Application a hybrid controller to a mobile robot

Application a hybrid controller to a mobile robotJ.-S Chiou, K. -Y. Wang,Simulation Modelling Pratice and Theory Vol. 16 pp. 783-795 (2008)

Professor: Juing-Shian Chiou

Student : Yu-Chia Hu

PPT製作 100%

學號 : M9820207

Outline Abstract

Introduction

Using generalized predictive control to predict the goal position

Using an SVM to improve the angle followed by the mobile robot to reach the target

Using a hybrid controller to improve the optimal velocity of the mobile robot

Experiments

Conclusions

References

Abstract

This paper presents the application of a hybrid controller to the optimization of the movement of a mobile robot. Through hybrid controller processes, the optimal angle and velocity of a robot moving in a work space was determined. More effective movement resulted form these hybrid controller processes.

The hybrid controller was able to choose a better position according to the circumstances encountered. The hybrid controller that is proposed includes a support vector machine and a fuzzy logic controller.

Introduction(1/3)

Fig. 1. Five-versus-five simulation platform.

Introduction(2/3)

Fig. 2. System architecture.

Introduction(3/3)

Section 2 describes the identification of the target position at the next sampling time using the GPC.

Section 3, the technique of the SVM is employed to determine the optimal angle of the robot’s movement.

Section 4 describes the determination of the optimal velocity of the robot using a hybrid controller that combines the SVM and GPC.

Section 5, the results of two experiments performed are presented. One of the experiments is a simulation using a FIRA five-versus-five simulation platform, whereas the other uses MATLAB.

Finally, conclusions are drawn Section 6.

Using generalized predictive control to predict the goal position(1/3)

Adaptive predictive control machines include a classified online structure and control system. The design parameters of the GPC include the autoregressive exogenous classification of online model levels and the controlled weighting of the control force.

Fig. 3. Sampling time.


Fig. 4. Subsequent position of the target.


Fig. 5. GPC system flowchart.

1

2/

L R

c

c

V VV

T d V

22

0( )

x x y y

y y y y

x x x x

d G GL G GL

GF G G GL

GF G G GL

Using an SVM to improve the angle followed by the mobile robot to reach the target (1/5)

For a mobile robot like the one illustrated in Fig. 6, choosing a path is very important. We designed an SVM to help our robot reach the target point in the shortest time.

Fig. 6. Relationship between d and


The SVM technique stems from attempts to identify the optimal classification of a hyperplane under conditions of linear division. The optimal hyperplane refers to the hyperplane which can correctly distinguish samples of two categories with a maximum margin. The SVM is shown in Fig. 7.

Fig. 7. Support vector machine.


Based on Fig. 6, we determined

In this case, training patterns were calculated according to

where were produced on the basis of 500 I at random.

Consider also

1tan y y

R

x x

b R

b R

' ' '

1 1 1 1 1( , ),..., ( , ), ; ,

2 2n

iy y R

　　 i=1,2,...,l,　y

'

'

'

( )2 2

( ) , 1,2,...,5002 2

i i

i i

w b y

w b y i


where w is the normal vector of the hyper plane, and b is the deviation value. In order to find the division of the hyper plane, we had to resolve the question of quadratic optimization. The constraints were

'( ) , 1,2,...,5002i i

y w b i

We also had to determine the minimum value of , because the equation above is quadratic with a linear constraint. This is a typical quadratic optimization problem. So, we used the Lagrange multiplier to resolve the question of quadratic optimization with linear constraints. We obtained

21( )

2w w

5002 '

1

1( , , ) ( ) , 0

2 2i i i ii

L w b a w a y w b a


However, using an SVM still did not produce the optimal solution. The way in which we dealt with this problem was to

After performing the substitution, we were left with the new equation

The following is the final function

500 500' '

11 1

500

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0

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i i i i ii i

i ii

Lw a y w a y

wL

a yb

' '1

2D i i j i j i jij

L a a a y y

500' '

11

( ) sgn[ ( ) ]i i

imf a y b

Using a hybrid controller to improve the optimal velocity of the mobile robot(1/7)

Fig. 8. The distance between the robot and the goal.

Fig. 9. The orientation of the robot with respect to the straight line path to the goal.


7

1

7

1

( )*

( )

n

i i i i

n

i i i

u v vCrisp

u v

We used the method of Center of Gravity Defuzzification to calculate the velocity of both wheels of the robot:


We defined the mathematical model of the equation of the robot’s movements as follows:

Having defined the state variables,

we were able to determine the state equation:

. .. . . .

_ _ _ _

.... .

( ) cos

sin cos sin

r l l x l y r x r y l

l r r r llr

y qx m n

wwpw s

rw w V V V V r w

D

r w r w r w a a

5 _ 6 _ 7 _ 8 _ 9 10 1, , , , ,

l x l y r x r y rx v x v x v x v x w x w

1 2 3 4, x , , x x y x m x n

. . . . . . .. . .

5 6 7 8 1 1

3 5 6 7 8 9 101 2 4[ ]

[ r cos sin cos sin ]

T

r r r l

x x x x x x xx x x

x x x x a r a r a r a a a


is a vector of the velocity along the horizontal axis of the robot’s left wheel.

is a vector of the velocity along the vertical axis of the robot’s left wheel.

is a vector of the velocity along the horizontal axis of the robot’s right wheel.

is a vector of the velocity along the vertical axis of the robot’s right wheel.

x is a vector of the displacement along the horizontal axis of the robot’s left wheel.

y is a vector of the displacement along the vertical axis of the robot’s left wheel.

m is a vector of the displacement along the horizontal axis of the robot’s right wheel.

_Vl x

_l yV

_r xV

_r yV


n is a vector of the displacement along the vertical axis of the robot’s right wheel.

Consequently, we identified the optimal vector of the velocity of the left wheel as , and that of the right wheel as

The support vector machine After having identified and

by means of the state equation, we used the SVM to improve the efficiency of the velocities ( and ) generated by the FLC. In this case, training patterns were calculated according to

5 6lGV x x 7 8rGV x x

lGV rGV

lV rV

1 1 1 1

( , ),..., ( , ), , 1,2,..., , 0,

( ) , 1,2,...,i i

n

l l l i

li l i l

V y V y V R i l y GV

w V b GV y GV i l


Fig. 11. (a) Before using the GPC to predict the next target position. (b) Using the GPC to predict the next target position


Fig. 12. (a) Before using the SVM to determine the heading angle in a MATLAB simulation. (b) Using the SVM to determine the optimal heading angle in a MATLAB simulation.

Experiments

Fig. 13. (a) Before using the SVM to determine the heading angle in a FIRA five-versus-five simulation platform. (b) Using the SVM to determine the heading angle in a FIRA five-versus-five simulation platform.

Conclusions

In our mobile robot, the SVM and the hybrid controller were applied for successful determination its optimal path and velocity.

Furthermore, the GPC was applied to predict the next target position. In the future, the computational time required by our SVM and hybrid controller will be reduced to increase the speed of the response of the mobile robot. The hybrid controller and the GPC will also be used in other systems to achieve optimization.

Documents

Application a hybrid controller to a mobile robot