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Markov Jump Linear Systems-Based Control

  • Adriano A. G. Siqueira
  • Marco H. Terra
  • Marcel Bergerman
Chapter

Abstract

In this chapter we deal with the problem of fault tolerant control of robotic manipulators. We present a fault-modeling framework based on Markovian jump linear systems. An important feature of this approach is that it does not require that the manipulator be stopped when a fault is detected, i.e., the manipulator can continue moving until all joints have reached their respective desired positions. We deal here with free joint faults, when joint actuators lose their ability to apply torque and only the joint’s on/off brake is operative. We present experimental results based on \({{\mathcal{H}}}_2,\;{{\mathcal{H}}}_{\infty},\) and mixed \({{\mathcal{H}}}_2/{{\mathcal{H}}}_{\infty}\) control-based approaches.

Keywords

Control Phase Joint Position Joint Torque Markovian State Output Feedback Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Arai H, Tachi S (1991) Position control of a manipulator with passive joints using dynamic coupling. IEEE Trans Rob Autom 7(4):528–534CrossRefGoogle Scholar
  2. 2.
    Bergerman M, Xu Y (1996) Optimal control sequence for underactuated manipulators. In: Proceedings of the IEEE international conference on robotics and automation, MinneapolisGoogle Scholar
  3. 3.
    Bergerman M, Xu Y (1996) Robust joint and cartesian control of underactuated manipulators. Trans ASME J Dyn Syst Meas Control 118(3):557–565CrossRefMATHGoogle Scholar
  4. 4.
    Costa OLV, do Val JBR (1996) Full information \({\mathcal{H}}_{\infty}\) control for discrete-time infinite Markov jump parameter systems. J Math Anal Appl 202:578–603MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Costa OLV, Fragoso MD, Marques RP (2005) Discrete-time Markov jump linear systems. Springer-Verlag, LondonMATHGoogle Scholar
  6. 6.
    Costa OLV, Marques RP (1998) Mixed \({\mathcal{H}}_2/{\mathcal{H}}_{\infty}\)-control of discrete-time Markovian jump linear systems. IEEE Trans Autom Control 43(1):95–100MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Costa OLV, Marques RP (2000) Robust \({\mathcal{H}}_2\)-control for discrete-time Markovian jump linear systems. Int J Control 73(1):11–21MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    de Farias DP, Geromel JC, do Val JBR, Costa OLV (2000) Output feedback control of Markov jump linear systems in continuous-time. IEEE Trans Autom Control 45(5):944–949CrossRefMATHGoogle Scholar
  9. 9.
    Dixon WE, Walker ID, Dawson DM, Hartranft JP (2000) Fault detection for robot manipulators with parametric uncertainty: a prediction-error-based approach. IEEE Trans Rob Autom 16(6):689–699CrossRefGoogle Scholar
  10. 10.
    Siqueira AAG, Terra MH (2004) A fault tolerant manipulator robot based on \({\mathcal{H}}_2,\;{\mathcal{H}}_{\infty},\) and mixed \({\mathcal{H}}_{2}/{\mathcal{H}}_{\infty}\) Markovian controls. In: Proceedings of the 2004 IEEE international conference on control applications (CCA), Taipei, Taiwan, pp 309–314Google Scholar
  11. 11.
    Siqueira AAG, Terra MH (2004b) Nonlinear and Markovian \({\mathcal{H}}_{\infty}\) controls of underactuated manipulators. IEEE Trans Control Syst Technol 12(6):811–826CrossRefGoogle Scholar
  12. 12.
    Siqueira AAG, Terra MH (2009). A fault tolerant manipulator robot based on \({{\mathcal{H}}}_2,\;{{\mathcal{H}}}_{\infty},\) and mixed \({{\mathcal{H}}}_2/{{\mathcal{H}}}_{\infty}\) Markovian jump controls. IEEE/ASME Trans Mechatron 14(2):257–263CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Adriano A. G. Siqueira
    • 1
  • Marco H. Terra
    • 1
  • Marcel Bergerman
    • 2
  1. 1.Engineering School of São CarlosUniversity of São PauloSão CarlosBrazil
  2. 2.CMU Robotics InstitutePittsburghUSA

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