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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).
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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

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