Partial Bi-Invariance of SE(3) Metrics1

@inproceedings{Chirikjian2015PartialBO,
  title={Partial Bi-Invariance of SE(3) Metrics1},
  author={Gregory S. Chirikjian},
  year={2015}
}
In a flurry of articles in the mid to late 1990s, various metrics for the group of rigid-body motions, SE(3), were introduced for measuring distance between any two reference frames or rigid-body motions. During this time, it was shown that one can choose a smooth distance function that is invariant under either all left shifts or all right shifts, but not both. For example, if one defines the distance between two reference frames to be an appropriately weighted Frobenius norm of the difference… CONTINUE READING

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