Theory of Applied Robotics: Kinematics, Dynamics, and Control

688 Pages·2007·20.56 MB·English

by  Reza N. Jazar

Theory of Applied
Robotics
Kinematics, Dynamics, and Control
Theory of Applied
Robotics
Kinematics, Dynamics, and Control
Reza N. lazar
DepartmentofMechanicalEngineering
Manhattan College
Riverdale,NY
~
Springer
Reza N.lazar
DepartmentofMechanical Engineering
ManhattanCollege
Riverdale, NY 10471
TheoryofAppliedRobotics:Kinematics,Dynamics,andControl
LibraryofCongressControlNumber:2006939285
ISBN-IO:0-387-32475-5 e-ISBN-IO:0-387-68964-8
ISBN-13:978-0-387-32475-3 e-ISBN-13:978-0-387-68964-7
Printedonacid-freepaper.
©2007SpringerScience+BusinessMedia,LLC
Allrightsreserved.Thisworkmaynotbetranslatedorcopied inwholeorinpartwithoutthewritten
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Dedicated to my wife,
Mojgan
and our children,
Vazan
and
Kavosh
and to my supportive father.
Everything depends on
"What youlike to do, what you have to do, and what you do."
Happiness means "what you do is what you liketo do."
Successmeans "what you do is what you have to do."
Preface
This book is designed to serve as a text for engineering students. It
introduces the fundamental knowledge used in robotics. This knowledge
can be utilizedto develop computer programs foranalyzingthekinematics,
dynamics, and control of robotic systems.
Thesubject ofrobotics mayappear overdosed by thenumberofavailable
texts because the field has been growing rapidly since 1970. However, the
topic remainsalivewith modern developments,which are closely related to
the classical material. It is evident that no single text can cover the vast
scope of classical and modern materials in robotics. Thus the demand for
new books arises because the field continues to progress. Another factor
is the trend toward analytical unification of kinematics, dynamics, and
control.
Classical kinematics and dynamics ofrobots has its roots in the work of
great scientists ofthe past four centuries who established the methodology
and understanding of the behavior of dynamic systems. The development
ofdynamicscience,since thebeginningofthe twentiethcentury,hasmoved
toward analysis ofcontrollable man-made systems.Therefore, merging the
kinematics and dynamics with control theory is the expected development
for robotic analysis.
The other important development is the fast growing capability of ac
curate and rapid numerical calculations, along with intelligent computer
programming.
Level ofthe Book
This book has evolved from nearly a decade of research in nonlinear
dynamic systems, and teaching undergraduate-graduate level courses in
robotics. It is addressed primarily to the last year of undergraduate study
and the first year graduate student in engineering.Hence, it is an interme
diate textbook. This book can even be the first exposure to topics in spa
tial kinematicsand dynamicsofmechanical systems.Therefore, it provides
both fundamentaland advanced topics on the kinematics and dynamics of
robots. The whole book can be covered in two successive courses however,
it is possible to jump over some sections and cover the book in one course.
The students are required to know the fundamentals of kinematics and
dynamics, as well as a basic knowledge of numerical methods.
x Preface
The contents ofthebook have been kept at a fairlytheoretical-practical
level. Many concepts are deeply explained and their use emphasized, and
most oftherelatedtheoryandformalproofshavebeenexplained. Through
out thebook,a strong emphasis isput on the physical meaningofthecon
cepts introduced.Topics that havebeen selected areofhigh interest in the
field. An attempt has been made to expose the students to a broad range
of topics and approaches.
Organization ofthe Book
The text is organized so it can be used for teaching or for self-study.
Chapter 1"Introduction," containsgeneralpreliminarieswith abriefreview
of the historical development and classification ofrobots.
Part I "Kinematics," presents the forward and inverse kinematics of
robots. Kinematics analysis refers to position, velocity, and acceleration
analysis of robots in both joint and base coordinate spaces. It establishes
kinematic relations among the end-effecter and the joint variables. The
method ofDenavit-Hartenberg for representing body coordinate frames is
introduced and utilized for forward kinematics analysis. The concept of
modular treatment ofrobots is wellcovered to show howwe may combine
simplelinksto maketheforward kinematicsofacomplexrobot.Forinverse
kinematicsanalysis,theideaofdecoupling,theinversematrix method, and
the iterative technique are introduced. It is shown that the presence of a
spherical wrist is what we need to apply analytic methods in inverse kine
matics.
Part II "Dynamics," presents a detailed discussion of robot dynamics.
An attempt is made to reviewthe basic approaches and demonstrate how
these can be adapted for the active displacement framework utilized for
robot kinematics in the earlier chapters. The concepts of the recursive
Newton-Euler dynamics, Lagrangian function, manipulator inertia matrix,
and generalizedforcesareintroduced and appliedforderivationofdynamic
equations of motion.
Part III "Control," presents the floating time techniquefor time-optimal
control of robots. The outcome of the technique is applied for an open
loop control algorithm.Then,a computed-torque method is introduced, in
which a combination of feedforward and feedback signals are utilized to
render the system error dynamics.
Method ofPresentation
The structure of presentation is in a "fact-reason-application" fashion.
The "fact" is the main subject we introduce in each section. Then the
reason isgiven as a "proof." Finallythe applicationofthe fact isexamined
insome"examples."The "examples"areavery important part ofthe book
becausethey showhowto implement the knowledge introduced in "facts."
They also cover some other facts that are needed to expand the subject.
Preface xi
Prerequisites
Sincethebookiswrittenforseniorundergraduate andfirst-year graduate
levelstudentsofengineering, theassumption isthat usersare familiar with
matrix algebra as well as basic feedback control. Prerequisites for readers
of this book consist of the fundamentals of kinematics, dynamics, vector
analysis, and matrix theory. These basics are usually taught in the first
three undergraduate years.
Unit System
Thesystemofunitsadopted in this book is,unlessotherwisestated,the
internationalsystemofunits (SI).The unitsofdegree (deg)or radian (rad)
are utilized forvariables representing angular quantities.
Symbols
• Lowercasebold letters indicatea vector.Vectorsmay beexpressed in
an n dimensional Euclidian space. Example:
r s d a b c
p q V w y z
w a € (J ~ cjJ
• Uppercase bold letters indicate a dynamic vector or a dynamic ma
trix, such as and Jacobian. Example:
F M J
• Lowercase letters with a hat indicate a unit vector. Unit vectors are
not bolded. Example:
i J k
j j k
• Lowercaseletters with a tilde indicatea 3x3skewsymmetricmatrix
associated to a vector. Example:
• An arrow above two uppercase letters indicates the start and end
points ofa position vector. Example:
--+
ON = a position vector from point 0 to point N
xii Preface
• A double arrow above a lowercase letter indicates a 4 x 4 matrix
associated to a quaternion. Example:
qO -ql -q2 -q3]
ql qo -q3 q2
f-q-+
q2 q3 qo -ql
[
q3 -q2 ql qo
q = qo+qli +q2j +q3k
• The length of a vector is indicated by a non-bold lowercase letter.
Example:
r = [r] a= [a] b= [b] s = lsi
• Capital letters A, Q, R, and T indicate rotation or transformation
matrices. Example:
-1]
Qz,o: = [ CSOi~SO0:: -cosoisn0:0: 0o] , GTB = [ Cs0Oo:: 001 -cosoo:: 00..25
1 0 0 o 1
• Capital letter B is utilized to denote a body coordinate frame. Ex
ample:
B(oxyz) B(Oxyz)
• Capital letter G is utilized to denote a global, inertial, or fixed coor
dinate frame. Example:
G G(XYZ) G(OXYZ)
• Right subscript on a transformation matrix indicates the departure
frames. Example:
T = transformation matrix from frame B(oxyz)
B
• Left superscript on a transformation matrix indicates the destination
frame. Example:
GT transformation matrix from frame B(oxyz)
B
to frame G(OXYZ)
• Whenever there isno sub or superscript,the matrices are shown in a
bracket. Example:
[ C~ ~ -so:
o -1 ]
[T] = 0.5
so: 0 CO: 0.2
o 0 o 1