Solving the inverse kinematics problem symbolically by means of knowledge-based and linear algebra-based methods

The construction of kinematics models by hand is often a tedious and error-prone process. This paper presents an overview of the Organic Robot Control project. One main goal of the project is to automate the computation of closed-formed solutions for both the forward and inverse kinematics of general industrial manipulators. For simple manipulator geometries, we use rule-based programming techniques to obtain a closed-form solution. For complicated geometries, we use elimination techniques based on the computation of Groebner basis. In so doing we convert a complicated coupled transcendental set of kinematics equations into a univariate polynomial. This polynomial can much easier be solved. The generated analytic models fulfill real time requirements and can be parallelized very well.