A new method for solving kinematic tasks for robots

J. F. Bitó, G. Y. Eröss, J. K. Tar

Research output: Contribution to journalArticle

2 Citations (Scopus)


The main difficulties in solving inverse kinematic tasks for robots are singularities and nonlinearities. In the first part of this paper practical conditions regarding singularities of 6 df wrist-joint structure robots are presented. These considerations are based on a simple iterative inversion method by the use of which introduction and characterization of the concepts of "essential" and "procedural" singularities are realized. The second part of the paper deals with the question of nonlinearities. It is pointed out that in robotics there are two different kinds of nonlinearities. The first type is present because the sine and cosine functions of the joint coordinates appear in the formulae of direct kinematic tasks. The second type is of finite polynomial nature, and originates from the quadratic functions of the unit vectors parallel to the rotation axes of the joints of the arm. The authors point out that an appropriate quaternion representation of the robot kinematics offers a convenient possibility to get rid of sine- and cosine-type nonlinearities. Those nonlinearities which remain are the results of simple quadratic operations (mainly multiplications and additions, subtractions and divisions); therefore the proposed method seems to be especially appropriate for realizations based on neural networks or particular hardwares using RISC processors. The advantages and disadvantages of this new method are compared to those of another solution recently published by the authors.

Original languageEnglish
Pages (from-to)459-465
Number of pages7
JournalEngineering Applications of Artificial Intelligence
Issue number6
Publication statusPublished - 1991


  • Robots
  • control nonlinearities
  • control theory
  • quaternions
  • singularities

ASJC Scopus subject areas

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

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