APPLICATION OF FUZZY LOGIC TO ROBOTIC ClONTROL
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APPLICATION OF FUZZY LOGIC TO ROBOTIC ClONTROL
Hammond V a s h i s t h and Peng-Yung WooDepartment of Electrical Engineering
Northern Illinois University, DeKalb, IL 60115
ABSTRACT
This paper describes how fuzzy
logic can be applied to robotic
control using software tools on
personal computers. First, the
fundamentals of fuzzy logic’and
robotics are discussed. Second, the
fuzzy controller designs for a two-
link manipulator and for robot PUMA
5 60 (the last three links locked)
are proposed. C language code is
developed to simulate the controller
designs. Fuzzy Inference DevelopmentEnvironment (FIDE) software from
Aptronix, Inc. is used for
development of fuzzy if-then rules.
The contribution of this paper is
the exploration of non-conventional
methods for control of highly non-
linear systems.
1. INTRODUCTION TO FUZZY LOGIC
Logic has been the essence of
scientific reasoning for centuries.
Fuzzy logic is a relatively new
concept initiated by Professor Lotfi
Zadeh of UC-Berkeley in the mid-
1 9 6 0 s [1,2]. Fuzzy logic uses the
technique of “approximate reasoning”
for making accurate decisions for
problems which are difficult to be
solved by conventional methods.
Fuzzy logic is a superset of
conventional, or Boolean logic. In
Boolean logic we talk about
“complete“ truth values of 0 and 1.
Boolean logic takes on the value of
0 and 1. Fuzzy logic enters the
domain of degrees of truth or false.
It investigates the partial truth
values - those between 0 and 1. Theintermediate values between 0 and 1
are used to represent Degrees of
Membership [1,21. Let us consider
six processors with different clock
rates. A fuzzy subset FAST can be
defined which would state ‘to what
degree is processor x fast?” The
subset FAST is called a Linguistic
Variable in fuzzy literature [1,2].
Every processor is assigned a degree
of membership in the fuzzy subset
FAST. We can define FAST(x) of speed
x as:
FAST(X) = 0 if x < 20 MHZ
= ( x - 2 0 ) / 3 0 if 20 MHZ <= x
= 1
<= 50 MHZ
if x > 50 MHZ
A graph of the above concept for
FAST(x) is shown in Figure 1.1.
Table 1.1 gives some example values
to interpret the meaning of the
membership functions and their
degrees.
The procedure for fuzzy
controller design involves three
steps: Fuzzication, Rule Evaluation
(Fuzzy Inference) and Defuzzication.
FUZZICATION is the initiating step
in fuzzy controller design wherein
the conventional crisp input
variables are converted to fuzzy
inputs by the input membership
function. In RULES EVALUATION, rules
are applied to these fuzzy inputs to
solve the control. problem.
DEFUZZICATION is the final step,
where the final crisp values of
output variables are derived from
the fuzzy values resulted in rule
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evaluation [1,2]. the vector of gravity terms. T is
the vector of joint torques.
2. ROBOT DYNAMICS FOR CONTROL
PURPOSE
A robot is defined as a
mechanical manipulator that can be
programmed according to the needs ofthe application by the end user,
which is used to move materials or
tools through planned trajectories
to perform the desired task [3,41.
The robotic system is a highly non-
linear coupled system. Various kinds
of actuators or motors can be used
in robot links, but primarily
electric, hydraulic and pneumatic
motors are used in industrial
robots. It is our aim to control the
motion of these motors which are
coupled to the robot joints. Thestudy of robotics considers the
kinematics and dynamics of the
manipulator [3,4]. Kinematics
relates to the position and velocity
of the links of the manipulator and
the related static forces. Dynamics
refers to the forces that are
required to cause the motion of the
manipulator. Usually the terms
robot and mechanical manipulator are
used interchangeably in literature.
The angular velocity of some
modern industrial robots is of the
order of 10 rad s - l , which has a
significant effect on the behavior
of the robotic manipulator. Hence,
study of control strategies is
really important. The dynamic
equation of the robotic manipulator
is usually symbolically represented
by Equation (2.1) [3,4].
T = M(@)@” + C ( 0 , e ’ ) + G(8)
where M ( 8 ) i s a mass matrix of
inertia terms of the manipulator,
C ( @ , @ ‘ )is the vector of Coriolis
and centrifugal terms and G ( 8 ) is
3. FUZZY CONTROLLER DESIGN FOR A
TWO-LINK MANIPULATOR
The robotic manipulator is a
non-linear device and conventionalcontrol methods either are not easy
to devise or make some major
approximations while developing the
controller. Fuzzy logic provides a
feasible means to deal with non-
linear systems. By using the three
steps mentioned in Section 1 of this
paper, a fuzzy controller is
designed to simulate the performance
of a two-link manipulator.
(1) The inputs to the fuzzy
controller are position errors andtheir time derivatives, that is, the
velocity errors. Since we consider
two links, in effect, there are four
inputs, namely:
e-thetal, error in position of link
1
e-theta2, error in position of link
Ld-thetal, error in velocity of link
1
d-theta2, error in velocity of link
2
We choose same membership functions(either for position error or for
velocity error) €or link 1 and link
2 of the two-link manipulator. They
are depicted in Figure 3.1 and
Figure 3.2.
(2) Table 3.1 shows the fuzzy
knowledge based control rules
developed for the two-link
manipulator. Again here we choose
the same rule base applied to both
link 1 and link 2. Generally, we do
not have to choose the rule base forlink 1 to be the same as that for
link 2.
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( 3 ) The outputs of the fuzzy
controller are joint torque 1 and
joint torque 2. We choose their
membership functions to be the same
and depict it in Figure 3 . 3 .
The rules in . (2) are
implemented with' the help ofsthe
personal computer and FIDE software.
The fuzzy controller fuzzifies the
input quantities through algorithms
that would operate on the input data
as specified by the membership
functions described in (1).The IF-
THEN decision rules can be
implemented using Table 3.1. And
finally the output is defuzzified
based on the membership functions
described in ( 3 ) .
The whole procedure is a standard
one for fuzzy controller designs
[ 1 , 2 1 .
4. FUZZY CONTROLLER DESIGN FOR
ROBOT PUMA 560
PUMA 56 0 is a popular
industrial robot. Its
characteristics are as follows:
* It is a medium-power robot;
* It is programmable either for
point-to-point or for continuous and
is computer controlled;
* It comes with a teach pendant andis powered by DC electric motors;
* It is widely used in manufactur-
ing process, for handling small
parts;
* It is actively used in
educational institutions for
research purposes.
We assume the first three links of
PUMA 560 have the same membership
functions while the last three links
are locked and therefore become the
load of the first three links.Figure 4.1 depicts the typical
coordinate frame assigned to the
links of PUMA 5 6 0 . Table 4.1 shows
the geometric and inertia parameters
of the robot [ S I . The membership
functions for PUMA 56 0 are presented
in Figure 4 . 2 through Figure 4 . 4 . By
using the same three steps as we did
for a two-link manipulator, we
design the fuzzy controller for PUMA
5 6 0 .
5. SOFTWARE IMPLEMENTATION ANDSIMULATION RESTJILTS
Fuzzy Inference Development
Environment (FIDE) software by
Aptronix, Inc. :is utilized for
implementing the fuzzy if-then rules
[ 61 . The two-link manipulator is
simulated by code written in clanguage [ 71 . The simulation of PUMA
56 0 is derived as an extension to
the simulation of the two-linkmanipulator. Space constraints force
the exclusion of the code in this
paper, but the reader can contact
the authors for more information on
this subject.
The previous sections describe
the membership functions for the
various input arid output variables
of the fuzzy coritroller. Nothing is
perfect in this world, and fuzzy
control tries to explore this
approximate, inexact nature of thereal world. A set of rules are
written for the robotic systems and
simulated in FIZ)E to give outputs.
Application of robots in industry
and other fields: depends on
efficiency, reliability and the
capabilities of the control system,
which has to ensure successful
application of robots in various
tasks. The control system of robots
can be realized in different ways,
with varying degrees of complexity
depending on the tasks imposed upona specific robot. Fuzzy logic
control can be considered as a nexus
between the conventional precise
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mathematical control and the human-
like decision making schemes. At
this time there is no systematic
procedure for the design of a fuzzy
controller and heuristic rules are
used for the control scheme.
Linguistic rules are the heart of
the fuzzy implementation. By a
linguistic variable we mean a
variable whose values are words or
sentences in a natural or artificial
language. For example, Age is a
linguistic variable if its values
are linguistic rather than
numerical, i.e. young, not young,
very young, quite young, old, not
very old, and not very young etc.
rather than 2 0 , 2 1 , 2 2 , 2 3 . . .
Using the fuzzy linguistic
rules, various conditions are
simulated to test the validity ofthe fuzzy controller. The behavior
of the two-link manipulator as well
as that of PUMA 5 6 0 are demonstrated
for either the fuzzy controller
applied or the conventional (PD and
PID) controller applied. The results
obtained for the two-link
manipulator are presented in Figure
5.1 through Figure 5.8 in the form
of plots of joint positions versus
time. Figure 5 . 9 through Figure 5 . 2 0
present the simulation results for
PUMA 5 6 0 . Basically four differentconditions are experimented
respectively:
Robot Unloaded
Robot in complex trajectory
Constrained motion of the
. Robot Loaded
situation
Robot.
(1) Figure 5 . 1 through Figure 5 . 2
and Figure 5.9 through Figure 5.11
show the situation when the robotsare unloaded. This is the simplest
case. We can see the fuzzy
controller does much better than
the conventional controller in the
sense that the position trajectories
of the robot joints with the fuzzy
controller is much closer to the
desired trajectories.
( 2 ) In Figure 5 . 3 through Figure
5 . 4 and Figure 5.12 through Figure
5.14, the desired trajectories
remain the same. The trajectories of
the robots with the fuzzy controller
when loaded still go convergent to
the desired trajectories, while the
conventional control plots show a
considerable discrepancy with the
desired plots.
( 3 ) Figure 5 . 5 through Figure 5 . 6
and Figure 5 . 1 5 through Figure 5.17
depict the situation when the
desired trajectories are sinusoidal
functions. Evidently, the
conventional controller can hardly
function then. The fuzzy controlleris still working very well to bring
the actual trajectories of the
robots to the desired trajectories.
(4) In robotic grinding, deburring
or assembly, smooth transition from
free to constrained motion is of
special interest. Figure 5 . 7 through
Figure 5 . 8 and Figure 5.18 through
Figure 5.20 present the results
obtained in these cases. Again, the
fuzzy plots are convergent to the
desired plots. The conventional
plots now show a total divergence.
NOTE: Due to limitation of space,
the simulation results cannot be
presented in this paper.
6. CONCLUSIONS
This paper proposes a new
fuzzy logic based strategy to
control a robotic manipulator in
order to overcome the disadvantages
of the existing conventional control
methods [ 8 , 9 1 . Two manipulators are
considered in this paper. One is a
two-link manipulator and the other
is PUMA 5 6 0 with the last three
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links locked. The performance of
these robots with a fuzzy controller
applied is found to be better than
with a conventional controller
applied. Moreover, this new approach
is easier to implement. Simulation
results for various conclitions for
the robots find that the fuzzy
controller provides a robust
control.
The main contribution of this
paper is the exploration of non-
conventional methods for control of
highly non-linear systems. A
successful simulation of a fuzzy
controller controlled two-link
manipulator and a fuzzy controller
controlled PUMA 560 is demonstrated.
REFERENCES
1. D. D riankov, H.Hellendoorn and M.
Reinfrank, An Introduction to Fuzzy Control,
Springer-Verlag, 1993
2 . T .J . Ross, Fuzzy Log ic w ith Engineering
Application, McGraw Hill, 1995
3. J.J. Craig, Introduction to R obotics -
Machanics and Control, Addision-Wesley, 1989
4. H. Asada and J.E. Slotine, Robot Analysisand Control, John-Wiley and Sons, 1987
5 . T.J. Tarn, A.K. Bejecy and X. Yun,
“Dynamic Equations for PUM A 560 Robot A rm”,
Dept. Of Systems, Science and Mathematics,
Washington University, St. Louis, M issouri 63 130.
6.
Manuals, Aptronix, Inc.
7.
Programming Language, Prentice Hall, 1978
8.
of Fuzzy Controller for Robotic Manipulators”,
IASTED International Conference on Applied
Modelling, Simulation and Optimization, Cacun,
Mexico, June, 1995
9. H. Vashisth “Implementation of Fuzzy
Logic for Control of a Robotic Manipulator and
Proposition of.Collision Avoidance Algorithm for
Flexible Assembly Cell ”, M.S . Thesis,
Electrical Engineering Department, Northern Illinois
University, Spring 1995
The FIDE Users, Reference and Quick Start
B.W. Kernigham and D.M. Ritchie, The C
H . Vashisth and P.-Y. Woo, “Simulation
Table 3.1 Tb eRule Base for llhe fuzzy kmowlcdgebasematrd
NegativeSmall
NegativeSmall Zero NegativeSmaU
Zero FmithSmal l
PositiveSmall
NegativeLarge
N e g a h M d i u miNegativeSmaIl
ZWJ
RxitkSmal l
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0.7764
1.18 0.- 0.0863 -0.00- 0.0119 0.0029 0.0118.0.61 O . mo 0 -a.o1o* 0.0013 0.0009 o.Oo0) O.uw9
0.16 0.- 0.- 0.0029 o . m e 0 . ~ 0 . 0 . ~ 0 4
0.1060
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