Advertisement

Robust Rotation Interpolation Based on SO(n) Geodesic Distance

  • Jin Wu
  • Ming LiuEmail author
  • Jian Ding
  • Mingsen Deng
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11754)

Abstract

A novel interpolation algorithm for smoothing of successive rotation matrices based on the geodesic distance of special orthogonal group SO(n) is proposed. The derived theory is capable of achieving optimal interpolation and owns better accuracy and robustness than representatives.

Keywords

Rotation interpolation Special orthogonal group Motion analysis 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgement

This work has been supported by National Natural Science Foundation of China under the grant of No. 41604025.

References

  1. 1.
    Chang, G.: Total least-squares formulation of Wahba’s problem. Electron. Lett. 51(17), 1334–1335 (2015)CrossRefGoogle Scholar
  2. 2.
    Wedel, A., Brox, T., Vaudrey, T., Rabe, C., Franke, U., Cremers, D.: Stereoscopic scene flow computation for 3D motion understanding. Int. J. Comput. Vis. 95(1), 29–51 (2011)CrossRefGoogle Scholar
  3. 3.
    Xu, S., Zhu, J., Li, Y., Wang, J., Lu, H.: Effective scaling registration approach by imposing emphasis on scale factor. Electron. Lett. 54(7), 422–424 (2018)CrossRefGoogle Scholar
  4. 4.
    Sabatini, A.M.: Quaternion based attitude estimation algorithm applied to signals from body-mounted gyroscopes. Electron. Lett. 40(10), 584–586 (2004)CrossRefGoogle Scholar
  5. 5.
    Niu, X., Wang, T.: C2-continuous orientation trajectory planning for robot based on spline quaternion curve. Assemb. Autom. 38(3), 282–290 (2018)CrossRefGoogle Scholar
  6. 6.
    Assa, A., Janabi-Sharifi, F.: Virtual visual servoing for multicamera pose estimation. IEEE/ASME Trans. Mech. 20(2), 789–798 (2015)CrossRefGoogle Scholar
  7. 7.
    Wu, J., Sun, Y., Wang, M., Liu, M.: Hand-eye calibration: 4D procrustes analysis approach. IEEE Trans. Instrum. Meas. (2019, in Press)Google Scholar
  8. 8.
    Shoemake, K.: Animating rotation with quaternion curves. ACM SIGGRAPH Comput. Graph. 19(3), 245–254 (1985)CrossRefGoogle Scholar
  9. 9.
    Park, F.C., Ravani, B.: Smooth invariant interpolation of rotations. ACM Trans. Graph. 16(3), 277–295 (1997)CrossRefGoogle Scholar
  10. 10.
    Leeney, M.: Fast quaternion SLERP. Int. J. Comput. Math. 86(1), 79–84 (2009)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Eberly, D.: A fast and accurate algorithm for computing SLERP. J. Graph. GPU Game Tools 15(3), 161–176 (2011)CrossRefGoogle Scholar
  12. 12.
    Wang, M., Tayebi, A.: Hybrid pose and velocity-bias estimation on SE(3) using inertial and landmark measurements. IEEE Trans. Autom. Control (2018, in Press)Google Scholar
  13. 13.
    Arun, K.S., Huang, T.S., Blostein, S.D.: Least-squares fitting of two 3-D point sets. IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9(5), 698–700 (1987)CrossRefGoogle Scholar
  14. 14.
    Bar-Itzhack, I.Y.: New method for extracting the quaternion from a rotation matrix. AIAA J. Guid. Control Dyn. 23(6), 1085–1087 (2000)CrossRefGoogle Scholar
  15. 15.
    Markley, F.L.: Unit quaternion from rotation matrix. AIAA J. Guid. Control Dyn. 31(2), 440–442 (2008)CrossRefGoogle Scholar
  16. 16.
    Wu, J.: Optimal continuous unit quaternions from rotation matrices. AIAA J. Guid. Control Dyn. 42(2), 919–922 (2019)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Electronic and Computer EngineeringHong Kong University of Science and TechnologyHong KongChina
  2. 2.International Joint Research Center for Data Science and High-Performance Computing, School of InformationGuizhou University of Finance and EconomicsGuizhouChina

Personalised recommendations

Cite paper

Buy options