GAFRO: Geometric Algebra for Robotics [Tutorial]

Abstract

Geometry is a fundamental part of robotics and there have been various frameworks of representation over the years. Recently, geometric algebra has gained attention for its property of unifying many of those previous ideas into one algebra. While there are already efficient open-source implementations of geometric algebra available, none of them is targeted at robotics applications. We want to address this shortcoming with our library <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gafro</i>. This article presents an overview of the implementation details as well as a tutorial of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gafro</i>, an efficient C++ library targeting robotics applications using geometric algebra. The library focuses on using conformal geometric algebra. Hence, various geometric primitives are available for computation as well as rigid body transformations. The modeling of robotic systems is also an important aspect of the library. It implements various algorithms for calculating the kinematics and dynamics of such systems as well as objectives for optimization problems. The software stack is completed by Python bindings in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pygafro</i> and a ROS interface in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gafro_ros</i>.