Minimum Degree Solutions for the Inverse Kinematics Problem by Application of the Buchberger Algorithm

  • Peter Kovács
Conference paper


A closed form solution of the inverse kinematics problem requires the derivation of a set of implicit determining equations for the joint variables. Depending on the sequence, in which joint variables are solved, different sets of equations will be obtained. The maximum polynomial degree among the equations in one set can be smaller than in other sets.

An approach for the symbolic computation of determining equations with minimum degree is presented. First a survey of the polynomial degrees of all equations in all possible solution sequences is obtained by application of the Buchberger Algorithm. This leads to the identification of optimal solution sequences for the joint variables. A basic technique is employed for actually calculating the equations in such a solution sequence.

The method can be used as well to examine arbitrary equation sub-system for extraneous roots. The presented strategies have been incorporated as components in an inverse kinematics expert system. This was used to verify that all closed form solutions for the general 6R robot must contain a determining equation of degree 16. An example of the application of the presented methods is given.


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Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • Peter Kovács
    • 1
  1. 1.Institut für Technische InformatikTechnische Universität BerlinWest Germany

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