Skip to main content
SpringerLink
Log in

Exponential Stabilization of Second-Order Nonholonomic Chained Systems

  • Conference paper
Book cover Intelligent Robotics and Applications (ICIRA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8103))

Included in the following conference series:

  • 8133 Accesses

Abstract

In this paper, an underactuated control method is considered for an X4-AUV with four thrusters and 6-DOFs. A second-order chained form transformation is introduced to the dynamical model by separating a system into three parts of controller model. Then, the Astolfi’s discontinuous control method is applied to realize an underactuated control method to stabilize the system. This approach is motivated by the fact that the discontinuous dynamic model without using a chained form transformation assures only a local stability (or controllability) of the dynamic based control system, instead of guaranteeing a global stability of the system. A computer simulation is presented to demonstrate the effectiveness of our approach.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ge, S.S., Sun, Z., Lee, T.H., Spong, M.W.: Feedback Linearization and Discontinuous Control of Second-Order Nonholonomic Chained Systems. In: Proc. of the 2001 IEEE International Conference on Control Applications, pp. 5–7 (2001)

    Google Scholar 

  2. Laiou, M., Astolfi, A.: A Local Transformations to Generalized Chained Forms. In: Sixteenth International Symposium on Mathematical Theory of Networks and Systems, MTNS 2004 (2004)

    Google Scholar 

  3. Murray, R., Sastry, S.S.: Nonholonomic Motion Planning: Steering Using Sinusoids. IEEE Transactions on Automatic Control 38, 700–716 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Xu, W.L., Ma, B.L.: Stabilization of Second-order Nonholonomic Systems in Canonical Chained Form. Original Research Article Robotics and Autonomous Systems 34(4), 223–233 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Zain, Z.M., Watanabe, K., Danjo, T., Izumi, K., Nagai, I.: Modeling an Autonomous Underwater Vehicle with Four-thrusters. In: The Fifteenth International Symposium on Artificial Life and Robotics (AROB 2010), pp. 934–937 (2010)

    Google Scholar 

  6. Zain, Z.M., Watanabe, K., Danjo, T., Izumi, K., Nagai, I.: A nonholonomic control method for stabilizing an X4-AUV. Artificial Life and Robotics 16(2), 202–207 (2011)

    Article  Google Scholar 

  7. Zain, Z.M., Watanabe, K., Izumi, K., Nagai, I.: A Discontinuous exponential stabilization law for an underactuated X4-AUV. Artificial Life and Robotics, 1–7 (December 11, 2012)

    Google Scholar 

  8. Zain, Z.M., Watanabe, K., Izumi, K., Nagai, I.: Stabilization of an underactuated X4-AUV using a discontinuous control law. Indian Journal of Geo-Marine Sciences (IJMS) 41(6), 589–598 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Electrical and Electronic Engineering, Universiti Malaysia Pahang, Pekan Branch, 26600, Pekan, Pahang, Malaysia

    Zainah Md. Zain

  2. Department of Intelligent Mechanical Systems, Division of Industrial Innovation Sciences, Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama, 700-8530, Japan

    Zainah Md. Zain, Keigo Watanabe & Isaku Nagai

  3. Department of Mechanical Engineering, Graduate School of Science and Engineering, Saga University, 1Honjomachi, Saga, 840-8502, Japan

    Kiyotaka Izumi

Authors
  1. Zainah Md. Zain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Keigo Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kiyotaka Izumi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Isaku Nagai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, Pusan National University, South Korea

    Jangmyung Lee

  2. School of Mechanical Engineering, Pusan National University, Busan, South Korea

    Min Cheol Lee

  3. Intelligent Systems & Biomedical Robotics Group, School of Creative Technologies, University of Portsmouth, PO1 2DJ, England, UK

    Honghai Liu

  4. School of Mechanical Engineering, Biorobotics Laboratory, Korea University of Technology and Education, Gajeon-ri Byeongcheon-myeon 307, 330-708, Cheonan, Korea

    Jee-Hwan Ryu

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zain, Z.M., Watanabe, K., Izumi, K., Nagai, I. (2013). Exponential Stabilization of Second-Order Nonholonomic Chained Systems. In: Lee, J., Lee, M.C., Liu, H., Ryu, JH. (eds) Intelligent Robotics and Applications. ICIRA 2013. Lecture Notes in Computer Science(), vol 8103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40849-6_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40849-6_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40848-9

  • Online ISBN: 978-3-642-40849-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation