How does the interaction radius affect the performance of intervention on collective behavior?

<div><p>The interaction radius <i>r</i> plays an important role in the collective behavior of many multi-agent systems because it defines the interaction network among agents. For the topic of intervention on collective behavior of multi-agent systems, does <i>r</i> also affect the intervention performance? In this paper we study whether it is easier to change the convergent heading of the group by adding some special agents (called shills) into the Vicsek model when <i>r</i> is larger (or smaller). Two kinds of shills are considered: fixed-heading shills (like leaders that never change their headings) and evolvable-heading shills (like normal agents but with carefully designed initial headings). We know that with the increase of <i>r</i>, two contradictory effects exist simultaneously: the influential area of a single shill is enlarged, but its influence strength is weakened. Which factor dominates? Through simulations and theoretical analysis we surprisingly find that <i>r</i> affects the intervention performance differently in different cases: when fixed-heading shills are placed together at the center of the group, larger <i>r</i> gives a better intervention performance; when evolvable-heading shills are placed together at the center, smaller <i>r</i> is better; when shills (either fixed-heading or evolvable-heading) are distributed evenly inside the group, the effect of <i>r</i> on the intervention performance is not significant. We believe these results will inspire the design of intervention strategies for many other multi-agent systems.</p></div

Nondestructive Intervention to Multi-Agent Systems through an Intelligent Agent

<div><p>For a given multi-agent system where the local interaction rule of the existing agents can not be re-designed, one way to intervene the collective behavior of the system is to add one or a few special agents into the group which are still treated as normal agents by the existing ones. We study how to lead a Vicsek-like flocking model to reach synchronization by adding special agents. A popular method is to add some simple leaders (fixed-headings agents). However, we add one intelligent agent, called ‘shill’, which uses online feedback information of the group to decide the shill's moving direction at each step. A novel strategy for the shill to coordinate the group is proposed. It is strictly proved that a shill with this strategy and a limited speed can synchronize every agent in the group. The computer simulations show the effectiveness of this strategy in different scenarios, including different group sizes, shill speed, and with or without noise. Compared to the method of adding some fixed-heading leaders, our method can guarantee synchronization for any initial configuration in the deterministic scenario and improve the <i>synchronization level</i> significantly in low density groups, or model with noise. This suggests the advantage and power of feedback information in intervention of collective behavior.</p></div

Examples of the moving route from location of agent 1 () to location of agent 2 () for the shill (starting from location ).

<p>The big dash-line square indicates the current group area (note that to show ideas of the shill route, for convenience, the group area shown here is supposed to be static. In fact, the actual consistent moving strategy considers the cases that normal agents are moving when the shill moves, i.e., the group area keeps changing, which is much more complicated.). Two moving routes for the shill are shown: <b>(a) a simple U-turn route</b>: first it goes forward to a location which is much far away from the whole group(dash line part (1)), then it makes a big U-turn (dash line parts of (2)–(3)–(4)) far away outside the group area and gets back to the left side of the whole group, finally goes forward and affects agent (dash line part (5)). Its heading is set to be zero in parts (1) and (5), while it can have different headings during (2)–(3)–(4) because there are no neighboring agents. <b>(b) A more efficient route</b> for the shill moving from agent to agent . Radius of the small dash line circle centered at the shill represents the neighborhood size which is the same as the radius of normal agents. The shill tries to find a shorter route which maintains a ‘safe’ distance (larger than ) away from any normal agent when its heading is not zero. It is much more efficient than the simple U-turn route.</p

Synchronization level(mean ) for respectively in the following cases: self-organized without any intervention; one intelligent shill with is added into the group; and fixed-heading simple shills are added into the group respectively.

<p>Synchronization level(mean ) for respectively in the following cases: self-organized without any intervention; one intelligent shill with is added into the group; and fixed-heading simple shills are added into the group respectively.</p

Comparisons of different soft control strategies in the <i>evolvable-heading-shill</i> scenario with <i>ρ</i>_<i>n</i> = 1 and <i>θ</i>_<i>s</i> = <i>π</i>/4.

<p>Comparisons of different soft control strategies in the <i>evolvable-heading-shill</i> scenario with <i>ρ</i>_<i>n</i> = 1 and <i>θ</i>_<i>s</i> = <i>π</i>/4.</p

Examples of initial positions of adding 25 shills into a group of 225 normal agents inside a 15 × 15 square.

<p>Blue dots represent normal agents. Red stars represent shills. Short lines connected to the blue dots or red stars represent their headings. Here initial headings of all normal agents are set as <i>zero</i> and initial headings of shills are <i>π</i>/2. (A) <i>Centered</i> shills; (B) <i>Distributed</i> shills.</p

System size effect on soft control performance (avg. <i>T</i>) in the <i>evolvable-heading-shill</i> scenario with <i>l</i> = 25.

<p>(A) and (C) show how soft control performance (avg. Δ<i>θ</i>) change when <i>n</i> increases (by increasing <i>M</i> with fixed <i>ρ</i>_<i>n</i>); (B) and (D) show how soft control performance (avg. Δ<i>θ</i>) change when <i>n</i> increases (by increasing <i>ρ</i>_<i>n</i> with fixed <i>M</i>).</p