Serre-Frenet Frame in n-dimensions at Regular and Minimally Singular Points

  • Ignacy DulebaEmail author
  • Iwona Karcz-Duleba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9520)


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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Electronics FacultyWroclaw University of TechnologyWroclawPoland

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