Spinor geometry based robots spatial rotations terminal control

  • Authors:

  • A. Milnikov;T. Natriashvili

  • Affiliations:

  • Department of Robotics, Institute of Mechanics of Machines, Tbilisi, Georgia;Department of Robotics, Institute of Mechanics of Machines, Tbilisi, Georgia

  • Venue:
  • MMES'11/DEEE'11/COMATIA'11 Proceedings of the 2nd international conference on Mathematical Models for Engineering Science, and proceedings of the 2nd international conference on Development, Energy, Environment, Economics, and proceedings of the 2nd international conference on Communication and Management in Technological Innovation and Academic Globalization
  • Year:
  • 2011

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Abstract

In the article, using spinor representation of orthogonal transformations, the expressions between second order complex unitary transformations matrixes and real orthogonal matrixes of spatial rotations in three dimensional Euclidean space L3 are received, that allows easily calculating of corresponding Euler's angles. The obtained results have enabled reducing the actually three-dimensional problem of spatial motion control to the one-dimensional problem; control kinematical functions of Euler's angles and control spinor matrix of rotation were constructed, by means of which control process of spatial rotations is completely determined.