Measures of Positional Error for a Rigid Body

[+] Author and Article Information
K. C. Gupta

University of Illinois at Chicago, Chicago, IL 60607-7022

J. Mech. Des 119(3), 346-348 (Sep 01, 1997) (3 pages) doi:10.1115/1.2826354 History: Received November 01, 1996; Revised June 01, 1997; Online December 11, 2007


Properties of Euclidean error measures for rigid body position are investigated. For two positions represented by 4 × 4 matrices A1 and A2 , it is shown that matrices [A2 − A1 ] and [(A1 )−1 A2 ] lead directly to desirable measures of rotational and translational errors, while the matrix [A2 (A1 )−1 ], although physically very meaningful, does not do so. With a proper choice of the origin of the body system, it is shown that the simple difference matrix [A2 − A1 ] leads to positional error measures which are meaningful both analytically and physically, and can be computed efficiently.

Copyright © 1997 by The American Society of Mechanical Engineers
Topics: Errors
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