In the last three decades, there has been a phenomenal growth of activity in robotics,
both in terms of research and in capturing the general public’s illusion of endless
futuristic possibilities.
Growth in robotics coincides with an increasing number of courses at most major
research universities on various aspects of the subject. These courses are available in
many departments, such as Systems Engineering and Automation, Computer Science,
Mathematics, or Electrical and Mechanical Engineering. Several excellent textbooks
support this education, covering different topics in kinematics, dynamics, control,
sensing, vision, AI, planning, and navigation for robotic mechanisms. Given the state
of knowledge on the robot subject and the vast diversity of students interested in the
field, there is an inherent utility for a book that presents the more abstract mathematical
formulation given by the screw theory in robotics. This work attempts to provide
a visual approach of this formulation to an audience who perhaps did not have enough
examples of building up the necessary knowledge.
Although the advantages of screw theory are obvious, few teach it in engineering
courses, so there are still proportionally few postgraduates who know how to apply
it. Some numerous projects and publications demonstrate the crucial advances
achieved when applying the geometric formalisms of Lie’s algebra in various robotics
specialties. The screw theory has proven superior to other mathematical techniques
in robotics. Therefore, it is essential to communicate and disseminate these
methodologies among as many students as possible who might be working with
robots in the future.
This book will emphasize geometric techniques and provide a modern visual presentation,
so concepts are better understood. We best capture the key physical features
of a robot with a geometric description. However, these screw theory tools,
inaccessible to many students, require a new language (e.g., screws, twists, wrenches,
adjoint transformation, geometric Jacobian, spatial vector algebra). The rules for the
manipulation of this language can seem kind of obscure. In fact, at the heart of the
screw theory, there is a high-level but straightforward geometric interpretation of
mechanics. The alternative is the most standard algebraic alternatives, which unfortunately
make us often buried in the calculation details.
When Brockett (1983) showed how to use the Lie group structure to describe
mathematically the kinematic chains in rigid bodies’ motion, there was a breakthrough
in making classical screw theory accessible to modern robotics. In presenting
it, we must highlight the powerful Product of Exponentials (POE) as a fundamental
tool of the screw theory.
Overall, we can realize that a good theory is the fastest way to obtain a better
functional performance, and the only thing to do in exchange is to study this mathematics.
The selection of topics for this text targets a modern screw theory approach
for robot mechanics. The content is an excellent introduction to the subject (e.g.,
mathematical tools, kinematics, differential kinematics, dynamics, trajectory generation,
simulation) and the best way to appreciate this approach’s benefits. Other
xviii Preface
aspects such as control are briefly introduced and used in simulations but left out to
a thorough extent for later works.
This book covers the screw theory fundamentals with a very graphical approach.
Its contents are very focused, practical, and visual so that any student can quickly
grasp the advantages of the theory and the algorithmic definitions. In the future, we
will be able to extend those possibilities to other problems and applications. The
main goal of this text is to provide valuable tools for roboticists. We present all necessary
basic theoretical notions but with great emphasis on applications and exercises
with real industrial manipulators. This choice permits that once we get the concepts
for these robot mechanics, it will be possible to expand the approach to a great variety
of robotics architectures.
The examples and exercises in this work demonstrate that geometric solutions
based on the screw theory are more suitable for real-time robotics applications compared
to typical numerical iterative algorithms.
In short, this text aims to help students, engineers, scientists, researchers, and
practitioners of robotics who want to develop their advanced projects toward the
application of screw theory methodologies. We will facilitate the comprehension and
access to the topics addressed through convenient examples presented in a clear
graphical structure. This book’s design intends to build a functional bridge between
the mathematical fundamentals, which are extensive, and the practical technological
robotic applications.
Another component of this book is the additional material included to reinforce
the knowledge-making operative of the formulations. Here, we grant access to code,
examples, and simulations for real manipulators, which help many robotics structure
applications, even outside the field of industrial manipulators. The MATLAB® environment,
including Simulink® and Simscape™, is also a valuable supplement for
robotics simulation, permitting students to explore robots’ mechanics interactively.
This book presents a personal visual approach on how to explain the fundamental
concepts of screw theory. The text is more a companion to essential and excellent
textbooks that thoroughly cover the subject’s mathematical foundations. Particularly
influential are those written by Corke; Davidson & Hunt; Lynch & Park; Mason;
Murray, Li, and Sastry; Selig; Siciliano and Khatib. All these have contributed to
modern robotics in an inspirational way.
In reading this book, we hope that many will feel the enthusiasm about robotics’
technological and social prospects, with the elegance of the underlying screw theory
for developing effective and efficient robotics algorithms, solutions, and
applications.