disturbance-Observer-Based MotionControl Systems. IEEE Trans. on Industrial Electronics 62(1): 414–422Google Scholar
  9. 9.
    Leena G and Ray G 2012 A set of decentralized PID controllers for an n-link robot manipulator Sadhana 37(3): 405–423CrossRefGoogle Scholar
  10. 10.
    Yoon Young-Doo, Eunsoo Jung and Seung-Ki Sul 2008 Application of a Disturbance Observer for a Relative Position Control System. IEEE Transactions on Industrial Electronics 46(2): 849–856Google Scholar
  11. 11.
    Zheng Qing Chen, Zhongzhou and Gao Zhiqiang 2009 A practical approach to disturbance decoupling control. Control Engineering Practice 17: 1016–1025CrossRefGoogle Scholar
  12. 12.
    Guo Lei and Cao Songyin 2014 Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions 53: 846–849CrossRefGoogle Scholar
  13. 13.
    Liu Chao, Jianhua Wu, Jia Liu and Zhenhua Xiong 2014 High acceleration motion control based on a time-domain identification method and the disturbance observer. Mechatronics 24: 672–678CrossRefGoogle Scholar
  14. 14.
    Zhang Zhengqiang and Xu Shengyuan 2015 Observer design for uncertain nonlinear systems with unmodeled dynamics. Automatica 51: 80–-84MathSciNetCrossRefGoogle Scholar
  15. 15.
    Kim Kyung-Soo and Rew Keun-Ho 2013 Reduced order disturbance observer for discrete-time linear systems. Automatica 49: 968–975MathSciNetCrossRefGoogle Scholar
  16. 16.
    Kapun A, Curkovic M, Ales Hace and Jezernik K 2008 Identifying dynamic model parameters of a BLDC motor. Simulation Modelling Practice and Theory 16: 1254–1265CrossRefGoogle Scholar
  17. 17.
    Xu Ling, Lei Chen and Weili Xiong 2015 Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration. Nonlinear Dynamics 79(3): 2155–2163MathSciNetCrossRefGoogle Scholar
  18. 18.
    Chan Linping, Fazel Naghdy and David Stirling 2013 Extended active observer for force estimation and disturbance rejection of robotic manipulators. Robotics and Autonomous Systems 61: 1277–1287CrossRefGoogle Scholar
  19. 19.
    Pan Yi-Ren, Yi-Ti Shih, Rong-Hwang Horng and An-Chen Lee 2009 Advanced Parameter Identification for a Linear-Motor-Driven Motion System Using Disturbance Observer. International Journal of precision Engineering and Manufacturing 10(4): 35–47CrossRefGoogle Scholar
  20. 20.
    Wang Dongqing, Feng Ding and Xinzhuang Dong 2012 Iterative Parameter Estimation for a Class of Multivariable Systems Based on the Hierarchical Identification Principle and the Gradient Search. Circuits Systems Signal Process 31: 2167–2177MathSciNetCrossRefGoogle Scholar
  21. 21.
    Liu C S and Peng H 2000 Disturbance observer based tracking control. ASME Transactions of the Dynamic Systems Measurement and Control 122: 332–335CrossRefGoogle Scholar
  22. 22.
    Shahi M and Mazinan A H 2015 Automated adaptive sliding mode control scheme for a class of real complicated systems. Sadhana 40(1): 51–74MathSciNetCrossRefGoogle Scholar
  23. 23.
    Karkar N, Benmhammed K and Bartil A 2014 Parameter Estimation of Planar Robot Manipulator Using Interval Arithmetic Approach. Arabian Journal for Science and Engineering 39: 5289–5295CrossRefGoogle Scholar
  24. 24.
    Cazalilla J, Marina Vallés, Vicente Mata and Ángel Valera 2014 Adaptive control of a 3-DOF parallel manipulator considering payload handling and relevant parameter models. Robotics and Computer-Integrated Manufacturing 30: 468–477CrossRefGoogle Scholar
  25. 25.
    JohnCorts-Romero, Germán A Ramos and HoracioCoral-Enriquez 2014 Generalized proportional integral control for periodic signals under active disturbance rejection approach. ISA Transactions 53: 1901–1909CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Division of MPAENetaji Subhas University of TechnologyNew DelhiIndia
  2. 2.Division of Electrical and Communication EngineeringNetaji Subhas University of TechnologyNew DelhiIndia

Personalised recommendations