a new path planning algorithm for mobile robot based on neural network

8/10/2019 A New Path Planning Algorithm for Mobile Robot Based on Neural Network

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A

NEW

PATH PLANNING ALGORITHM

FOR M O B n E R O BO T

BASEDON NEURAL

NETWORK

ZHU

Yonglie CHANG

Img

WANG Shuguo

(Robot

Insmute,

Harbm

InStlNte of Technology,

Harbm Chma 150001)

zhuyongliel@yahoo

corn

cu

Abstract : In

this paper, a new path-planning algorithm

based on neural network is proposed for mobile robots.

Neural network is used in the algorithm to model the

environment and calculate the collision energy function

(CEF) which

is

the dominating term in the cost function.

To implement the pathplanning procedure, rather than

calculating the minimum v alue of the cost function directly,

a discrete method is used

to

approximate the minus

gradient direction of the cost function in order to

determine the motion tendency of the point set along the

path. Finally, the performance and efficiency of the

algorithm are estimated through computer simulation. As

can be seen from the results, the algorithm is very efficient

in

siblatiom wh ae real-time operation is required

Key words:

mob ile robo t patlkplanning neural

network

1 Introduction

In this paper, a

new path-planning

algorithm based on

neural network is proposed for mobile robot s aim@ at the

global

pathplaMing problem. Different methods

for

solving

the

problem of path-planning by using neural

network have been discussed in many literatures

1 1[21,

In

literature

[ I ]

the neural network is used to describe the

restrictions of the environment and calculate

the

collision

'

energy function (CEF). The sum

of

the CEF of the iterative

point set aloni the path and the distance function is defined

as

the cost function. Then the motion equation of the

points

set

can be determined by resolve the minimum

value of the cost func tion. After iterations, th e point set

will tend to he the optimum path. While in this paper, the

environmental model of

[I]

s used for reference, but rather

than calculating the minimum value of the cos t function

directly, a discrete method is used to approximate the

minus gradient direction of the cost function in order to

'

determine the motion tendency

of

the point set along the

path. Finally, the performance and efficiency of the

algorithm are estimated through computer simulation.

As

can be seen from the results, the algorithm is very efficient

in situations where real-time o p t i o n is required.

2. EnvironmentModeling by Neural Network

Suppose the workspace for robot is shown in Fig.

1

i the shadowed parts represent the barrieryl

In

the

discussion o f the algorithms, the m obile robot is regarded

as a particle.

In

practice, the harriers should be expanded

according o the

radium

ofthe robot.

Y

x

Fig.1 The workspace for

robot

Accordingto

[ I ] ,

the environmental model can be set

up as the follow ings: First, the restriction conditions of the

barriers

can

he represented by inequations

( 1

and

( 2)

Where,

x

and

y

are any point in the workspace. Points

meeting the inquatiom fall in the haniers .

x - 2 > 0

x - 6 > 0

- x + 9 > 0

(2)

[o

(1)

- 5 > 0

- y + 4 > 0 - y + 7 > o

The neural network used to calculate the collision

penalty function is shown in Fig.2. The two nodes of the

input layer represent th e coordinates of the points along the

path. The eight nodes of the medium layer represent the

eight restrict conditions of the barriers. The outputs of the

0-7803-7490-8/02/ 17.0002002 IEEE.

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nodes of the top layer represent the collision penalty

function corresponding to ea ch

Mer

Fig.2 The neural network

used to

calculate the collision

penalty function

Now the calculation

of

the collision energy function

of

the fust barrier

c:

is illustrated as an example. The

calculation

is

done

accnrding

to

equation

(3136).

c:= f T , ) (3)

Where,

c:

is the output of the nodes of the top layer,

T,

is the input of the nodes of the top layer,

e,

is the

threshold of the nodes. of the top layer (e qu al

to

-(N-0.5),

where

N

is the number of the inequations),

OM,

s the

output

of

the mth node of medium layer,

I,,

is the input

of the mth node of the medium layer, is the

threshold of the mt h node (equal to the constant term in

inequations),

Wvv

nd

W

is the coeficient of the

restriction condition of the mth inequation, the weighted

coefficients of the connection of the medium and top layer

is the excited function,

s 1. f ~ ) = -

parameter

T

influents the shape

of

the penalty function.

The penalty function is flat with larger T and has smooth

,

1

1

e 3

slope

on

the edge of the barriers. The penalty function is

steep with sm aller T and similar to the s tep function on the

edge of the barriers. The parameter

T

influents the results

and efficiency of the path-planning. This can be seen from

the simulation results in section 3 . For the workspace of

this paper, the penalty functions with differentT are shown

in

Fig.3 and Fig.4.

As

can

he

seen from the figures, the

collision penalty function becomes very steep with

T

equal

to 0.1 and

has

ittle fluctuation inside or outs ide the

barria.

Fig.3

Collisionpenalty

function

T=0.3

. .

M

86 A

- , - :

Fig.4 Collision

penalty

fnnction T=0.1

3.

Algorithm for path-planning

In

the new algorithm for path-planning, rather than

calculating the minimum value of the cost function, a

discrete method is used to approximate the minus

gradient direction of th e cost function i n. order to

determine the motion tendency of the point set along the

path. The detailed procedure can be stated

as

follow:

Input the coordinates of the start point and the target

point and connec t th e two points to get a segment.

Divide the segment equally by a serial

of

points and

calculate the coordinates of these points. These points

will be made as the original point set for

iteration.

Choose 6

adjacent area around each point

( .E)

n

point set as Fig5 and define eight directions as

E. NE.

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N NW W SW

S SE ,

Thecollisionenergy Function

E,

and the distance energy Function

F.i

of the eight

vertexes to the target point are calculated with equation

(7)

and (8). The directional derivatives of the collision

energy function at point X , F j with regard to the eight

direction

can he

calculated fiom

equation

9)

sw s SE

Rg.5 The 6 adjacent area at point

XIYi

1

(7)

Where,

c; is the collision penalty function of point

tX,,Y,) with regard to the kth barrier. K is the number of.

the ban ias.

E , ( X , , T )

= J ( X , - X , ) + ( r :

- q ) 2 (8)

Where,

X, ,Y, )

is coordinates of the target point and

( X z , r )sthecoordinates ofthee ightvatex es.

with regard to

directions

( E ,N ,

S)

IYliere,

(xi ,

) is the coordinate of the eight vertexes.

Equation (9) can be used to approximate the eight

directioiml derivatives of collision energy function at point

X.8) hen

6

is small enough. The direction with

smallest directional derivative is more likely the direction

of minus gradient at this point. This is the so called

discrete method used to approximate the direction of minus

gradient. Take the distance energy into account, w e choose

the cost function

E [XI, ,

at point X, , YJ

as:

Where.

w

and 1

are

the weighted coefficients of

directional derivative and distance energy Function. From

the principle of the algorithm, we h o w that the term

E,(X,,YJ makes less contribution to the decision when 6

is very small. Generally, we cho ose o ~ uch smaller than

14 C.

Based on the analysis above, we first calculate the

cost function E, [XI, i

at any point in the iteration point

set. It is the function of the eight directions. The direction

with the smallest cost Function is the motion tendency at

this point. The corresponding vertex is the original point

for the next iteration. The same operation is done at each

point in the point set during every iteration. The operation

gceson and a collision-fie path

will e

generated

The iteration termination condition for the algorithm

is that the cost function of the co nsecutiv e iterations meet:

Where, En Xi,) and En+,X i , ) are the cost

function of nth and n+l)th iteration at

point

(X., ).is

a

small

value which

is

chosen according to the practical

situation.

For the pathplanning algorithm, because the optimal

decision is made

at

every local point, so the path generate

is

not always the optimum in the global sense But in

situations where the distance optimum is not

so

important,

the

algorithm has advantages of high speed and hizh

efficiency. Th is can

be

seen from the simulation results in

section 3.

4. Results

of

simulation

Based

on

the principle of algorithm, the simulation

results for different parameter is shown in fig.6-9. Where

represent the transition track for each iteration. Fig.6 and

'n'

epresent the result of the final iteration and

0

1572



f i g 7 are the simulation results with T=0.1 and different 1

0.la nd 0.05 Fig.6 and fig.7 are the result after

5

and 9

times iteration respectively. As can he seen, when keep T

unchanged, decrease of can reduce the computation

burden and improve the efficiency of path-planning. But

smaller 6 leads to more optimal planning path. This is

easy to understand, because when

6

is getting smaller

the effect of approximating minus gradient direction

becomes reliable and the fluctuation of the path becomes

smaller by using the discrete method. Large may leads

to the iteration divergent ,and no optimal path can he found.

Fig.8-9 is- the simulation results when T=0 .4 and with

different

,I.

0.1 and 0.05). Compared with fig.6-7, we can

see, for larger T, the point set along the path can depart

quickly from the barrier. The fluctuation of the planning

path is smaller. This is reasonable because for smaller T,

the collision energy function is steeper with smaller

fluctuations,

so

the slid ing effect

arises

and the

planning

path shows more fluctuations. For larger T, the collision

energy function is flat with larger fluctuations, so the

smooth motion tendency is ersy to be found for the point

set. Thus the planning path

is

generated with smaller

fluctuations

c m , n

1.0

I . o n . . e ,

lnk

/ T .

I

6 :

0

I ,

o o u o

n

4 u o

Fig.6

Simulation result 1 Fig.7 Simulation result 2

(T=0.1.

=O.l. n=5)

(T=O.I,

=0.05,

n=9)

5 .

Conclusions

In this paper, a newp ath-plann ing algorithm based on

neural network is proposed for mobile robots. Neural

network is used in the algorithm to model the environment

and calculate the collision energy function. To implement

the path-planning for mob ile robot, rather, than calculating

the minimum value of the cost function directly, a discrete

method is used to approximate the minus gradient

direction of the CEF in order to determine the motion

tendency of the point set of the path. The influences of T

and

on

the efficiency and effect of the algorithm are

evaluated through computer simulation. As can be seen

from the results, the algorithm is very efficient in

situations where real-time Operation is required.

References

(Tz0.4. 4 . 1 , I F 5 ) ,

( T 4 . 4 ,

=0.05, n=9)

Sun

zeng qi.

Intelligerit

orztrol

Th eow

ami

Teckrrique.

Publishing House of Tsinghua University, 1997.

R.Glasius, A.Komoda,S.C.A.M.Gielen, Neural network

dynamics fo rpath planningandobstacle avoidance. Neural

Networks. 1995, vol.

8.

Zhu D. Latombe J.C., New Heuristic Algorithms for

Eflcient Hierarchical Path Planning,

IEEE

Trans.

On

Robotics and Automation, 1991,7(1), 9-19.

Nguyen D.H. Widrow B., Neural Networks for

SelJLearning Control Systems, IEEE Control System

Magazine, 1990, lO(3).

Fig.8 Simulation result

3

Fig.9 Simulation result

4

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a new path planning algorithm for mobile robot based on neural network

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