Motion Interpolation in Lie Subgroups and Symmetric Subspaces

Conference paper

Selig, JM, Wu, Y and Carricato, M (2017). Motion Interpolation in Lie Subgroups and Symmetric Subspaces. 7th IFToMM International Workshop of Computational Kinematics. Futurescope, Poitiers, France 22 - 24 May 2017 Springer. https://doi.org/10.1007/978-3-319-60867-9_53
AuthorsSelig, JM, Wu, Y and Carricato, M
TypeConference paper
Abstract

We show that a map defined by Pfurner, Schrocker and Husty, mapping points in 7-dimensional projective space to the Study quadric, is equivalent to the composition of an extended inverse Cayley map with the direct Cayley map, where the Cayley map in question is associated to the adjoint representation of the group SE(3). We also verify that subgroups and symmetric subspaces of SE(3) lie on linear spaces in dual quaternion representation of the group. These two ideas are combined with the observation that the Pfurner-Schrocker-Husty map preserves these linear subspaces. This means that the interpolation method proposed by Pfurner et al can be restricted to subgroups and symmetric subspaces of SE(3).

KeywordsMotion interpolation; Lie triple systems; Symmetric subspaces; Cayley maps
Year2017
PublisherSpringer
Journal citationpp. 467-474
Digital Object Identifier (DOI)https://doi.org/10.1007/978-3-319-60867-9_53
Accepted author manuscript
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Publication dates
Print05 Jul 2017
Publication process dates
Deposited03 Apr 2017
Accepted28 Feb 2017
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