Skip to main content
SpringerLink
Log in
Book cover

International Conference on Computer Aided Systems Theory

EUROCAST 2003: Computer Aided Systems Theory - EUROCAST 2003 pp 337–348Cite as

Using Fractional Calculus for Lateral and Longitudinal Control of Autonomous Vehicles

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2809))

Abstract

Here it is presented the use of Fractional Order Controllers (FOC) applied to the path-tracking problem in an autonomous electric vehicle. A lateral dynamic model of a industrial vehicle has been taken into account to implement conventional and Fractional Order Controllers. Several control schemes with these controllers have been simulated and compared . First, different controllers with similar parameters have been implemented and then they have been improved by using optimization methods. The preliminary results are presented here.

This work has been partially supported by Research Grant DPI 2002-04064C05-03 (MCYT).

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ollero, A.: Robotica. Manipuladores y Robots Moviles. Marcombo (2001)

    Google Scholar 

  2. Wit, J.S.: Vector Pursuit Path Tracking for Autonomous Ground Vehicles. PhD thesis, University of Florida (2000)

    Google Scholar 

  3. Davidson, M., Bahl, V.: The Scalar ε-Controller: A Spatial Path Tracking Approach for ODV, Ackerman, and Differentially-Steered Autonomous Wheeled Mobile Robots. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 175–180 (2001)

    Google Scholar 

  4. Manabe, S.: The Non-Integer Integral and its Application to Control Systems. JIEE (Japanese Institute of Electrical Engineers) Journal 80, 589–597 (1960)

    Google Scholar 

  5. Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)

    MATH  Google Scholar 

  6. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives and Some of Their Applications. Nauka i technika, Minsk (1987)

    Google Scholar 

  7. Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)

    MATH  Google Scholar 

  8. Podlubny, I.: Fractional Differential Equations, vol. 198. Academic Press, London (1999)

    MATH  Google Scholar 

  9. Lurie, B.J.: Three-Parameter Tunable Tilt-Integral-Derivative (TID) Controller. US Patent US5371670 (1994)

    Google Scholar 

  10. Podlubny, I.: Fractional-Order Systems and PI λ D μ-Controllers. IEEE Trans. Automatic Control 44, 208–214 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Oustaloup, A., Mathieu, B., Lanusse, P.: The CRONE Control of Resonant Plants: Application to a Flexible Transmission. European Journal of Control 1 (1995)

    Google Scholar 

  12. Oustaloup, A., Moreau, X., Nouillant, M.: The CRONE Suspension. Control Engineering Practice 4, 1101–1108 (1996)

    Article  Google Scholar 

  13. Raynaud, H., ZergaInoh, A.: State-Space Representation for Fractional Order Controllers. Automatica 36, 1017–1021 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Vinagre, B.M., Petrás, I., Podlubny, I., Chen, Y.Q.: Using Fractional Order Adjustment Rules and Fractional Order Reference Model in Model-Reference Adaptative Control. Nonlinear Dynamics 29, 269–279 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Manabe, S.: The non-Integer Integral and its Application to Control Systems. ETJ of Japan 6, 83–87 (1961)

    Google Scholar 

  16. Oustaloup, A.: Fractional Order Sinusoidal Oscilators: Optimization and Their Use in Highly Linear FM Modulators. IEEE Transactions on Circuits and Systems 28, 1007–1009 (1981)

    Article  Google Scholar 

  17. Axtell, M., Bise, E.M.: Fractional calculus applications in control systems. In: Proceedings of the IEEE 1990 Nat. Aerospace and Electronics Conf., New York, USA, pp. 563–566 (1990)

    Google Scholar 

  18. Vinagre, B.M., Chen, Y.: Lecture Notes on Fractional Calculus Applications in Automatic Control and Robotics. The 41st IEEE CDC2002 Tutorial Workshop #2 (2002), http://mechatronics.ece.usu.edu/foc/cc02tw/cdrom/lectures/book.pdf or http://eii.unex.es/isa/LasVegas/

  19. Orsoni, B., Melchior, P., Oustaloup, A.: Davidson-Cole Transfer Function in Path Tracking Design. In: Proceedings of the 6th European Control Conference, Porto, Portugal, pp. 1174–1179 (2001)

    Google Scholar 

  20. Orsoni, B., Melchior, P., Oustaloup, A., Badie, T., Robin, G.: Fractional motion control: Application to an xy cutting table. Nonlinear Dynamics 29, 297–314 (2002)

    Article  MATH  Google Scholar 

  21. Bahl, V.: Modeling and Control of a Class of Autonomous Wheeled Mobile Robots. Master’s thesis, Department of Electrical and Computer Engineering, Utah State University, Logan, Utah (2002)

    Google Scholar 

  22. Brennan, S.: Modeling and control issues associeted with scaled vehicles. Master’s thesis, University of Illinois (1999)

    Google Scholar 

  23. Vinagre, B.M., Podlubny, I., Hernandez, A., Feliu, V.: Some Approximations of Fractional Order Operators Used in Control Theory and Applications. Fractional Calculus and Applied Analysis 3, 231–248 (2000)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EII, Universidad de Extremadura, Badajoz, Spain

    J. I. Suárez, B. M. Vinagre, A. J. Calderón & C. A. Monje

  2. CSOIS, Utah State University, Logan, Utah, USA

    Y. Q. Chen

Authors
  1. J. I. Suárez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. M. Vinagre
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. J. Calderón
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. A. Monje
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Y. Q. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Cybernetics, Universidad de Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Systems Theory, Johannes Kepler University Linz, Altenbergerstrasse 69, A-4040, Linz, Austria

    Franz Pichler

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Suárez, J.I., Vinagre, B.M., Calderón, A.J., Monje, C.A., Chen, Y.Q. (2003). Using Fractional Calculus for Lateral and Longitudinal Control of Autonomous Vehicles. In: Moreno-Díaz, R., Pichler, F. (eds) Computer Aided Systems Theory - EUROCAST 2003. EUROCAST 2003. Lecture Notes in Computer Science, vol 2809. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45210-2_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45210-2_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20221-9

  • Online ISBN: 978-3-540-45210-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation