DQ Robotics: a Library for Robot Modeling and Control Using Dual Quaternion Algebra

Dual quaternion algebra and its application to robotics have gained considerable interest in the last two decades. Dual quaternions have great geometric appeal and easily capture physical phenomena inside an algebraic framework that is useful for both robot modeling and control. Mathematical objects, such as points, lines, planes, infinite cylinders, spheres, coordinate systems, twists, and wrenches are all well defined as dual quaternions. Therefore, simple operators are used to represent those objects in different frames and operations such as inner products and cross products are used to extract useful geometric relationships between them. Nonetheless, the dual quaternion algebra is not widespread as it could be, mostly because efficient and easy-to-use computational tools are not abundant and usually are restricted to the particular algebra of quaternions. To bridge this gap between theory and implementation, this paper introduces DQ Robotics, a library for robot modeling and control using dual quaternion algebra that is easy to use and intuitive enough to be used for self-study and education while being computationally efficient for deployment on real applications.