-74- Chapter 6 Simulation Results. 6.1 Simulation Results by Applying UGV theories for USV

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tested for UGV is given below. Figure 6.1 shows planed paths with obstacles having 5m safety distance.

1 Chapter 6 Simulation Results 6.1 Simulation Results by Applying UGV theories for USV The path planning with two obstacles by utilizing algorithms which are developed and tested for UGV is given below. Figure 6.1 shows planed paths with obstacles having 5m safety distance. The safety distance is equal to 6m of the obstacles which are utilized for the next simulations, presented in figure e 35 3 "ii Obstacle 1 Obstacle X..Coordinate[m] Figure 6.1- Obstacle avoidance using UGV algorithms (Safety distance from Obstacles= 5m) -74-

45 4 35 3 E Q; iii 25 u.;. 2 15 Obstacle 1 Obstacle 2 1 5 5 1 15 2 25 X-Coordinate[m] 3 35 4 45 Figure 6.

2 Simulation Results from the Novel Algorithm Possible paths have to generate first to choose

So that possible paths of the USV are generated as shown in Figure 6.3.

2 E Q; iii 25 u.; Obstacle 1 Obstacle X-Coordinate[m] Figure 6.2- Obstacle avoidance using UGV algorithms (Safety distance from Obstacles= 6m) 6.2 Simulation Results from the Novel Algorithm Possible paths have to generate first to choose the best among them as discussed in the Chapter 5. So that possible paths of the USV are generated as shown in Figure 6.3. All possible paths are generated in a 2x2 matrix. That can be used to presents a 2x2m area or multiples of that similarly ( 4x4m) on the Sea or water

2 4 6 -ro c E 1 (.) 12 ct 14 CD 8 16 18 2 2 4 6 8 1 12 14 16 18 2 Column Coordinate Figure 6.

But those obstacles data have to interpret to the algorithm. Figure 6.4 to 6.

Then square shape obstacles were placed on different locations of the grid.

3 ro c E 1 (.) 12 ct 14 CD Column Coordinate Figure Possible paths matrix of the USV Obstacle in sea can identify by utilizing Radars, stereo vision or any other methods successfully. But those obstacles data have to interpret to the algorithm. Figure 6.4 to 6.7 is presented different obstacle matrix for different obstacle positions. The whole path matrix is plotted there with red color paths. Then square shape obstacles were placed on different locations of the grid. t obviously should be a 2x2 matrix since the dimensions of the possible path matrix should be equals to the dimensions of the obstacle matrix. Relavent MatLab program is given with appendix D. 2r , &. B Hl u! 12 H & B :.1] 2 & B C H & B OlD c...,"c.nj.. Figure 6.4- Obstacle on the Obstacle matrix A - 76-

2 E., B l! D u! 12 H ::J ;zn 2 4 E B ll 12 H E B Zl co... "c_.,.., Figure 6.

6- Obstacle on the Obstacle matrix C 2 E B. i ll u! 12 H E B ;zn 2 E B D 12 H E m ;zn CL.ftn C_.

7- Obstacle on the Obstacle matrix D Table 1 presents the maximum traveling units on each and every path.

4 2 E., B l! D u! 12 H ::J ;zn 2 4 E B ll 12 H E B Zl co... "c_.,.., Figure 6.5- Obstacle on the Obstacle matrix B 21 4 E E 18 ;zn2=-,,-s=-d e--b=-;zn Clll..mnC-Nie Figure 6.6- Obstacle on the Obstacle matrix C 2 E B. i ll u! 12 H E B ;zn 2 E B D 12 H E m ;zn CL.ftn C_.lllle Figure 6.7- Obstacle on the Obstacle matrix D Table 1 presents the maximum traveling units on each and every path. Then those table data is utilized to calculate path values. After considering path values ninth path is chosen for the obstacle matrix A. 5th, 1st and 2nd paths are chosen for the obstacle matrices B, C and D respectively. -77-

r1 1 2 3 4 5 6 7 8 9 X A 4 4 4 4 4 4 4 4 17 B 4 4 4 4 18 4 4 4 4 c 3 4 4 4 4 4 4 4 4 D

5 r X A B c D Table 6.1- Maximum Safe traveling distance on each path Figure 6.8 and 6.9 presents path planning with obstacles which are having safety distances 4m and 6m respectively E 3oo ar ro.!::: 25 E y 2 >- 15 Obstacle 1 Obstacle Starting point X-Coordinate[m] Figure 6.8- Obstacle avoidance using the Naval algorithm (Safety distance from Obstacles= 4m) -78-

6 45 4 E ;; c 2 25 > Obstacle 1 Obstacle L i L X-Coordinate[m] Figure 6.9- Obstacle Avoidance using the Naval Algorithm based on Morphin Algorithm (Safety distance from Obstacles= 6m) - 79-

6.3 Simulation Results from Potential Field Method Already developed software

11 present the contour map and 3 dimensional surfaces of 3 obstacles.

7 6.3 Simulation Results from Potential Field Method Already developed software is employed for path planning with PFM. Figure 6.1 and 6.11 present the contour map and 3 dimensional surfaces of 3 obstacles. Path planning with PFM is processed by considering minimum potential from starting point y J a -..._J..._, Figure 6.1- Contour map of Potential field with 3 obstacles - 8-

.....,......... -- 15 1 5... : ;...... -5 w o...... :............. :. :.......:..._................,............."i.

. u ;;:m 15 1 5......,......,...,.........,.,. - -... l.

8 ....., : ; w o : :. : :..._ , "i., n Figure D surface of Potential field with 3 obstacles!3ll 46 «XX ::a!.,.3) i :.EO.. u ;;:m ,......,..., ,., l...., :a:jo 25 :xjo X-Ctoullnntes(nlJ Figure Obstacle avoidance using PFM (Safety distance from Obstacles= 5m)

6.4 Comparison of Obstacle avoidance methods The other two obstacle avoidance methods were compared and results are presented in Figure 6.13 and 6.14.

According to the results which are presented in the figure shows that Novel algorithm is capable of achieving the target with minimum traveling distance.

9 6.4 Comparison of Obstacle avoidance methods The other two obstacle avoidance methods were compared and results are presented in Figure 6.13 and The travel distance verses safety distance is compared in the Figure According to the results which are presented in the figure shows that Novel algorithm is capable of achieving the target with minimum traveling distance. Potential field method shows minimum travet distance at 5m safety distance since it was changed its traveling path between two obstacles to another path which was away from the two obstacles. Distance towards obstacles verses time were taken for all three methods and results are given using three different colors in the figure t shows that the generated paths utilizing potential field method is far away from the safety area of the obstacle compared with other methods. That is the main reason for traveling longer when the potential field is used. 85 BOO 75 - Potential field me thod for USV - ugv algorithms for USV - Novel algothm for USV -.. ::! 7 ;:;. "" ""., -.;.= D S.1fety disto111ce Figure Comparison of safety distances - 82-

10 55 Distance towards obstacles 45 Novel algorithm ApplingUGVtheories PFM 4 35 J!l 3 r 2so r c5 2 " 15 Obstacle 1 Obstacle time[s) Figure Comparison of distances towards two obstacles - 83-

6.5 Simulation Results for Dynamic Obstacles Avoidance Figure 1 and 2 present the make use of static obstacle avoidance for dynamic obstacles.

Dynamic obstacles can freeze on their moving path with time. So they become another static obstacle at the end.

Simulation results from the path prediction methods which are discussed above are presented below.

11 6.5 Simulation Results for Dynamic Obstacles Avoidance Figure 1 and 2 present the make use of static obstacle avoidance for dynamic obstacles. The time information ofthe USV and the obstacle} are shown in the figure 1 for the convenience. Dynamic obstacles can freeze on their moving path with time. So they become another static obstacle at the end. But it is required to predict the moving path of the obstacle before hand. Simulation results from the path prediction methods which are discussed above are presented below. Effective area prediction is also equally important as path prediction. So set of simulations have done on that and those simulation results are presented after the path prediction results as shown below. 8 7.s ll " - 4 u >- :nj Obstacle \ \ Obstacle :nj 4 X-Coordinates [m] 7 8 Figure Dynamic obstacle avoidance with time values - 84-

$Obstacle 1 e 8 >- 4 Obstacle 31 i \Om 35.$ (35,35) v (325,33) 3 25 3 35 4 45 55 6 65

12 6 - Goal 55 t Obstacle 2 (625,59) ll i14so Obstacle 1 e 8 >- 4 Obstacle 31 i \Om 35. (35,35) v (325,33) X<:oodnates lm] Figure Dynamic obstacle avoidance with 3 obstacles

6.5.1 Simulation Results for path prediction of Dynamic Obstacles For the simulations of path prediction, Octomorphic path is generated as

But the path planning module is only supplied with past 1 coordinates ofthe obstacle movements in USV frame.

1 Polynomial approximation method for path prediction Simulations done utilizing Polynomial approximation method considering sensor noise

13 6.5.1 Simulation Results for path prediction of Dynamic Obstacles For the simulations of path prediction, Octomorphic path is generated as the actual path of the obstacle. But the path planning module is only supplied with past 1 coordinates ofthe obstacle movements in USV frame. Then path prediction module is predicted another 5 coordinates. Then those coordinates and the error values are plotted Polynomial approximation method for path prediction Simulations done utilizing Polynomial approximation method considering sensor noise and without noise Simulations without sensor noise 4 :s D -e } -1-2, -3.4Q L llme [S] Figure Longitudinal coordinates of actual path j Cii!:l -2-4, c llme [S] Figure Lateral coordinates of actual path _j BOO - 86-

and 6.18 presents the lateral and longitudinal value changes respect to time.

Predicted paths after changing the degree of the polynomials are presented in a same figure

14 Figure Actual path and Predicted paths of the Obstacle for different degrees of Polynomials Figure 6.17 and 6.18 presents the lateral and longitudinal value changes respect to time. Then Figure 6.19 shows the actual Octomorphic path of the obstacle. Predicted paths after changing the degree of the polynomials are presented in a same figure to compare the effect of the degree. Figure 6.2 and 6.21 shows the lateral and longitudinal errors after changing the degree of the polynomial. A developed MatLab program for this is given in appendix E

2 - Longitudinal error of predicted paths for different degrees of Polynomials.5 OA.

15 4 3 2 Degree= 3 Degree= 8 Degree= 5 E... g w "iii c 6 ::J g, -1 _J -2 --< Time [S] Figure Longitudinal error of predicted paths for different degrees of Polynomials.5 OA.3 Degree= 3 Degree= 5 Degree= E.1... g w Q) iii -.1 _J -.2 " J -.3 f -, Time [S] Figure Lateral error of predicted paths for different degrees of Polynomials - 88-

$J - ttl 1 el (jj y Cii \ c 1- ft 5 t.a - "g> -1,,,, l 1 _J,l, r \ -2 " ll.r r -3 ( t t -,f (. ( 1 t f W1,\,,... j.\ -4 1 2 3 4 6 7 8 Time [S] Figure 6.$ $.. \,,, l ( J r 11 r, 1L t l f \1 1t i 1.. r \1 1,1 1;, J:l.!,.;ly.,,.\ J ll" l lijll -,.,._.1 8 5 1 15 2 25 lime [SJ 3 35 4 45 Figure 6.$

16 Simulations with sensor noise 5 ltv ) 4 1 r lt 11,.;" r,.,,1,, J r 3 rj d E ; , Q) u c,. J - ttl 1 el (jj y Cii \ c 1- ft 5 t.a - "g> -1,,,, l 1 _J,l, r \ -2 " ll.r r -3 ( t t -,f (. ( 1 t f W1,\,,... j.\ Time [S] Figure Longitudinal coordinates of actual path with noise (noise=sm) " ) ( ;. },Ji! lfr - V.rlli lyl -).l;, r11"1,.. i \,,, l ( J r 11 r, 1L t l f \1 1t i 1.. r \1 1,1 1;, J:l.!,.;ly.,,.\ J ll" l lijll -,.,._ lime [SJ Figure Lateral coordinates of actual path with noise (noise=sm) - 89-

$- " u 2 c: 2! en i:s!!! n; "... 1 8 L y- 7 --...:.: - " 6 _:;Y,:.. 4-2 4 \-1 " -"---... :. -6 \,.-:->. "" < l c-- <---- :::;r--.. " \o ::--- -----".,._ -8 4-3 -2 j - -1.::-t K.$ $.{ _, 1 2 3 4 Loogitudinal Distance [m] 5 Figure 6.24- Actual path of the Obstacle with noise (noise=5m) Figure 6.22 and 6.$

17 - " u 2 c: 2! en i:s!!! n; " L y :.: - " 6 _:;Y,: \-1 " -" :. -6 \,.-:->. "" < l c-- <---- :::;r--.. " \o :: ".,._ j - -1.::-t K. -- Actual Path,_ ""v -"<) "),..._,. " LS,_, xf;4 \ -,.7\- Y, - -,? \: 1-1\ -- \ - v.,.t:.";;><. y_ --;7. "",-f< -:..._ 7 " \-..{ _, Loogitudinal Distance [m] 5 Figure Actual path of the Obstacle with noise (noise=5m) Figure 6.22 and 6.23 shows the lateral and longitudinal value changes with noise respect to the time. Then Figure 6.24 presents the actual Octomorphic path of the obstacle with respect to time_ Then predicted path is generated for noisy data with 6 degree polynomial. That is given in Figure Then that degree is changed to 5 and 4 respectively as shown in the Figure 6.26 and

$Actual Path g 1 8,, - -Q) c: " 6 iii i5 Q) iii - 4 2 \ \ \" \ <.$ .-- -- """ -2-1 - Longitudinal Distance [m] 1 1 2 Figure 6.

18 14 12 Actual and Predicted Path Predicted Path ( Degree=6,Noise =1 m) l Actual Path g 1 8,, - -Q) c: " 6 iii i5 Q) iii \ \ \" \ < """ Longitudinal Distance [m] Figure Actual and Predicted path of the Obstacle (Degree of Polynomial= 6, noise = lm)

$15 E :::1 Q) u c:: ll " :l 5 ;; - J "! \,.$ $.. - - f - " -5, -,, )i ( l - j \ v 1 -,,._.,_,L,.$

19 25 Actual and Predicted Path 2 Predicted Path ( Degree=5,Noise = 1m) Actual Path 15 E :::1 Q) u c:: ll " :l 5 ;; - J "! \, f - " -5, -,, )i ( l - j \ v 1 -,,._.,_,L,. \ Longitudinal Distance [m] 25 3 Figure Actual and Predicted path of the Obstacle (Degree of Polynomial= 5, noise= lm) - 92-

$.. 1 8 6 4 E 2,...r- - Actual and Predicted Path < -...:,. - - -,_" " -,"" ; \,, \ ".",,"-. Predicted Path ( Degree=4,Noise = 1m) l Actual Path,, f s -Q) - ::::.";!.!!! Cl Q) <;; -2 _J "-.$

20 E 2,...r- - Actual and Predicted Path < -...:, ,_" " -,"" ; \,, \ ".",,"-. Predicted Path ( Degree=4,Noise = 1m) l Actual Path,, f s -Q) - ::::.";!.!!! Cl Q) <;; -2 _J "-. < "" t,..-r_ " y \. t: - -{ :--...,. > -1-6 J Longitudinal Distance [m] Figure Actual and Predicted path of the Obstacle (Degree of Polynomial = 4, noise= lm)

4 Actual and Predicted Path Predicted Path (Degree 4. Noise Sm) Actual Path 3 - " g! Cl) " 2 1-1 t: M.A- -->..;:s_,..;, -......,-.".i-t< C. r... <...... "?:- --1-2, -3-4 -15-1 -5 5 1 15 2 25 3 Longitudinal Distance [m] 35 Figure 6.

Quite improved predicted path is received with small (lm) noise when degree ofthe polynomial is equal to four. Then noise is increased by 4m to analyze the effect of noise.

21 4 Actual and Predicted Path Predicted Path (Degree 4. Noise Sm) Actual Path 3 - " g! Cl) " t: M.A- -->..;:s_,..;, ,-.".i-t< C. r... < "?: , Longitudinal Distance [m] 35 Figure Actual and Predicted path of the Obstacle (Degree of Polynomial = 4, noise = 5m) One meter noise is added to the figure 6.25,6.26 and Quite improved predicted path is received with small (lm) noise when degree ofthe polynomial is equal to four. Then noise is increased by 4m to analyze the effect of noise. Normally even the improved GPS receivers are having error of two or three meters alone. So the noise is changed from lm to 5m of 4th degree polynomial. That result is given in figure 6.28 and it proves that the polynomial approximations methods are not good with noise

2.1 Simulations without sensor noise - Actual and Predicted Paths 8-6, ",..._ -------- --":", -------- -... 4...,.. " 2 E.

22 RBNN method for path prediction Simulations are done utilizing RBNN method considering and without considering sensor noise Simulations without sensor noise - Actual and Predicted Paths 8-6, ",..._ ":", ,.. " 2 E. Actual Path - spread = 1 Ql <J c: spread= 5 spread= 1 " i5 T!! Ql iii..j _ " «... ;; Longitudinal Distance [m] Figure Actual path and Predicted paths of the Obstacle for different Spreads - 95-

$iii c: 6 f, \ ::J \ - \, l c;, c: -5 _J -1 f. 1, j -15-2 1 2 3 4 6 7 8 Time [S) Figure 6.$ $spread= 5 E.... 1 g w Q) c;; _J -1 i1 ; 1 \ -2-3 -4 1 2 3 4 Time [S] 6 7 8 Figure 6.$

23 2, spread= spread= 1 spread= j E... 5 g. w J. iii c: 6 f, \ ::J \ - \, l c;, c: -5 _J -1 f. 1, j Time [S) Figure Longitudinal error of predicted paths for different Spreads spread= 1 spread= 1 spread= 5 E g w Q) c;; _J -1 i1 ; 1 \ Time [S] Figure Lateral error of predicted paths for different Spreads 96

$2 Simulations with sensor noise Actual and Predicted Paths 1 T T -, Actual Path r Noise= Om 8 Noise= 5m _H:<- ""--, Noise = 1Om 6 \\$

24 ,._, Actual and predicted paths for different spreads are given in figure 6.29 to analyze the effect of spread value efficiently. The number of neuron enrollments can be increased by increasing the spread value. That predicted path can be smoothed more by increasing the spread value. Longitudinal and Lateral error changes for different spread values are presented in Figure 6.3 and 6.31 respectively Simulations with sensor noise Actual and Predicted Paths 1 T T -, Actual Path r Noise= Om 8 Noise= 5m _H:<- ""--, Noise = 1Om 6 \\. 4 E " Q) 2 u c:: ", X ( ".\.( -6 \ "" Longitudinal Distance [ m] Figure Actual path and Predicted paths of the Obstacle for different noise values - 97-

The data without sensor noise can not be expected in the field. So that the noise is introduced to the actual path data and then predicted paths are taken for different noise values with 3m spread.

$1 1 Noise= Om 3 Noise= 5m l l r V 2 tllll : l i f,[r, if J i n ".s 1,. 1 r J rr r,. j ( \ t\j,,,, r 1.., l,....... tj t. 1r -.!. ;: 11 i,,, ll>.., l :J,\ \ 1\1 j.!, :!::: J.$

25 The data without sensor noise can not be expected in the field. So that the noise is introduced to the actual path data and then predicted paths are taken for different noise values with 3m spread. Those results are given below in Figure t proves the validity of the RBNN method for successful path prediction with noises. Longitudinal and lateral errors for different noise values are given in Figure 6.33 and 6.34 respectively. MatLab program for this is given in appendix F. 4 Noise= 1m f. 1 1 Noise= Om 3 Noise= 5m l l r V 2 tllll : l i f,[r, if J i n ".s 1,. 1 r J rr r,. j ( \ t\j,,,, r 1.., l, tj t. 1r -.!. ;: 11 i,,, ll>.., l :J,\ \ 1\1 j.!, :!::: J. t y t g> - 1 ;, tr1 l \1 i t r\. i. ;...J H. t) j h!j 1, -2o t1 1 tt )1\ l t J lt Time [S] Figure Longitudinal error of predicted paths for different noise values - 98-

$E -... g 4 3 2 1 w Q). j -1 l. " ;\( j., -2,, il. -3, l i f (,1 - i_,,.. tl. J,i t 1. Jlil \1,,, 1:. 1, r. { 1, J. t. A \ -l i )" t, Noise= 1m Noise= 5m Noise= Om,. j... nt 1 h ill t M,... i. rl tl 1 1,.$

26 E -... g w Q). j -1 l. " ;\( j., -2,, il. -3, l i f (,1 - i_,,.. tl. J,i t 1. Jlil \1,,, 1:. 1, r. { 1, J. t. A \ -l i )" t, Noise= 1m Noise= 5m Noise= Om,. j... nt 1 h ill t M,... i. rl tl 1 1,. :..., v \iji, ru. t.,.., lhl r\1, r\1 \ (1\ 1 \ i \ \ ) \, :, n t lime [S] Figure Lateral error of predicted paths for different noise values Summary of Simulation Results for path prediction Path predictions of dynamic obstacles are very important for dynamic obstacle avoidance. Polynomial approximation method is tried for that initially. ts quite good method and gave very good results at the beginning, without noises. But position data can not be expected without noise from the field. So noise was introduced and polynomial approximation method is not able to give considerable results as expected. RBNN method which is famous for function approximation is tried after that. t shows very good results with noises. Those predicted paths can smoothen more by increasing the spread value

6.5.2 Simulation Results for Obstacle area prediction of Dynamic Obstacles 6.5.2.1 Simulation Results from Velosity obstacle method Velocity obstacle method is a conventional method which is employed for Dynamic obstacle area predictions.

27 6.5.2 Simulation Results for Obstacle area prediction of Dynamic Obstacles Simulation Results from Velosity obstacle method Velocity obstacle method is a conventional method which is employed for Dynamic obstacle area predictions. t predicts triangular areas for Dynamic obstacles. The size of that area is depends on a constant. Following figures present the simulation results from that conventional method. A novel obstacle area prediction method is simulated after that. The main objective of that proposed method is to predict the areas of dynamic obstacle movements effectively. So that novel method is compared with the conventional method at the end. Those simulation results are presented finally lime [s] Figure Longitudinal velocity of the obstacle - 1-

2 i 1.5 1 V..._.s.5..._.?:- g Qi > -.5 Q) iii _.J -1-1.

$36- Lateral velocity of the obstacle 4 Ac tual Path 3 k =.6 1 1 k = 1.2 l 1 c,.!. l \ l.$

28 2 i V..._.s.5..._.?:- g Qi > -.5 Q) iii _.J Time [s] Figure Lateral velocity of the obstacle 4 Ac tual Path 3 k = k = 1.2 l 1 c,.!. l \ l.. : l.. r j l - J k =.9 \ >! 1 ". i, ime]S] Figure Upper and Lower Boundaries of Predicted Obstacles Area towards Longitudinal direction - -

$soo, Actual Path 1 4 3 2 ( k l l f. "-,\,, k =.6 k =.9 k = 1.2 1 j f cs -1 L ""- \ 1 1-2 -3-4,"" ""- --- f r, r j, - j -soo 1 2 3 4 lime[s) 7 BOO Figure 6.$ 38 present upper and lower boundaries of predicted obstacle areas utilizing conventional method towards Longitudinal and Lateral directions.

38 present upper and lower boundaries of predicted obstacle areas utilizing conventional method towards Longitudinal and Lateral directions.

29 soo, Actual Path ( k l l f. "-,\,, k =.6 k =.9 k = j f cs -1 L ""- \ ,"" ""- --- f r, r j, - j -soo lime[s) 7 BOO Figure Upper and Lower Boundaries of Predicted Obstacles Area towards Lateral direction Figure 6.37 and 6.38 present upper and lower boundaries of predicted obstacle areas utilizing conventional method towards Longitudinal and Lateral directions. Those boundaries are generated for different constant values. This constant can be adjusted to take the efficient predicted area. The actual path may deviate out from the predicted obstacle areas. That mean those obstacles may collide with the USV. So those types of situations are calculated and plotted with time for Longitudinal and Lateral directions as shown in Figure 6.39 and

$39 - Error towards Longitudinal direction E 1 9 8 7 6 5 w J 4 3 1 r k =.6 k =.9 k = 1.2 2..\) 1,.$

30 E i 5 w ; i! l, : =ll.l> k =.9 k = BOO lime(s( :)1 - Figure Error towards Longitudinal direction E w J r k =.6 k =.9 k = \) 1,.,Y \ l BOO lime(s) Figure Error towards Lateral direction

6.5.2.2 Simulation Results from the novel method The predicted areas generated from the novel method are depending on the relative velocity of the obstacles as discussed in previous chapters.

$Then the Sea condition factor is changed and those simulation results are presented in Figure 6.45, 6.46, 6.47, 6.48 and 6.49. 3 2,- Q) t.l " 1;j " i5 1i! C" c;, s " 1-1.. \ \ \. < \, A.$

31 Simulation Results from the novel method The predicted areas generated from the novel method are depending on the relative velocity of the obstacles as discussed in previous chapters. The relative velocity variation of the obstacle is presented in Figure 6.35 and That variation is directly effecting the area prediction. So the upper and lower boundaries of predicted areas by means of novel method are presented in Figure 6.41 and The error values of those are shown in figure 6.43 and Then the Sea condition factor is changed and those simulation results are presented in Figure 6.45, 6.46, 6.47, 6.48 and ,- Q) t.l " 1;j " i5 1i! C" c;, s " \ \ \. < \, A. 1 \, """" 1 " Time [S] 6 7 BOO Figure Upper and Lower Boundaries of Predicted Obstacles Area towards Longitudinal direction ( S =.5 ) - 14-

4 -l 3 2 1 CD!! ;)! i5 jj! CD -1.1-2 -3-4 1 2 3 4 6 lime[s] Figure 6.

32 4 -l CD!! ;)! i5 jj! CD lime[s] Figure Upper and Lower Boundaries of Predicted Obstacles Area towards Lateral direction ( S =.5 ) j_ , 6 s g 5 w i 1 ( ime [S] Figure Error towards Longitudinal direction ( S =.5 )

$1 : -1 9 8 7 6 E... 5 g w 4 3 2 1 1 2 3 4 lime [S] 6 7 8 Figure 6.44 - Error towards Lateral direction ( S =.5 ) 3 2,Y"\ l Actual Path 1 l 1 l y =.4 l s =.6. "- : " H" A E f \ 1 \ \" 1 \ 1 " " r \.$

33 1 : E... 5 g w lime [S] Figure Error towards Lateral direction ( S =.5 ) 3 2,Y"\ l Actual Path 1 l 1 l y =.4 l s =.6. "- : " H" A E f \ 1 \ \" 1 \ 1 " " r \.. \ 1 )!l \ y. 1 ".. r.,, 1., t i -2 3 S } lime[s] Figure Upper and Lower Boundaries of Predicted Obstacles Area towards Longitudinal direction for different Sea condition values - 16-

46- Upper and Lower Boundaries of Predicted Obstacles Area towards Lateral direction for different Sea condition

34 4 3 2 too., ll u c 1ij 1!! ll j -1-2 Actual Path s =.4 s =.6 l s =.8 - "" r l ;, l; "-, :,, >, y BOO Time (S] Figure Upper and Lower Boundaries of Predicted Obstacles Area towards Lateral direction for different Sea condition values 7 6 S=O s =.6 s =.8 J 4oo ;; " 3 " 2 1 t 1. r l l l llme[s] Figure Width of Predicted Obstacles Area towards Longitudinal direction for different Sea condition values - 17-

$1 9 8 7 6 E... 5 g w 4 r i 3o 2 1; ( J \ S = OA s =.6 s =.$ 48- Error towards Longitudinal direction for different Sea condition E 1 9 8 7 6 g

35 E... 5 g w 4 r i 3o 2 1; ( J \ S = OA s =.6 s = Time [S] Figure Error towards Longitudinal direction for different Sea condition E g 5 w 4o 3o 2 1 o J, values S = OA s =.6 s = Time [S] Figure Error towards Lateral direction for different Sea condition values - 18-

The upper and lower bounds of the predicted obstacle areas from both methods are shown in figure 6.5 and 6.51 and errors are presented in figure 6.52 and 6.53.

The area reduction from the novel method is inspired from the differences between the widths of the novel method and conventional method.

36 Comparison Results The proposed novel algorithm for obstacle area prediction is compared with the conventional method to prove the effectiveness of the novel method. The upper and lower bounds of the predicted obstacle areas from both methods are shown in figure 6.5 and 6.51 and errors are presented in figure 6.52 and Width of the predicted area from both methods towards longitudimrl direction is given in figure The area reduction from the novel method is inspired from the differences between the widths of the novel method and conventional method. That difference is given in figure 6.55 and that proves the improvements from the novel method. Matlab program which is developed for this is given with appendix G. 4, Actual Path 3 N1.el Method 2 1 <.l " c: " g! J -1 r _r "". 1 ""--- Con-lntional Method r,,, r,, lime [S) 6 l 7 8 Figure Upper and Lower Boundaries of Predicted Obstacles Area towards Longitudinal direction from Conventional and Novel Methods - 19-

$_ " "" --; "-"-- -4 \, - 1 2 3 4 Time [S] 6 7 BOO Figure 6.$ 51- Upper and Lower Boundaries of Predicted Obstacles Area towards Lateral direction from Conventional and

37 4 Actual Path N<Mll Method 3 Comentional Method 2 1 " ffi Ui i5 " "..: "-._ " "" --; "-"-- -4 \, Time [S] 6 7 BOO Figure Upper and Lower Boundaries of Predicted Obstacles Area towards Lateral direction from Conventional and Novel Methods 1()() 9 NoYel Method Conventional Method g 5 w 4 3 ; 2,o.i lime[s] 6 7 BOO Figure Error towards Longitudinal direction for Conventional and Novel Methods - 11-

$1 9 NoYel Method Conwntional MethOO 8 7 6 E i 5 w 4 3 2 1 \; 1 2 3 4 lime(s] 6 7 8 Figure 6.$

38 1 9 NoYel Method Conwntional MethOO E i 5 w \; lime(s] Figure Error towards Lateral direction for Conventional and Novel Methods 45 Nowl Method Conwntional Method 4 35 :[3 i5 325 " g 2 15,! lime(s] Figure Width of Predicted Obstacle Area towards Longitudinal direction from Conventional and Novel Methods

1 8 6 4 " 5 3:: 2 al 1.1 :J al a: -2-4 -6 1 2 3 4 6 7 BOO lime[s) Figure 6.

39 " 5 3:: 2 al 1.1 :J al a: BOO lime[s) Figure Predicted Distance reduction from Novel Method Above figure presents the effectiveness of employing Novel method for Dynamic obstacle avoidance well. But the Novel method is not reducing the predicted area totally. t may increase that area at sharp turns respect to the conventional method. t can be observed from the lower side of the graph given in Figure But the overall performance of the proposed method is better than conventional one at the end

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