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research-article

Pose Changes From a Different Point of View

[+] Author and Article Information
Gregory S. Chirikjian

Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland, USA 21218
gchirik1@jhu.edu

Robert Mahony

College of Engineering and Computer Science, The Australian National University, Canberra, ACT, 2601, Australia
robert.mahony@anu.edu.au

Sipu Ruan

Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland, USA 21218
ruansp@jhu.edu

Jochen Trumpf

College of Engineering and Computer Science, The Australian National University, Canberra, ACT, 2601, Australia
jochen.trumpf@anu.edu.au

1Corresponding author.

ASME doi:10.1115/1.4039121 History: Received September 22, 2017; Revised December 22, 2017

Abstract

For more than a century, rigid-body displacements have been viewed as affine transformations described as homogeneous transformation matrices wherein the linear part is a rotation matrix. In group-theoretic terms, this classical description makes rigid-body motions a semi-direct product. The distinction between a rigid-body displacement of Euclidean space and a change in pose from one reference frame to another is usually not articulated well in the literature. Here we show that, remarkably, when changes in pose are viewed from a space-fixed reference frame, the space of pose changes can be endowed with a direct product group structure, which is different than the semi-direct product structure of the space of motions. We then show how this new perspective can be applied more naturally to problems such as monitoring the state of aerial vehicles from the ground, or the cameras in a humanoid robot observing motions of its hands.

Copyright (c) 2018 by ASME
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