Serre-Frenet Frame in n-dimensions at Regular and Minimally Singular Points
In contemporary robotics more and more complicated systems are considered. To plan their motions, well-known coordinate frames, living in natural, three-dimensional spaces, should be modified to cover multidimensional spaces as well. In this paper an algorithm is proposed to determine the Serre-Frenet frame in high dimensional spaces. The frame is examined at regular points where consecutive derivatives of a given curve, the robot moves along, are independent of each other. An interpolation procedure is provided when a minimally singular points appear and dimensionallity of the space spanned by the derivatives drops by one with respect to the regular, full dimensional space.
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