Modeling & Simulation of UAV Trajectory Planning on GAs

7/30/2019 Modeling & Simulation of UAV Trajectory Planning on GAs

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Modeling & Simulation of UAV Trajectory Planning on GAs

CHEN Zhiqiu LIU Yun LUO Jianjun JIANG HongAstronautic School

Northwestern Polytechnical UniversityXian, China

[email protected]

AbstractAccording to the design requirement of UAV (The

unmanned aircraft vehicle)the models of threat, UAVsdynamics, guidance and trajectory planning are established.

Trajectory planning adopts genetic algorithms(GAs) and

genetic coding uses distance, corner program. Through

simulating by Matlab/Simlink software, the result proves the

trajectory planning according with dynamics characteristic.

Keywords-UAV;GAs;Trajectory Planning

I. INTRODUCTIONUAV mentioned in this paper is a type of no remote

sensing and no remote controlling equipments, auto guidingafter takeoff and auto working after flying into the workingspace. UAV adopts GPS and the voyage forecast guidancemethod. The information of GPS is basic guidanceparameters. When GPS information loses, the voyageforecast guidance method works to guide it flying on thescheduled path by the information of estimated wind velocitybefore failing or weather forecast before takeoff or thesensors on UAV. Guiding paths include a cruising path, aworking path, and a self-destruction path. Every path can

upload over 3 voyage points in advance. The required pathmainly is a cruising path between takeoff and arriving atworking area. The main target is to avoid threat area,adapting flight capability and improving survival capabilityof UAVs.

II. THE MODEL OF THREATIn order to save fuel and reach the maximal distance,

UAVs always fly with a fixed height, leveling off and smallyaw angles. The threat sources mainly are the radar fence,the aerial defence, the climate condition, etc. Because UAVsfly in a high altitude, the terrain threat will not be effective.The 3D path planning problem can be changed to the 2Dplane.

All the threat sources shape can be simplified to thecombination of columns and tapers. The main danger forUAVs is the effect of the radar fence and the aerial defence.

There are the assumptions of the threat model sources.1. The character of radar detection does not change.

There are no communications between them.2. UAVs Radar Cross-Sections(RCS) are same. UAV

can be considered as particle.3. All the threat sources can be considered as a rotundity

an its radius is0r .

4. The damage probability of the threat source can beregarded as aim condition coordinate damage probabilities

which formula is

20

2

0( )rG r e

= .

The UAVs damage probability of all the threat sourcescan be expressed as

2 2

1 1

1 1

2 22 2

2 2

2 2

( , ) 1 1

1 1

m m

mn mnm m

n n

x x y y

r r

n

x x y yx x y y

r rr r

f x y e

e e

=

"

.

Hence, the average damage probability of UAV in the

flight course can be expressed as1 2 1( , , )

1

1

( , )

n

n

l d d d

n n

i

i

f x y dl

P

d

+

+

=

=

.

III. THE MODEL OF DYNAMICSThere are the assumptions of the dynamics model.1. UAV is a rigid body with changing weight for fuel

consuming.2. The wing and body do not have elasticity. There are no

peg-top effects on the circumrotating parts of UAVs body.3.The assumption is an instantaneous balance.4. UAVs always fly with a fixed height, small attack and

yaw angles. sin ,sin ,cos cos 1 .

5. The control is almost perfect.Then the model of dynamics can be given.1. The dynamics formula for the center of mass in the

flight path coordinate.

V

dVm P X

dt

dmV P Z

dt

=

= +

2

2

1

2

1

2y

y

D

Z

Z Z Z y

y

y

y

X V SC

Z V SC

C C C

m

m

=

=

= +

=

International Conference on Computer Modeling and Simulation

978-0-7695-3562-3/09 $25.00 2009 IEEE

DOI 10.1109/ICCMS.2009.34

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2. The kinematics formula for the center of mass in theground coordinate.

cos

sin

x V

V

dxV V

dt

dzV V

dt

= =

= =

V

=

= + 3. The thrust model of engine

NT

V

=

is the thrust of engine

0HN A N= is the power of engine with the changingheight.

0 01.11( / ) / 0.11H HA T T =

0N

is the power of ground.

HN is the power in the sky.

4. The control model of engineIn order to ensure the flight in the sky to reach the

maximal distance, the thrust in Z axes and the lift must bebigger than the weight of UAV.

21

2y

mg P Y

Y C V S

= +

=

IV. THE MODEL OF GUIDANCEBecause the position parameters are precise in GPS, in

the simulation the parameters can be considered as no error.

Through integral ,dx dy the position parameters ( , y ) can

be calculated. UAVs fly in the beelines between theguidance points and with horizontal swerving between thestraight flight course.

The s tart of

cruise

Read a new point

on the trajectory

Yaw or not

Go s traight

Calculate the distance

to the next point

The confirming

distance

Guidance end on

this point

N ex t G ui da nc e pa th

Y aw

Yaw end

Y

N

Y

Y

N

>

< OR =

Figure 1. The flow chart of guidance

V. THE MODEL OF GENE CODETrajectory planning adopts genetic GAs and genetic

coding uses distance, corner[1] program. ThePoint A is the starting point. Then point B,C,D can be

expressed in the formulas.

1111 sin,cos dydx DD == )cos( 212 ++= dxx DC )sin( 212 ++= dyy DC

Therefore, point n can also be expressed in the formulas.

1111 sin,cos dydx nn ==

)cos(1

1

11 +

=

+++=

in

j

jinii dxx

1

1 1

1

sin( )n i

i i n i j

j

y y d +

+ +

=

= + , ( 1,2, n 1)i =

A

4

3

2

1

B

CD

E x

y

4

d3d

2d

1d

Figure 2. The model of gene code

The codings use read coded genes. Every individual is atrajectory. There are n points in the trajectory. The coding is

,1 ,2 , ,n 1 ,1 ,2 , ,n 1

k k k k k k k k k

i i i i n i i i i n ix d d d d + += .k

ix is No. i individual

in No. k generation population.

VI. INITIALIZATION POPULATIONranL is the maximal voyage in the cruise path.

max

is themaximal yaw angles.

minL is the minimal flight distance. The

chromosomes in 0 ( 1, 2, , )ix i N= can be expressed as

0 min, min

2 [ ( 1) ]

1

Rani j

L n ld L

n

+= +

+

( 1,2, , )j n= ,

0

, max max2

i j = ( 1, 2,3, , )j n= . is a normal random

number in ( )0,1 .

VII. SELECTION OPERATIONThe fitness function for ( 1,2, )kix i N= is

( )ki Ang Ang Dis Dis

f x T p F p F= . In the formula T is the

individual evaluation function. AngF is a sign which is biggerthan normal in the first yaw angle. When it is bigger than

normal or not,Ang

F will be 1 or 0. DisF is a sign which is

longer than normal for distance. When it is longer than

normal or not DisF

will be 1 or 0. Angp and Disp are penalty

functions.

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Roulette wheel selection is adopted in the selection

operation. The selected probability is

1

( )

( )

kk i

i nk

i

i

f xP

f x=

=

.

( )ki

f x is the fitness function fori.

VIII. CROSSOVER OPERATIONThe crossover operator adopts arithmetic crossover.

k

ji

k

ji

k

ji ddd ,2,1,1 )1( +=

,

k

ji

k

i

k

ji ddd ,22,2 )1( +=

),,2,1( nj =

k

ji

k

ji

k

ji ,2,1,1 )1( +=

,

k

ji

k

i

k

ji ,22,2 )1( +=

),,2,1( nj =

is a random number in ( )0,1 .

IX. MUTATION OPERATIONThe mutation operator adopts Gaussian mutation for

every chromosome.

1,, n

k

ji

k

ji dd +=

),2,1( nj = ;

2,, n

k

ji

k

ji += ),2( nj = ;

1n and 2n obey )10,0(2N , )2,0( 2N Gaussian

distribution.

X. EVALUATION FUNCTION T The multi-object optimization is used for this function.

1 1 2 2

m ax( )n n n n

L LP P P P

T = + +

1nP

2nP

L are weighing coefficient.

1nP

+2nP

+ L =1

Pn is the level of satisfaction for the average damage

probability and voyage.

( )

'' 0( '')

''( ' '')

'' '( ')

' 1

nn n

n nP x n n n

n n

n n

n

PP P

P PP P P

P PP P

P

=

= <

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Modeling & Simulation of UAV Trajectory Planning on GAs