IDEAS home Printed from https://ideas.repec.org/a/hin/jnlamp/6302430.html
   My bibliography  Save this article

Intrinsic Optimal Control for Mechanical Systems on Lie Group

Author

Listed:
  • Chao Liu
  • Shengjing Tang
  • Jie Guo

Abstract

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on , the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

Suggested Citation

  • Chao Liu & Shengjing Tang & Jie Guo, 2017. "Intrinsic Optimal Control for Mechanical Systems on Lie Group," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-8, July.
    • Handle: RePEc:hin:jnlamp:6302430
    DOI: 10.1155/2017/6302430
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AMP/2017/6302430.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AMP/2017/6302430.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/6302430?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jnlamp:6302430. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.