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Chapter One


General Introduction and Review




1

Chapter One

General In
troduction and Review



1.1
Introduction

T
he term 'robotics' refers to the study and use of robots. The term was coined
and first used by the Russian
-
born American scientist and writer Isaac Asimov

[
1
]
.

The science of robotics has grown tremendously over the past twenty years,

fueled
by

rapid advances in computer and sensor technology as well as theoretical advances
in control

and computer vision

[2]
.
The Robot Industries Association (RIA) has
defined an industrial robot as "a reprogrammable multi
-
functional manipulator
designe
d to move material, parts, tools or specialized devices, through variable
programmed motions for the performance of a variety of tasks"

[
3
].
The
robot

has
been applied to a great variety of mechanical devices, such

as teleoperators,
underwater vehicles, a
utonomous land rovers, etc.


Robotic systems play an essential role in our society, and their presence and
our

dependence on them are increasingly growing.

Robotic systems

are the best and
most of the time the only replacement to human beings in applicatio
ns

where human
presence is either not possible or harmful

[2,4].
Understanding the complexity of
robots and their applications requires knowledge of electrical engineering,

mechanical engineering, systems and industrial engineering, computer science,
econo
mics, and mathematics. The relevant areas include mechanics, mechanical
design, electronics, embedded systems, dynamics, control, and artificial intelligence

[
5
]
.


1.2 Robot Control


Robots are classified by control method into servo and non
-
servo robots.
The
earliest robots were non
-
servo robots. These robots are

essentially open
-
loop

devices
whose movement is limited to predetermined mechanical stops, and they

are useful

primarily for materials transfer. Servo robots use closed
-
loop computer

control to
Chapter One


General Introduction and Review




2

d
etermine their

motion and are thus capable of being truly multifunctional,
reprogrammable devices.

Servo controlled robots are further classified according to
the method that the controller

uses to guide the end
-
effector.

The simplest type of
robot in this

class is the point
-
to
-
point

robot

[
2
]
.

The robot's control system is
responsible for producing actual robot behavior that matches the desired behavior as
closely as possible.

Once a nominal trajectory is determined, there remains the
problem of issuing th
e commands to the joint actuators that will cause the
manipulator to faithfully
"track
"

or follow the planned

trajectory
. This is called the
robot control problem

[
6
].

Control of an industrial

robot is mainly a problem of dynamics. It includes
non
-
linearit
ies, uncertainties

and

external perturbations that should be considered in
the design of control
laws
.

The block diagram of a typical robot control is shown in
F
ig.

(
1.1).

The figure shows that ther
e

are

four

basic
components:

i) manipulator,

ii)
sensors,

iii)

actuators and drives

and

iv) controllers.

The following is a brief
description of these components

[7
,8
]
:

i.

Manipulator:

A robot manipulator manipulates a tool or gripper in 3
-
dimensional
space to accomplish a task. A typical robot is comprised of
several major linkages
responsible for positioning the end
-
effector in space, and a wrist assembly for
orienting the end
-
effector
.

Using R and P to designate rotary and prismatic motion,
t
he majority of the manipulators fall into one of five geometric type
s: articulate
(RRR), spherical (RRP),
SCARA

(Selective Compliance Arm for Robotic
Assembly) (RRP), cylindrical (RPP), or cartesian (PPP).

ii.
Feedback devices
: Transducers that sense the position of various linkages and/or
joints that transmit this informa
tion to the controller. The robot needs a variety of
sensors in order to adapt to disturbances and unpredictable changes in the work
environment so as to obtain information
both about the environment (using external
Chapter One


General Introduction and Review




3

sensors, such as

cameras or touch sensor
s) and
a
bout itself (using internal sensors,
such as joint encoders or joint torque sensors)
.

iii.


Actuators and Drives
:

They are basically a
n assembly of mechanical and
electrical components that allow a robot to physically act upon itself or the
environment
. Joint actuators can be either a

pneumatic, hydraulic or electric
device
.

They are operated by

a control system that furnishes the power to change
and/or maintain the position of an element (such as an end
-
effector) that performs
a task. The actuator res
ponds to a signal received from the control system.


iv.

Controller:
The controller is the brain or computer center of the robot. It
controls the robot's movement and timing.

An intelligent industrial robot is a remarkably useful combination of a
manipulat
or, sensors and controls.

Controllers typically use feedback from a variety
of sensors to compare the robot's actual behavior to the desired behavior. The
controller uses this information to generate control inputs to the robot, in the form of


q
d

Desired joint position

velocity & acceleration

Controller



Joint torques

Link parameters

Actuators

q

Actual joint position

velocity & acceleration


Loading condition

Manipulator

Sens
ors

Fig.

(1.1) Block
d
iagram of
r
obot
c
ontrol [
5
]
.


-

+

Chapter One


General Introduction and Review




4

actuator
torques/forces
.

The use of these machines in factory automation can
improve productivity, increase product quality and improve competitiveness.

Robots
have been created to

perform a wide variety of tasks spanning from educational
robots in classrooms, to a
rc welding robots in the automobile industry, to
teleoperated robot arms and mobile robots in space

[
2
,
5
].


1.3 Trajector
y
Tracking
a
nd Control

T
he term trajectory is defined as follows by Brady (1983):"a trajectory is the
time sequence of intermediate con
figurations of the arm between the source and the
destination, the space curve traced by the end effector is called the path of the
trajectory"

[
9
].

Because of the complexity of both the kinematics and dynamics of
the manipulator and of the task

to be car
ried out, the motion control problem is
generally decomposed into three stages, Motion

Planning, Trajectory Generation,
and Trajectory Tracking. In the motion planning stage, desired

paths are generated
in the Task Space
,

without timing information, i.e.,
without specifying

velocity or
acceleration along the paths.
o
f

primary concern is the generation
s

of collision free
paths

in the workspace. In the trajectory generation stage, the desired position,
velocity, and acceleration

of the manipulator along the p
ath as a function of time or
as a function of arc

length along the

path are computed
.
In

t
he
manipulator trajectory
tracking control
, the

problem revolves around computing the

torques to be applied to
achieve accurate tracking

and

consists of following a g
iven time


varying trajectory
q
d
(t) and its successive derivatives

and

which respectively describe
the desired velocity and acceleration

[1
0
]
.


In order to compute a
j
oint
s
pace trajectory, the given end

e
ff
ector path must
be transformed into

a
j
oint
s
pace path via the inverse kinematics mapping. Because
of the di
f
ficulty of computing this

mapping on

line, the usual approach is to compute
a discrete set of joint vectors along the end

e
ff
ector path and to perf
orm an
Chapter One


General Introduction and Review




5

interpolation in
j
oint
s
pace among these points in order to complete

the
j
oint
s
pace
trajectory. The computed reference trajectory is then presented to the controller,
whose function is to cause

the robot to track the given trajectory as closely as
possible.

To achieve high precision tracking control, the coupling

between the joints,
the unmodeled disturbances, and

the payload changes must be taken into
consideration.

This is a challenging task in control theory. So far, a

number of
control schemes
have been developed, such

as

[
11
]
:


*
Inverse dynamics control
:
known also under the name of computed torque
control which

relies on the exact cancelation of the nonlinear dynamics

of the
manipulator system, requires the exact dynamic

model
,

and decoupling

robot
manipulator dynamics; nonlinearities such as Coriolis and centrifugal terms as well
as gravity terms can be simply compensated by adding these forces to the control
input. H
owever, this type of feedback linearizing controller is more complicated

and

its conception is no longer straightforward for the robot manipulator dynamics if
mechanical (joint and/or link) flexibility is considered
.

The performance of this
method is degraded

by the unmodeled dynamics and payload variation

*
Lyapunov
-
based control
:
does seek neither to linearize nor to decouple the
system nonlinear dynamics. The idea

is only to search for asymptotic stability
-
exponentially, if possible
.

* Passivity
-

based control:

exploits the passivity properties of the robot
manipulator dynamics.

Like the previous class of control schemes, it does not
achieve exact cancellation of the nonlinearities and then it is expected to be more
robust than inverse dynamics control
.

*Adaptive control

and iterative control strategies
:

require no a priori knowl
edge of
unknown parameters
.


Chapter One


General Introduction and Review




6

1.4 Neural Networks

(NNs)

Artificial intelligence is the science of making machines to do things that
would
require intelligence if done by humans. The artificial intelligence

is used to
shed light on the human variety of inte
lligence by attempting to model it with

computers, make computers easier to use by making them operate more like human

users and solve complex problems that traditional programming methods can not
solve efficiently or not at all

[
1
2
]
.

NNs

referred to a te
chnique for using physical
hardware or computer software to model computational properties analogous to
some that have been postulated for real networks of nerves, such as the ability to
learn and store relationships

[
1
3
]
. NNs

have been widely adopted in t
he field of
nonlinear system identification and control since the 1970's.
In the mid 1980s,
interest in NNs grew when it was shown that nonlinear NN architectures could be
trained to produce desired outputs

[
1
4
]
.


NNs
are used instead of more traditional c
omputation methods when the
system studied is complex or the actual mathematical function is unknown.

Currently,
NNs

are used in two main areas of application, i.e. approximation and
classification problems.
NN

control designs are divided into

two major ca
tegories

[
1
5
]
:

(1) The direct design where the controller is a
NN
.


(2) The indirect design where the controller is not itself a

NN
, but uses

NNs

in its
design and adaptation
.

NNs

can be applied in two ways in the design of the robot controller
that
descr
ibed

in Fig
. (
1.
2
)
: (1) system identification model and (2) control. NNs can be
used to obtain

the system identification
model
which can be used to design the
appropriate
controll
er.

They can also be used directly in
the
design of the controller
once the r
eal system model is available.
T
he

more popular
NN

architectures for
system

identification and control

are
[
5,
16
]
:

Chapter One


General Introduction and Review




7

1. Fixed Stabilizing Controllers
:

this scheme

uses the desired trajectory as

the input
and the feedback control as an error signal.

As

the NN

(
inverse dynamics model
)

training advances

that input will converge

to zero. The
NN

controller will

learn to
take over from the feedback controller.


2. Adaptive Inverse Control
:

The

idea

of this scheme
is to cancel the disturbance
and the noise

present i
n the plant

and the
alternative which allows
this cancellation
includes a

NN

plant model in parallel with the

plant


3. Nonlinear Internal Model Control
:

consists of a
NN

controller, a

NN

plant
model

which
can be trained off
-
line, using

data collected from

plant operations, and
a robustness filter

with a single tuning parameter

which is
a first order filter whose
time constant is selected

to ensure closed loop stability.

4. Model Predictive Control
:

This architecture requires a
NN
plant model

used to
predic
t the plant response, a
NN
controller

learns to produce the input selected by
the optimization

process,

a performance function to evaluate system

responses, and
an optimization procedure to select

the best control input.

-

Sensors

Primary controller

Secondary controller


q
d


Robot

+

+

+



q

Fig. (1.2) Controller decomposition in primary and secondary controllers[5].


Chapter One


General Introduction and Review




8

5. Model Reference Control or Neu
ral Adaptive Control
:

T
wo
NNs are used:

a
controller network and a

model network. The model network

can be trained off
-
line
using historical plant measurements.

The controller is adaptively trained to

force the

plant output to track a reference model outpu
t.

The model network is used to predict
the effect

of controller changes on plant output, which allows

the updating of
controller parameters.

6. Adaptive Critic
:

This scheme
consists of two
NNs
. The first

network operates as
an inverse controller and is

ca
lled the Action or Actor network. The second network,

called the Critic Network, predicts the future

performance of the system. The Critic
network is

trained to optimize future performance. The training

is performed using
reinforcement learning, which is

a
n approximation to dynamic programming.

7. Neural Adaptive Feedback Linearization
:

It is
based on the standard feedback
linearization

controller technique

that
produces a control signal with two
components. The

first component cancels out the nonlineariti
es in the

plant, and the
second part is a linear state feedback

controller.

8. Stable Direct Adaptive Control
:

The controller consists

of three parts: linear
feedback, a nonlinear sliding mode controller and an adaptive
NN

controller. The
sliding mode con
troller is used to keep the system

state in a region where the
NN

can

be accurately trained to achieve optimal control.

The

sliding mode controller is
turned on (and the neural

controller is turned off) whenever the system drifts

outside
this region. The c
ombination of controllers

produces a stable system which adapts to
optimize

performance.


1.5 Literature Survey

The motion control of industrial manipulators is a central

issue in the robotic
area and has received a great deal

of attention in the past deca
de
.

Many approaches
have been

introduced to treat this control problem and various control

algorithms
Chapter One


General Introduction and Review




9

have also been proposed in the literature.

The literature of adaptive control and NN
application to trajectory tracking will be reviewed next.


1.5.1 Ada
ptive Control

The

problem

of robot motion

consists
of

obtaining dynamic model of
manipulator and using this model to determine the control inputs
The main task of
control system is to track the required trajectory with given accuracy

even in the
presence o
f disturbances
.

This task is often referred to as the dynamic control.
When
the model is exactly known, the technique of feedback linearization in nonlinear
systems, which is also called
computed torque method
, has been developed to deal

with the control o
f robotics. If knowledge of an
a priori
bound of uncertainty
is

known
, then
robust controll
ers can be
u
sed

to treat the tracking of robot motion

[17]
.

The problem
s

of constructing non
-
linear adaptive control schemes

for robotic
manipulators were considered

when

Miyasato and Oshima

in
1989

proposed

a
non
-
linear

adaptive control scheme where only seven adjustable parameters were
needed at most and the quality dynamic performance was achieved without exact
knowledge of non
-
linear coupling terms

[
1
8
].





Leung, Zhou and Su

[
19
]

in
1991

presented an adaptive variable structure
model following control design for the nonlinear robot manipulator system by using
the

theory of
Variable Structure Control (
VSC
)
.

The

derivation

of

the

VSC did not

require any

knowl
edge

of nonlinear robotic system

by adaptation of scalar gain

and
d
id

not necessarily need the occurrence of a sliding mode at each individually stable
discontinuity surface.
T
he problem of chattering was reduced by the introduction of
a boundary layer
.

An

adaptive controller was developed by
Yuan

[2
0
]

in

1995

for a third
-
order
robot model which included the motor dynamics. The adaptive technique

enabled

the controller to deal with uncertain payloads without requiring exact knowledge of
Chapter One


General Introduction and Review




10

the robot dynamics
.

T
he proposed controller used an adaptive acceleration observer
to estimate the acceleration, avoiding the noise probing acc
eleration feedback and
was proven to be globally stable in the Lyapunov sense
.


The velocity

measurement, obtained by sensors such as

tachometers, is often
contaminated by

noise. This circumstance may reduce the dynamic performance of
the manipulator,

because in practice the values of the controller gain matrices are
limited by the noise

present in the velocity measurement
[
21
]
.

In robo
t control,

velocity sensors are often omitted to save cost and to lessen weight and volume.
This

problem can be solved by using observers to estimate velocities
.
I
n

1997
,

L
ee

and K
halil

designed an adaptive output feedback controller for rigid

robots that
asymptotically recovers the performance achieved under state feedback

control.
High
-
gain observers were used to estimate joint velocities. The control inputs were
saturated outside a domain of interest and used an adaptive law with a parameter
projection f
eature

[
2
2
]
.

A nonlinear adaptive controller with velocity observer

was
designed and implemented on a 6
DOF

parallel

manipulator with direct drive
actuators

by
Honegger
in

1998
. The experiments

showed that the nonlinear
controller reduced the tracking

erro
rs by a factor of about 10 relative to linear joint
controllers,

whe
n fast movements were performed [
2
3
]
.



Many researchers developed an a
daptive robust control schemes for the
trajectory tracking control of robot manipulators.

Yao

[2
4
]

in

1998

used t
wo

schemes:
adaptive sliding mode control

based on the conventional adaptation
structure and
desired compensation adaptive robust control

based on the desired
compensation

adaptation structure. A dynamic sliding mode
was

used to enhance

the
system re
sponse
.

T
he work serve
d

for

the two purposes: improving tracking
performance of robot control systems and setting up a

standard with which various
control

al
gorithms could be compared
.

Keleher and Stonier
in

2002

incorporated

p
hysical state constraints

Lya
punov

function

from which
they

obtain
ed

analytic
Chapter One


General Introduction and Review




11

control laws that drive the robot's end

e
ffe
ctor into a desired
fi
xed target within
fi
nite time

[
2
5
]
.

In

2003

Tayebi

[2
6
]

derived an
A
daptive
I
terative
L
earning
C
ontrol
scheme with unknown parameters, perfor
m
ed

repetitive tasks. The control scheme
was nothing else but a PD controller plus an iteratively updated term designed to
cope with the unknown parameters and disturbances
.

The
research
er

showed

that it
was

possible to use a single iterative variable

in t
he control scheme at the expense of
the knowledge
of

some bounds of the system parameters.


1.5.2 Neural Networks

Control

For the past several years, there have been a lot of interests in applying
i
ntelligent control schemes,

such as
NN

control scheme,
to
solve the problem of
identification and control of complex nonlinear systems by exploiting the nonlinear
mapping abilities of the NN
. A new trend in control of nonlinear systems tries to
combine both adaptive control and the robust control technologies for

designing
NN

controller. Where, the
NNs

are used to

approximate the uncertainty with only
unknown linear weights, the adaptive

technologies can then be adopted to update the
weights and the residual modeling

error is controlled by a robust control scheme
.

The application of NNs

in the area of robotic

control

has a high
potential

[
2
7
]
.

Various design methods have

been proposed in the application of NN to the robot
control

field. The differences in those schemes are largely in the

role that NN is
applied to

the control system and the way it

is trained
.

Due to the structure of
NNs
,

such a

controller

was
designed for trajectory
tracking for manipulator by
Hace
et al

[
2
8
]
in

1994

that
allow
ed

the elimination of
structured and unstructured inaccuracies.

Lyapunov'
s stability theory was used to
design the adaptive law for a computed torque method
based
NN

controller. A joint
space control scheme was used to test this type of controller
.


Chapter One


General Introduction and Review




12

Jung and Hsia

[
29
]

in

1995

presented a comprehensive study of NN
controller for

a
robot

manipulator
.
The

NN control
ler

served as the inverse model of
the
computed
-
torque controlled robot system
. A new

teaching signal
was
developed
for the back
-
propagation algorithm, and delayed joint variables were proposed as
inputs to the NN.

In

19
95, P
ham and
L
iu

[3
0
]

employed

three NNs that
were

based on input
-
output identification, the first to learn the dynamics of the robot, the second to model
its inverse dynamics and the third, a copy of the second NN, to control the robot.

L
ewis

et al
.

[3
1
]

designed
in

1996

a NN controller

on a

rigid

link robot arms
that g
a
ve

guaranteed closed
-
loop performance in terms of small tracking errors and
bounded controls and
reported that there was a trade
-
o
ff
between the
m
agnitudes of
tracking error and weight

err
or.

An adaptive robust compensator for a class on
nonlinear
MIMO nonlinear system was proposed by
Meddah and Benallegue

[32]
in
199
7
. They used a NN
-
based adaptive compensator to improve the tracking
performance. Both of strong robustness with respect to u
nknown dynamics and
asymptotic convergence to zero of the output tracking error was obtained
.



In

1997,
a
n adaptive neural tracking control problem for robotic

systems
under plant uncertainties and external disturbances

ha
d

been proposed and solv
ed
from the
viewpoint of the H


tracking performance by

Chang and Chen

[
1
7
]
.

Ge
and Lee

[
3
3
]

presented a robust model reference adaptive controller for robots
based on applying direct adaptive techniques to an additional parallel NN to provide
adaptive enh
ancements to a fixed controller for better control performance, while a
sliding mode control was introduced to guarantee robust closed
-
loop stability.

A

Radial Base Function (
RBF
)

NNs

were used to adaptively

learn system
uncertainty bounds in the Lyapunov

sense by
Zhihong

et al

[
3
4
]
.

T
he

outputs of the
NNs were used as the parameters of the controller to compensate

for the effects of
system uncertainties. This scheme obtained strong robustness with respect to
Chapter One


General Introduction and Review




13

uncertain dynamics and nonlinearities, and the
output tracking error between the
plant output and the desired reference output can asymptotically converge to zero.


Xiao
et al
.

[
3
5
]

in
199
9

presented an iterative learning controller using
NN for the robot trajectory tracking control. Basic co
ntrol configuration was briefly
presented and a new weight
-
tuning algorithm of NN was proposed with a dead
-
zone
technique
.

I
n

1999
,
Poznyak

et al

[
3
6
]

discussed the

adaptive nonlinear identification

and trajectory tracking via
D
ynamic
NNs
, and
Sun

et al

[
3
7
]

present
ed

a stable
adaptive control approach based on D
ynamic
NNs for

robot manipulators with
unknown dynamics nonlinearities. The robot control
was

composed of

the dynamic
inversion of the D
ynamic
NN system, adaptive compensation and a sliding control
.

They

proved that the tracking

error metric, the state deflection metric of the
D
ynamic
NN system

from the robot system, and the NN weights are convergen
t.



The work of

Li

and

Wang

[
3
8
]

in
2000

showed that
tracking error bound
wa
s completely det
ermined by
NN

approximation error bound, disturbance

bound,
as well as a control design parameter

when proposed

a robust
NN

control scheme for
robot tracking tasks. The
NN

wa
s trained on
-
line and the weight tuning algorithm
ha
d
a small dead zone to overcom
e bounded disturbances.




A

stable adaptive dynamic friction

compensator for motion control systems
based on

NN parameterization
was

proposed

by
Wang et al

[
39
]

in

2001

to cope
with both

dynamic friction uncertainty and system inertia uncertaint
y
.

N
Ns

we
re
used to parameterize the unknown system

nonlinear function and the unknown

dynamic friction

bounding function respectively. Based on Lyapunov

synthesis, the
adaptive control algorithms
we
re

designed to achieve asymptotic tracking of the
desired

trajectory and guarantee the boundedness of

all the signals in the closed
-
loop
system.

Chapter One


General Introduction and Review




14

Choi

et al

[4
0
]

in

2001
present
ed

an adaptive NN compensator
to
reduce

the
control errors of

the conventional control systems which
we
re

not completely
known
. The prop
osed

adaptive NN compensator generate
d

a new command signal to
the

conventional control system using the control error that
wa
s the difference

between the desired reference input and the actual system

response. The proposed
NN
-
compensated control system
wa
s adaptable

to the environment changes and
wa
s
more robust than the conventional

control systems.

A control system using
Radial Base Function (
RBF
)

NN

with a

simple
controller
was

developed

by
Chen

[4
1
]

in

2002

to generate control

signals to control
a SCA
RA robot. The control signals

generated by the
NN

were

quite close
to
the
actual control signals.

This means the developed control system using RBF
NN

achieve
d
satisfactory results
.




The development

of

a robust neural net
-
based MRAC scheme f
or a class
of MIMO nonlinear plants to the control of an industrial robotic manipulator

was
discussed by
Zhang, So, and Cai

[4
2
]

in

2002
.

VSC technique was incorporated
and by use of

Lyapunov

direct

method
, they proved that the whole closed
-
loop
system und
er the proposed scheme was stable and the tracking error would
asymptotically
approach

to zero even in the presence of bounded external
disturbances.



1.6 Scope of the Work


The main
objective of the work
is

to

study the dynamic equations for two
-
axis

(plan
a
r robot)

and three
-
axis SCARA robot

and t
o develop
a robust adaptive
controller

for them
. The system is treated as a partially known system

for them
. The
known dynamics are used to design a nominal controller based on the feedback
linearization

method, to stabilize the nominal system
.

NNs are
to be
used to
approximate the unmodeled dynamics in order to eliminate the effect of the system
Chapter One


General Introduction and Review




15

uncertainties and to improve the tracking performances. The
use of a finite number
of components in NNs, in re
ason of implementation constraints, introduces

approximation errors. This problem
sha
ll be addressed by using a sliding component
in the control law.


1.7 Thesis Organization



By now the reader have realized that

c
hapter
o
ne is a general introduction to the

robot definition,

robot control system
, trajectory tracking,
NNs

and the available
literature survey.



Chapter two introduces the equation
s

of motion
(dynamics and kinematics
equations)
of
a

two
-
axis

(planar)

and three
-
axis

SCARA robot
.



Chapter three appli
es
the
proportional plus derivative

control

and variable
structure control

to the two robots
.




Chapter four applies
NN

technology to the problem of robot control.




F
inally, conclusions and suggestions for future work are given in chapter five.