Chirikjian, Gregory S.; Mahony, Robert; Ruan, Sipu; Trumpf, Jochen
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,...[Show more]
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