IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i7p757-d528177.html
   My bibliography  Save this article

A Lie Group-Based Iterative Algorithm Framework for Numerically Solving Forward Kinematics of Gough–Stewart Platform

Author

Listed:
  • Binhai Xie

    (The State Key Laboratory of VR Technology & Systems, Beihang University, Beijing 100191, China
    Jiangxi Research Institute, Beihang University, Beijing 100191, China)

  • Shuling Dai

    (The State Key Laboratory of VR Technology & Systems, Beihang University, Beijing 100191, China
    Jiangxi Research Institute, Beihang University, Beijing 100191, China)

  • Feng Liu

    (The State Key Laboratory of VR Technology & Systems, Beihang University, Beijing 100191, China
    Jiangxi Research Institute, Beihang University, Beijing 100191, China)

Abstract

In this work, we began to take forward kinematics of the Gough–Stewart (G-S) platform as an unconstrained optimization problem on the Lie group-structured manifold SE(3) instead of simply relaxing its intrinsic orthogonal constraint when algorithms are updated on six-dimensional local flat Euclidean space or adding extra unit norm constraint when orientation parts are parametrized by a unit quaternion. With this thought in mind, we construct two kinds of iterative problem-solving algorithms (Gauss–Newton (G-N) and Levenberg–Marquardt (L-M)) with mathematical tools from the Lie group and Lie algebra. Finally, a case study for a general G-S platform was carried out to compare these two kinds of algorithms on SE(3) with corresponding algorithms that updated on six-dimensional flat Euclidean space or seven-dimensional quaternion-based parametrization Euclidean space. Experiment results demonstrate that those algorithms on SE(3) behave better than others in convergence performance especially when the initial guess selection is near to branch solutions.

Suggested Citation

  • Binhai Xie & Shuling Dai & Feng Liu, 2021. "A Lie Group-Based Iterative Algorithm Framework for Numerically Solving Forward Kinematics of Gough–Stewart Platform," Mathematics, MDPI, vol. 9(7), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:757-:d:528177
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/7/757/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/7/757/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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:gam:jmathe:v:9:y:2021:i:7:p:757-:d:528177. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.