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PSO-based Motion Fuzzy Controller
Design for Mobile Robots
International Journal of Fuzzy Systems, Vol.10, No. 1, March 2008
Master : Juing-Shian Chiou
Student : Yu-Chia Hu(胡育嘉)
PPT
: 100%製作
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Outline
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Abstract
Introduction
Motion Fuzzy Control Structure
PSO-based Fuzzy Controller Design Method
Simulation Results
Conclusions
References
2
Abstract
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A motion control structure with a distance fuzzy
controller and an angle fuzzy controller is proposed to
determine velocities of the left-wheeled motor and
right-wheeled motor of the two-wheeled mobile robot.
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A PSO-based method is proposed to automatically
determine appropriate membership functions of these
two fuzzy systems so that the controlled robot can
move to any desired position effectively in a twodimensional space.
3
Introduction(1/3)
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In this paper, a PSO-based motion fuzzy controller
design method is proposed to automatically determine
appropriate membership functions of fuzzy systems to
control a two-wheeled mobile robot so that it move
efficiently in a two-dimensional space.
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Introduction(2/3)
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In Section 2, a two-wheeled mobile robot is described
and a motion fuzzy control structure is proposed to
determine velocities of its left-wheeled motor and
right-wheeled motor.
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In Section 3, a PSO-based fuzzy controller design
method with a ratio coefficient coding method and a
variable fitness function is proposed to automatically
select the input and output membership functions of
these two fuzzy systems.
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Introduction(3/3)
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In Section 4, some results simulated in the 3D robot
soccer simulator of FIRA [19] are presented to
illustrate the efficiency of the proposed method
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Finally, some conclusions are made in Section 5.
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Motion Fuzzy Control Structure(1/9)
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Motion Fuzzy Control Structure(2/9)
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Motion Fuzzy Control Structure(3/9)
d  ( xd  x) 2  ( yd  y ) 2
   , if   180    180
 (   )  360, if 180      180

 
a (t )  a (t )  a (t  1)
d (t )  d (t )  d (t  1)
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Motion Fuzzy Control Structure(4/9)
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Motion Fuzzy Control Structure(5/9)
Ry1 ( j1 , j2 ) : if x1 is A(1, j1) AND x2 is A(2, j 2) ,then
y1 is y1( j1, j2 ) j1 , j2 {3, 2, 1,0,1, 2,3}
Ry 2 ( j3, j4 ) : If x3 is A(3, j 3) and x4 is A(4, j 4) ,then
y2 is y2( j3, j4 ) j3 , j4 {3, 2, 1,0,1, 2,3}
Where x1 , x2 , x3 and x4 are input variables, y1 and y2
Are output variables
A(1, j1 )  T ( x1 ), A(2, j2 )  T ( x2 ), y1( j1 , j2 )  T ( y1 )
A(3, j3 )  T ( x3 ), A(4, j4 )  T ( x4 ), y2( j3 , j4 )  T ( y2 )
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Motion Fuzzy Control Structure(6/9)
T ( xi )  {NB, NM , NS , Z , PS , PM , PB}, i  1, 2,3, 4
 { A( i ,3), A( i ,2), A( i ,1), A( i ,0), A( i ,1), A( i ,2), A( i ,3), }
T ( ym )  {NB, NM , NS , Z , PS , PM , PB}, m  1, 2
 { y( i ,3), y( i ,2), y( i ,1), y( i ,0), y( i ,1), y( i ,2), y( i ,3), }
y1 
y2 
3
3
 w
y
 w
y
j1 3 j2 3
3
3
j1 3 j2 3
( j1 , j2 ) 1( j1 , j2 )
( j3 , j4 ) 1( j3 , j4 )
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Motion Fuzzy Control Structure(7/9)
Where w( j1 , j2 ) and w( j3 , j4 ) are respectively described by
w( j1 , j2 ) 
min(u A(1, j1 ) ( x1 ), u A(2, j2 ) ( x2 ))
3
3
  min min(u
j1 3 j2 3
w( j3 , j4 ) 
A (1, j1 )
( x1 ), u A(2, j2 ) ( x2 ))
min(u A(3, j3 ) ( x3 ), u A(4, j4 ) ( x4 ))
3
3
  min min(u
j3 3 j4 3
A (3, j 3)
( x3 ), u A(4, j4 ) ( x4 ))
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Motion Fuzzy Control Structure(8/9)
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Motion Fuzzy Control Structure(9/9)
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PSO-based Fuzzy Controller Design
Method(1/11)
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The PSO algorithm is a computation technique
proposed by Kennedy and Eberhart. Its development
was based on observations of the social behavior of
animals such as bird flocking and fish schooling of the
swarm theory.
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PSO-based Fuzzy Controller Design
Method(2/11)
Step 1: Initialize the PSO algorithm by setting ,
F1 pbest  F2pbest   FNpbest  0 g=1,
the maximum number of generation (G),
the number of particles (N),
and four parameter values of , c1 , c2 , max
and . min
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PSO-based Fuzzy Controller Design
Method(3/11)
Step 2: Generate the initial position vector
p1h  p1h ,1 , p1h ,2 , , p1h , j  , , p1h ,n  and the initial



1
1
1
1
v

v
,
v
,
,
v
velocity vector h
 h ,1  h ,2 
 h, j  ,
of N particles randomly by
max
min
p1h , j   p min

p

p
j
j
 j  rand ()
max
min
v

v


j
j
1
and v h , j  
rand ()
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
, v1h ,n 


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PSO-based Fuzzy Controller Design
Method(4/11)
Step 3: Calculate the fitness value of each particle
in the g-th generation by
F  phg   fit  phg  , h  1, 2,
,N
where is the fitness function.
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PSO-based Fuzzy Controller Design
Method(5/11)
Step 4: Determine FhPbest and phPbest for each particle by
g
Pbest
g

F
,
if
F

F
 h
h
h
FhPbest   Pbest
 Fh , otherwise
h  1, 2, , N 
g
Pbest
g

p
,
if
F

F
 h
h
h
Pbest
ph   Pbest
 ph , otherwise
h  1, 2, , N 
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PSO-based Fuzzy Controller Design
Method(6/11)
Step 5: Find an index q of the particle with the highest
fitness by q  arg max F Pbest
h
h

1,2,
,
N


and determineand Gbest and Gbest by
P
F
Gbest
Pbest
Pbest
F

F

max
F
and
q
h
h1,2, , N 
Gbest
Pbest
p

p
q
and
Gbest
p
where
is the position vector of the particle with the
global best fitness value F Gbest from the beginning to the
current generation.
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PSO-based Fuzzy Controller Design
Method(7/11)
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Step 6: If g=G, then go to Step 12, Otherwise, go to
Step 7.
Step 7: Update the velocity vector of each particle by
vhg 1    vhg  c1  rand1()   p Gbest  phg 
c2  rand 2()   phPbest  phg 
  max 
max  min
G
g
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PSO-based Fuzzy Controller Design
Method(8/11)
Step 8: Check the velocity constraint by
g 1
max
v max
,
if
v

v
j
j
 h, j 

 g 1
g 1
g 1
max
v h , j   v h , j  , if v min

v

v
j
j
h, j 
 min
g 1
min
v
if
v

v
 j
j
 h, j 
h  1, 2, , N , j  1, 2, , n
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PSO-based Fuzzy Controller Design
Method(9/11)
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Step 9: Update the position vector of each particle by
phg 1  phg  vhg 1
g
p
Where h is the current position vector of the h-th
particle in the g-th generation.
phg 1 is the next position vector of the h-th
particle in the (g+1)-th generation.
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PSO-based Fuzzy Controller Design
Method(10/11)
Step 10: Bound the updated position vector of
each particle in the searching range by
 p max
j ,

 g 1
g 1
p h , j    p h , j  ,
 min
 p j ,
h  1,2, , N ,
if
pgh, 1j   p max
j
if
g 1
max
p min

p

p
j
j
h, j 
if
pgh, 1j   p min
j
j  1,2, , n
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PSO-based Fuzzy Controller Design
Method(11/11)
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Step 11: Let g=g+1 and go to Step 3.
Step 12: Determine the corresponding fuzzy controller
based on the position of the particle p Gbest with the best
fitness value F Gbest .
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Simulation Results(1/3)
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Simulation Results(2/3)
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Simulation Results(3/3)
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Conclusions
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A PSO-based motion fuzzy controller design method
is proposed to determine velocities of the left-wheeled
motor and right-wheeled motor of the two-wheeled
mobile robot so that the controlled robot can move to
any desired position effectively in a two-dimensional
space.
In the practical application, the proposed fuzzy
controller design method has been successfully
applied to control two-wheeled mobile robots for the
actual FIRA robot soccer tournament and it also has a
good performance.
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References
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Thank of your attention
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