Die theoretischen grundlagen zur behandlung algebraischer singularitäten der kinematischen koordinatenumkehr in der robotertechnik

Abstract

Discussed in this paper is the difference between kinematic and algebraic singularities in the realm of robotics inverse kinematics. Since singularities of the first kind have been discussed extensively in the specialized literature, this paper focuses on those of the second kind. Presented in the paper are the theoretical foundations pertaining to algebraic singularities, along with practical guidelines for their elimination. Two methods are presented to cope with algebraic singularities in this paper. The simpler of these is introduced first. It is shown that a case exists in which these singularities cannot be eliminated using this method. This case is fully identified and shown to be very unlikely in practice. Nevertheless, it can be handled with the introduction of Euler parameters, as fully discussed in this paper.