The De Casteljau algorithm on SE(3)

Claudio Altafini

In A. Isidori, F. Lamnabhi-Lagarrigue and W. Respondek (eds.) Nonlinear Control in Year 2000, Springer-Verlag, 2000.

Smooth closed-form curves on the Lie group of rigid body motions are constructed via the De Casteljau algorithm. Due to the lack of a bi-invariant metric on $SE(3) $, the resulting curve depends on the choice of the metric tensor. The two most common cases are analyzed

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