PSO-based Motion Fuzzy Controller Design for Mobile Robots

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PSO-based Motion Fuzzy Controller Design for Mobile Robots

Master : Juing-Shian ChiouStudent : Yu-Chia Hu( 胡育嘉 )PPT : 100% 製作

International Journal of Fuzzy Systems, Vol.10, No. 1, March 2008

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Outline

Abstract Introduction Motion Fuzzy Control Structure PSO-based Fuzzy Controller Design Method Simulation Results Conclusions References

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Abstract 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.

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 two-dimensional space.

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Introduction(1/3)

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) 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.

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)

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

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)

, 180 180( ) 360, 180 180

ifif

( ) ( ) ( 1)( ) ( ) ( 1)

a t a t a td t d t d t

2 2( ) ( )d dd x x y y

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Motion Fuzzy Control Structure(4/9)

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Motion Fuzzy Control Structure(5/9)

: if is AND is ,then is

1 1 2( , )yR j j 1x (1, 1)jA 2x (2, 2)jA1y

1, 21( ) 1 2, { 3, 2, 1,0,1,2,3}j jy j j

2 3, 4( )yR j j : If is and is ,then is

3x (3, 3)jA 4x (4, 4)jA2y

3, 42( ) 3 4, { 3, 2, 1,0,1,2,3}j jy j j

Where and are input variables, Are output variables

1 2 3, ,x x x 4x 1 2y and y

1 2 1 2

3 4 3 4

(1, ) 1 (2, ) 2 1( , ) 1

(3, ) 3 (4, ) 4 2( , ) 2

( ), ( ), ( )

( ), ( ), ( )j j j j

j j j j

A T x A T x y T y

A T x A T x y T y

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Motion Fuzzy Control Structure(6/9)

( , 3), ( , 2), ( , 1), ( ,0), ( ,1), ( ,2), ( ,3),

( ) { , , , , , , }, 1,2,3,4{ }

i

i i i i i i i

T x NB NM NS Z PS PM PB iA A A A A A A

( , 3), ( , 2), ( , 1), ( ,0), ( ,1), ( ,2), ( ,3),

( ) { , , , , , , }, 1,2{ }

m

i i i i i i i

T y NB NM NS Z PS PM PB my y y y y y y

1 2 1 2

1 2

3 3

1 ( , ) 1( , )3 3

j j j jj j

y w y

3 4 3 4

1 2

3 3

2 ( , ) 1( , )3 3

j j j jj j

y w y

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Motion Fuzzy Control Structure(7/9)

1 2( , )j jw3 4( , )j jw

1 2

1 2

1 2

1 2

(1, ) 1 (2, ) 2( , ) 3 3

(1, ) 1 (2, ) 23 3

min( ( ), ( ))

min min( ( ), ( ))

A j A jj j

A j A jj j

u x u xw

u x u x

3 4

3 4

4

3 4

(3, ) 3 (4, ) 4( , ) 3 3

(3, 3) 3 (4, ) 43 3

min( ( ), ( ))

min min( ( ), ( ))

A j A jj j

A j A jj j

u x u xw

u x u x

Where and are respectively described by

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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)

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 , g=1, the maximum number of generation (G), the number of particles (N), and four parameter values of ,

and .

1 2 0pbest pbest pbestNF F F

1 2 max, ,c c min

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PSO-based Fuzzy Controller Design Method(3/11)

Step 2: Generate the initial position vector and the initial

velocity vector of N particles randomly by

and

1 1 1 1 1,1 ,2 , ,, , , , ,h h h h j h np p p p p

1 1 1 1 1,1 ,2 , ,, , , , ,h h h h j h nv v v v v

1 min max min, ()j jh j jp p p p rand

max min

1, ()

20j j

h j

v vv rand

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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

where is the fitness function.

, 1,2, ,g gh hF p fit p h N

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PSO-based Fuzzy Controller Design Method(5/11)

Step 4: Determine and for each particle byPbesthF

Pbesthp

,

,

1,2, ,

g Pbest gh h hPbest

h Pbesth

F if F FF

F otherwise

h N

,

,

1,2, ,

g Pbest gh h hPbest

h Pbesth

p if F Fp

p otherwise

h 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

and determineand and by

and

andwhere is the position vector of the particle with the

global best fitness value from the beginning to the current generation.

1,2, ,arg max Pbest

hh Nq F

GbestFGbestP

1,2, ,maxGbest Pbest Pbest

q hh NF F F

Gbest Pbestqp p

GbestpGbestF

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PSO-based Fuzzy Controller Design Method(7/11) 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

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2

1()

2()

g g Gbest gh h h

Pbest gh h

v v c rand p p

c rand p p

max minmax g

G

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PSO-based Fuzzy Controller Design Method(8/11)Step 8: Check the velocity constraint by

max 1 max,

1 1 min 1 max, , ,

min 1 min,

,

,

1,2, , , 1,2, ,

gj jh j

g g gj jh j h j h j

gj jh j

v if v v

v v if v v v

v if v v

h N j n

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PSO-based Fuzzy Controller Design Method(9/11) Step 9: Update the position vector of each particle by

1 1g g gh h hp p v

Where is the current position vector of the h-th particle in the g-th generation. is the next position vector of the h-th particle in the (g+1)-th generation.

ghp

1ghp

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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

max 1 max,

1 1 min 1 max, , ,

min 1 min,

,

,

,

1,2, , , 1,2, ,

gj jh j

g g gj jh j h j h j

gj jh j

p if p p

p p if p p p

p if p p

h N j n

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PSO-based Fuzzy Controller Design Method(11/11) 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 with the best fitness value .

GbestpGbestF

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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 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 [1] M. Bowling and M. Veloso, “Motion control in dynamic multi-robot environments,” IEEE International Symposium on Computational Intelligence in Robotics and Automation, pp. 168-173, 1999. [2] W. R. Hwang and W. E. Thompson, “Design of intelligent fuzzy logic controllers using genetic algorithms,” IEEE World Congress on Computational Intelligence, pp. 2144-1388, 1994. [3] T. H. Lee, F. H. F. Leung, and P. K. S. Tam, ”Position control for wheeled mobile robots using a fuzzy logic controller," IEEE International Conference on Industrial Electronics Society, pp. 525-528, 1999. [4] Y. Lee and S. H. Zak, “Genetic fuzzy tracking controllers for autonomous ground vehicles,” American Control Conference, pp. 2144-2149, 2002. [5] C. Lin, A. B. Rad, W. L. Chan, and K. Y. Cai, “A robust fuzzy PD controller for automatic steering control of autonomous vehicles,” IEEE International Conference on Fuzzy Systems, pp. 549-554, 2003

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References [6] F. Solc and B. Honzik, “Modeling and control of a soccer robot,” IEEE International Workshop in Advanced Motion Control, pp. 506-509, 2002. [7] C. C. Wong, H. Y. Wang, S. A. Li, and C. T. Cheng “Fuzzy controller designed by GA for two-wheeled mobile robots,” International Journal of Fuzzy Systems, vol. 9, no. 1, pp. 22-30, 2007 [8] W. L. Xu, S. K. Tso, “Real time self reaction of a mobile robot in unstructured environments using fuzzy reasoning,” Engineering Applications of Artificial Intelligence, vol. 9, no. 5, pp. 475-485, 1996. [9] C. C. Chen and C. C. Wong, “Self-generating rule-mapping fuzzy controller design using a genetic algorithm,” IEE Proceedings: Control Theory and Applications, vol. 149, pp. 143-148, 2002. [10] C. C. Wong and S. M. Her, “A self-generating method for fuzzy system design,” Fuzzy Sets and Systems, vol.103, no.1, pp.13-25, 1999. [11] C. C. Wong and C. C. Chen, “A GA-based method for constructing fuzzy systems directly from numerical data,” IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics, vol. 30, no. 6, pp. 904-911, 2000. [12] C. C. Wong, B. C. Lin, S. A. Lee, and C. H. Tsai, “GA-based fuzzy system design in FPGA for an omni-directional mobile robot,” Journal of Intelligent & Robotic Systems, vol.44, no.4, pp.327-347, 2005.

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References [13] J. Kennedy and R. Eberhart, “Particle swarm optimization,” IEEE International Conference Neural Network, pp. 1942-1948. 1995 [14] R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” Sixth International Symposium on Micro Machine and Human Science, Nagoya Japan, pp.39-43,1995. [15] J. Kennedy, “The particle swarm: Social adaptation of knowledge,” International Conference on Evolutionary Computation, pp. 303-308, 1997. [16] Z. L. Gaing, “A particle swarm optimization approach for optimum design of PID controller in AVR system,” IEEE Trans. on Energy Conversion, vol. 19, no. 2, pp.384-391, 2004. [17] M. Clerc and J. Kennedy, “The particle swarm-explosion, stability, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, pp.58-73, 2002. [18] F. Ye, C. Y. Chen, and H. M. Feng, “Automatic evolutional clustering-based fuzzy modeling system design,” International Journal of Fuzzy Systems, vol. 7, no.4, pp. 182-190, 2005. [19] http://www.fira.net/soccer/simurosot/overview.html

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Thank of your attention