Algebraic methods for computing inverse kinematics

Abstract

Inverse kinematics computation is one of the challenging topics in robot control and simulation. The description of the kinematics of a robot leads to an algebraic system of equations when trigonometric functions are avoided by certain substitutions. Solving the inverse kinematics problem can so be reduced to solving a system of algebraic equations. In order to keep numerical errors small, one should try to transform the system of equations into an equivalent but ‘simpler’ one by some algebraic method. Gröbner bases are an algebraic technique that transform algebraic equations into a ‘standard form’, the Gröbner basis, that has certain properties concerning the solvability and the solutions of an algebraic system of equations. In this paper, we give an introduction to the formulation of the kinematic equations and to the method of Gröbner bases, and discuss how Gröbner bases can be applied to this specific class of problems.