DEM 型歩行者モデルによる回避シミュレーション

!"# ဳᱠⴕ⠪ࡕ࠺࡞ߦࠃࠆ࿁ㆱࠪࡒࡘ࡟࡯࡚ࠪࡦ$
ዊᴰቁਯ %㧘ㄞౝિᅢ %㧘⿒Ⴆㆯᄙ &$
% หᔒ␠ᄢቇ
Ꮏቇㇱ$
Ꮏቇ⎇ⓥ⑼$
& หᔒ␠ᄢቇᄢቇ㒮
᭎ⷐ$
☳૕Ꮏቇ߿࿯⾰ജቇߢᵈ⋡ߐࠇߡ޿ࠆ !"# ߦ '( ࡕ࠺࡞ࠍេ↪ߒ㧘ⴕേ․ᕈࠍ⹦⚦ߦ⴫⃻ߒߚ !"#
ဳᱠⴕ⠪ࡕ࠺࡞ߦߟ޿ߡㅀߴࠆ‫ߚߞⴕߡ޿↪ࠍ࡞࠺ࡕߩߘޔߦࠄߐޕ‬㓚ኂ‛߿ઁߩᱠⴕ⠪ࠍ࿁ㆱߔࠆࠪ
ࡒࡘ࡟࡯࡚ࠪࡦࠍ⚫੺ߔࠆ‫ޕ‬$
)*+,-./01$2,345.6,+/$78$!"#$9++6$:;.<<,0$#+-15$
:.=.84=,$>+,?43,%@$A+746.=.$:B4C,40D,%@$E8+6.$)=.6B4=.&$
%!1F.;631/6$+<$:10D/+5+G8@$!+BD,BD.$H/,*1;B,68$
$
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)7B6;.06$
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B,345.6,+/$.*+,-,/G$+7B6.051$./-$+6D1;$<++61;$78$4B,/G$6D1$3+-15J$
$
1 ߪߓ߼ߦ
㆏〝‫✼߿࡞࡯ࡕࠣࡦࡇ࠶࡚ࠪޔ‬ᣣ‫ߪߚ߹ޔ‬࿾㔡߿Ἣ
ἴߥߤߩἴኂᤨߥߤ‫ޔ‬᭽‫ߥޘ‬႐㕙ߢᷦṛ߿ᷙ㔀߇⊒
↢ߔࠆ‫ߥ߁ࠃߩߎޕ‬ᷦṛ߿ᷙ㔀ߣ޿ߞߚ߽ߩߪੱߦ
OV ࡕ࠺࡞ࠍេ↪ߔࠆ‫ޕ‬OV ࡕ࠺࡞ߪ೨ᣇ☸ሶߣߩ〒
㔌߆ࠄᦨㆡߥ☸ሶㅦᐲࠍ᳞߼‫☸ޔ‬ሶࠍടㅦ߅ࠃ߮ᷫ
ㅦߐߖࠆ⸘▚ᣇᴺߢ޽ࠆ[4]‫ ޕ‬x ߦ૏⟎ߔࠆ☸ሶടㅦ
ᐲ a ߪ☸ሶ㑆〒㔌 'x ࠍ↪޿ߡએਅߩᑼߢ⴫ߐࠇࠆ‫ޕ‬
a D V 'x v (1)
♖␹⊛ࠬ࠻࡟ࠬࠍਈ߃‫ޔ‬੤ㅢ੐᡿ߩ⊒↢₸ࠍ㜞߼ࠆ‫ޕ‬
ߎߎߢ‫ ޔ‬D ߪᗵᐲଥᢙ㧘 v ߪ☸ሶㅦᐲ㧘 V 'x ߪ☸
ࠃߞߡ‫ޔ‬ᷦṛࠍ⸃ᶖ࡮✭๺ߒ‫ߦ࠭࡯ࡓࠬ߇ੱޔ‬⒖േ
ሶ 㑆 〒㔌 ߆ࠄ ᳞ ߼ࠄ ࠇࠆ ᦨ ㆡㅦ ᐲ㑐 ᢙ ߢ޽ ࠆ‫ޕ‬
ߢ߈ࠆⅣႺࠍ⸳⸘ߔࠆߚ߼੤ㅢࡕ࠺࡞ߦࠃࠆ੤ㅢᵹ
⸃ᨆ߇㊀ⷐߣߥࠆ‫ޕ‬
⃻࿷ߢߪゞ߿ੱߥߤߩኻ⽎‛ࠍ☸ሶߢ⴫⃻ߒ‫ޔ‬୘‫ޘ‬
V 'x ߪએਅߩᑼߢ᳞߼ࠄࠇࠆ‫ޕ‬
V 'x v max
2
§
§ d ··
§ 'x d ·
¨¨ tanh¨
¸ tanh¨ ¸ ¸¸ (2)
© w ¹¹
© w ¹
©
ߩ☸ሶ᜼േࠍㅊ〔ߔࠆࡒࠢࡠࡕ࠺࡞ࠍ↪޿ߚ⸃ᨆ߇
ߎߎߢ‫ޔ‬v max ߪ೙㒢ㅦᐲ‫'ޔ‬x ߪ☸ሶ㑆〒㔌‫ޔ‬d, w ߪ
৻⥸⊛ߢ޽ࠆ[1,2]‫⎇ᧄޕ‬ⓥߢߪⓨ㑆ࠍㅪ⛯⊛ߦᝒ߃‫ޔ‬
ቯᢙߢ޽ࠆ‫⎇ᧄޕ‬ⓥߢߪ d
0.47, w
0.45 ߣߒߚ‫ޕ‬
ℂ⺰ߦၮߠ߈☸ሶ᜼േࠍ⸘▚ߔࠆ DEM (Distinct
ᰴߦ‫ޔ‬DEM ߦߟ޿ߡ⺑᣿ߔࠆ‫ޕ‬DEM ߣߪ‫⸃ޔ‬ᨆኻ
Element Method‫ޔ‬୘೎ⷐ⚛ᴺ) [3]ࠍ↪޿ߡⴕേ․ᕈࠍ
⽎ߩ᭴ㅧ૕ࠍㅪ⛯૕ߣߒߡߪขࠅᛒࠊߕ‫ޔ‬୘‫☸ߩޘ‬
⹦⚦ߦ⴫⃻ߒߚᱠⴕ⠪ࡕ࠺࡞ࠍ᭴▽ߔࠆ‫☸ޔߚ߹ޕ‬
ሶⷐ⚛߆ࠄߥࠆ㓸ว૕ߢࡕ࠺࡞ൻߒ‫ߩߘޔ‬㓸ว૕ࠍ
ሶߩടㅦᐲ⸘▚ߦߪ OV (Optimal Velocity‫ᦨޔ‬ㆡㅦᐲ)
㔌ᢔ⊛ߦ⸃ᨆߔࠆᚻᴺߢ޽ࠆ[3]‫ޕ‬DEM ߢߪ☸ሶട
&
ㅦᐲ a ࠍᓸዊᤨ㑆Ⴧಽ 't ߢᏅಽㄭૃߒߡ⸘▚ߔࠆ‫ޕ‬
&
*
ߘߒߡ‫ޔ‬ㅦᐲ v ߅ࠃ߮૏⟎ x ࠍએਅߩᑼߢ᳞߼☸ሶ
ࡕ࠺࡞[4]ࠍេ↪ߔࠆ‫ޕ‬
ߘߒߡ‫ޔ‬᭴▽ߒߚࡕ࠺࡞ࠍ↪޿ߡ㓚ኂ‛߿ઁߩᱠⴕ
⠪ࠍ੤߃ߚ㓚ኂ࿁ㆱࠪࡒࡘ࡟࡯࡚ࠪࡦࠍⴕߞߚ‫ߐޕ‬
ࠄߦࠪࡒࡘ࡟࡯࡚ࠪࡦห᭽ߩታ㛎ࠍⴕ޿‫⚿ޔ‬ᨐࠍᲧ
セߒߡࡕ࠺࡞ߩ᦭ലᕈࠍᬌ⸽ߒߚ‫ޕ‬
& !"# ဳᱠⴕ⠪ࡕ࠺࡞ߩ᭎ⷐ$
DEM ဳᱠⴕ⠪ࡕ࠺࡞ߩ᭴▽ࠍⴕ߁ߦ޽ߚࠅ‫ޔ‬ᱠⴕ
⠪ࠍ☸ሶߣߒߡࡕ࠺࡞ൻߒߚ☸ሶߩടㅦᐲ⸘▚ߦߪ
ࠍᤨ‫ޘ‬ೞ‫ޘ‬⒖േߐߖࠆ‫ޕ‬
&
&
*
v t 't v t a t 't 't
&
&
&
x t 't x t v t 't 't
(3)
(4)
ߎߩࠃ߁ߦᣂߒ޿ᤨೞ t 't ߦ߅ߌࠆടㅦᐲࠍᢙ
୯Ⓧಽߔࠆߣ‫ᤨޔ‬ೞ t 't ߦ߅ߌࠆᄌ૏߅ࠃ߮ㅦᐲ
߇ᓧࠄࠇࠆ‫' ࠍ▚⸘ߩߎޕ‬t ߢ➅ࠅ㄰ߔߎߣߦࠃߞߡ
☸ሶߩㆇേ゠〔߇⸘▚ߢ߈ࠆ‫ޕ‬
ᧄ᧪ DEM ߢߪ☸ሶห჻߇ធ⸅ߒߚ㓙‫ޔ‬Voigt ࡕ࠺
ߥࠆน⢻ᕈ߇޽ࠆߣ⠨߃ࠄࠇࠆ‫ߢߎߘޕ‬㧘 i o j ᣇ
࡞ࠍ↪޿ߡធ⸅ജࠍ⸘▚ߒടㅦᐲࠍ᳞߼ࠆ߇‫ޔ‬ᱠⴕ
ะߦኻߒߡ☸ሶ i, j ߇ធ⸅ߔࠆᤨ㑆 't ij ࠍએਅߩᑼ
⠪ࡕ࠺࡞ߢߪ㕖ធ⸅⁁ᘒߢ☸ሶߩടㅦᐲࠍ⸘▚ߔࠆ
ࠃࠅ᳞߼ࠆ‫ޕ‬
ᔅⷐ߇޽ࠆ‫ޔߢߎߘޕ‬਄ㅀߩ OV ࡕ࠺࡞ࠍ↪޿ߡട
ㅦᐲ⸘▚ࠍⴕ߁ߎߣߢ DEM ဳᱠⴕ⠪ࡕ࠺࡞ࠍ᭴▽
& &
xi x j ri r j
&
&
v ni cos T ni v nj cos T nj
't ij
ߔࠆ‫ޕ‬
⛯޿ߡ‫ޔ‬᭴▽ߒߚࡕ࠺࡞ࠍ↪޿ߚ㓚ኂ࿁ㆱࠕ࡞ࠧ࡝
࠭ࡓߦߟ޿ߡㅀߴࠆ‫☸ޔߪߢ࡞࠺ࡕߩߎޕ‬ሶ i ߩ⋡
ᮡᣇะߦኻߒߡㅴⴕߩᅹߍߣߥࠆน⢻ᕈߩ޽ࠆ㓚ኂ
☸ሶࠍ್೎ߔࠆⷞ㊁㗔ၞ‫ⷞޔ‬㊁㗔ၞߦ฽߹ࠇࠆ☸ሶ
&
ߩౝታ㓙ߦᷫㅦࡌࠢ࠻࡞ v o ߩᓇ㗀ࠍฃߌࠆ☸ሶࠍ
್೎ߔࠆ⊒⃻㗔ၞࠍቯ⟵ߔࠆ[1]‫ⷞޕ‬㊁㗔ၞ߅ࠃ߮⊒
⃻㗔ၞࠍ࿑ 1 ߦ␜ߔ‫ޕ‬
i
ߘߒߡ‫ᤨޔ‬ೞ t ߢߩ☸ሶߩ૏⟎߅ࠃ߮ㅦᐲᖱႎ߆ࠄ
& &
't ij ᓟߩ☸ሶ i, j ߩ૏⟎ xic , x cj ࠍߘࠇߙࠇ᳞߼ࠆ‫ޕ‬
☸ሶ i c, j c ߩ૏⟎㑐ଥࠃࠅ☸ሶ i c ߩ⊒⃻㗔ၞౝߦ☸ሶ
j c ߩਛᔃ߇ሽ࿷ߔࠆ߆ุ߆್ቯߔࠆ‫☸ޕ‬ሶ j c ߇ሽ࿷
ߒߥ޿႐ว(࿑ 3(a))‫☸ޔ‬ሶ j ߪ☸ሶ i ߦᐓᷤߒߥ޿ߣ
&
⠨߃ࠄࠇࠆߚ߼‫ޔ‬ᷫㅦࡌࠢ࠻࡞ v o ߩᓇ㗀ࠍฃߌߥ޿
ߣߒߡ☸ሶ i ߩ⋡ᮡᣇะߦኻߒᦨ㜞ㅦᐲ v i max ࠍਈ
30
4ri
(5)
$
߃ࠆ‫৻ޕ‬ᣇ‫ޔ‬ሽ࿷ߒߚ႐ว(࿑ 3(b))‫☸ޔ‬ሶ j ߪ☸ሶ i
ߩㅴⴕߩᅹߍߦߥࠆߣ⠨߃ࠄࠇࠆߚ߼‫ޔ‬ᷫㅦࡌࠢ࠻
&
࡞ v o ߩᓇ㗀ࠍฃߌࠆ‫ޕ‬
3d
6d
Target direction
jc
i
i
j
ic
ic
: affected area
j
jc
: area of field of view
࿑ 1: ⷞ㊁㗔ၞ߅ࠃ߮⊒⃻㗔ၞ
&
(a) v o
㧔 ri ߪ☸ሶ i ߩ☸ሶඨᓘ㧕
&
(b) v o z 0
0
࿑ 3: ⊒⃻㗔ၞߢߩ㓚ኂ☸ሶ್ቯ
Obstacle
&
vo
i
j
T j T ni
T nj
&
vnj
Target
&
Movement vni
࿑ 2: ☸ሶ i, j ߩ☸ሶ૏⟎߅ࠃ߮ㅦᐲߩ㑐ଥ
㧔㤛⦡⍫ශߪ☸ሶߩㅴⴕㅦᐲࡌࠢ࠻࡞㧕
ⷞ㊁㗔ၞౝߦ㓚ኂ☸ሶ j ߩਛᔃ߇ሽ࿷ߒߥ޿႐ว‫ޔ‬
☸ሶ i ߪ๟ࠅߩ☸ሶ߆ࠄߩᓇ㗀ࠍฃߌߥ޿ߣߒߡ☸
ሶ i ߩ⋡ᮡᣇะߦኻߒᦨ㜞ㅦᐲ vi max ࠍਈ߃ࠆ‫৻ޕ‬ᣇ‫ޔ‬
ⷞ㊁㗔ၞౝߦ޽ࠆ☸ሶ j ߩਛᔃ߇ሽ࿷ߔࠆ႐ว‫ᤨޔ‬
ೞ t ߢ ߩ i o j ᣇ ะ ߦ ኻ ߔ ࠆ ☸ ሶ i, j ߩ ㅦ ᐲ
&
&
v ni cos T ni 㧘 v nj cos T nj ࠍߘࠇߙࠇ᳞߼ࠆ(࿑ 2)‫ޕ‬
&
&
v ni cos T ni d v nj cos T nj ߩ႐ว‫☸ޔ‬ሶ i ߪ☸ሶ j ߦㅊ
޿ߟ߆ߥ޿ߚ߼‫ޔ‬ᓇ㗀ࠍฃߌߥ޿ߣߒߡ☸ሶ i ߩ⋡
ᮡ ᣇ ะ ߦ ኻ ߒ ᦨ 㜞 ㅦ ᐲ v i max ࠍ ਈ ߃ ࠆ ‫ ޕ‬ㅒ ߦ
&
&
v ni cos T ni ! v nj cos T nj ߩ႐ว‫ ޔ‬i o j ᣇะߦኻߒߡ
☸ሶ i ߪ☸ሶ j ߦㄭߠ޿ߡ޿ߊߚ߼‫ޔ‬ㅴⴕߩᅹߍߦ
&
ᷫㅦᐲ v o ߪᑼ(2)ߩᦨㆡㅦᐲ㑐ᢙࠍ೑↪ߒߡએਅ
ߩᑼࠃࠅ᳞߼ࠆ(࿑ 4(a))‫ޕ‬
D V 'xij v ni ˜ cos T nic ˜ 't
&
vo
'x
&
ij
& & & &
min xi x j , xi x cj
$
$
OPQ$
&
ߐࠄߦ‫ ޔ‬vo ࠍ↪޿ߡ‫ᤨޔ‬ೞ t 't ߦ߅ߌࠆ i o j ᣇ
ะߦኻߔࠆㅴⴕᣇะ T nic ࠍ
T nic
t 't
&
&
§ v ni ˜ cosT nic t v o · sin T jc
¸˜
$ ORQ$
cos 1 ¨
¨
¸ sin T
vi max
jc
©
¹
&
ߣߒ‫ޔ‬ㅴⴕㅦᐲ v ni ߪએਅߩࠃ߁ߦ᳞߼ࠆ(࿑ 4(b))‫ޕ‬
­ v&ni
°
®&
° v ni
¯
vi max
T
ni c
T jc d S 6
S·
§
vi max ˜ cos¨ T nic T jc ¸
6¹
©
T
ni c
T jc ! S 6
$ OSQ$
ߎߩࠕ࡞ࠧ࡝࠭ࡓࠍ↪޿ࠆߎߣߢ‫⋡ޔ‬ᮡᣇะ਄ߦ㓚
ኂ‛߇ሽ࿷ߒߡ߽ή㚝ߥᷫㅦ߿㕒ᱛࠍߖߕ‫ޔ‬ㅴⴕᣇ
ะߩߺࠍ೙ᓮߒߡ㓚ኂࠍ࿁ㆱߢ߈ࠆߣ⠨߃ࠄࠇࠆ‫ޕ‬
Condition
X-Y coordinate([m], [m])
Target direction
Max speed ( v max ) [m/s]
No.
No.1
No.2
No.1
No.2
No.1
No.2
(1)
(-2,0)
(0,0)
X
0
0.86
0
(2)
(-2,0)
(-2,0)
X
X
0.86
0.43
(3)
(-2,0)
(2,0)
X
-X
0.86
0.86
⴫ 1: ࿁ㆱࠪࡒࡘ࡟࡯࡚ࠪࡦࡄ࡜ࡔ࡯࠲
Obstacle
&
vo
T jc
i
T ni
jc
ࠍ࿑ 5 ߦ␜ߔ‫ޕ‬ᱠⴕ⠪ߩ᜼േߪ࿑ 6 ߦ␜ߔࠃ߁ߦⵍ
Target
j
&
vni
㛎⠪߹ߚߪ㓚ኂ‛ߩೋᦼ૏⟎߅ࠃ߮ㅴⴕᣇะߪࠪࡒ
ࡘ࡟࡯࡚ࠪࡦߣห᭽ߣߒ‫ⵍޔ‬㛎⠪ߦߪ⋡ᮡᣇะߦኻ
(a) t
Obstacle
i
ࡊ࠴ࡖࠪࠬ࠹ࡓࠍ↪޿ߡ⸘᷹ߒߚ‫⸘ޕ‬᷹ᤨߩࠨࡦࡊ
࡝ࡦࠣ๟ᵄᢙߪ 200[Hz]ߣߒߚ‫ޕ‬ฦ᧦ઙߦ߅ߌࠆⵍ
Movement
&
vo
㛎⠪ߦ 4 ߟߩࡑ࡯ࠞ࡯ࠍขࠅઃߌ‫ࡖࠠࡦ࡚ࠪ࡯ࡕޔ‬
T jc
ߒߡ⥄ὼߦᱠߊࠃ߁ᜰ␜ߒߚ‫ⵍޔߚ߹ޕ‬㛎⠪ߦߪ⋡
jc
Target
ᮡᣇะ߇᣿⏕ߦߥࠆࠃ߁‫ߡ޿↪ࠍࡦ࡯ࠦ࡯࡜ࠞޔ‬᏷
j
3[m]ߩㅢ〝ࠍ⸳ߌߚ(࿑ 5)‫ޕ‬
T ni
1.5m
1.5m
Movement&
vni
y
(b) t 't
x
࿑ 4: ☸ሶ i ߩㅦᐲࡌࠢ࠻࡞⸘▚
࿑ 5: ታ㛎ߩ᭽ሶ((1)㓚ኂ࿁ㆱߩ႐ว)
T 㓚ኂ࿁ㆱ⹜㛎$
᭴▽ߒߚࡕ࠺࡞ߩ᦭ലᕈࠍᬌ⸽ߔࠆߚ߼‫ޔ‬㓚ኂ‛߿
ઁߩᱠⴕ⠪ࠍ࿁ㆱߔࠆࠪࡒࡘ࡟࡯࡚ࠪࡦ߅ࠃ߮ታ㛎
ࠍⴕߞߚ‫⹜ߩࠄࠇߎޕ‬㛎ߢߪ‫(ޔ‬1)㕒ᱛߒߚ㓚ኂ‛ࠍ
࿁ㆱߔࠆ႐ว(㓚ኂ࿁ㆱ)‫(ޔ‬2)㓚ኂ߇ห৻ᣇะߦ⒖േ
ߒߡ޿ࠆ႐ว(ㅊ޿⿧ߒ)‫(ޔ‬3)෻ኻᣇะߦ⒖േߒߡ޿
ࠆ႐ว(ߔࠇ㆑޿)ߦߟ޿ߡᬌ⸽ߒߚ‫ޕ‬એਅߦ࿁ㆱࠪ
ࡒࡘ࡟࡯࡚ࠪࡦ߅ࠃ߮ታ㛎ߦߟ޿ߡㅀߴࠆ‫ޕ‬
TJ% ࿁ㆱࠪࡒࡘ࡟࡯࡚ࠪࡦ$
(a) ᱜ㕙
(b) ஥㕙
(c) ⢛㕙
࿑ 6: ⵍ㛎⠪ߩࡑ࡯ࠞ࡯ขࠅઃߌ૏⟎
㧔ฝ⢋‫ޔ‬Ꮐ⢋‫ޔ‬⢛ਛ‫࠻࠶࠮ࡈࠝޔ‬㧕
⴫ 1 ߦฦ᧦ઙߢߩ 2 ☸ሶߩ X-Y ೋᦼᐳᮡ‫⋡ޔ‬ᮡᣇ
ะ߅ࠃ߮ᦨᄢㅦᐲࠍ␜ߔ‫ߪߢࡦ࡚ࠪ࡯࡟ࡘࡒࠪᧄޕ‬
☸ሶඨᓘࠍ 0.2[m]‫ᤨޔ‬㑆Ⴧಽࠍ 1.0˜10-4[s]ߣߒߚ‫ޕ‬
TJ& ࿁ㆱታ㛎$
ࠪࡒࡘ࡟࡯࡚ࠪࡦห᭽ߩታ㛎ࠍⴕߞߚ‫ޕ‬ታ㛎ߩ᭽ሶ
U ⚿ᨐ߅ࠃ߮⠨ኤ$
ฦ᧦ઙߦ߅ߌࠆ࿁ㆱࠪࡒࡘ࡟࡯࡚ࠪࡦߩ 5 ⑽㑆ߩ
☸ሶ゠㆏ࠍ࿑ 7 ߦ␜ߔ‫☸⊕ޕ‬ሶߪ NO.1‫ޔ‬㤥☸ሶߪ
No.2 ߩ☸ሶࠍߘࠇߙࠇ⴫ߒߡ޿ࠆ‫ޕ‬ᰴߦ‫ޔ‬࿁ㆱታ㛎
ߦ߅ߌࠆⵍ㛎⠪ߩᱠⴕ゠〔ࠍ࿑ 8 ߦ␜ߔ‫ޕ‬࿑ 7,8 ࠃ
੹ᓟߪოߩᓇ㗀ࠍ⠨ᘦߒߚࡕ࠺࡞ࠍ⠨߃ࠆ‫ߦࠄߐޕ‬
ࠅ‫ޔ‬࿁ㆱࠪࡒࡘ࡟࡯࡚ࠪࡦߩ☸ሶ゠㆏ߪ࿁ㆱታ㛎ߩ
ኻ⽎ᢙࠍჇ߿ߒ⟲㓸ߢߩⴕേ․ᕈࠍ⺞ᩏߒ‫ޔ‬ᱠⴕ⠪
ᱠⴕ゠㆏ߣࠃߊ৻⥌ߒߡ޿ࠆ‫ޔߚ߹ޕ‬ฦ࿑ߪ৻ቯᤨ
ߩⴕേ․ᕈࠍ⹦⚦ߦ⴫⃻ߒߚࡕ࠺࡞ߩ᭴▽ࠍ⋡ᜰߔ‫ޕ‬
㑆㑆㓒ߢ૏⟎ᐳᮡࠍࡊࡠ࠶࠻ߒߡ޿ࠆ‫࠻࠶ࡠࡊޕ‬㑆
㓒ࠍ⷗ࠆߣࡃ࡜ߟ߈߇⷗ࠄࠇߥ޿ߚ߼‫࡯࡟ࡘࡒࠪޔ‬
ෳ⠨ᢥ₂$
࡚ࠪࡦߣታ㛎ߩ෺ᣇߦ߅޿ߡ৻ቯㅦᐲߢ⒖േߒߡ޿
[1] E. Harada, H. Gotoh, Y. Maruyama, Proposal of
ࠆߎߣ߇ࠊ߆ࠆ‫ޕ‬એ਄ߩ⚿ᨐ߆ࠄ‫⎇ᧄޔ‬ⓥߢ᭴▽ߒ
DEM-base Crowd Refuge Model with the Optimal
ߚ DEM ဳᱠⴕ⠪ࡕ࠺࡞ߪ᦭ലߢ޽ࠆߣ⸒߃ࠆ‫ޕ‬
Velocity Model, Japan Society of Civil Engineers,
߹ߚ‫ޔ‬ታ㛎ߢߪⵍ㛎⠪߇⒖േᓟߦ x =2[m]ઃㄭߦ೔
Vol.51 (2007) 553-558.
㆐ߒߚᤨ‫࠻࠶ࡠࡊޔ‬㑆㓒߇⁜ߊߥࠅ‫ޔ‬ᱠⴕㅦᐲ߇ૐ
[2] K. Nishinari, Jammology Physics of Self-driven
ਅߔࠆ௑ะ߇⷗ࠄࠇࠆ‫࠴ࡊࡖࠠࡦ࡚ࠪ࡯ࡕߪࠇߎޕ‬
Particles Toward Solution of All Jams, Tenth Annual
ࡖߩࡑ࡯ࠞ࡯⹺⼂▸࿐ߩ೙㒢߇޽ߞߚߚ߼‫ޔ‬
Japanese-American Frontiers of Science Symposium
x =2[m]ߢ㕒ᱛߔࠆࠃ߁ᜰ␜ߒߚߚ߼ߢ޽ࠆ‫ࡒࠪޕ‬
(2007).
ࡘ࡟࡯࡚ࠪࡦߢߪ⋡ᮡᣇะߦ⒖േߒ⛯ߌࠆࠃ߁ߦ⸳
[3] P.A. Cundall, O.D.L.Strack, A Discrete Numerical
ቯߒߡ޿ࠆ߇‫ޔ‬㓚ኂߩ࿁ㆱᓟߥߩߢ㓚ኂࠍ࿁ㆱߔࠆ
Model for Granular Assemblies Geo-technique, Vol.29
⚿ᨐߦᄢ߈ߥᓇ㗀ߪߥ޿ߣ⠨߃ࠄࠇࠆ‫ޕ‬
No.1 (1979) 47-65.
[4] M. Bando, K. Hasebe, A. Nakayama, A. Shibata and
V ߹ߣ߼$
Y. Sugiyama, Dynamical model of traffic congestion
ᧄ⎇ⓥߢߪ‫ޔ‬DEM ߦ OV ࡕ࠺࡞ࠍេ↪ߔࠆߎߣߢ‫ޔ‬
DEM ဳᱠⴕ⠪ࡕ࠺࡞ߩ᭴▽ࠍⴕߞߚ‫ࠍ࡞࠺ࡕߩߘޕ‬
and numerical simulation. Phys. Rev. E, Vol.51 No.2
(1995) 1035- 1042.
↪޿ߡ㓚ኂࠍ࿁ㆱߔࠆࠪࡒࡘ࡟࡯࡚ࠪࡦࠍⴕߞߚ⚿
ᨐ‫ޔ‬ታ㓙ߩᱠⴕ⠪ห᭽ߩᱠⴕ᜼േ߇⷗ࠄࠇߚ‫ޕ‬
1.5m
1.5m
1.5m
2m
-2m
y
-1.5m
2m
-2m
x
y
-1.5m
2m
x
(a) Condition No.1
-2m
y
-1.5m
(b) Condition No.2
(c) Condition No.3
࿑ 7: ࿁ㆱࠪࡒࡘ࡟࡯࡚ࠪࡦߦ߅ߌࠆ☸ሶ゠㆏
(a) Condition No.1
(b) Condition No.2
࿑ 8: ࿁ㆱታ㛎ߦ߅ߌࠆⵍ㛎⠪ߩᱠⴕ゠㆏
(c) Condition No.3
x