text: Unraveling the nature of the communication model that governs which two individuals in a swarm interact with each other is an important line of inquiry in the collective behavior sciences. A number of models have been proposed in the biological swarm literature, with the leading models being the metric, topological, and visual models. The hypothesis evaluated in this manuscript is whether the choice of a communication model impacts the performance of a tasked artificial swarm. The biological models are used to design coordination algorithms for a simulated swarm, which are evaluated over a range of six swarm robotics tasks. Each task has an associated set of performance metrics that are used to evaluate how the communication models fare against each other. The general findings demonstrate that the communication model significantly affects the swarm's performance for individual tasks, and this result implies that the communication model-task pairing is an important consideration when designing artificial swarms. Further analysis of each tasks' performance metrics reveal instances in which pairwise considerations of model and one of the various experimental factors becomes relevant. The reported research demonstrates that the artificial swarm's task performance can be increased through the careful selection of a communications model.
  @cite_28: Schools of fish and flocks of birds are examples of self-organized animal groups that arise through social interactions among individuals. We numerically study two individual-based models, which recent empirical studies have suggested to explain self-organized group animal behavior: (i) a zone-based model where the group communication topology is determined by finite interacting zones of repulsion, attraction, and orientation among individuals; and (ii) a model where the communication topology is described by Delaunay triangulation, which is defined by each individual's Voronoi neighbors. The models include a tunable parameter that controls an individual's relative weighting of attraction and alignment. We perform computational experiments to investigate how effectively simulated groups transfer information in the form of velocity when an individual is perturbed. A cross-correlation function is used to measure the sensitivity of groups to sudden perturbations in the heading of individual members. The results show how relative weighting of attraction and alignment, location of the perturbed individual, population size, and the communication topology affect group structure and response to perturbation. We find that in the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction. This phenomenon has been seen in self-organized animal groups in both experiments and nature.
  @cite_48: Social transmission of information is vital for many group-living animals, allowing coordination of motion and effective response to complex environments. Revealing the interaction networks underlying information flow within these groups is a central challenge [1]. Previous work has modeled interactions between individuals based directly on their relative spatial positions: each individual is considered to interact with all neighbors within a fixed distance (metric range [2]), a fixed number of nearest neighbors (topological range [3]), a ‘shell’ of near neighbors (Voronoi range [4]), or some combination (Figure 1A). However, conclusive evidence to support these assumptions is lacking. Here, we employ a novel approach that considers individual movement decisions to be based explicitly on the sensory information available to the organism. In other words, we consider that while spatial relations do inform interactions between individuals, they do so indirectly, through individuals’ detection of sensory cues. We reconstruct computationally the visual field of each individual throughout experiments designed to investigate information propagation within fish schools (golden shiners, Notemigonus crysoleucas). Explicitly considering visual sensing allows us to more accurately predict the propagation of behavioral change in these groups during leadership events. Furthermore, we find that structural properties of visual interaction networks differ markedly from those of metric and topological counterparts, suggesting that previous assumptions may not appropriately reflect information flow in animal groups.
  @cite_36: In a recent Physical Review Letters article, propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors." In their paper, provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
  @cite_42: The aggregate motion of a flock of birds, a herd of land animals, or a school of fish is a beautiful and familiar part of the natural world. But this type of complex motion is rarely seen in computer animation. This paper explores an approach based on simulation as an alternative to scripting the paths of each bird individually. The simulated flock is an elaboration of a particle systems, with the simulated birds being the particles. The aggregate motion of the simulated flock is created by a distributed behavioral model much like that at work in a natural flock; the birds choose their own course. Each simulated bird is implemented as an independent actor that navigates according to its local perception of the dynamic environment, the laws of simulated physics that rule its motion, and a set of behaviors programmed into it by the "animator." The aggregate motion of the simulated flock is the result of the dense interaction of the relatively simple behaviors of the individual simulated birds.
  @cite_21: Numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional positions of individual birds in airborne flocks of a few thousand members, we show that the interaction does not depend on the metric distance, as most current models and theories assume, but rather on the topological distance. In fact, we discovered that each bird interacts on average with a fixed number of neighbors (six to seven), rather than with all neighbors within a fixed metric distance. We argue that a topological interaction is indispensable to maintain a flock's cohesion against the large density changes caused by external perturbations, typically predation. We support this hypothesis by numerical simulations, showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one.
  @cite_54: This paper addresses the connectedness issue in multiagent coordination, i.e., the problem of ensuring that a group of mobile agents stays connected while achieving some performance objective. In particular, we study the rendezvous and the formation control problems over dynamic interaction graphs, and by adding appropriate weights to the edges in the graphs, we guarantee that the graphs stay connected.
  @cite_19: A computer simulation was performed to examine the schooling mechanism. The model uses the basic assumptions that the speed and direction of individual movements are stochastic variables, and that the direction of movement is related to the location and heading of the neigh-bors. Three behavioral interactions between individuals and the were considered approach avoidance and parallel orientation movements Individual movements and tje resultant group movement were simulated by repeatedly generating random numbers. It was found that group movements in unity could occur despite each indicidual lacking knowledge of movement of the entire school, and in the absence of a consistent leader. The results lead to the following conclusions: for effective schooling to occur, individuals must pissess two types of behavior; 1. approach movement to allow aggregation, and 2. parallel orientation movement to allow the group ro move cohesively. Experiments were also performed with varied combinations of model parameters, and a wide variation in the movement pattern of the simulated schoolwas obtained.
  @cite_27: 
  @cite_58: In this note, we specify an "individual-based" continuous-time model for swarm aggregation in n-dimensional space and study its stability properties. We show that the individuals (autonomous agents or biological creatures) will form a cohesive swarm in a finite time. Moreover, we obtain an explicit bound on the swarm size, which depends only on the parameters of the swarm model.
summary: The metric model is one of the earliest models developed to represent range-limited communication between biological swarm agents @cite_27 @cite_19 @cite_42 . This model is used as a benchmark for comparison testing relatively newer communication models @cite_48 @cite_21 @cite_28 . The model is widely-used in the field of multi-robot systems, as well, due to its ability to capture sensor range constraints @cite_58 @cite_36 @cite_54 . However, a field study of European starlings, Sturnus vulgaris , indicates that the swarm uses a topological, rather than a range limited model @cite_21 . Specifically, starlings coordinate with their nearest six to seven neighbors (topological distance). An artificial swarm, in response to a simulated predator, decomposes into fewer groups, and produces more cohesive swarms, when using the topological model compared to the metric model @cite_21 . Strandburg-Peshkin @cite_48 introduced the visual model, and show that it best predicts how golden shiners, Notemigonus crysoleucas , behave in response to stimuli. The model's low clustering makes it fundamentally different from the metric and topological models, from a network-theoretic perspective.