Flocking System Research Articles

The structure inference of flocking systems based on the trajectories.

The interaction between the swarm individuals affects the dynamic behavior of the swarm, but it is difficult to obtain directly from outside observation. Therefore, the problem we focus on is inferring the structure of the interactions in the swarm from the individual behavior trajectories. Similar inference problems that existed in network science are named network reconstruction or network inference. It is a fundamental problem pervading research on complex systems. In this paper, a new method, called Motion Trajectory Similarity, is developed for inferring direct interactions from the motion state of individuals in the swarm. It constructs correlations by combining the similarity of the motion trajectories of each cross section of the time series, in which individuals with highly similar motion states are more likely to interact with each other. Experiments on the flocking systems demonstrate that our method can produce a reliable interaction inference and outperform traditional network inference methods. It can withstand a high level of noise and time delay introduced into flocking models, as well as parameter variation in the flocking system, to achieve robust reconstruction. The proposed method provides a new perspective for inferring the interaction structure of a swarm, which helps us to explore the mechanisms of collective movement in swarms and paves the way for developing the flocking models that can be quantified and predicted.

Robust flocking of multiple intelligent agents with multiple disturbances

The cooperation control of multiple intelligent agents (MIAs), which can solve complex engineering problems in practice, has received increasing attention. However, there are multiple disturbances in wireless sensor networks, which has a great effect on the collaboration of MIAs. In this paper, the problem of the flocking motion of second-order MIAs is addressed with collision avoidance and multiple disturbances. To estimate the matched/mismatched disturbances, the disturbance observers are designed. It is noted that the assumption that the differentials of disturbances converge to zeros in the literature is removed. A novel compound strategy is designed by using the robust auxiliary function and the potential function. The asymptotic properties of the flocking system are studied based on the Input-to-State Stability Theorem and the robust stability. Numerical simulation results verify the validity of the proposed protocol.

Coordination of a Semi-Informed Flocking System via Model Predictive Control

Coordination of mobile multi-agent systems has been studied intensively for many different purposes. These include swarm robotics, transportation, control of human crowds, and even understanding of collective behavior of animal groups. Mainly, the flocking behavior of multiple agents has been investigated under usually idealized conditions regarding information availability. This paper proposes a model predictive control framework to control flocking agents with limited information. The flocking system is composed of a leader agent and agents that have no information about the group objective and cannot perceive the unknown operation area. The leader agent is a part of the group. However, it has prior information about the group objective and can sense the environment. With the proposed control scheme, the leader steers the flocking agents like a shepherd dog to accomplish the group goal. The presented control scheme is validated in simulation examples.

A Software Framework for Self-Organized Flocking System Motion Coordination Research

We describe and analyze the basic algorithms for the self-organization of a swarm of robots in coordinated motion as a flock of agents as a strategy for the solution of multi-agent tasks. This analysis allows us to postulate a simulation framework for such systems based on the behavioral rules that characterize the dynamics of these systems. The problem is approached from the perspective of autonomous navigation in an unknown but restricted and locally observable environment. The simulation framework allows defining individually the characteristics of the basic behaviors identified as fundamental to show a flocking behavior, as well as the specific characteristics of the naviga-tion environment. It also allows the incorporation of different path planning approaches to enable the system to navigate the environment for different strategies, both geometric and reactive. The basic behaviors modeled include safe wandering, following, aggregation, dispersion, and homing, which interact to generate flocking behavior, i.e., the swarm aggregates, reach a stable formation and move in an organized fashion toward the target point. The framework concept follows the principle of constrained target tracking, which allows the problem to be solved similarly as a small robot with limited computation would solve it. It is shown that the algorithm and the framework that implements it are robust to the defined constraints and manage to generate the flocking behavior while accomplishing the navigation task. These results provide key guidelines for the implementation of these algorithms on real platforms.

Network community detection via iterative edge removal in a flocking-like system

We present a network community-detection technique based on properties that emerge from a nature-inspired flocking system. Our algorithm comprises two alternating mechanisms: first, we control the particles alignment in higher dimensional space and, second, we present an iterative process of edge removal. These mechanisms together can potentially reduce accidental alignment among particles from different communities and, consequently, the model can generate robust community-detection results. In the proposed model, a random-direction unit vector is assigned to each vertex initially. A nonlinear dynamic law is established, so that neighboring vertices try to become aligned with each other. After some time, the system stops and edges that connect the least-aligned pairs of vertices are removed. Then, the evolution starts over without the removed edges, and after enough number of removal rounds, each community becomes a connected component. The proposed approach is evaluated using widely accepted benchmarks and real-world networks. Experimental results reveal that the method is robust and excels on a wide variety of networks. For large sparse networks, the edge-removal process runs in quasilinear time, which enables application in large-scale networks. Moreover, the distributed nature of the process eases the parallel implementation of the model.

Effect of temperature on flocking propensity and species interactions in a subtropical mixed-species flocking system

Increased participation in mixed-species flocks is one hypothesized behavioral tactic used by forest birds to adjust to cold temperatures in winter. This phenomenon has been documented in temperate North America, but not at subtropical latitudes where temperatures are less extreme. To understand how temperature structures the size, richness, flocking propensity, and species interactions of subtropical mixed-species flocks, we performed paired mixed-species flock and point count surveys in upland hardwood forests in north-central Florida, USA. We described the composition of 92 mixed-species flocks across a ∼20 °C range of daytime temperatures, using linear mixed models and network analyses to test for effects of temperature. We found that both flock species richness and size were significantly smaller at higher temperatures while statistically controlling for effects of time of day, canopy height, and local site effects. Thirteen of 14 flocking species showed decreases in within-flock abundance with increasing temperature, although this effect was only significant for the nuclear Carolina Chickadee (Poecile carolinensis). Flock composition and species flocking propensities were less plastic than in temperate systems. By comparing metrics from 7 social networks corresponding to temperature ranges, we found that strength of flocking interactions was lower and that species were significantly less likely to co-occur with similarly foraging species at temperatures above 20 °C. Flocking propensities were lower for many species in the warmest temperature range. Thirteen of 14 species joined flocks in all 7 networks, and dissimilarity of social networks was consequently best explained by changes in species co-occurrence patterns rather than species turnover within flocks. In contrast to boreal flocking systems, changes to flocking behavior were prompted by unseasonably warm weather rather than cold spells, which suggests that warming winter temperatures could lead to breakdown of social behaviors in our system.

Cucker–Smale flocking subject to random failure on general digraphs

This paper studies the Cucker–Smale (C–S) flocking subject to random failure under general interaction topologies, which contain the hierarchical leadership and rooted leadership as special cases. Furthermore, at each time step, each of the agents can fail to interact with any of its neighbors. The random failures are assumed to be not independent. We prove that the flocking would occur almost surely under some conditions on the initial state of the flock only. The result suggests that the C–S flocking system on general digraphs can endure random failure in interactions. Finally, several numerical simulations are provided to illustrate the obtained results.

Vision-Aided Multi-UAV Autonomous Flocking in GPS-Denied Environment

This paper presents a sophisticated vision-aided flocking system for unmanned aerial vehicles (UAVs), which is able to operate in GPS-denied unknown environments for exploring and searching missions, and also able to adopt two types of vision sensors, day and thermal cameras, to measure relative motion between UAVs in different lighting conditions without using wireless communication. In order to realize robust vision-aided flocking, an integrated framework of tracking-learning-detection on the basis of multifeature coded correlation filter has been developed. To achieve long-term tracking, a redetector is trained online to adaptively reinitialize target for global sensing. An advanced flocking strategy is developed to address the autonomous multi-UAVs' cooperative flight. Light detection and ranging (LiDAR)-based navigation modules are developed for autonomous localization, mapping, and obstacle avoidance. Flight experiments of a team of UAVs have been conducted to verify the performance of this flocking system in a GPS-denied environment. The extensive experiments validate the robustness of the proposed vision algorithms in challenging scenarios.

Leader-follower multi-agent flocking with bounded missing data and random communication radius

In this paper, the leader-follower Cucker–Smale flocking system with bounded missing data and random communication radius is studied. The communication network is determined by the stochastic distance radii between agents. The process by which data are lost in the communication network is independent and identically distributed. The goal of this paper is to determine a lower bound on the probability that the agents asymptotically achieve a flocking behaviour, i.e. the relative velocities between the leader agent and other agents asymptotically vanish and the relative positions converge. Finally, a numerical simulation example is provided to illustrate the obtained results.

A survey of mathematical modeling based on flocking system

Based on the basics of the flocking, the concept and relationship of individual, cluster and flocking behavior are introduced. Two research methods, which are the macroscopic Angle of Euler method and the Lagrangian method of microcosmic Angle, are elaborated in detail. Then several flocking models and their improvement applications are summarized, the model among them based on dynamic principle is widely used, so the basic mode of its behavior, the following mechanism of an individual in an orderly procession, the mechanism for avoiding obstacles, and the causes of fission behavior are discussed in this paper. Finally, some problems in current researches of flocking are presented and future development are prospected.

Flocking of Mobile Agents Using a New Interaction Model: A Cyber-Physical Perspective

The attraction repulsion (AR) model has been a common mathematical framework to emulate the interactions among mobile agents and to design rigid flocking laws. A main drawback of the AR model is that environment effects are not taken into account in the model. This means that rigid flocking laws can not react to the change of environments. In this paper, we make an attempt to design flocking systems that are adaptive to the change of communication environments. The flocking system is modeled as a cyber-physical system, where the cyber layer and control layer are designed systematically. In the cyber layer, a new interaction model is proposed by considering communication parameters of the environment. In the control layer, distributed controllers are designed for mobile agents with switching topology using the proposed interaction model. It is shown that the proposed flocking law can react to change of communication environments and guarantee the optimal communication link between agents. The stability and convergence of the flocking system are analyzed with nonsmooth techniques. Numerical simulations are provided to illustrate the effectiveness of the design.

Evolutionary game theory for multiple-mobile-robot flocking systems containing mutations

This paper studies some major issues encountered in the evolution of strategy choice for a multiple-mobile-robot flocking system that contains mutated individuals. The main objectives of the study are to analyse the effects of mutated strategies on the dynamic performance of the system (i.e., the convergence time and stabilisation time) and to explore the strategy evolution and distributions in flocking movement. Accordingly a payoff matrix directly related to these dynamic performance indicators is designed. The simulation results indicate that the system can achieve common consistency for any given initial conditions, and the final evolution reveals some degree of inherent regularity in the values of the payoff matrix elements. Furthermore, the simulation results confirm the validity of evolutionary game theory to enhance the dynamic performances of a system. The procedure developed from the work can facilitate group-based strategy selection as a creative solution.

Strategic Adjustment Capacity, Sustained Competitive Advantage, and Firm Performance: An Evolutionary Perspective on Bird Flocking and Firm Competition

Imitating the positioning rules in the bird flocking system, the strategic adjustment capacity is decomposed into three aspects, which are the organizational learning capacity from the top firms, the extent to which firms maintain or rely on the best operational capacity vector in history, and the ability to overcome the disadvantage while maintaining the advantage of the operational capacity vector from the previous years, respectively. Financial vectors are constructed to represent the results of corporate strategic adjustment and listed firms in the China A stock are chosen as the samples. As empirical analysis reveals, there is a positive correlation between the organizational learning capacity from the top firms and the firm performance and a U-shaped relation between the learning capability from the previous best operational capacity vector and the firm performance. However, no significant correlation between the inertia control ability of the current operational capacity vector of the firms and their performance improvement can be observed. This study verifies that the issue of corporate competitiveness and performance can be investigated by utilizing the principles of competition in nature. Moreover, a firm can obtain a sustainable competitive advantage by improving its ability to learn from top firms in the industry.

Cucker–Smale flocking with randomly failed interactions

We consider the Cucker–Smale model consisting of interacted particles involving random failure. More precisely, each pair of neighboring agents can fail to interact with a certain probability. Two cases are considered: undirected connected interactions and directed rooted interactions. Our results show that the unconditional flocking for long-range communication rate is still true independently of the failure rate probability. For short-range communication rate, conditional flocking can be established. These results, together with the previous study of Dalmao and Mordecki (2012) [8], suggest that the C–S flocking system under various interaction topologies can endure random failure in interactions.

Modeling and control through leadership of a refined flocking system

A new refined flocking model that includes self-propelling, friction, attraction and repulsion, and alignment features is presented. This model takes into account various behavioral phenomena observed in biological and social systems. In addition, the presence of a leader is included in the system in order to develop a control strategy for the flocking model to accomplish desired objectives. Specifically, a model predictive control scheme is proposed that requires the solution of a sequence of open-loop optimality systems. An accurate Runge–Kutta scheme to discretize the optimality systems and a nonlinear conjugate gradient solver are implemented and discussed. Numerical experiments are performed that investigate the properties of the refined flocking model and demonstrate the ability of the control strategy to drive the flocking system to attain a desired target configuration and to follow a given trajectory.

Hydrodynamic limit of the kinetic Cucker–Smale flocking model

The hydrodynamic limit of a kinetic Cucker–Smale flocking model is investigated. The starting point is the model considered in [Existence of weak solutions to kinetic flocking models, SIAM Math. Anal.45 (2013) 215–243], which in addition to free transport of individuals and a standard Cucker–Smale alignment operator, includes Brownian noise and strong local alignment. The latter was derived in [On strong local alignment in the kinetic Cucker–Smale equation, in Hyperbolic Conservation Laws and Related Analysis with Applications (Springer, 2013), pp. 227–242] as the singular limit of an alignment operator first introduced by Motsch and Tadmor in [A new model for self-organized dynamics and its flocking behavior, J. Stat. Phys.141 (2011) 923–947]. The objective of this work is the rigorous investigation of the singular limit corresponding to strong noise and strong local alignment. The proof relies on a relative entropy method. The asymptotic dynamics is described by an Euler-type flocking system.

Environment orientation: a structured simulation approach for agent-based complex systems

Complex systems are collections of independent agents interacting with each other and with their environment to produce emergent behaviour. Agent-based computer simulation is one of the main ways of studying complex systems. A naive approach to such simulation can fare poorly, due to large communication overhead, and due to the scope for deadlock between the interacting agents sharing a computational platform. Agent interaction can instead be considered entirely from the point of view of the environment(s) within which the agents interact. Structuring a simulation using such Environment Orientation leads to a simulation that reduces communication overhead, that is effectively deadlock-free, and yet still behaves in the manner required. Additionally the Environment Orientation architecture eases the development of more sophisticated large-scale simulations, with multiple kinds of complex agents, situated in and interacting with multiple kinds of environments. We describe the Environment Orientation simulation architecture. We report on a number of experiments that demonstrate the effectiveness of the Environment Orientation approach: a simple flocking system, a flocking system with multiple sensory environments, and a flocking system in an external environment.

Virtual Fish Interaction

Digital media is currently used for learning and entertainment purposes. This paper describes an interactive installation that allows participants to play with virtual water and a group of koi fish. The installation manipulates recombinant information between person and virtual fish consisting of new media. The virtual fish are used in a flocking system which simulates flocking behavior via the use of the FLOSC, which is commination between Max/MSP and Macromedia Flash. The main sensor is a webcam that tracks the presence and the position of the person which will determine the fish flocking movements and behavior.

Mean-field limit for a collision-avoiding flocking system and the time-asymptotic flocking dynamics for the kinetic equation

A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field limit of the particle system is obtained. Furthermore, the time-asymptotic flocking behavior of the solution to the kinetic equation is also derived. The technics used for local wellposedness and stability follow from similar ideas to those have been used in [3,14,22]. While in order to extend the local result globally, the main contribution here is to generate a series of new estimates for this Vlasov type equation, which imply that the growing of the characteristics can be controlled globally. Further estimates also show the long time flocking phenomena.

A mathematical model for multi-name credit based on community flocking

We present a new mathematical model for multi-name credit that employs stochastic flocking. Flocking mechanisms have been used in a variety of models of biological, sociological and physical aggregation phenomena. As a direct application of a flocking mechanism, we introduce a credit risk model based on community flocking for a credit worthiness index. Correlations between different credit worthiness indices are explained in terms of communication rates and coupling strengths from the flocking system. Based on the flocking model, we compute credit curves for individual names and default time distributions. We also apply the proposed model to the pricing of credit derivatives such as credit default swaps and collateralized debt obligations.