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Reconciling Distance Metric Methods for Rigid Body Displacements

[+] Author Affiliations
Anurag Purwar, Qiaode Jeffrey Ge

Stony Brook University, Stony Brook, NY

Paper No. DETC2009-87718, pp. 1295-1304; 10 pages
  • ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7: 33rd Mechanisms and Robotics Conference, Parts A and B
  • San Diego, California, USA, August 30–September 2, 2009
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4904-0 | eISBN: 978-0-7918-3856-3
  • Copyright © 2009 by ASME


In the last twenty years, researchers have proposed a few different methods to establish a norm (or, metric) for both planar and spatial rigid body displacements. Desire to meaningfully quantify a displacement composed of rotation and translation stems from a requirement to ascertain “distance” between two given displacements in applications, such as motion approximation and interpolation, mechanism synthesis, collision avoidance, positioning, and robot calibration and control. In this paper, we show that the various seemingly different shape independent norm calculation methods based on approximating displacements with higher dimensional rotations via orthogonal matrices, or polar decomposition (PD) and singular value decomposition (SVD) can be reconciled and unified in the mathematically compact and elegant framework of biquaternions. In the process, we also propose an elegant and fast method for such norm calculations.

Copyright © 2009 by ASME



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