IEEE Robotics & Automation Magazine - September 2021 - 102
A Library for Robot
Modeling and Control
DQ Robotics
By Bruno Vilhena Adorno and Murilo Marques Marinho
D
ual quaternion algebra and its application to
robotics have attracted considerable interest in
the last two decades. Dual quaternions have great
geometric appeal and easily capture physical
phenomena inside an algebraic framework,
which 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 among them.
Nonetheless, dual quaternion algebra is not as widespread
as it could be, not only because classic matrix algebra
on real numbers is very mature and provides the backbone
of most robotics textbooks [4]-[6] but also because efficient
and easy-to-use computational tools are not abundant and
usually are restricted to the particular algebra of
Digital Object Identifier 10.1109/MRA.2020.2997920
Date of current version: 7 July 2020
102 * IEEE ROBOTICS & AUTOMATION MAGAZINE * SEPTEMBER 2021
quaternions. To bridge this gap between theory and implementation,
this article introduces DQ Robotics, a library for
robot modeling and control employing dual quaternion
algebra that is easy to use, intuitive enough to be utilized for
self-study and education, and computationally efficient for
deployment on real applications.
A Library for Robot Modeling and Control
Far from being an abstract mathematical tool, dual quaternions
easily capture geometric and physical phenomena
and thus can be applied to robot modeling and
control. Some authors consider the particular set of dual
quaternions with a unit norm, known as unit dual quaternions,
to be the most efficient and compact tool for
describing rigid transformations [1], [2]. For instance,
homogeneous transformation matrices (HTMs) have 16
elements, whereas dual quaternions have eight, and dual
quaternion multiplications are less expensive than those
for HTM [3, p. 42]. Moreover, it is easy to extract geometric
parameters from a given unit dual quaternion
(translation, axis of rotation, angle of rotation). Nonetheless,
they are easily mapped into a vector structure, which
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IEEE Robotics & Automation Magazine - September 2021
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