25

2011 3 11

1 RoboCup Rescue Simulation [1]

RoboCup Rescue Simulation

RoboCup Rescue Simulation

RoboCup Rescue Simulation

1

RoboCup Rescue Simulation

26

A*[2] [3]

2

A* D* [4]

Adaptive A* [5]

A*

27

G

1

G= V, E, C

V node E edge

C

2

V = {v1, v2,…, vn}

3

E = {ei, j vi, vj V, vi vj }

4

C : E R+

ei, j ci, j

G vs vg

5

vs, vs+1, … , vg-1, vg vi vi+1

ei, i+1

vs, vs+1, … , vg-1, vg

6

cs, s+1+cs+1, s+2+…+cg-2, g-1+ cg-1, g

vs vg

28

7

vs vg

8

9

●

10

29

11

12

13

A* [2] 1968 Hart

A*

30

A*

p

p f p

　　　f p = g p + h p

g p h p

g p p

h p p

p p

g p h p

h p h* p

p

　　　f* p = g p + h* p

h* p

h* p p, 0 ≤ h* p ≤ h p

A*

31

f* p

f* p

h* p

A*

D* [4] 1994 Anthony Stentz

D* A*

A*

Adaptive A* [5] 2006 Sven

Adaptive A*

A*

A*

32

G'

33

14

G'= V, E, C, B

V, E , C 2, 3, 4

B

15

B : E R+

ei, j bi, j

34

A* 3

A*

A* h* p h*

p p

v1, v2, v3, …

1. p

2.

3. 1 2

4. vi vi vi+1

5. 3

6. 3 5 h* p

35

4.1 7 8

1. 3 h* 3

a

0.98 0.98 1 3 = 2.8812

b

0.02 3 + 0.98 0.02 4 + 0.98 0.98 0 7 = 0.1384

c h* 3 = 2.8812 + 0.1384 = 3.0196

2. 0 h* 0 3.19

3. f * p

a f* 3 = g 3 + h* 3 = 1 + 3.0196 = 4.0196

36

b f * 0 = g 0 + h* 0 = 1 + 3.19 = 4.194

4. f * p

3

5. 6 4 7 f* p

6. 6 f * p 4 f * p

6

7. 5 3 f * p

8. 5

9. 8 8

10.

A*

A*

A*

A*

A*

37

A*

A* h* p p

1 5.1

C++ Visual Studio

2010

OS Windows 7CPU AMD Athlon X2 Dual Core Processor 5200+

Memory 3GB

3[8]

1%

38

A*

5.1 5.2 5.2

39

1-1 1 20 4 1 1000

1-2 2 20 4 10 1000

2-1 1 20 4 1 1000

2-2 2 20 4 10 1000

5.3 .

40

sA* 66.499 12.23 0.00021

35.958 2.192 0.0003034.927 - -

1-1 5.3 .

A*

t = 34.106, P = 0.000 A*

5.4

0

100

200

300

400

500

600

700

800

900

34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70

t�

@ABC/�

A* YZ[\ ]^_

41

sA* 42.327 3.716 0.00112

35.393 1.050 0.0018640.516 2.790 0.0015634.934 - -

1-2 5.5

3 5.5

t PA* 3.1954 0.000

A* 11.505 0.00031.635 0.000

0

100

200

300

400

500

600

700

800

900

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

t�

@ABC/�

A* YZ[\ � ]^_

42

5.6

sA* 42.370 14.671 0.00031

35.945 5.399 0.0001734.090 - -

2-1 5.5

A*

t = 18.175, P = 0.000 A*

0100200300400500600700800900

1000

34 37 40 43 46 49 52 55 58 61 64 67 70

t�

@ABC/�

A* YZ[\ ]^_

43

5.7

sA* 35.432 2.736 0.00096

35.237 1.024 0.0016335.178 2.018 0.0015434.071 - -

2-2 5.6

3 5.8

0100200300400500600700800900

1000

34 35 36 37 38 39 40 41 42 43 44 45 46

t�

@ABC/�

A* YZ[\ � ]^_

44

t PA* 19.004 0.000

A* 9.977 0.00016.974 0.000

2003 [6]

G' = V, E, C, B V E

C B

B[7] 5.9

45

3 1 10004 1 1000

5-1 3 1 10005-2 3 10 10005-3 3 100 10005-4 3 20 10005-5 3 30 10006-1 1 1 10006-2 1 10 10006-3 1 20 1000

m

5.10

m m sA* 998.50 122.8 0.00185

998.35 122.6 0.00789932.38 - -

m 5.7

46

A*

t = 0.054, P = 0.998 A*

m

5.11

m m sA* 2390.45 363.9 0.00626

2355.78 325.6 0.787071980.52 - -

m 5.8

050

100150200250300350400450500

t�

@ABC/�(m)

A* YZ[\ ]^_

47

A*

t = 1.807, P = 0.167 A*

m

5.12

m m sA* 2209.74 411.41 0.00553

1631.94 237.29 0.058721518.90 - -

m 5.9

0

50

100

150

200

250

300

t�

@ABC/�(m)

A* YZ[\ ]^_

48

A*

t = 33.116, P = 0.000 A*

m

5.13

m m sA* 1697.09 123.61 0.02049

1621.50 178.60 0.316061633.02 99.90 0.105121517.91 - -

m 5.10

0

50

100

150

200

250

300

350

400

1400 1550 1700 1850 2000 2150 2300 2450 2600 2750 2900 3050 3200 3350 3500

t�

@ABC/�(m)

]^_ A* YZ[\

49

3 5.14

t PA* 17.239 0.000

A* 13.346 0.00010.340 0.000

m

5.15

0

50

100

150

200

250

300

350

400

450

1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500

>�

@ABC/�(m)

A* YZ[\ � ]^_

50

m m sA* 1537.18 56.28 0.17054

1632.04 255.3 3.149191529.91 55.07 0.678861519.17 - -

m 5.11

3 5.16

t PA* 2.296 0.000

A* 5.086 0.0005.592 0.000

0

100

200

300

400

500

600

1400

1450

1500

1550

1600

1650

1700

1750

1800

1850

1900

1950

2000

2050

2100

2150

2200

2250

2300

2350

2400

2450

2500

2550

2600

2650

2700

2750

2800

2850

2900

2950

t�

@ABC/�(m)

A* YZ[\ � ]^_

51

m

5.17

m m sA* 1062.39 91.04 0.03772

1032.76 88.14 0.438291049.27 86.83 0.16579963.05 - -

m 5.12

3 5.18

050

100150200250300350400450500

750

800

850

900

950

1000

1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

1550

1600

1650

1700

1750

t�

@ABC/�(m)

A* YZ[\ � ]^_

52

t PA* 9.277 0.000

A* 3.744 0.0005.705 0.000

m

5.19

m m sA* 1007.80 85.58 0.05782

993.70 82.23 0.43575990.04 74.28 0.17549930.66 - -

m 5.13

050

100150200250300350400450500

t�

@ABC/�(m)

A* YZ[\ � ]^_

53

3 5.20

t PA* 4.677 0.000

A* 5.290 0.0000.599 0.932

m

5.21

m m sA* 2210.89 485.2 0.00586

1916.49 397.5 0.109261706.52 - -

m 5.14

0

100

200

300

400

500

600

700

1650 1800 1950 2100 2250 2400 2550 2700 2850 3000 3150 3300 3450 3600

t�

@ABC/�(m)

A* YZ[\ ]^_

54

A*

t = 18.731, P = 0.000 A*

m

5.22

m m sA* 1848.07 148.1 0.02639

1824.26 227.9 0.414191798.80 126.0 0.156691704.31 - -

m 5.15

A*

5.23

0

100

200

300

400

500

600

700

1600 1700 1800 1900 2000 2100 2200 2300 2400 2500

>�

@ABC/�(m)

A* YZ[\ � ]^_

55

t P

A* 9.671 0.000

A* 8.168 0.000

4.535 0.000

m

5.24

m m sA* 1773.49 95.77 0.04951

1768.35 146.7 0.636501749.46 87.65 0.219191704.07 - -

m 5.16

0

100

200

300

400

500

600

700

165017001750180018501900195020002050210021502200225023002350

t�

@ABC/�(m)

A* YZ[\ � ]^_

56

3 5.25

t PA* 8.260 0.000

A* 6.691 0.0003.426 0.000

A*

A*

A*

A*

A*

A*

A*

A*

57

A*

A*

A*

A*

A*

A*

A*

58

2

C-168

2012

1 Robocup rescue simulation, http://roborescue.sourceforge.net/.

2 P.E. Hart, N.J. Nilsson, and B. Raphael, A formal basis for the heuristic determination of

59

minimum cost paths , Systems Science and Cybernetics, IEEE Transactions on, 4 2 : pp. 100-107,

1968.

3 E.W.Dijkstra, A note on two problems in connexion with graphs , Numerische mathematic,

1 1 : pp. 269-271, 1959.

4 A. Stentz, Optimal and efficient path planning for partially-known environments , In Robotics

and Automation, 1994. Proceedings, 1994 IEEE International Conference on, pp. 3310-3317. IEEE,

1994.

5 S. Koenig and M. Likhachev, A new principle for incremental heuristic search: Theoretical results , In

Proceedings of the International Conference on Automated Planning and Scheduling, pp. 410-413,

2006.

6 25000.

7

http://www.city.nagoya.jp/kurashi/category/20-2-5-6-0-0-0-0-0-0.html.

8 1997