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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
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