  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.
