Application of Conformal Geometric Algebra in Robotics: DH-Parameters Extraction from Joint Axes Poses

Conformal geometric algebra (CGA) contains rounds (points, spheres, circles, point-pairs ...) and flats (planes, lines, ...) just as transformations (translations, rotations, scalors, ...) between them, directly as its elements. This allows very elegant and intuitive modeling and implementation of frequently used algorithms in robotics. Unfortunately there is a steep learning curve working the first time with this algebra. Thats why the purpose of this paper is to collect the missing parts from several books and papers which are needed for practical usage and than to use them in a concrete example application: Determination of Denavit-Hartenberg parameters and also the modified version of them. The CGA solution is then compared with an implementation based on well known vector algebra and a more elegant known solution based on dual vector algebra. Furthermore an overview about available tools to work with CGA is given and a new object oriented class library and a new syntax to formulate mathematical expressions in CGA is introduced.