Advertisement

Dual quaternions for absolute orientation and hand-eye calibration

  • Konstantinos Daniilidis
Conference paper
Part of the Advances in Computing Science book series (ACS)

Abstract

Many computer vision problems involving three dimensional motion necessitate an efficient representation for 3D displacement that enhances the understanding of the problem and facilitates linear solutions of low complexity. The most common representation is a rotation about an axis through the origin followed by a translation and represented by an orthogonal matrix and a vector, respectively. An alternative representation to orthogonal matrices are the unit quaternions already used in several vision algorithms [4] which still use the translation as a separate unknown. From Chasles’ theorem [1] it is known that a rigid transformation can be modeled as a rotation about an axis not through the origin and a translation along this axis. This well known screw transformation can be algebraically modeled using dual vectors, matrices or quaternions [5].

Keywords

Scalar Part Rigid Transformation Dual Vector Unit Quaternion Screw Axis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    O. Bottema and B. Roth. Theoretical Kinematics. North-Holland Publishing Company, Amsterdam New York London, 1979.MATHGoogle Scholar
  2. [2]
    H. Chen. A screw motion approach to uniqueness analysis of head-eye geometry. In IEEE Conf. Computer Vision and Pattern Recognition, pages 145–151, Maui, Hawaii, June 3–6, 1991.Google Scholar
  3. [3]
    J.C.K. Chou and M. Kamel. Finding the position and orientation of a sensor on a robot manipulator using quaternions. Intern. Journal of Robotics Research, 10 (3): 240–254, 1991.CrossRefGoogle Scholar
  4. [4]
    O. Faugeras. Three-dimensional Computer Vision. MIT-Press, Cambridge, MA, 1993.Google Scholar
  5. [5]
    J. Funda and R.P. Paul. A computational analysis of screw transformations in robotics. IEEE Trans. Robotics and Automation, 6: 348–356, 1990.CrossRefGoogle Scholar
  6. [6]
    R. Horaud and F. Dornaika. Hand-eye calibration. Intern. Journal of Robotics Research, 14: 195–210, 1995.CrossRefGoogle Scholar
  7. [7]
    B.K.P. Horn. Robot Vision. MIT Press, Cambridge, MA, 1986.Google Scholar
  8. [8]
    J. Kim and V.R. Kumar. Kinematics of robot manipulators via line transformations. Journal of Robotic Systems, 7: 649–674, 1990.MATHCrossRefGoogle Scholar
  9. [9]
    M. Li and D. Betsis. Hand-eye calibration. In Proc. Int. Conf. on Computer Vision, pages 40–46. Boston, MA, June 20–23, 1995.Google Scholar
  10. [10]
    J.M. McCarthy. Dual orthogonal matrices in manipulator kinematics. Intern. Journal of Robotics Research, 5 (2): 45–51, 1986.CrossRefGoogle Scholar
  11. [11]
    T.Q. Phong, R. Horaud, A. Ya.ssine,, and D.T. Pham. Optimal estimation of object pose from a single perspective view. In Proc. Int. Conf. on Computer Vision, pages 534–539. Berlin, Germany, May 11–14, 1993.Google Scholar
  12. [12]
    B. Sabata and J.K. Aggarwal. Estimation of motion from a pair of range images: a review. CVGIP: Image Understanding, 54: 309–324, 1991.MATHCrossRefGoogle Scholar
  13. [13]
    Y.C. Shiu and S. Ahmad. Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form ax = xb. IEEE Trans. Robotics and Automation, 5: 16–27, 1989.CrossRefGoogle Scholar
  14. [14]
    R.Y. Tsai and R.K. Lenz. A new technique for fully autonomous and efficient 3d robotics hand/eye calibration. IEEE Trans. Robotics and Automation, 5: 345–358, 1989.CrossRefGoogle Scholar
  15. [15]
    M.W. Walker. Manipulator kinematics and the epsilon algebra. IEEE Journal of Robotics and Automation, 4: 186–192, 1988.CrossRefGoogle Scholar
  16. [16]
    C.C. Wang. Extrinsic calibration of a vision sensor mounted on a robot. IEEE Trans. Robotics and Automation, 8: 161–175, 1992.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1997

Authors and Affiliations

  • Konstantinos Daniilidis

There are no affiliations available

Personalised recommendations