Flocking with Confrontation
xi (t  1)  xi (t )  vi (t )t
Vicsek model (Vicsek T, PRL, 1995)
 The only rule of the model is at each time step a given
particle driven with a constant absolute velocity assumes
that average direction of motion of the particles in its
neighborhood of radius r with some random perturbation
added.
• Particles are driven with a constant absolute
velocity and at each time step assume the
average direction of motion of the particles in
their neighborhood with some random
perturbation added.
• Numerical evidence: kinetic phase transtition
from no transport (zero average velocity, |va|=0)
to finite net transport through spontaneous
symmetry breaking of the rotational symmetry.
The transition is continuous
• Net momentum of the interacting particles
is not conserved, va~0,1.
• 社会力的概念是Helbing在研究人群流动时提出的。
由于微观个体之间存在着内在的协同性和排斥性，
造成了群体流动的整体复杂性，他提出以社会力
（Social Force）的形式对行人间相互作用具体化
和模型化，并用Langevin方程描述行人移动的动
力学过程。这一问题研究的标志性工作是Helbing
于1995年在PRE上发表的文章。2000年Helbing
等人又以社会力模型为基础，在Nature上发表了
关于恐慌人群疏散的研究工作，引起了多个体领
域研究者们的广泛响应。
• If r is the next edge of this polygon to reach, his/her
desired direction e (t) of motion will be where r~(t)
denotes the actuaL position of pedestrian n at time t.
• repulsive effects
• the repulsive potential
is a monotonic
decreasing function of b with equipotential
lines having the form of an ellipse that is
directed into the direction of motion.
Flocking with Confrontation
Social force model for pedestrian dynamics (Helbing D.,
Molnar P., Phys Rev E, 1995)
Simulating dynamical features of escape panic. (Helbing
D., Farkas I., Vicsek T, Nature, 2000)
Optimal traffic organization in ants
under crowded conditions
•
Audrey Dussutour1,2, Vincent
Fourcassie´ 1, Dirk Helbing3
& Jean-Louis Deneubourg2
NATURE |VOL 428 | 4 MARCH 2004
• Hierarchical group dynamics in pigeon
flocks
• Vicsek，2010 nature
Effective leadership and decision making in animal groups on the
move， I. D. Couzin, Nature, 2005.
Interaction & information
It may be unreasonable to assume that group members have
the capacity for individual recognition.
Asumptions:
 the absence of complex signalling mechanisms
 not possible for group members to establish who has
and has not got information
Questions:
How information about the location of resources, or of a
migration route, can be transferred within groups;
How individuals can achieve a consensus when informed
individuals differ in their preferences;
Starting conditions:
Each simulation run was started with randomized individual positions and
orientations.
Group size
Group sizes here are comparable to the size of schools, flocks or herds, of
many species1–4,13,19, but smaller than large aggregates such as honeybee
colonies7,8, owing to the nonlinear increase in computer processing time
required as N increases. Our results, however, are likely to be independent of
absolute group size, within the constraints of maintaining cohesion of group
members22. To automatically test whether groups remained cohesive we used
the equivalence class technique described in refs 18, 19.
Group direction
To quantify group direction h we create a vector extending from the group’s
centroid calculated at time tft-50t to the centroid calculated at tft, where tf,
the final time step, is 2,500. In Figs 1 and 2 we calculated the mean angular
deviation s for 400 replicates, equivalent to calculating the linear standard
deviation20, which we normalized so that its minimum value is 0, corresponding
to no information transfer (groups move in random directions), and its maximum
value is 1, corresponding to the motion of the simulated groups always being
exactly aligned with g.
Elongation
Elongation was measured by creating a bounding box around the group aligned
with the direction of travel and calculating the ratio of the length of the axis
aligned with the group direction, to that perpendicular to group direction.
The Local Interactions
Groups are composed of N individuals. Each individual with
position vector ci(t), direction vector vi(t), and speed si, attempts
to maintain a minimum distance a between itself i and others j at all
times by turning away from neighbours within that range
Avoidance is the highest priority
Attractions
Informed individuals balance the influence of preferred direction and
social interactions
nonlinear effect of group size
As group size became larger this relationship became increasingly nonlinear
(Fig. 1a), meaning that the larger the group, the smaller the proportion of
informed individuals needed to guide the group with a given accuracy.
400 replicates, w=0.5; a=1, r =6, g =0, t =0.2 s, q 2, si =as-1
corresponding to fish
In a given time step, informed individuals find themselves moving in a similar
direction (here within a 20-degree arc) to their preferred direction, w is reinforced (by
winc, up to a maximum, wmax), otherwise it is reduced (by wdec, to a minimum of 0)
w, wmax = 0.4
n1 = 5, n2 = 5
n1 = 6, n2 = 5
n1 = 5, n2 = 5
n1 = 6, n2 = 5
n1 = 6, n2 = 4
n1 = 11, n2 = 10
n1 = 11, n2 = 9
n1 = 6, n2 = 4
winc =0.012
wmax = 0.0008
winc =0.012
wmax = 0.0008
w-> w:winc :wmax
or w-> w:-wdec :0
n1 = 10, n2 = 10
• Hunting in groups for
gregarious prey is
such a widespread
phenomenon in the
animal kingdom that it
comes as a surprise
that the first simple
model of the process
has only just been
published, in the New
Journal of Physics1.
• Bonabeau, E., Theraulaz, G. & Deneubourg,
J.-L, : a model of division of labor in social
insects.
• Perspective of seeing the systems as the
emergence of macroscopic patterns out of
processes and interactions defined at the
microscopic level.
• Can be extended to social insects to show
that complex collective behavior may emerge
from interactions among individuals that
exhibit simple behaviors.
•
•
Bonabeau, E., Sobkowski, A. Theraulaz, G., Denebourg, J.-L., Adaptive Task Allocation
Inspired by a Model of Division of Labor in Social Insects, in Lundh, D. et al. (Eds.):
Biocomputing and Emergent Computation: Proceedings of BCEC'97, pp. 36-45, 1997.
Bonabeau, E., Theraulaz, G. & Deneubourg, J.-L. (1996). Quantitative study of the fixed
threshold model for the regulation of division of labour in insect societies. Proc. Roy. Soc.
London B 263, 1565-1569.
• Bonabeau et al,:
• Information sharing: pheromone
(hormone).
• Threshold: The more individual
performs a task, the lower is its
response threshold with respect to
stimuli associated with this task, and
vice-versa.
• Learn to update the threshold.
• Some follow up works using pheromone
in task allocation
Stick pulling experiment
•
•
Ling Li, Alcherio Martinoli, and Yaser S. Abu-Mostafa, Emergent Specialization in
Swarm Systems, H. Yin et al. (Eds.): IDEAL 2002, LNCS 2412, pp. 261–266.
Martinoli, A., Mondada, F.: Collective and cooperative group behaviours:
Biologically inspired experiments in robotics. In Khatib, O., Salisbury, J.K., eds.:
Proceedings of the Fourth International Symposium on Experimental Robotics
(1995). Lecture Notes in Control and Information Sciences, Vol. 223. SpringerVerlag, Berlin (1997) 3–10
• a team of robots search a circular arena and pull
sticks out of holes in the ground.
• The length of a stick has been chosen so that a
single robot is incapable of pulling a stick out of
the ground completely on its own, but
collaboration between two robots is sufficient for
solving this task.
• Agents learn the maximal length of time that a
robot waits for the help of another robot while
holding a sick (gripping time parameter, GTP).
• Researchers have all agreed that Specialization
and division of labor should not be a priori,
should develop in the process of system
development.
• Initially homogenous agents turn to be
heterogeneous agents. Must involve adaptation,
learning.
• We do not favor central planning, or global
information sharing
• ULB的Deneubourg与EPFL的Matinoli等人
进行了机器人与生物融合的第一个实验。
他们将有蟑螂2倍大小的机器人，覆盖上具
有蟑螂体味的滤纸，与蟑螂一起放在一个
实验平台上，观察有机器人时和没有机器
人时，蟑螂在两个遮光板下躲藏的个数的
区别。发现蟑螂很好地接受了机器人（如
图）。