Skip to main content
SpringerLink
Log in

Continuum Arm Control with Constraints on the Driving Forces via Fractional Order Models

  • Conference paper
  • First Online:
New Advances in Mechanisms, Mechanical Transmissions and Robotics (MTM&Robotics 2020)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 88))

  • 607 Accesses

Abstract

The paper presents an extension of the Circle Criterion for the dynamic models of the continuum robots. This technique is applied to the control of the fractional order model system with constraints of the driving forces. It is demonstrated that the stability of the closed loop control system requires that the arm frequency plot does not intersect the circle of driving constraints. It is shown that nonlinear components worsen the stability of the system. The proposed methods are illustrated by numerical simulation and experimental tests.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Robinson, G., Davies, G.B.C.: Continuum robots – a state of the art. In: Proceedings of the IEEE International Conference on Robotics and Automation, Detroit, May 1999, pp. 2849–2854 (1999)

    Google Scholar 

  2. Gravagne, I.A., Walker, I.D.: On the kinematics of remotely - actuated continuum robots. In: Proceedings of the 2000 IEEE International Conference on Robotics and Automation, San Francisco, April 2000, pp. 2544–2550 (2000)

    Google Scholar 

  3. Gravagne, I.A., Walker, I.D.: Kinematic transformations for remotely- actuated planar continuum robots. In: Proceedings of the 2000 IEEE International Conference on Robotics and Automation, San Francisco, April 2000, pp. 19–26 (2000)

    Google Scholar 

  4. Gravagne, I.A., Walker, I.D.: Uniform regulation of a multi-section continuum manipulators. In: Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington DC, May 2002, pp. 1519–1525 (2002)

    Google Scholar 

  5. Gravagne, I., Walker, I.D.: Manipulability and force ellipsoids for continuum robot manipulators. In: 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, Hawaii, 29–31 October, pp. 304–310 (2001)

    Google Scholar 

  6. Chirikjian, G.S., Burdick, J.W.: An obstacle avoidance algorithm for hyper-redundant manipulators. In: Proceedings of the IEEE International Conference on Robotics and Automation, Cincinnati, Ohio, May 1990, pp. 625–631 (1990)

    Google Scholar 

  7. Mochiyama, H., Kobayashi, H.: The shape Jacobian of a manipulator with hyper degrees of freedom. In: Proceedings of the 1999 IEEE International Conference on Robotics and Automation, Detroit, May 1999, pp. 2837–2842 (1999)

    Google Scholar 

  8. Li, J., Xiao, J.: Determining grasping configurations for a spatial continuum manipulator. In: 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, 25–30 September 2011, San Francisco, pp. 4207–4213 (2011)

    Google Scholar 

  9. Walker, I., Hannan, M.: A novel elephant’s trunk robot. In: AIM 1999, pp. 410–415 (1999)

    Google Scholar 

  10. Jones, B., Walker, I.D.: Practical kinematics for real-time implementation of continuum robots. IEEE Trans. Robotics 22(6), 1087–1099 (2006)

    Article  Google Scholar 

  11. Kapadia, A.D., Walker, I., Dawson, D.: A model – based sliding mode controller for extensible continuum robots. In: Recent Advances in Signal Processing, Robotics and Automation, ISPRA Conference, pp. 103–120 (2009)

    Google Scholar 

  12. Rucker, D.C., Webster III, R.J., Chirikjian, G.S., Cowan, N.J.: Equilibrium conformations of concentric-tube continuum robots. Int. J. Robot. Res. 29(10), 1263–1280 (2010)

    Article  Google Scholar 

  13. Popescu, N., Popescu, D., Ivanescu, M.: A spatial weight error control for a class of hyper-redundant robots. IEEE Trans. Robot. 29(4), 1043–1050 (2013). ISSN 1552-3098

    Google Scholar 

  14. Ivanescu, M., Popescu, N., Popescu, D.: The shape control of a tentacle arm. Robotica Cambridge J. 33(03), 684–703 (2015)

    Google Scholar 

  15. Ivanescu, M., Popescu, N., Popescu, D.: A decoupled sliding mode control for a continuum arm. Adv. Robot. Spec. Issue Continuum Robots Manipulation 29(13), 831–845 (2015)

    Google Scholar 

  16. Diethelm, K.: The Analysis of Fractional Differential Equations. Springer, London (2004)

    Google Scholar 

  17. Petras, I: Fractional-Order Nonlinear Systems, Modeling, Analysis and Simulation. Higher Education Press, Beijing (2011). Springer

    Google Scholar 

  18. Monje, C., Chen, Y.Q., Vinagre, B., Hue, D., Feliu, V.: Fractional-Order Systems and Controls. Springer, London (2010)

    Google Scholar 

  19. Aguila-Camacho, N., Duarte-Mermoud, M., Callegos, J.: Lyapunov functions for fractional order systems. Commun. Nonlinear Sci Numer. Simulat. 19, 2951–2957 (2014)

    Article  MathSciNet  Google Scholar 

  20. Khalil, H.: Nonlinear Systems. Prentice Hall, New Jersey (2003)

    Google Scholar 

  21. Li, Y., Chen, Y.Q., Podlubny, I.: Stability of fractional order nonlinear systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. 59, 1810–1821 (2010)

    Article  MathSciNet  Google Scholar 

  22. Agarwal, R., Hristova, S., O’Regan, D.: Lyapunov functions and strict stability of Caputo fractional differential equations. Advances in Difference Equations 2015(1), 1–20 (2015). https://doi.org/10.1186/s13662-015-0674-5

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhao, Y., Wang, Y., Liu, Z.: Lyapunov function method for linear fractional order systems. In: Proceedings of the 34th Chinese Control Conference, pp. 1457–1463 (2015)

    Google Scholar 

  24. Dadras, S., Malek, H., Chen, Y.: A note on the Lyapunov stability of fractional order nonlinear systems. In: Proceedings of the ASME Cleveland, Orlando, August 2017, pp. 123–129 (2017)

    Google Scholar 

  25. Al-Saggaf, U.M., Mehedi, I.M., Mansouri, R., Bettayeb, M.: Rotary flexible joint control by fractional order controllers. Int. J. Control Autom. Syst. 15(6), 2561–2569 (2017)

    Article  Google Scholar 

  26. Rhong, L., Peng, X., Zhang, B.: A reduced-order fault detection filter design for polytopic uncertain continuous-time Markovian jump systems with time-varying delays. Int. J. Control Autom. Syst. 16(5), 2021–2032 (2018)

    Article  Google Scholar 

  27. Khimani, D., Patil, M.: High performance super-twisting control for state delay systems. Int. J. Control Autom. Syst. 16(5), 2063–2073 (2018)

    Article  Google Scholar 

  28. Wu, B., Wang, C.-L., Hu, Y.-J.: Stability analysis for time-delay systems with nonlinear disturbances via new generalized integral inequalities. Int. J. Control Autom. Syst. 16(6), 2772–2780 (2018)

    Article  Google Scholar 

  29. Heymann, N., Podlubni, I.: Physical interpretation of initial conditions for fractional differential with Riemann-Liouville fractional derivatives. Rheologica Acta 17(23), 45–63 (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechatronics, University of Craiova, Craiova, Romania

    Mircea Ivanescu & Mircea Nitulescu

  2. Electrical Engineering Department, University of Craiova, Craiova, Romania

    Cristian Vladu

Authors
  1. Mircea Ivanescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mircea Nitulescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cristian Vladu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mircea Ivanescu .

Editor information

Editors and Affiliations

  1. Department of Mechatronics, Polytechnic University of Timişoara, Timișoara, Romania

    Erwin-Christian Lovasz

  2. Department of Mechatronics, Polytechnic University of Timişoara, Timișoara, Romania

    Inocentiu Maniu

  3. Department of Mechanical Engineering, Mechatronics and Robotics, Gheorghe Asachi Technical University of Iasi, Iași, Romania

    Ioan Doroftei

  4. Mechatronics, University of Craiova, Craiova, Romania

    Mircea Ivanescu

  5. Department of Mechatronics, Polytechnic University of Timişoara, Timișoara, Romania

    Corina-Mihaela Gruescu

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ivanescu, M., Nitulescu, M., Vladu, C. (2021). Continuum Arm Control with Constraints on the Driving Forces via Fractional Order Models. In: Lovasz, EC., Maniu, I., Doroftei, I., Ivanescu, M., Gruescu, CM. (eds) New Advances in Mechanisms, Mechanical Transmissions and Robotics . MTM&Robotics 2020. Mechanisms and Machine Science, vol 88. Springer, Cham. https://doi.org/10.1007/978-3-030-60076-1_38

Download citation

Publish with us

Policies and ethics

Search

Navigation