Quaternion representations of the O+(3) group, and their applications in robotics

J. F. Bitó, G. Y. Eröss, J. K. Tar

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4 Citations (Scopus)


Abstract algebraic methods for solving different mathematical tasks have found widespread applications in theoretical physics and in several technical applications. Though group theory can be used to achieve the most simple and transparent formulation of different tasks, it is not very well known by engineers. The aim of this paper is to discuss quaternion representations of the O+(3) Lie group from the aspect of robotics. The main features of these representations, as well as their advantages over the pure 3 × 3 matrix (self-)representation, are discussed in the formulation and solution of the direct and inverse kinematic tasks for robots of general wrist-joint structure. To illustrate the convenience of quaternion formulations a particular solution of the inverse kinematic task has been developed on the basis of the concept of non-Euclidean (curved) spaces. A possible Hopfield-type neural-network application appropriate to the proposed solution is also considered.

Original languageEnglish
Pages (from-to)453-458
Number of pages6
JournalEngineering Applications of Artificial Intelligence
Issue number6
Publication statusPublished - 1991



  • Group theory
  • Lie algebra
  • inverse kinematic task
  • quaternions
  • robots

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Artificial Intelligence
  • Electrical and Electronic Engineering

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