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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
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    References listed on IDEAS

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    1. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
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