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Robot calibration using least-squares and polar-decomposition filtering

  • Section 4: Kinematics
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Experimental Robotics I

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 139))

Abstract

This paper reports the experimental results of a novel method to calibrate geometric errors of multi-axis robotic manipulators. The method proposed by the authors is based on a least-square estimation of the rotation matrix of a rigid body in three-dimensional Cartesian space. The error is filtered by imposing the orthogonality constraint on the rotation matrix, using the polar-decomposition theorem. The axis of rotation of the rigid body, then, is computed from the linear invariants of the rotation matrix. Finally, the wrist of the Yaskawa Motoman Robot was calibrated. The measurements of the Cartesian coordinates of points were performed using a computer vision system and LED markers on a rigid body grasped by the end-effector.

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References

  1. An, C.H., Atkeson, C.G. and Hollerbach, J.M. 1988, “Model-Based Control of a Robot Manipulator”, The MIT Press, ambridge, Massachusetts.

    Google Scholar 

  2. Angeles, J., 1985., “On the Numerical Solution of the Inverse Kinematics Problem”, The International Journal of Robotics Research, Vol. 4, No. 2, Summer 1985.

    Google Scholar 

  3. Angeles, J., 1986, “Automatic Computation of the Screw Parameters of Rigid-Body Motions. Part I: Finitely-Separated Positions”, ASME Journal of Dynamic Systems, Measurement and Control. Vol. 108, March 1986.

    Google Scholar 

  4. Angeles, J., and Ioannides, G. 1989., “Calibration of a Robot Wrist with an Offset Axis”, ASME Winter Annual Meeting. (To be presented.)

    Google Scholar 

  5. Golub, G., and Van Loan. C., 1983. Matrix Computations, The Johns Hopkins University Press, Baltimore, MD.

    Google Scholar 

  6. Halmos, P. R., 1974. Finite-Dimensional Vector Spaces, Springer-Verlag, New York.

    Google Scholar 

  7. Hayati, S.A. “Robot Arm Geometric Link Calibration.”, Proceedings of the 22nd IEEE Conference on Decision and Control, pp.1477–pp.1483, December 1983.

    Google Scholar 

  8. Higham, N. J., 1986, “Computing the Polar Decomposition — with Applications”, SIAM J. Sci. Stat. Comput., Vol. 7, No. 4, October.

    Google Scholar 

  9. Kirchner H. O. K., Gurumoorthy, B., and Prinz, F. B., 1987, “A Perturbation Approach to Robot Calibration”, The International Journal of Robotics Research, Vol. 6, No. 4, Winter.

    Google Scholar 

  10. Kumar, A. and Waldron, K.J., 1981. “Numerical Plotting of Positioning Accuracy of Manipulators.” Mechanism Machine Theory Vol. 16, No 4, pp. 361–368.

    Google Scholar 

  11. Laub, A. J. and Schifflet, G. R. 1983., “A Linear Algebra Approach to the Analysis of Rigid-Body Displacement from Initial and Final Position Data”, ASME Journal of Dynamic Measurements and Control, Vol. 105, June.

    Google Scholar 

  12. Mooring, B. W., 1983, (August 7–11,Chicago). “The Effect of Joint Axis Misalignment on Robot Positioning Accuracy.”, Proc. 1983 ASME Int. Conf. on Computers in Enginnering. New York: ASME, pp. 151–155.

    Google Scholar 

  13. Nothern Digital Inc., 1986, “The WATerloo Spatial Motion Analysis and Recording Technique”, Technical Description, August 1986.

    Google Scholar 

  14. Shapiro, R., 1978. “Direct Linear Transformation Method for Three-Dimensional Cinematography”, The Research Quarterly, Vol. 49, No. 2, pp. 197–205.

    Google Scholar 

  15. Veitschegger, W. K. and Wu, C. H., 1986, “Robot Accuracy Analysis Based on Kinematics”, IEEE Journal of Robotics and Automation, Vol. RA-2, No. 3, Fall.

    Google Scholar 

  16. Veitschegger, W. K. and Wu, C. H., 1987, “A Method for Calibrating and Compensating Robot Kinematic Errors”, IEEE International Conference on Robotics and Automation, Vol. 1, pp. 39–44.

    Google Scholar 

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Vincent Hayward Oussama Khatib

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© 1990 Springer-Verlag

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Ioannides, G., Angeles, J., Flanagan, R., Ostry, D. (1990). Robot calibration using least-squares and polar-decomposition filtering. In: Hayward, V., Khatib, O. (eds) Experimental Robotics I. Lecture Notes in Control and Information Sciences, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042541

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  • DOI: https://doi.org/10.1007/BFb0042541

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52182-2

  • Online ISBN: 978-3-540-46917-9

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