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Technical Briefs

A Coordinate Frame Useful for Rigid-Body Displacement Metrics

[+] Author and Article Information
Venkatesh Venkataramanujam, Pierre M. Larochelle

Department of Mechanical and Aerospace Engineering, Robotics and Spatial Systems Laboratory, Florida Institute of Technology, Melbourne, FL 32901

J. Mechanisms Robotics 2(4), 044503 (Sep 30, 2010) (5 pages) doi:10.1115/1.4002245 History: Received July 25, 2008; Revised July 19, 2010; Published September 30, 2010; Online September 30, 2010

This paper presents the definition of a coordinate frame, entitled the principal frame (PF), that is useful for metric calculations on spatial and planar rigid-body displacements. Given a set of displacements and using a point mass model for the moving rigid-body, the PF is determined from the associated centroid and principal axes. It is shown that the PF is invariant with respect to the choice of fixed coordinate frame as well as the system of units used. Hence, the PF is useful for left invariant metric computations. Three examples are presented to demonstrate the utility of the PF.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

SE(N−1) to SO(N)

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Figure 2

Mapping to SO(N)

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Figure 3

Unit point mass model

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Figure 4

Unit point mass model and associated PF

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Figure 5

Four possible orientations for the PF

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Figure 6

Principal frame for eleven desired locations

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Figure 7

Principal frame for ten desired locations

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Figure 8

Principal frame for the pick and place task

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