Computation of Spatial Displacements from Redundant Geometric Features

[+] Author and Article Information
Q. J. Ge

Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794

B. Ravani

Computer Integrated Design and Manufacturing Laboratory, Department of Mechanical and Aeronautical Engineering, University of California-Davis, Davis, CA 95616

J. Mech. Des 116(4), 1073-1080 (Dec 01, 1994) (8 pages) doi:10.1115/1.2919489 History: Received October 01, 1993; Revised May 01, 1994; Online June 02, 2008


This paper follows a previous one on the computation of spatial displacements (Ravani and Ge, 1993). The first paper dealt with the problem of computing spatial displacements from a minimum number of simple features of points, lines, planes, and their combinations. The present paper deals with the same problem using a redundant set of the simple geometric features. The problem for redundant information is formulated as a least squares problem which includes all simple features. A Clifford algebra is used to unify the handling of various feature information. An algorithm for determining the best orientation is developed which involves finding the eigenvector associated with the least eigenvalue of a 4 × 4 symmetric matrix. The best translation is found to be a rational cubic function of the best orientation. Special cases are discussed which yield the best orientation in closed form. In addition, simple algorithms are provided for automatic generation of body-fixed coordinate frames from various feature information. The results have applications in robot and world model calibration for off-line programming and computer vision.

Copyright © 1994 by The American Society of Mechanical Engineers
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