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1 Vol. 29 No. 4, pp , Optimization of Personal Distribution for Evacuation Guidance basedonvectorfield Masafumi Okada and Teruisa Ando It is an important issue to make a disaster reduction plans for overcrowded population in urban cities. In tis paper, we focus on evacuation guidance to prevent te damage from spreading. Te personal navigation system cannot deal wit evacuation guidance for te uman crowd wit large numbers of individuals because of time constrain and extraordinary communication error. An implicit guidance based on dynamical caracteristic of swarm beavior is efficient and effective by a few guidance operators. We propose a modeling and control metod of swarm based on vector field. Te evacuee beavior model contains intention of evacuation, field of view, collision avoidance and evacuee group, wic are represented by vector field. Te guidance operator model contains indicating direction. By giving te desired vector field tat indicates te safe route for evacuation, te position of guidance operators are optimally distributed. Moreover, te number of guidance operators is minimized based on te contribution index. Te proposed modeling and control metod is applied to te swarm robot and te effectiveness is evaluated by te experiments. Key Words: Disaster Reduction, Evacuation Guidance, Vector Field, Swarm Robot 1. [1] [2] [3] [4] Tokyo TECH [5] [6] Fink [7] Kerr [8] Simizu [9] Pimenta [10] [11] SPH Smooted Particle Hydrodynamics Vaugan [12]

2 Fig. 1-(a) Fig. 1-(b) Reynolds Boid model [13] (a) Collision Avoidance (b) Velocity Matcing (c) Flock Centering [14] Boid model (b) (a) (c) 2. 2 x v f = v f (x) v f (x) x v f (x) =a0 + a1x + a2x 2 + a3x 3 =Θφ(x) 1 2 Θ= φ(x) = a0 a1 a2 a3 1 x T x 2 T x 3 T i i T 3 4 ai (i =0, 1, 2 ) x x i = x i x i 1 y x i 2 y 2 y i i T 5 x = x y i T 6 v f Fig. 2 ξ j i (j =1, 2) (i =1, 2, 3, ) ξ j i xi v = ξ j i+1 xi 7 xi (v, xi) 2 Θ Fig. 2 Fig Boid model (a) x xj =[x j y j ] T j v p j Fig. 2 Defined evacuation route Fig. 1 Evacuation and non-available routes Fig. 3 Obtained evacuation vector field JRSJ Vol. 29 No May, 2011

3 397 Fig. 4 Parameter definition for collision avoidance v p j p c (x) = 1+exp{a p ( rj b p )} r p j = xj x r j r j 8 9 a p c p b p Fig. 5 Human flow wit large number of persons b p (Δθ p j )= γ p Φ Ψ 1+exp α p (Δθ p j βp ) + δp fi fififi ρ fffi Δθ p j = tan 1 yj y fififi θ p x j x α p β p γ p δ p δ p b p v p j j Δθ p j x i vf θ p r p j Fig. 4 0 π β p 120 ±60 [15] β p = π/3 v p j 120 i j x v w c w v w (x) = 1+exp{a w ( r w b w )} r w r w 12 a w b w c w r w x 8 a p c p 10 γ p 12 a w b w c w Fig. 5 Fig Mawson [16] Affiliative model Boid model (c) v a i Fig. 6 Simulation result of swarm beavior v a i (x) =c a r a 13 r a = x a x 14 x a x c a 2. 5 xi i xi[k +1]=xi[k]+vi(xi[k])T vi = v f + nx v p j + lx j i j=1 15 v w j + v a i 16 T n l Fig Fig. 6 vi

4 v g x v g (x) = c g 1+exp{a g ( r g b g )} R(θg ) r g = x g x " 1 0 # Fig. 7 Vector field via guidance operator a g c g x g b g b g (Δθ g )= γ g 1+exp{α g (Δθ g β g )} 19 Δθ g x vi r g a g c g α g γ g β g β p π/3 R(θ) R(θ) = " cos θ sin θ sin θ cos θ # 20 θ g R(θ g ) Fig. 7 i vi vi = v f + nx lx mx v p j + v w j + v g j + va i j i j=1 j=1 m bv f 2. 1 Fig. 8 bv f (x) =b Θφ(x) 22 bv f 21 bv f J x r J = kx fl fl fl fl flbv f (x r j) vi(x r j ) j=1 fl 2 23 Fig. 8 Definition of modified evacuation routes J a b c x g θ g T J x g x g δx 24 x g J θ g θ g δθ 25 θ g δx δθ x r Fig JRSJ Vol. 29 No May, 2011

399 Fig. 11 Appearance of swarm robot Fig. 9 Positional and directional optimization of guidance operators Fig. 10-4 2 Fig. 10-4 Fig. 10-1 Fig. 10-4 4. Fig. 10 Optimization of position direction number of guidance operators W = nx i=1 c g 1+exp{a g ( r p i bg )} 26 Fig.

5 399 Fig. 11 Appearance of swarm robot Fig. 9 Positional and directional optimization of guidance operators Fig Fig Fig Fig Fig. 10 Optimization of position direction number of guidance operators W = nx i=1 c g 1+exp{a g ( r p i bg )} 26 Fig. 10 W Fig. 11 [17] SH-2 StarGazer LAN v f 120 v p LAN Fig

400 Fig. 12 Guidance experiment wit 13 evacuees and 2 guidance operators 3. 4 2 Fig. 10-4 Fig. 12-4 5. 1 2 3 4 5 CREST [1] 2001. [2] vol.45, no.11, pp.1164 1174, 2004. [3] vol.45, no.12, pp.

of 2008 International Conference on Robotics and Automation, pp.1471 1476, 2008. [ 8 ] W. Kerr and D.F. Spears: Robotic simulation of gases for a surveillance task, Proc.

6 400 Fig. 12 Guidance experiment wit 13 evacuees and 2 guidance operators Fig Fig CREST [1] [2] vol.45, no.11, pp , [3] vol.45, no.12, pp , [4] 2004, pp.55 56, [5] [6] DEWS [ 7 ] J. Fink, M.A. Hsie and V. Kumar: Multi-robot manipulation via caging in environments wit obstacles, Proc. of 2008 International Conference on Robotics and Automation, pp , [ 8 ] W. Kerr and D.F. Spears: Robotic simulation of gases for a surveillance task, Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp , [ 9 ] M. Simizu, A. Isiguro, T. Kawakatsu, Y. Masubuci and M. Doi: Coerent swarming from local interaction by exploiting molecular dynamics and stokesian dynamics metods, Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp , [10] L.C.A. Pimenta, M.L. Mendes, R.C. Mesquita and G.A.S. Pereira: Fluids in electrostatic fields: An analogy for multirobot control, IEEE TRANSACTIONS ON MAGNETICS, vol.43, no.4, pp , [11] L.C.A. Pimenta, N.Micael, R.C. Mesquita, G.A.S. Pereira and V. Kumar: Control of swarms based on ydrodynamic models, Proc. of 2008 International Conference on Robotics and Automation, pp.1 6, [12] R. Vaugan, N. Sumpter, J. Henderson, A. Frost and S. Cameron: Robot control of animal flocks, Proc. of te 1998 IEEE ISIC/CIRA/ISAS Joint Conference Gaitersburg, pp , [13] C.W. Reynolds: Flocks, erds, and scools:a distributed beavioral model, Computer Grapics, vol.21, no.4, pp.25 34, July [14] 26 CD ROM 3O1 06, [15] [16] A.R. Mawson: Mass Panic and Social Attacment : Te Dynamics of Human Beavior. Asgate Pub Co, [17] A2 F13, JRSJ Vol. 29 No May, 2011

7 401 Masafumi Okada PD IEEE Teruisa Ando

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