Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-21T18:06:13.586Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematic calibration using the product of exponentials formula

Published online by Cambridge University Press:  09 March 2009

Koichiro Okamura  and
F.C. Park
Koichiro Okamura
Affiliation:
Department of Precision Machinery Engineering, The University of Tokyo, 7–3–1 Hongo, Bunkyo-ku, Tokyo 113 (Japan).
F.C. Park
Affiliation:
Mechanical Design and Production Engineering Seoul National University, Kwanak-Ku Shinlim-Dong San 56–1, Seoul 151–742, (Korea).
Get access Rights & Permissions [Opens in a new window]

Summary

We present a method for kinematic calibration of open chain mechanisms based on the product of exponentials (POE) formula. The POE formula represents the forward kinematics of an open chain as a product of matrix exponentials, and is based on a modern geometric interpretation of classical screw theory. Unlike the kinematic representations based on the Denavit- Hartenberg (D-H) parameters, the kinematic parameters in the POE formula vary smoothly with changes in the joint axes, ad hoc methods designed to address the inherent singularities in the D-H parameters are therefore unnecessary. Another important advantage is that simple closed-form expressions can be obtained for the derivatives of the forward kinematic equations with respect to the kinematic parameters. After introducing the POE formula, we derive a least-squares kinematic calibration algorithm for general open chain mechanisms. Simulation results with a 6-axis open chain are presented.

Keywords

Exponentials formulaKinematic calibrationOpen-chain mechanisms.
Type
Article
Information
Robotica , Volume 14 , Issue 4 , July 1996 , pp. 415 - 421
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Whitney, D.E., Lozinski, CA. and Rourke, J.M., “Industrial robot forward calibration method and results” J. Dynamic Systems, Meas., Control 108, 1–8 (1986).CrossRefGoogle Scholar
2.Hayati, S., “Robot arm geometric parameter estimation” Proc. 22nd IEEE Int. Conf. Decision and Control (1983) pp. 1477–1483.CrossRefGoogle Scholar
3.Stone, H.W., Kinematic Modeling, Identification, and Control of Robot Manipulators (Kluwer, Boston, 1987).CrossRefGoogle Scholar
4.Zhuang, H., Roth, Z.S. and Hamano, F., “A complete and parametrically continuous kinematic model for robot manipulators” IEEE Trans. Robotics Autom. 8, 451–463 (1992).CrossRefGoogle Scholar
5.Mooring, B.W. and Tang, G.R., “An improved method for identifying the kinematic parameters in a six axis robot” Proc. Int. Comput. in Eng. Conf. Exhibit, Las Vegas, (1984) pp. 79–84.Google Scholar
6.Brockett, R.W., “Robotic manipulators and the product of exponentials formula” Proc. Int. Symp. Math. Theory of Networks and Systems, Beer Sheba, Israel (1983) pp. 120–129.Google Scholar
7.Park, F.C., “Computational aspects of the product-ofexponentials formula for robot kinematics” IEEE Trans. Auto. Contr. 39, No. 3, 643–647 (03, 1993).CrossRefGoogle Scholar
8.Curtis, M.L, Matrix Groups, (Springer-Verlag, New York, 1984).CrossRefGoogle Scholar
9.Park, F.C., “The Optimal Kinematic Design of Mechanisms”, Ph.D. Thesis (Harvard University, 1991).Google Scholar
10.Paden, B. and Sastry, S.S., “Optimal kinematic design of 6R manipulators” Int. J. Robotics Research 7, No. 2, 43–61 (04, 1988).CrossRefGoogle Scholar
11.Paul, R.P., Robot Manipulators: Mathematics, Programming and Control (MIT Press Cambridge, 1982).Google Scholar
12.Park, F.C., Bobrow, J.E. and Ploen, S.R., “A Lie group formulation of robot dynamics” Proc. 3rd Int. Workshop on Advanced Motion Control, Berkeley, CA., (1994) pp. 13–22.Google Scholar
13.Hollerbach, J.M., “A survey of kinematic calibration” In: (Khatib, O., Craig, J.J. and Lozano-Perez, T., eds.) The Robotics Review I (MIT Press, Cambridge, 1989).Google Scholar