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 semidirect 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 from the semidirect 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 pose changes of its hands.
Pose Changes From a Different Point of View
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 22, 2017; final manuscript received December 22, 2017; published online February 27, 2018. Assoc. Editor: Andrew P. Murray.
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Chirikjian, G. S., Mahony, R., Ruan, S., and Trumpf, J. (February 27, 2018). "Pose Changes From a Different Point of View." ASME. J. Mechanisms Robotics. April 2018; 10(2): 021008. https://doi.org/10.1115/1.4039121
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