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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., (© 2024 Massachusetts Institute of Technology.)

This study proposes a method for uniformly revolving swarm robots to entrap multiple targets, which is based on a gene regulatory network, an adaptive decision mechanism, and an improved Vicsek-model. Using the gene regulatory network method, the robots can generate entrapping patterns according to the environmental input, including the positions of the targets and obstacles. Next, an adaptive decision mechanism is proposed, allowing each robot to choose the most well-adapted capture point on the pattern, based on its environment. The robots employ an improved Vicsek-model to maneuver to the planned capture point smoothly, without colliding with other robots or obstacles. The proposed decision mechanism, combined with the improved Vicsek-model, can form a uniform entrapment shape and create a revolving effect around targets while entrapping them. This study also enables swarm robots, with an adaptive pattern formation, to entrap multiple targets in complex environments. Swarm robots can be deployed in the military field of unmanned aerial vehicles' (UAVs) entrapping multiple targets. Simulation experiments demonstrate the feasibility and superiority of the proposed gene regulatory network method. [ABSTRACT FROM AUTHOR]

The thermodynamic Cucker–Smale model (TCS model) describes dynamic consistency caused by different temperatures between multi-agent particles. This paper studies the flocking behaviors of the TCS model with multiplicative white noise under hierarchical leadership. First, we introduce the corresponding model of two particles. Then, by using mathematical induction and considering the properties of differential functions, it is proved that, under certain conditions, the group can achieve flocking. Finally, we verify the conclusion through numerical simulation results. Similarly, this paper studies the above model with perturbation functions. [ABSTRACT FROM AUTHOR]

This paper addresses the leaderless and leader-followers flocking motion problems of multi-agent systems in a workspace with obstacles. We consider inertial agents with equally limited communication radius and heterogeneous input constraints. Using the notion of proximity graphs, we provide distributed controllers to induce the desired flocking behaviour. Unlike previous results, our controller designs do not require predicted states or a target determination scheme and allow edge deletions. Also, by taking advantage of the group's heterogeneity, our controllers allow agents with less restrictive input constraints to compensate for the control effort that their less capable neighbours cannot provide. We illustrate the effectiveness of our proposals through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of finite-time flocking in the multi-agent nonholonomic system with proximity graph. With the aid of singular communication function and results from graph theory, a novel distributed control protocol is proposed, where each agent merely obtains state information of its neighbors. Based on the theory of finite-time stability, the proposed protocol can achieve flocking within a finite-time and an upper bound on the setting time can be derived. Furthermore, we can deduce several sufficient conditions to the problem under the assumption that the positions and relative distances of agents are unknown. These sufficient conditions show that there are always suitable gains that enable our proposed protocol to perform finite-time flocking control and maintain the connectivity of the graph for any given initial connected graphs. Finally, the theoretical results are validated by numerical simulations. [ABSTRACT FROM AUTHOR]

Dealing with the flocking problems of Cucker-Smale systems is a challenging issue. In this paper, the finitetime and fixed-time flocking problems of the Cucker-Smale system are investigated. By designing new continuous non-Lipschitz pinning controllers and using the theory of differential equations, sufficient conditions for the flocking of Cucker-Smale systems are obtained. Besides, sufficient conditions are given to ensure that there is no collision during the process of flocking. The effect of control parameters on the convergence speed is also investigated. The results show that the convergence time is related to control parameters and the density of pinned nodes. Finally, some numerical simulations are used to verify the theoretical results. [ABSTRACT FROM AUTHOR]

We study the comparison between the phenomenological and kinetic models for a mixture of gases from the viewpoint of collective dynamics. In the case in which constituents are Eulerian gases, balance equations for mass, momentum, and energy are the same in the main differential part, but production terms due to the interchanges between constituents are different. They coincide only when the thermal and mechanical diffusion are sufficiently small. In this paper, we first verify that both models satisfy the universal requirements of conservation laws of total mass, momentum, and energy, Galilean invariance and entropy principle. Following the work of Ha and Ruggeri (ARMA 2017), we consider spatially homogeneous models which correspond to the generalizations of the Cucker Smale model with thermal effect. In these circumstances, we provide analytical results for the comparison between two resulting models and also present several numerical simulations to complement analytical results. [ABSTRACT FROM AUTHOR]

We introduce and analyze a model for the dynamics of flocking and steering of a finite number of agents. In this model, each agent's acceleration consists of flocking and steering components. The flocking component is a generalization of many of the existing models and allows for the incorporation of many real world features such as acceleration bounds, partial masking effects, and orientation bias. The steering component is also integral to capture real world phenomena. We provide rigorous sufficient conditions under which the agents flock and steer together. We also provide a formal singular perturbation study of the situation where flocking happens much faster than steering. We end our work by providing some numerical simulations to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

We study emergent behaviors of thermomechanical Cucker-Smale (TCS) ensemble confined in a harmonic potential field. In the absence of external force field, emergent dynamics of TCS particles has been extensively studied recently under various frameworks formulated in terms of initial configuration, system parameters and network topologies. Moreover, the TCS model does not exhibit rotating motions in the absence of an external force field. In this paper, we show the emergence of periodically rotating one-point cluster for the TCS model in a harmonic potential field using elementary energy estimates and continuity argument. We also provide several numerical simulations and compare them with analytical results. [ABSTRACT FROM AUTHOR]

We study the inertial spin model which consists of two variables: velocity as a mechanical observable and spin as an internal variable. In this paper, we slightly modified the original inertial spin model where the spin in the dynamics of the velocity is replaced by the average of spins. Moreover, by introducing two external control functions (rotation control and alignment control), we show the emergence of velocity and spin alignments mainly depends on these control functions. Finally, we perform numerical simulations that support and complement our theoretical results. [ABSTRACT FROM AUTHOR]

We study the pattern formation problem of the Cucker--Smale (CS) flocking model. A distributed CS type flocking model for formation control is introduced based on our previous collision-avoiding model. We present two sufficient frameworks guaranteeing the emergence of flocking and formation achievement in terms of the initial state and system parameters. In the first framework, we show a threshold phenomenon between unconditional and conditional flocking, embodying all three rules of Reynolds: velocity alignment, cohesion, and collision avoidance. Furthermore, with an additional condition on the initial state and system parameters, we show that the agents also converge to a desired spatial configuration in the second framework. Finally, we perform some numerical simulations to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

As we known, it is popular for a designed system to achieve a prescribed performance, which have remarkable capability to regulate the flow of information from distinct and independent components. Also, it is not well understand, in both theories and applications, how self propelled agents use only limited environmental information and simple rules to organize into an ordered motion. In this paper, we focus on analysis the flocking behaviour and the line-shaped pattern for collective motion involving time delay effects. Firstly, we work on a delayed Cucker-Smale-type system involving a general communication weight and a constant delay τ > 0 for modelling collective motion. In a result, by constructing a new Lyapunov functional approach, combining with two delayed differential inequalities established by L2-analysis, we show that the flocking occurs for the general communication weight when ττ is sufficiently small. Furthermore, to achieve the prescribed performance, we introduce the line-shaped inner force term into the delayed collective system, and analytically show that there is a flocking pattern with an asymptotic flocking velocity and line-shaped pattern. All results are novel and can be illustrated by numerical simulations using some concrete influence functions. Also, our results significantly extend some known theorems in the literature. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to investigate the flocking behavior of the discrete-time Cucker-Smale(C-S) model under general interaction network topologies with agents having their free-will accelerations. We prove theoretically that if the free-will accelerations of agents are summable, then, for any given initial conditions, the solution achieves flocking with a finite moving speed by suitably choosing the time step as well as the communication rate β of the system or the strength of the interaction between agents. In particular, if the communication rate of the system is subcritical, i.e., β is less than a critical value βc, then flocking holds for any initial conditions regardless of the strength of the interaction between agents. While, if the communication rate is critical (β = βc) or supercritical (β > βc), then flocking can only be achieved by making the strength of the interaction large enough. We also present some numerical simulations to support our obtained theoretical results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper investigates the flocking problem of quad-rotor UAVs. Considering the actual situations, we derived a new simplified quad-rotor UAV model which is more reasonable. Based on the model, the T-S fuzzy model of attitude dynamic equation and the corresponding T-S fuzzy feedback controller are discussed. By introducing a double-loop control construction, we adjust its attitude to realize the position control. Then a flocking algorithm is proposed to achieve the flocking of the quad-rotor UAVs. Compared with the flocking algorithm of the mass point model, we dealt with the collision problem of the quad-rotor UAVs. In order to improve the airspace utilization, a more compact configuration called quasi e-lattice is constructed to guarantee the compact flight of the quad-rotor UAVs. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

A generalization of the Cucker-Smale model for collective animal behavior is investigated. The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in animal decision making, but are often neglected in modeling: (i) stochasticity (imperfections) of individual behavior and (ii) delayed responses of individuals to signals in their environment. Sufficient conditions for flocking for the generalized Cucker-Smale model are derived by using a suitable Lyapunov functional. As a by-product, a new result regarding the asymptotic behavior of delayed geometric Brownian motion is obtained. In the second part of the paper, results of systematic numerical simulations are presented. They not only illustrate the analytical results, but hint at a somehow surprising behavior of the system--namely, that the introduction of an intermediate time delay may facilitate flocking. [ABSTRACT FROM AUTHOR]

The paper presents a method for decentralized flocking and global formation building for a network of unicycle-like robots described by the standard kinematics equations with hard constraints on the robots linear and angular velocities. We propose decentralized motion coordination control algorithms for the robots so that they collectively move in a desired geometric pattern from any initial position. There are no predefined leaders in the group and only local information is required for the control. The effectiveness of the proposed control algorithms is illustrated via computer simulations and experiments with real robots. [ABSTRACT FROM AUTHOR]

In this paper, we study the flocking problem of multi-agent systems with obstacle avoidance, in the situation when only a fraction of the agents have information on the obstacles. Obstacles of arbitrary shape are allowed, no matter if their boundary is smooth or non-smooth, and no matter it they are convex or non-convex. A novel geometry representation rule is proposed to transfer obstacles to a dense obstacle-agents lattice structure. Non-convex regions of the obstacles are detected and supplemented using a geometric rule. The uninformed agents can detect a section of the obstacles boundary using only a range position sensor. We prove that with the proposed protocol, uninformed agents which maintain a joint path with any informed agent can avoid obstacles that move uniformly and assemble around a point along with the informed agents. Eventually all the assembled agents reach consensus on their velocity. In the entire flocking process, no distinct pair of agents collide with each other, nor collide with obstacles. The assembled agents are guaranteed not to be lost in any non-convex region of the obstacles within a distance constraint. Numerical simulations demonstrate the flocking algorithm with obstacle avoidance both in 2D and 3D space. The situation when every agent is informed is considered as a special case. [ABSTRACT FROM AUTHOR]

We present a mathematical model for stock market volatility flocking. Our proposed model consists of geometric Brownian motions with time-varying volatilities coupled with Cucker-Smale (C-S) flocking and regime switching mechanisms. For all-to-all interactions, we assume that all assets' volatilities are coupled to each other with a constant interaction weight, and we show that the common volatility emerges asymptotically and discuss its financial applications. We also provide several numerical simulations and compare them to existing analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the flocking problem of multi-agent systems with multiple groups. First, some algorithms using local information are designed to divide the agents into any pre-assigned number of groups in fixed and switching heterogeneous networks, respectively. Based on algebraic graph theory and Barbalat’s lemma, convergence criteria are established to ensure velocity alignment and cohesion of each subgroup as well as collision avoidance between any agents in the whole group. Second, an algorithm for homogeneous networks is studied. Simulation examples are finally presented to verify the effectiveness of our theoretical results. [ABSTRACT FROM PUBLISHER]

This paper presents the experimental implementation of a flocking algorithm for multiple robotic fish governed by extended second-order unicycles. Combing consensus protocols with attraction/repulsion functions, a flocking algorithm is proposed to make the agents asymptotically converge to swim with consistent velocities and approach the equilibrium distances to their neighbors. The LaSalle–Krasovskii invariance principle is applied to verify the stability of the system. Besides numerical simulations, platform simulations involving robotic fish kinematic constraint and control mechanism are shown. An experiment with three robotic fish is implemented to illustrate the effectiveness of the proposed flocking algorithm in the presence of external disturbance and boundary collision. [ABSTRACT FROM AUTHOR]

In order to study the influence of external force or external perturbation on flocking behavior, a Cucker–Smale flocking model with singular communication weight and perturbation functions is proposed. By imposing appropriate restrictions on the perturbation functions, we first prove the system does not allow any collisions between agents under certain initial conditions. Moreover, under the same conditions, we obtain the system has an asymptotic flocking. Last, we give specific examples of perturbation functions and verify the correctness of the results through numerical simulations. • Propose a Cucker–Smale flocking model with singular communication weight and perturbation functions. • Under some certain conditions, the system has an asymptotic flocking without collision between any agent. • Give specific perturbation functions and verify the reliability of the results through numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates a flocking problem of multiple agents with heterogeneous nonlinear dynamics. In order to avoid fragmentation, we construct a potential function and a connectivity-preserving flocking algorithm to enable the multiple agents to move with the same velocity while preserving the connectivity of underlying networks with a mild assumption that the initial network is connected and the coupling strength of the initial network of the nonlinear velocity consensus term is larger than a threshold value. Furthermore the proposed flocking algorithm is extended to solve the problem of multi-agent systems with a nonlinear dynamical virtual leader. The result is that all agents' velocities asymptotically approach to the velocity of the virtual leader, and the distance between any two agents is asymptotically stabilized to avoid collisions among agents. Finally, some numerical simulations are presented to illustrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: We have developed numerical simulations of three dimensional suspensions of active particles to characterize the capabilities of the hydrodynamic stresses induced by active swimmers to promote global order and emergent structures in active suspensions. We have considered squirmer suspensions embedded in a fluid modeled under a Lattice Boltzmann scheme. We have found that active stresses play a central role to decorrelate the collective motion of squirmers and that contractile squirmers develop significant aggregates. [Copyright &y& Elsevier]

In a multi-agent system, the number and initial position of informed agents play a major role in the convergence of unin-formed agents. In this paper, three different patterns of informed agents' initial positions are studied to see how the convergence percentage can be affected by the number of informed agents. The proposed initial locations are intuitive and inferred from the col-lective behavior in humans. To evaluate efficiency of the proposed methods and to compare them from different points of view, large number of computer simulations is peiformed and results are analyzed. [ABSTRACT FROM AUTHOR]

The splitting and joining capabilities of a previously designed framework for the collective movement of mobile robots are studied. This framework is implemented in a distributed manner among the robots and allows scalability with increasing number of robots. It is expandable with new functionalities through the inclusion of new modules. Splitting functionality is created by including a new module, while joining does not need new structures. A total of 130 systematic experiments, grouped in six different sets, were undertaken to test the splitting and joining functions of the framework, yielding results in which robots behaved as expected. Four of the sets correspond to experiments in simulation using up to 40 robots. The remaining sets use eight real robots. [ABSTRACT FROM AUTHOR]

We present a class of extended Kuramoto models describing a flocking motion of particles on the infinite cylinder and provide sufficient conditions for the asymptotic formation of locked solutions where the distance between particles remains constant. Our proposed model includes the complex Kuramoto model for synchronization. We also provide several numerical simulation results and compare them with analytical results. [ABSTRACT FROM AUTHOR]

This paper presents a bio-inspired controller capable of controlling a swarm of unmanned aerial vehicles (UAVs) to provide a visual representation of an invisible airborne hazardous substance such as a chemical cloud. By using this approach, the position of the individuals in the swarm of UAVs forms a distribution map without the need for transmitting sensor data to a base station for chemical map generation. A behaviour-based approach is adopted to develop this controller so that it is computationally cheap and highly effective, compared to other coverage methods such as Voronoi partition or simulated annealing. Simulation results show that the approach is highly responsive to dynamic changes in the environment. [ABSTRACT FROM AUTHOR]

This article introduces a novel approach to increase the performances of multi-agent based simulations. We focus on a particular kind of multi-agent based simulation where a collection of interacting autonomous situated entities evolve in a situated environment. Our approach combines the fast multipole method coming from computational physics with agent-based microscopic simulations. The aim is to speed up the execution of a multi-agent based simulation while controlling the precision of the associated approximation. This approach may be considered as the first step of a larger effort aiming at designing a generic kernel to support efficient large-scale multi-agent based simulations. This approach is illustrated in this paper by the simulation of large scale flocking dynamical systems. [ABSTRACT FROM AUTHOR]

Very recently, a model for flocking was introduced by Cucker and Smale together with a proof of convergence. This proof established unconditional convergence to a common velocity provided the interaction between agents was strong enough and conditional convergence otherwise. The strength of the interaction is measured by a parameter β ≥ 0 and the critical value at which unconditional convergence stops holding is β = 1/2. This model was extended by Shen to allow for a hierarchical leadership structure among the agents and similar convergence results were proved. But, for discrete time, unconditional convergence was proved only for $\beta < \frac{1}{2k}$ (k being the number of agents). In this note we improve on this result showing that unconditional convergence holds indeed for β < 1/2. [ABSTRACT FROM AUTHOR]

Flocking, arguably one of the most fascinating concepts in nature, has in recent times established a growing stature within the field of robotics. In this paper, we control the collective motion of a flock of nonholonomic car-like vehicles in a constrained environment. A continuous centralized motion planner is proposed for split/rejoin maneuvers of the flock via the Lyapunov-based control scheme to anchor avoidance of obstacles intersecting the paths of flockmates. The control scheme inherently utilizes the artificial potential fields, within a new leader-follower framework, to accomplish the desired formations and reformations of the flock. The effectiveness of the proposed control laws are demonstrated through computer simulations. [ABSTRACT FROM AUTHOR]

Most existing flocking algorithms rely on information about both relative position and relative velocity among neighbouring agents. In this article, we investigate the flocking problem with only position measurements. We propose a provably-stable flocking algorithm, in which an output vector is produced by distributed filters based on position information alone but not velocity information. Under the assumption that the initial interactive network is connected, the flocking algorithm not only can steer a group of agents to a stable flocking motion, but also can preserve the connectivity of the interactive network during the dynamical evolution. Moreover, we investigate the flocking algorithm with a virtual leader and show that all agents can asymptotically attain a desired velocity even if only one agent in the team has access to the information of the virtual leader. We finally show some numerical simulations to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations. [ABSTRACT FROM AUTHOR]

A model for the displacement of self-driven organisms is studied by means of extensive computer simulations. Local interactions influenced by noisy communications among organisms, leads to the onset of collective motion at low noise levels. When the noise is increased the system undergoes first-order transitions into disordered states of motion. We have also studied the relaxation process between these states. By fitting the time dependence of the order parameter when the system is annealed from a state below coexistence to another above it, we conclude that the relaxation can be well described by means of a stretched exponential. In this way the characteristic relaxation times are obtained. [ABSTRACT FROM AUTHOR]