Flocking Model Research Articles

Pigeon interaction mode switch-based UAV distributed flocking control under obstacle environments

Unmanned aerial vehicle (UAV) flocking control is a serious and challenging problem due to local interactions and changing environments. In this paper, a pigeon flocking model and a pigeon coordinated obstacle-avoiding model are proposed based on a behavior that pigeon flocks will switch between hierarchical and egalitarian interaction mode at different flight phases. Owning to the similarity between bird flocks and UAV swarms in essence, a distributed flocking control algorithm based on the proposed pigeon flocking and coordinated obstacle-avoiding models is designed to coordinate a heterogeneous UAV swarm to fly though obstacle environments with few informed individuals. The comparative simulation results are elaborated to show the feasibility, validity and superiority of our proposed algorithm.

An Alternative Approach to Mean Field Game with Major and Minor Players, and Applications to Herders Impacts

The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean–Vlasov dynamics in some of the players’ optimization problems. We apply this approach to linear quadratic models for which we recover the existing solutions for open loop equilibria, and we show that we can also provide solutions for closed loop versions of the game. Finally, we implement numerically our theoretical results on a simple model of flocking.

Effects of agent's orientation in 2D flocking models

Various different types of collective motions have attracted attention from physicists; this is a fascinating phenomenon, resulting from the very simple interactions between individuals (particles/cells). Our aim is to contribute to elucidating the motion of collective behavior of a non-equilibrium multi-agent system. In this context, the topic of this manuscript is to study the effect of the zone of orientation on the collective motion in two-dimensional space. In this investigation, we extend the model suggested by Viscek et al. for only a single interaction radius. In our proposed model, the particles corresponding to agents locally interacting with their neighbors according to simple rules depending on the particular condition. At each time step the velocity of an agent depends on their direction and is perturbed by an external noise η. Particularly, we show that with a specific fixed parameter a phase transition can be achieved, from disordered motion of particles to ordered motion, by varying the radius of orientation R2 and the value of the density. Furthermore, the value of R2 at which the transition emerges depends strongly on the size of repulsion zone R1. The study is performed over different situations via a numerical simulation technique. Implications of these findings are discussed in the section of simulation results.

A new flocking model through body attitude coordination

We present a new model for multi-agent dynamics where each agent is described by its position and body attitude: agents travel at a constant speed in a given direction and their body can rotate around it adopting different configurations. In this manner, the body attitude is described by three orthonormal axes giving an element in [Formula: see text] (rotation matrix). Agents try to coordinate their body attitudes with the ones of their neighbours. In this paper, we give the individual-based model (particle model) for this dynamics and derive its corresponding kinetic and macroscopic equations.

A discontinuous Galerkin method on kinetic flocking models

We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker–Smale [Emergent behaviors in flocks, IEEE Trans. Autom. Control. 52 (2007) 852–862] and Motsch–Tadmor [A new model for self-organized dynamics and its flocking behavior, J. Statist. Phys. 144 (2011) 923–947] models. We first establish a well-posedness theory and large-time flocking behavior for the kinetic systems, which indicates a concentration in velocity variable in infinite time. We then apply a discontinuous Galerkin method to treat the asymptotic [Formula: see text]-singularity, and construct high-order positive-preserving schemes to solve kinetic flocking systems.

Sharp conditions to avoid collisions in singular Cucker–Smale interactions

We consider the Cucker–Smale flocking model with a singular communication weight ψ(s)=s−α with α>0. We provide a critical value of the exponent α in the communication weight leading to global regularity of solutions or finite-time collision between particles. For α≥1, we show that there is no collision between particles in finite time if they are placed in different positions initially. For α≥2 we investigate a version of the Cucker–Smale model with expanded singularity i.e. with weight ψδ(s)=(s−δ)−α, δ≥0. For such model we provide a uniform with respect to the number of particles estimate that controls the δ-distance between particles. In case of δ=0 it reduces to the estimate of collision avoidance.

An Adaptive Agent-Based Model of Homing Pigeons: A Genetic Algorithm Approach

Conventionally, agent-based modelling approaches start from a conceptual model capturing the theoretical understanding of the systems of interest. Simulation outcomes are then used “at the end” to validate the conceptual understanding. In today’s data rich era, there are suggestions that models should be data-driven. Data-driven workflows are common in mathematical models. However, their application to agent-based models is still in its infancy. Integration of real-time sensor data into modelling workflows opens up the possibility of comparing simulations against real data during the model run. Calibration and validation procedures thus become automated processes that are iteratively executed during the simulation. We hypothesize that incorporation of real-time sensor data into agent-based models improves the predictive ability of such models. In particular, that such integration results in increasingly well calibrated model parameters and rule sets. In this contribution, we explore this question by implementing a flocking model that evolves in real-time. Specifically, we use genetic algorithms approach to simulate representative parameters to describe flight routes of homing pigeons. The navigation parameters of pigeons are simulated and dynamically evaluated against emulated GPS sensor data streams and optimised based on the fitness of candidate parameters. As a result, the model was able to accurately simulate the relative-turn angles and step-distance of homing pigeons. Further, the optimised parameters could replicate loops, which are common patterns in flight tracks of homing pigeons. Finally, the use of genetic algorithms in this study allowed for a simultaneous data-driven optimization and sensitivity analysis.

Existence of weak solutions to a kinetic flocking model with cut-off interaction function

Existence of weak solutions to a kinetic flocking model with cut-off interaction function

Large-Scale Patterns in a Minimal Cognitive Flocking Model: Incidental Leaders, Nematic Patterns, and Aggregates.

We study a minimal cognitive flocking model, which assumes that the moving entities navigate using the available instantaneous visual information exclusively. The model consists of active particles, with no memory, that interact by a short-ranged, position-based, attractive force, which acts inside a vision cone (VC), and lack velocity-velocity alignment. We show that this active system can exhibit-due to the VC that breaks Newton's third law-various complex, large-scale, self-organized patterns. Depending on parameter values, we observe the emergence of aggregates or millinglike patterns, the formation of moving-locally polar-files with particles at the front of these structures acting as effective leaders, and the self-organization of particles into macroscopic nematic structures leading to long-ranged nematic order. Combining simulations and nonlinear field equations, we show that position-based active models, as the one analyzed here, represent a new class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems. The reported results are of prime importance in the study, interpretation, and modeling of collective motion patterns in living and nonliving active systems.

Clusterflock: a flocking algorithm for isolating congruent phylogenomic datasets.

BackgroundCollective animal behavior, such as the flocking of birds or the shoaling of fish, has inspired a class of algorithms designed to optimize distance-based clusters in various applications, including document analysis and DNA microarrays. In a flocking model, individual agents respond only to their immediate environment and move according to a few simple rules. After several iterations the agents self-organize, and clusters emerge without the need for partitional seeds. In addition to its unsupervised nature, flocking offers several computational advantages, including the potential to reduce the number of required comparisons.FindingsIn the tool presented here, Clusterflock, we have implemented a flocking algorithm designed to locate groups (flocks) of orthologous gene families (OGFs) that share an evolutionary history. Pairwise distances that measure phylogenetic incongruence between OGFs guide flock formation. We tested this approach on several simulated datasets by varying the number of underlying topologies, the proportion of missing data, and evolutionary rates, and show that in datasets containing high levels of missing data and rate heterogeneity, Clusterflock outperforms other well-established clustering techniques. We also verified its utility on a known, large-scale recombination event in Staphylococcus aureus. By isolating sets of OGFs with divergent phylogenetic signals, we were able to pinpoint the recombined region without forcing a pre-determined number of groupings or defining a pre-determined incongruence threshold.ConclusionsClusterflock is an open-source tool that can be used to discover horizontally transferred genes, recombined areas of chromosomes, and the phylogenetic ‘core’ of a genome. Although we used it here in an evolutionary context, it is generalizable to any clustering problem. Users can write extensions to calculate any distance metric on the unit interval, and can use these distances to ‘flock’ any type of data.

A new discrete Cucker-Smale flocking model under hierarchical leadership

This paper studies the flocking behavior in a new discrete-time Cucker-Smale model under hierarchical leadership. The features of this model are that each individual has its own intrinsic nonlinear dynamics and the interaction between individuals follows a hierarchical leadership structure. Based on a specific matrix norm, we prove that the conditional flocking indeed occurs. Numerical experiments are given to confirm the theoretical results.

A weighted adaptive-velocity self-organizing model and its high-speed performance

This paper proposed an improved adaptive-velocity self-organizing model as a prospective candidate in order to enhance high-speed convergence and accelerate convergence. Moreover, weights are assigned to reinforce convergence under super high-speed circumstances. Convergence performance is assessed via group polarization, convergence ratio and convergent time. As verified by numerical experiments, superior high-speed performance and fast convergence are achieved simultaneously in the improved adaptive-velocity model. The weighted adaptive model prominently improved super high-speed performance with short convergent time and low energy consumption. Then, the parameter space of the weighted adaptive flocking model is investigated.

Combined fitness function based particle swarm optimization algorithm for system identification

An improved particle swarm optimization (PSO) algorithm, called combined fitness function based particle swarm optimization algorithm is presented in this investigation. PSO algorithm originated from bird flocking models and is effective in solving system identification problems. However in the identification process, single measure like the squared error between the measured values and the modeled ones may be not a sufficient criterion. The improved PSO algorithm adopts a combined fitness function to solve this problem. Mean Square Error (MSE) and Grey Absolute Relational Grade (GARG) are employed as evaluation measures, and entropy method is used to determine the relative weights of the two measures. Numerical simulations and experiments are carried out to evaluate the performance of the improved PSO. Consistent results demonstrate that combined fitness function based PSO algorithm is feasible and efficient for system identification, and can achieve better performance over conventional PSO algorithm.

Flock Leadership: Understanding and influencing emergent collective behavior

This study introduces Flock Leadership, a framework for understanding and influencing emergent collective behavior in the context of human organizing. Collective capacities emerge when interactions between individuals enact divergent and convergent ways of perceiving and responding to reality. An agent-based flocking model is employed to represent these interactive dynamics and emergent processes. This study explicates the model's constructs, translating its algorithms into behavioral norms at the individual level and its outcomes into collective behaviors at the group level. Phenomena-based simulation modeling links two collective states—technical capacity and adaptive capacity—to the specific underlying norm configurations from which they emerge. Flock Leadership provides a unique theoretical framing of emergent collective behavior in organizational settings, a new methodology for analyzing relationships between those emergent behavioral patterns and the interaction norms underlying them, and a useful means for identifying leadership opportunities.

The combined effect of attraction and orientation zones in 2D flocking models

In nature, many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex motion of these systems, we study the Vicsek model of self-propelled particles (SPP) which is an important tool to investigate the behavior of collective motion of live organisms. This model reproduces the biological behavior patterns in the two-dimensional (2D) space. Within the framework of this model, the particles move with the same absolute velocity and interact locally in the zone of orientation by trying to align their direction with that of the neighbors. In this paper, we model the collective movement of SPP using an agent-based model which follows biologically motivated behavioral rules, by adding a second region called the attraction zone, where each particles move towards each other avoiding being isolated. Our main goal is to present a detailed numerical study on the effect of the zone of attraction on the kinetic phase transition of our system. In our study, the consideration of this zone seems to play an important role in the cohesion. Consequently, in the directional orientation, the zone that we added forms the compact particle group. In our simulation, we show clearly that the model proposed here can produce two collective behavior patterns: torus and dynamic parallel group. Implications of these findings are discussed.

A Flocking Model of Human Organizing: Leadership Implications

This study uses flock modeling to advance understanding of emergent collective behavior in contexts of human organizing. Collective capacities emerge from interactions between individuals. An agent...

Phase Transitions in a Kinetic Flocking Model of Cucker--Smale Type

We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change phenomenon takes place as diffusion decreases, bringing the system from a "disordered" to an "ordered" state. This effect is related to recently noticed phenomena for the diffusive Vicsek model. We also carry out numerical simulations of the system and give further details on the phase transition.

A model-sensor framework to predict homing pigeon flights in real time

Advances in sensor technology have triggered the development of model-sensor frameworks that integrate real-time sensor data into simulation models. Successful implementations include sensor streams of physical properties of the environment, and traces of human mobility as captured by mobile devices. Implementation of real-time sensor-data streams from tagged animals is not yet in place. However, these are anticipated in the near future. In this research, we explore a model-sensor framework with a novel agent-based flocking model for homing pigeons and an emulated sensor stream that is derived from a previously recorded GPS track. Results point to conceptual shortcomings but also opportunities in transferring conventional models to an integrated model-sensor framework. From these insights, directions for further research towards automatic model-calibration and adaptive rulesets were identified.

Topological-distance-dependent transition in flocks with binary interactions.

We have studied a flocking model with binary interactions (binary flock), where the velocity of an agent depends on the velocity of only another agent and its own velocity, topped by the angular noise. The other agent is selected as the nth topological neighbor; the specific value of n being a fixed parameter of the problem. On the basis of extensive numerical simulation results, we argue that for n = 1, the phase transition from the ordered to the disordered phase of the flock is a special kind of discontinuous transition. Here, the order parameter does not flip-flop between multiple metastable states. It continues its initial disordered state for a period t(c), then switches over to the ordered state and remains in this state ever after. For n = 2, it is the usual discontinuous transition between two metastable states. Beyond this range, the continuous transitions are observed for n≥3. Such a system of binary flocks has been further studied using the hydrodynamic equations of motion. Linear stability analysis of the homogeneous polarized state shows that such a state is unstable close to the critical point and above some critical speed, which increases as we increase n. The critical noise strengths, which depend on the average correlation between a pair of topological neighbors, are estimated for five different values of n, which match well with their simulated values.

Flocking with discrete symmetry: The two-dimensional active Ising model.

We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams inthevicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.