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Several simulation models have demonstrated how flocking behavior emerges from the interaction among individuals that react to the relative orientation of their neighbors based on simple rules. However, the precise nature of these rules and the relationship between the characteristics of the rules and the efficacy of the resulting collective behavior are unknown. In this article, we analyze the effect of the strength with which individuals react to the orientation of neighbors located in different sectors of their visual fields and the benefit that could be obtained by using control rules that are more elaborate than those normally used. Our results demonstrate that considering only neighbors located on the frontal side of the visual field permits an increase in the aggregation level of the swarm. Using more complex rules and/or additional sensory information does not lead to better performance. [ABSTRACT FROM AUTHOR]

In this work, we propose a minimalistic swarm flocking approach for multirotor unmanned aerial vehicles (UAVs). Our approach allows the swarm to achieve cohesively and aligned flocking (collective motion), in a random direction, without externally provided directional information exchange (alignment control). The method relies on minimalistic sensory requirements as it uses only the relative range and bearing of swarm agents in local proximity obtained through onboard sensors on the UAV. Thus, our method is able to stabilize and control the flock of a general shape above a steep terrain without any explicit communication between swarm members. To implement proximal control in a three-dimensional manner, the Lennard-Jones potential function is used to maintain cohesiveness and avoid collisions between robots. The performance of the proposed approach was tested in real-world conditions by experiments with a team of nine UAVs. Experiments also present the usage of our approach on UAVs that are independent of external positioning systems such as the Global Navigation Satellite System (GNSS). Relying only on a relative visual localization through the ultraviolet direction and ranging (UVDAR) system, previously proposed by our group, the experiments verify that our system can be applied in GNSS-denied environments. The degree achieved of alignment and cohesiveness was evaluated using the metrics of order and steady-state value. [ABSTRACT FROM AUTHOR]

The physics of active biological matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Current theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these approaches do not seem to recognize explicitly their critical feature: namely, the role of survival-driven purpose and the attendant pursuit of maximum utility. Here, we propose a game-theoretic framework, statistical teleodynamics, that demonstrates that the bird-like agents self-organize dynamically into flocks to approach a stable arbitrage equilibriumof equal effective utilities. This is essentially the invisible handmechanism of Adam Smith's in an ecological context. What we demonstrate is for ideal systems, similar to the ideal gas or Ising model in thermodynamics. The next steps would involve examining and learning how real swarms behave compared to their ideal versions. Our theory is not limited to just birds flocking but can be adapted for the self-organizing dynamics of other active matter systems. [ABSTRACT FROM AUTHOR]

The physics of active biological matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Current theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these approaches do not seem to recognize explicitly their critical feature: namely, the role of survival-driven purpose and the attendant pursuit of maximum utility. Here, we propose a game-theoretic framework, statistical teleodynamics, that demonstrates that the bird-like agents self-organize dynamically into flocks to approach a stable arbitrage equilibriumof equal effective utilities. This is essentially the invisible handmechanism of Adam Smith’s in an ecological context. What we demonstrate is for ideal systems, similar to the ideal gas or Ising model in thermodynamics. The next steps would involve examining and learning how real swarms behave compared to their ideal versions. Our theory is not limited to just birds flocking but can be adapted for the self-organizing dynamics of other active matter systems.

Complex patterns of collective behaviour may emerge through self-organization, from local interactions among individuals in a group. To understand what behavioural rules underlie these patterns, computational models are often necessary. These rules have not yet been systematically studied for bird flocks under predation. Here, we study airborne flocks of homing pigeons attacked by a robotic falcon, combining empirical data with a species-specific computational model of collective escape. By analysing GPS trajectories of flocking individuals, we identify two new patterns of collective escape: early splits and collective turns, occurring even at large distances from the predator. To examine their formation, we extend an agent-based model of pigeons with a ‘discrete’ escape manoeuvre by a single initiator, namely a sudden turn interrupting the continuous coordinated motion of the group. Both splits and collective turns emerge from this rule. Their relative frequency depends on the angular velocity and position of the initiator in the flock: sharp turns by individuals at the periphery lead to more splits than collective turns. We confirm this association in the empirical data. Our study highlights the importance of discrete and uncoordinated manoeuvres in the collective escape of bird flocks and advocates the systematic study of their patterns across species.

The collective motion of animal groups often exhibits velocity–velocity correlations between nearest neighbours, with the strongest velocity correlations observed at the shortest inter-animal spacings. This may have been a motivational factor in the development of models based primarily on short-ranged interactions. Here we ask whether such observations necessarily mean that the interactions are short-ranged. We develop a minimal model of collective motion capable of supporting interactions of arbitrary range and show that it represents a counterexample: the strongest velocity correlations emerge at the shortest distances, even when the interactions are explicitly non-local.

Animal groups frequently move in a highly organized manner, as represented by flocks of birds and schools of fish. Despite being an everyday occurrence, we do not fully understand how this works. In particular, what social interactions between animals give rise to the flock structures we observe? This question is often investigated using self-propelled particle models where particles represent the individual animals. These models differ in the social interactions used, individual particle properties, and various technical assumptions. One particular technical assumption relates to whether all particles update their headings and positions at exactly the same time (synchronous update) or not (asynchronous update). Here, we investigate the causal effects of this assumption in an attraction-only model and find that it has a dramatic impact. Polarized groups do not form when synchronous update is used, but are produced with asynchronous update, and this phenomenon is robust with respect to variation in particle displacements and inclusion of noise. Given that many important models have been implemented with synchronous update only, we speculate that our understanding of the social interactions on which they are based may be incomplete. Perhaps previously unobserved phenomena will emerge if other potentially more realistic update schemes are used.

The balletic motion of bird flocks, fish schools, and human crowds is believed to emerge from local interactions between individuals in a process of self-organization. The key to explaining such collective behavior thus lies in understanding these local interactions. After decades of theoretical modeling, experiments using virtual crowds and analysis of real crowd data are enabling us to decipher the “rules of engagement” governing these interactions. On the basis of such results, my students and I built a dynamical model of how a pedestrian aligns his or her motion with that of a neighbor and how these binary interactions are combined within a neighborhood of interaction. Computer simulations of the model generate coherent motion at the global level and reproduce individual trajectories at the local level. This approach has yielded the first experiment-driven, bottom-up model of collective motion, providing a basis for understanding more complex patterns of crowd behavior in both everyday and emergency situations. [ABSTRACT FROM AUTHOR]

It is commonly believed that global patterns of motion in flocks, schools and crowds emerge from local interactions between individuals, through a process of self-organization. The key to explaining such collective behaviour thus lies in deciphering these local interactions. We take an experiment-driven approach to modelling collective motion in human crowds. Previously, we observed that a pedestrian aligns their velocity vector (speed and heading direction) with that of a neighbour.Herewe investigate the neighbourhood of interaction in a crowd: which neighbours influence a pedestrian's behaviour, how this depends on neighbour position, and howthe influences ofmultiple neighbours are combined. In three experiments, a participant walked in a virtual crowd whose speed and headingwere manipulated.We find that neighbour influence is linearly combined and decreases with distance, but not with lateral position (eccentricity).We model the neighbourhood as (i) a circularly symmetric region with (ii) aweighted average of neighbours, (iii) a uni-directional influence, and (iv)weights that decay exponentially to zero by 5 m. Themodel reproduces the experimental data and predicts individual trajectories in observational data on a human 'swarm'. The results yield the first bottom-up model of collective crowd motion. [ABSTRACT FROM AUTHOR]

Collective migration of animals in a cohesive group is rendered possible by a strategic distribution of tasks among members: some track the travel route, which is time and energy-consuming, while the others follow the group by interacting among themselves. In this paper, we study a social dynamics system modeling collective migration. We consider a group of agents able to align their velocities to a global target velocity, or to follow the group via interaction with the other agents. The balance between these two attractive forces is our control for each agent, as we aim to drive the group to consensus at the target velocity. We show that the optimal control strategies in the case of final and integral costs consist of controlling the agents whose velocities are the furthest from the target one: these agents sense only the target velocity and become leaders, while the uncontrolled ones sense only the group, and become followers. Moreover, in the case of final cost, we prove an 'Inactivation' principle: there exist initial conditions such that the optimal control strategy consists of letting the system evolve freely for an initial period of time, before acting with full control on the agent furthest from the target velocity. [ABSTRACT FROM AUTHOR]

This issue is devoted to complex systems in life sciences. Some perspective ideas on possible objectives of future research are extracted from the contents of this issue and brought to the reader's attention. The final ambitious aim is the development of a mathematical theory for complex living systems. [ABSTRACT FROM AUTHOR]

This brief note is an introduction to the special issue devoted to modeling, qualitative analysis and simulations of vehicular traffic, crowds and swarms, viewed as living, hence complex, systems. The first part focuses on the conceptual difficulties to be tackled when dealing with the most challenging topics of this subject, mainly on interactions and complexity features. The second part provides a brief overview and critical analysis of the contents. Finally, some perspective ideas on conceivable future research objectives are brought to the reader's attention. [ABSTRACT FROM AUTHOR]

Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group often turns giving rise to more complicated dynamics, still keeping strong polarization of the flock. Here we propose novel dynamical equations for the collective motion of polarized animal groups that account for correlated turning including solely social forces. We exploit rotational symmetries and conservation laws of the problem to formulate a theory in terms of generalized coordinates of motion for the velocity directions akin to a Hamiltonian formulation for rotations. We explicitly derive the correspondence between this formulation and the dynamics of the individual velocities, thus obtaining a new model of collective motion. In the appropriate overdamped limit we recover the well-known Vicsek model, which dissipates rotational information and does not allow for polarized turns. Although the new model has its most vivid success in describing turning groups, its dynamics is intrinsically different from previous ones in a wide dynamical regime, while reducing to the hydrodynamic description of Toner and Tu at very large length-scales. The derived framework is therefore general and it may describe the collective motion of any strongly polarized active matter system. [ABSTRACT FROM AUTHOR]

In this work, we investigate the possibility of using inspiration from the self-organizing property of organisms in nature for providing visual representation of an invisible pollutant profile. We present a novel mathematical model of the bacterium and use it to find pollutants in the environment. This model has the capability of exploring the environment to search for sparsely distributed pollutants or food sources and then subsequently exploiting them upon discovery. We also combine the bacterium model in a bacterium–flock algorithm for the purposes of preventing collisions between robots or organisms in addition to providing coverage to a pollutant. By adjusting the velocity of individuals, we show that we are able to control the coverage provided by the population as a whole. Furthermore, we compare the bacterium–flock algorithm with a novel gradient-ascent-flocking algorithm and the well established Voronoi partition algorithm. Results show that bacterium–flock algorithm and the Voronoi partition algorithm are capable of adapting the distribution of the individuals of a population based upon the underlying pollutant profile while the gradient-ascent-flocking algorithm is not. This shows that the bacterium–flock and the Voronoi partition algorithms can potentially be used to track a spatiotemporal function. On the other hand, the gradient-ascent-flock algorithm has a faster convergence time in some cases with the Voronoi partition algorithm having the slowest convergence time overall. [ABSTRACT FROM AUTHOR]

We propose a self-adaptive communication strategy for controlling the heading direction of a swarm of mobile robots during flocking. We consider the problem where a small group of informed robots has to guide a large swarm along a desired direction. We consider three versions of this problem: one where the desired direction is fixed; one where the desired direction changes over time; one where a second group of informed robots has information about a second desired direction that conflicts with the first one, but has higher priority. The goal of the swarm is to follow, at all times, the desired direction that has the highest priority and, at the same time, to keep cohesion. The proposed strategy allows the informed robots to guide the swarm when only one desired direction is present. Additionally, a self-adaptation mechanism allows the robots to indirectly sense the second desired direction, and makes the swarm follow it. In experiments with both simulated and real robots, we evaluate how well the swarm tracks the desired direction and how well it maintains cohesion. We show that, using self-adaptive communication, the swarm is able to follow the desired direction with the highest priority at all times without splitting. [ABSTRACT FROM AUTHOR]

This brief note is an introduction to the papers published in this special issue devoted to complex systems in life sciences. Out of this presentation some perspective ideas on conceivable future research objectives are extracted and brought to the reader's attention. The final (ambitious) aim is to develop a mathematical theory for complex living systems. [ABSTRACT FROM AUTHOR]

In flocking, a swarm of robots moves cohesively in a common direction. Traditionally, flocking is realized using two main control rules: proximal control, which controls the cohesion of the swarm using local range-and bearing information about neighboring robots; and alignment control, which allows the robots to align in a common direction and uses more elaborate sensing mechanisms to obtain the orientation of neighboring robots. So far, limited attention has been given to motion control, used to translate the output of these two control rules into robot motion. In this paper, we propose a novel motion control method: magnitude-dependent motion control (MDMC). Through simulations and real robot experiments, we show that, with MDMC, flocking in a random direction is possible without the need for alignment control and for robots having a preferred direction of travel. MDMC has the advantage to be implementable on very simple robots that lack the capability to detect the orientation of their neighbors. In addition, we introduce a small proportion of robots informed about a desired direction of travel. We compare MDMC with a motion control method used in previous robotics literature, which we call magnitude-independent motion control (MIMC), and we show that the swarms can travel longer distances in the desired direction when using MDMC instead of MIMC. Finally, we systematically study flocking under various conditions: with or without alignment control, with or without informed robots, with MDMC or with MIMC. [ABSTRACT FROM PUBLISHER]

This brief note presents the papers published in a special issue devoted to complex systems in life sciences. Out of the set of papers some perspective ideas on conceivable future researches are extracted and brought to the attention of the readers. The final ambitious aim is to contribute to the development of a mathematical theory for complex living systems. [ABSTRACT FROM AUTHOR]

This paper deals with the modeling and simulation of swarms viewed as a living, hence complex, system. The approach is based on methods of kinetic theory and statistical mechanics, where interactions at the microscopic scale are nonlinearly additive and modeled by stochastic games. [ABSTRACT FROM AUTHOR]

The formation of waves is a vivid example of collective behaviour occurring in insects, birds, fish and mammals, which has been interpreted as an antipredator response. In birds a quantitative characterization of this phenomenon, involving thousands of individuals, is missing and its link with predation remains elusive. We studied waves in flocks of starlings, a highly gregarious species, by both direct observation and quantitative computer vision analysis of HD video recordings, under predation by peregrine falcons, Falco peregrinus. We found that waves originated from the position of the attacking predator and always propagated away from it. We measured their frequency and velocities, the latter often being larger than the velocity of the flock. A high positive correlation was found between the formation of waves and reduced predation success. We suggest that the tendency of a prey to escape, when initiated even by a few individuals in a cohesive group, elicits self-organized density waves. Such evident fluctuations in the local structure of the flocks are efficient in confusing predators. [Copyright &y& Elsevier]

We explain the physical motivation for studying the collective coherent motion of large numbers of self-propelled biological organisms. Starting from a well-known discrete model, we discuss the fundamental microscopic mechanisms leading to collective behavior in bird flocks, and how appropriate behavioral rules for the individuals can determine specific features of the aggregation at the group level. We further discuss the theoretical, experimental, and computational effort undertaken to explore this phenomenon together with possible directions for future research in this area. [ABSTRACT FROM AUTHOR]

In this paper, we study how a self-organized mobile robot flock can be steered toward a desired direction through externally guiding some of its members. Specifically, we propose a behavior by extending a previously developed flocking behavior to steer self-organized flocks in both physical and simulated mobile robots. We quantitatively measure the performance of the proposed behavior under different parameter settings using three metrics, namely, (1) the mutual information metric, adopted from Information Theory, to measure the information shared between the individuals during steering, (2) the accuracy metric from directional statistics to measure the angular deviation of the direction of the flock from the desired direction, and (3) the ratio of the largest aggregate to the whole flock and the ratio of informed individuals remaining with the largest aggregate, as a metric of flock cohesion. We conducted a systematic set of experiments using both physical and simulated robots, analyzed the transient and steady-state characteristics of steered flocking, and evaluate the parameter conditions under which a swarm can be successfully steered. We show that the experimental results are qualitatively in accordance with the ones that were predicted in Couzin et al. model (Nature, 433:513–516, 2005) and relate the quantitative differences to the differences between the models. [ABSTRACT FROM AUTHOR]

From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behavior have aimed to understand how a globally ordered state may emerge from simple behavioral rules. Less effort has been devoted to understanding the origin of collective response, namely the way the group as a whole reacts to its environment. Yet, in the presence of strong predatory pressure on the group, collective response may yield a significant adaptive advantage. Here we suggest that collective response in animal groups may be achieved through scale-free behavioral correlations. By reconstructing the 3D position and velocity of individual birds in large flocks of starlings, we measured to what extent the velocity fluctuations of different birds are correlated to each other. We found that the range of such spatial correlation does not have a constant value, but it scales with the linear size of the flock. This result indicates that behavioral correlations are scale free: The change in the behavioral state of one animal affects and is affected by that of all other animals in the group, no matter how large the group is. Scale-free correlations provide each animal with an effective perception range much larger than the direct interindividual interaction range, thus enhancing global response to perturbations. Our results suggest that flocks behave as critical systems, poised to respond maximally to environmental perturbations. [ABSTRACT FROM AUTHOR]

In this paper, we study self-organized flocking in a swarm of mobile robots. We present Kobot, a mobile robot platform developed specifically for swarm robotic studies. We describe its infrared-based short range sensing system, capable of measuring the distance from obstacles and detecting kin robots, and a novel sensing system called the virtual heading system (VHS) which uses a digital compass and a wireless communication module for sensing the relative headings of neighboring robots. We propose a behavior based on heading alignment and proximal control that is capable of generating self-organized flocking in a swarm of Kobots. By self-organized flocking we mean that a swarm of mobile robots, initially connected via proximal sensing, is able to wander in an environment by moving as a coherent group in open space and to avoid obstacles as if it were a “super-organism”. We propose a number of metrics to evaluate the quality of flocking. We use a default set of behavioral parameter values that can generate acceptable flocking in robots, and analyze the sensitivity of the flocking behavior against changes in each of the parameters using the metrics that were proposed. We show that the proposed behavior can generate flocking in a small group of physical robots in a closed arena as well as in a swarm of 1000 simulated robots in open space. We vary the three main characteristics of the VHS, namely: (1) the amount and nature of noise in the measurement of heading, (2) the number of VHS neighbors, and (3) the range of wireless communication. Our experiments show that the range of communication is the main factor that determines the maximum number of robots that can flock together and that the behavior is highly robust against the other two VHS characteristics. We conclude by discussing this result in the light of related theoretical studies in statistical physics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the self-propulsion and interaction potential parameters. In this paper, we utilize a procedure which connects a class of individual-based models to their continuum formulations and determine criteria for the validity of the latter. -stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions. We perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual-based one. [Copyright &y& Elsevier]

Drawing inspiration from social interactions in nature, the field of swarm intelligence has presented a promising approach to the design of complex systems consisting of numerous, usually homogeneous, simple parts, to solve a wide variety of problems. Like cellular automata, swarm-intelligence systems involve highly parallel computations across space, based heavily on self-organization, the emergence of global behavior through local interactions of components, and the absence of centralized or global control. However, this has a disadvantage as the desired behavior of a system becomes hard to predict or design based on its local interaction rules. In our ongoing research, we propose to provide greater control over a system, and potentially more useful, goal-oriented behavior, by introducing layered, hierarchical controllers in the particles or components. The layered controllers allow each particle to extend their reactive behavior in a more goal-oriented style, while keeping the locality of the interactions and the general simplicity of the system. In this paper, we present three systems designed using this approach: a competitive foraging system, a system for the collective transport and distribution of goods, and a self-assembly system capable of creating complex structures in a 3D world. Our simulation results show that in all three cases it was possible to guide the self-organization process at different levels of the designated task, suggesting that the self-organizing behavior of swarm-intelligence systems may be extendable to support problem solving in various contexts, such as coordinated robotic teams. [ABSTRACT FROM AUTHOR]

This article proposes three control algorithms for the emergence of self-organized behaviours, including aggregation, flocking and rendezvous, in swarm robotics systems. The proposed control algorithms are based on a local polar coordinates' control law available in the literature for posture regulation; this law is adapted to work in a self-organized robotic swarm using distance and bearing as coupling information. Therefore, the robots only need to know the radial distance and orientation to the goal; additionally, the three algorithms are based on self-organization, eliminating the need for a preset coupling topology among the robots. In particular, the flocking algorithm has a first stage for topology creation, while the rendezvous and aggregation algorithms change the topology on every iteration depending on the local interactions of the robots. The effectiveness of the algorithms was evaluated through numerical simulations of swarms of up to 100 differential traction wheeled mobile robots. [ABSTRACT FROM AUTHOR]