Proceedings
of~the Second International Conference
on
Machine
Learning
and Cybanetics,
Wan,
25
November
2003
ROUGH SET AND GENETIC ALGORITHMS IN PATH
PLANNING
OF
ROBOT
YING
ZHANG,
CHENGDONG
WU,
MENGXIN
LI
Shen Yang Architectural And Civil Engineering Institute, Shenyang,
110068,
Liaoning, China
EMAIL: zyllZO@sina.com
Abstract:
A
hybrid
method
of
rough set
and
genetic algorithms is
presented
to
raise the speed and accuracy
of
path planning of
robot. Firstly, gain the decision rule
by
rough set theory.
And then, come to a series
of
available paths
by
training the
gained minimal decision rule. Finally, optimize the
population
of
the paths above using genetic algorithms, and
obtain the most excellent path. The results
show
that
the
hybrid method is good at raising the speed
of
path planning of
robot.
Keyword
Rough set;Genetic a1gorithms;RroboG;Path planning
1
Introduction
Robot is the outgrowth of traditional mechanism and
neoletterday electronics technology. And the use of robot
is
enlarging time after time.
So
the performance
of
robot
must be raised. Among them, path planning technology is
more important.
At present, the path planning methods inside and
outside the country have been divided into two
parts:
the
traditional methods and the intelligent methods. The
traditional methods include: gradient method, grid metho4
enumeration method, manmade potential method, and A
p p h research method etc.. But the gradient method
is
easy
to
sink into the local minimum point. And graph research
method and enumeration method can’t be used to settle the
optimization problems, which have higher dimensionality.
And potential method may lose some useful information of
solution. The intelligent methods used in path planning
including
fuzzy
control method , neural network method,
and genetic algorithms are in common use recently. And
genetic algorithms are more useful than others. But gaining
the population randomly leads into bigger research space,
and the ability of deleting redundant individual
is
lower, all
of
which influence the planning speed. Especially, when the
environment is complicated
or
there are many robots, the
shortcoming of genetic algorithms
is
fairly clearer.
So
based
on the genetic algorithms, rough set
is
led to improve the
population initialization process, and then
to
raise the speed
and ability of robot path planning.
2
Rough set theory
In
1982,
Z.Pawlak proved rough set theory, which put
forward the concept of the inaccurate category reference to
the defmitions of inaccuracy and
fuzzy
in logic, and on this
foundation formed a complete system, i.e. rough set theory.
In recent years, rough set theory has been a new systematic
research hot spot
of
artificial intelligence domain., and
has
been used in pattern recognition, machine learning,
knowledge representation, knowledge discovery and
decision analysis etc..
2.1
The knowledge representation system
It is necessary
to
use
symbol to represent knowledge
for
dealing
with
intelligent
data.
The basic composition of
the knowledge representation system is the set of research
objects, in which the knowledge is presented by appointing
the basic character and the attribute value. And a
knowledge representation system can be indicated by:
S=U,C,D,V,P
Where
U
is the set of object, CUDA is the set
of
characters, and the subset
C
and subset D
are
called
condition attribute and result attribute respectively. V=
U
is the set
of
attribute values, V.indicates the category
of a€A, f:
UxAV
is an information function, which
appoint the attribute value
of
every object x in
U.
This definition of knowledge representation system
can be expressed conveniently by using table. The method
of expressing knowledge by using table may be regarded as
a special formal language. When we express the relation of
equivalence by symbols, the
data
should be called
knowledge representation system, i.e.
KEG
or
amibute
values table of information system.
0780378652/03/$17.00 02003 IEEE
698
Proceedings
of
the
Second International Conference on Machine
Learning
and Cybernetics,
Xi”,
25 November 2003
2.2
The simplification
of
knowledge and core
In the use of rough set theory,
it
needs to delete
abundant basic category frequently to simplify the
knowledge in the circumstance of keeping the initial
category in knowledge basis. To finish the simplification of
knowledge needs
two
basic concept: simplification and core,
which
are
two
very important concepts. Based on these
two
concepts, abundant attributes
are
analyzed, and knowledge
is handled at the same time. Firstly, the repetitive examples
and abundant attributes and abundant attribute values of
every example are deleted. Then, the minimal
simplification is gained, in terms of which the logical rules
are gained. Fmally,
draw
the minimal rules to deal with the
data.
3
The derivation
of
the decision rules
of
robot paths
3.1
Establish decision table
The workspace of robot
is
indicated by
grids.
We
assume the sequence number
of
the
present location of
robot i sp, (except the boundary points), and assume the
sequence number of goal grid
is
99.
Then, there
are
8
possible directions that the robot
may
pass by. See figure 1.
I
1
Figure 1. the possible directions of paths
These
8
directions are regarded as condition attributes
(C={X,,X,,X,,&, X5,X6,X7,Xs}) to be quantified, and the
condition attribute values is expressed by
13.
Thus,
the
initial decision table is established (see table 1).
3.2
The simplification
of
decision table
The simplification of decision table
is
to simplify the
Table 1 the initial decision table of path planning
...
...
...
... ... ... ... ...
...
...
437411
1 3 1 3 1 3 1 3
1 3
( 3 1 3
18
condition attributes in decision table, and after that the
decision table possesses the ability of the decision table
before simplification, but possesses less condition
attributes.
The step of simplifying the decision table is as
follows:
(1)simplify the condition attributes, i.e. deleting some
columns
from
decision table;
(Ddelete the repetitive rows;
(3)delete the abundant amibnte values.
The simplification of condition attributes need to
delete some condition attributes in the condition of keeping
the consistence of decision table. That is to say, after one of
the condition attributes
is
deleted, investigate that if the
condition attribute with same row can decide the same
decision value
as
before. For compatible data table, the
most excellent attribute set is selected by rough set theory.
Quality
:
C={X,,X2;,X.} is the attribute set, if
n
(C(Xi})=
n
C, then Xi can be omitted from C; on the
contrary, Xi can not be omit from C.
Firstly, the repetitive samples in decision table are
merged. And the attributes of samples based
on
character
are simplified to delete every attribute column. Then, the
consistence of decision table is investigated. After
calculating, attribute {&},{X6},{X8} are abundant
attributes, which should be deleted. Finally, the repetitive
rows of decision table are merged once more.
The number of samples is decreased to
162
after
deleting the abundant attribute. See table
2.
699
ProceedJngs of the Second Internadonal Conference on
Macbine
Lea..%
and
Cybernetics,
Wan,
25
November
2003
Table
2.
the decision table after the abundant attributes
are deleted
I
I
I
I I
I
1621 1 1 3
1 3
1 3
1 3
18
3.3
The minimal decision rules
It
is clear that not all decision rules are necessary in
decision algorithms, some rules can be deleted and the
decision progress will not be affected. The method can be
respected
as
follows:
Order
F
is a basic algorithms,
S=(U,A)
is a howledge
representation system,
F
possesses the basic rule sets which
have the same result
y
,
which can be represented
as
F,
.
The cause sets of decision rules belong
to
F,
can be
representedas
P,
When
IsV
P,
V{
P,
:(
0
}],
the basic decision
rules
0

y
in
F
can be omitted. Where V
p,
is the
decomposition of all formula. Otherwise, the basic decision
rules
in
F
can
not
be omitted, then the decision rules set
F,
is regarded as independent.
If all rules
of
the subset
Fi
of
decision rule set
F,
are
independent, and
IsV
P,
V
Pi
,
then the subset
Fi
of
decision rule set
F,
call the simplification of
Fv.
When decision rules in basic algorithms
F
are all
simplified rules, and each basic decision rule
0
.
I
in
F
F,
is simplified one, the basic algorithms
F
is the minimal.
The decision table like table
3
is the minimal decision
rule, which can not be simplified again.
’
Table
3
the table of minimal decision rule
4
Simulation result
The hybrid method of rough set and genetic algorithms
can be represented
as
follows:
(1)establish the work model of robot by grid method,
among which the barrier grid is tumed out randomly;
(2)the initial population of the fixed scale is tumed out
randomly, and is trained by rough set path decision rule,
then a series of available paths are gained;
(3)
initialize the counter of genetic generations,
options=O;
(4)plan the path
by using
genetic algorithms including
select operator, crossover operator and mutation operator.
The crossover rate in crossover operator
can
be defined by
the selfadapt selection formula as follows:
P,
=
6

f ’ ) U

f mi n
+
‘2
where
f,,
is the maximal value of the fimess function,
and
f,,
is the minimal value of the fitness function, and
f ’
is the bigger one of the individuals that
cross,
and
k,
and
k,
are
the
contraction
coefficients
of
the
algorithms, furthermore,
k,
+
k,
=
1
.
Assume
k,
=0.3
and
k,
=0.7
here.
In terms of the algorithms progress above, the
simulation experiments are done. A’grid of
I O
X
I O
is
selected to indicate the work environment of robot, and the
population scale is 30, i.e. popsize=30, and the length of
individuals is 100, i.e. stringlength=lOO.
In
addition, the mutation rate is selected
to
he
0.01.
The positions and
quantity
of barriers
‘turn
out randomly.
See figure
2,
the result in figure 2(a) is gained by 13
700
Proceedings
of
the
Second International Conference on Machme Learning
and
Cybernetics,
Xi’an,
25
November
2003
’
generations, i.e. options=13, and where
the
quantity
of
the
barrier is 7a=35, and the fitness function value is
f=0.1786.
In
figure 2(b),
the
result is gained by
10
generations, i.e. options=l0, and where the quantity of the
barrier is za=32, and the fitness function value is
.f=O.l734.
Table
4.
the contrast results between the new method
and the traditional method
I
Method
I
1
Method2
I
Method
I
I
Method2
in
I
99.999
I
9985
1
125
I
I2
15
199x17
I
9976
I
217
I
15
Figure 2.
the
simulation results gained by Matlab
Besides, the planned path can back space voluntarily
when there is a barrier pi d ahead, and can start to research
the new path voluntarily just as
the
grid (5.5,4.5)
in
fig 2(a),
and
the
grid (3.555) in fig 2(b).
Using the hybrid method proposed here
plans
the
work
model,
in
which there are
IO,
15,
20, 25
and 30 barriers
respectively, and the position of the barriers
all
turn
out
randomly. The simhlation results are shown in table 4,
except
the
result gained by the proposed new method,
there
are
the results gained by traditional genetic algorithms. And
the contrast between the two methods is showed in table
4
too.
Where
f
is the average fitness value,
fop,
is the
most excellent fitness value,
N,,
is the average
generations when reach the most excellent results. And
method
1
indicates the traditional method, and method
2
indicates
the
new hybrid method.
From the contrast results, it is clearly that the new


..
.. ..
20
I
99.821
I
99.31
I
378
I
22
30
I
99.797
I
99.42
I
439
I
24
25
1
99.796
I
99.02
I
295
I
19
method has the higher planning speed than the traditional
algorithms.
5
Conclusion
In this paper, a new hybrid method of rough set and
genetic algorithms for robot’s path planning is proposed.
Rough set is good at dealing with a large of incomplete data.
The genetic algorithms
are an
excellent research method,
which can research a bigger space than other algorithms
,
The new hybrid method proposed here interfuses the merits
of the above two methods. And finally, the simulation
results show
the
superiority of the hybrid method.
Acknowledgments
Thank the natural scientific foundation of Liaoning
province and the Chinese construction ministry
for
their
help.
References
Pawlak Z.Rough
Sets.
Theoretical Aspects of
Reasoning about Data. Nowowiejska 1519, 1990
Sugibara
K
,
Smith
J.
Genetic Algorithms for
Adaptive Motion Planning of an Autonomous Mobile
Robots. IEEE TransSMC: 138143,1997
Shibata, T, Fukuda T
,
Intelligent Motion Plannin
by Genetic Algorithm with Fuzzy Critic. In Proc, 8
IEEE
Symp.
on Intelligent and Control. Chicago, IL:
565569, August, 1993
Goldberg
D
E. Genetic Algorithms in Search.
Optimization an Machine Learning. Massachusetts:
AddisonWesiey, 1989
Beasley D, David R, Martin R.
An
Overview
of
Genetic Algorithms
,
University Computing,
15(2):5869,1993
[6] Xiangrong Xu, Yaobin Chen. A Method
for
Trajectory Planning of Robot Manipulators
in
Cartesian Space. Hefei, China: Proceedings of the 3d
World Congress on Intelligent Control and
Automation: 12201225,2000
701
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