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.

Flocking with Confrontation

Vicsek model (Vicsek T, PRL, 1995)

ttvtxtx iii )()()1(

• 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

Simulating dynamical features of escape panic. (Helbing D., Farkas I., Vicsek T, Nature, 2000)

Social force model for pedestrian dynamics (Helbing D.,

Molnar P., Phys Rev E, 1995)

Optimal traffic organization in antsunder 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.

Asumptions: the absence of complex signalling mechanisms not possible for group members to establish who has and has not got information

Interaction & information

It may be unreasonable to assume that group members have the capacity for individual recognition.

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 sizeGroup 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 directionTo quantify group direction h we create a vector extending from the group’s centroid calculated at time tft-50t to the centroid calculated at tft, 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.

ElongationElongation 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 InteractionsGroups 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, =0.5; =1, =6, =0, t =0.2 s, 2, si =s-1 corresponding to fish

, max = 0.4

In a given time step, informed individuals find themselves moving in a similar directio

n (here within a 20-degree arc) to their preferred direction, is reinforced (by inc, up t

o a maximum, max), otherwise it is reduced (by dec, to a minimum of 0)

inc =0.012

max = 0.0008

n1 = 5, n2 = 5 n1 = 6, n2 = 5 n1 = 6, n2 = 4

n1 = 5, n2 = 5 n1 = 6, n2 = 5 n1 = 6, n2 = 4

n1 = 10, n2 = 10 n1 = 11, n2 = 10 n1 = 11, n2 = 9

inc =0.012

max = 0.0008

:inc :max or :-dec :0

• 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 (hormo

ne). • Threshold: The more individual perform

s 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. Springer-Verlag, 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）。