Stable Flocking of Multiple Inertial Agents on Balanced Graphs

In this note, we consider the flocking of multiple agents which have significant inertias and evolve on a balanced information graph. Here, by flocking, we mean that all the agents move with a common velocity while keeping a certain desired internal group shape. We first show that flocking algorithms that neglect agents' inertial effect can cause unstable group behavior. To incorporate this inertial effect, we use the passive decomposition, which decomposes the closed-loop group dynamics into two decoupled systems: a shape system representing the internal group shape and a locked system describing the motion of the center-of-mass. Then, analyzing the locked and shape systems separately with the help of graph theory, we propose a provably stable flocking control law, which ensures that the internal group shape is exponentially stabilized to a desired one, while all the agents' velocities converge to the centroid velocity that is also shown to be time-invariant. This result still holds for slow-switching balanced information graphs. Simulation is performed to validate the theory.     

基于有向网络的智能群体群集运动控制

对具有二次积分动态的智能群体(flock/swarm),在有向网络取得群集运动(flocking/swarming)进行了研究．提出了一个分散控制方法对智能群体进行分散控制．用有向图模型表示智能体之间的相互作用及通信关系．对固定的网络拓扑,控制互连拓扑是固定的,时不变的,运用传统的LaSalle不变集原理,代数图论的有关技巧进行了稳定性分析,并得到以下主要结论:i)智能群体速度方向渐进收敛,并保持方向一致;ii)智能群体速度大小渐进收敛,并保持大小相等;iii)有邻接关系的智能体(Agent)之间没有碰撞发生;iv)智能群体的势场函数被最小化．理论分析显示,有向图的弱连通性及一种称为平衡图的有向图在系统的稳定性分析中扮演着关键角色．最后,给出了一个仿真例子对理论结果进行了验证．     

Hybrid Control for Connectivity Preserving Flocking

In this technical note, we address the combined problem of motion and network topology control in a group of mobile agents with common objective the flocking behavior of the group. Instead of assuming network connectivity, we enforce it by means of distributed topology control that decides on both deletion and creation of communication links between agents, adapting the network to the group's spatial distribution. With this protocol ensuring network connectivity, a decentralized motion controller aligns agent velocity vectors and regulates inter-agent distances to maintain existing network links. The stability of the flocking controller is established in continuous time by means of an observability argument on a quadratic form of the graph Laplacian that exploits the time delay between link deletion and creation caused by the topology control protocol, which induces a dwell time between network switches.      

Stable Flocking Motion of Mobile Agents Following a Leader in Fixed and Switching Networks

Multiple mobile agents with double integrator dynamics, following a leader to achieve a flocking motion formation, are studied in this paper. A class of local control laws for a group of mobile agents is proposed. Prom a theoretical proof, the following conclusions are reached: (i) agents globally align their velocity vectors with a leader, (ii) they converge their velocities to the leaders velocity, (iii) collisions among interconnected agents are avoided, and (iv) agent's artificial potential functions are minimized. We model the interaction and/or communication relationship between agents by algebraic graph theory. Stability analysis is achieved by using classical Lyapunov theory in a fixed network topology, and differential inclusions and nonsmooth analysis in a switching network topology respectively. Simulation examples are provided.     

A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements

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.     

Generating and analyzing hierarchical interaction in a flock of robotic swarms

One of the popular approaches for the self-organized flocking of artificial agents is based on a computer animation model called Boid. This model reproduces flocking motion using three simple behavioral rules: repulsion, attraction, and alignment. However, the flocking performance largely depends on how these rules are configured, and no general guideline exists for the configuration. This paper introduces hierarchical interaction-based flocking by employing individuals that can switch their roles. Robots can move as leaders or followers depending on the situation. The flocking performance is evaluated, and the swarming behavior is analyzed in a scenario where robots travel alternately between two landmarks.     

Flocking of multi‐agent nonholonomic systems with unknown leader dynamics and relative measurements

In this paper, we consider the distributed flocking control problem of multi‐agent nonholonomic systems with a virtual leader whose dynamics is unknown; state information is time varying and not available to all agents under both fixed and switching topologies. On the basis of the relative velocity and orientation information of neighboring agents, two distributed discontinuous control protocols are designed for fixed and switching topologies, respectively. By using tools from algebraic graph theory and nonsmooth analysis, the proposed distributed discontinuous control protocols guarantee that the velocities and orientations of the agents exponentially converge to the velocity and orientation of the virtual leader, respectively, while ensuring collision avoidance of the whole group, if the interaction graph among agents is undirected and the virtual leader with bounded time‐varying velocity has directed paths to other agents. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Topology-preserving flocking of nonlinear agents using optimistic planning

We consider the generalized flocking problem in multiagent systems, where the agents must drive a subset of their state variables to common values, while communication is constrained by a proximity relationship in terms of another subset of variables. We build a flocking method for general nonlinear agent dynamics, by using at each agent a near-optimal control technique from artificial intelligence called optimistic planning. By defining the rewards to be optimized in a well-chosen way, the preservation of the interconnection topology is guaranteed, under a controllability assumption. We also give a practical variant of the algorithm that does not require to know the details of this assumption, and show that it works well in experiments on nonlinear agents.     

Adaptive Flocking Control with a Minority of Informed Agents

In this paper, we address the flocking problem of multiple dynamic mobile agents with a virtual leader in a dynamic proximity network. To avoid fragmentation, we propose a novel flocking algorithm that consists of both an adaptive controller for followers and a feedback controller for the virtual leader. Based on our algorithm, all agents in the group can form a network, maintain connectivity, and track the virtual leader, even when only a minority of agents have access to the information of the virtual leader. Finally, several convincing simulation results are provided that demonstrate 2‐D flocking of a group of agents using the proposed algorithm.     

An overview on optimal flocking

The decentralized aggregate motion of many individual robots is known as robotic flocking. The study of robotic flocking has received considerable attention in the past twenty years. As we begin to deploy flocking control algorithms on physical multi-agent and swarm systems, there is an increasing necessity for rigorous promises on safety and performance. In this paper, we present an overview the literature focusing on optimization approaches to achieve flocking behavior that provide strong safety guarantees. We separate the literature into cluster and line flocking, and categorize cluster flocking with respect to the system-level objective, which may be realized by a reactive or planning control algorithm. We also categorize the line flocking literature by the energy-saving mechanism that is exploited by the agents. We present several approaches aimed at minimizing the communication and computational requirements in real systems via neighbor filtering and event-driven planning, and conclude with our perspective on the outlook and future research direction of optimal flocking as a field.     

Flocking of Multi-Agents With a Virtual Leader

All agents being informed and the virtual leader traveling at a constant velocity are the two critical assumptions seen in the recent literature on flocking in multi-agent systems. Under these assumptions, Olfati-Saber in a recent IEEE Transactions on Automatic Control paper proposed a flocking algorithm which by incorporating a navigational feedback enables a group of agents to track a virtual leader. This paper revisits the problem of multi-agent flocking in the absence of the above two assumptions. We first show that, even when only a fraction of agents are informed, the Olfati-Saber flocking algorithm still enables all the informed agents to move with the desired constant velocity, and an uninformed agent to also move with the same desired velocity if it can be influenced by the informed agents from time to time during the evolution. Numerical simulation demonstrates that a very small group of the informed agents can cause most of the agents to move with the desired velocity and the larger the informed group is the bigger portion of agents will move with the desired velocity. In the situation where the virtual leader travels with a varying velocity, we propose modification to the Olfati-Saber algorithm and show that the resulting algorithm enables the asymptotic tracking of the virtual leader. That is, the position and velocity of the center of mass of all agents will converge exponentially to those of the virtual leader. The convergent rate is also given.      

Multiagent flocking with formation in a constrained environment

We consider the problem of controlling a group of mobile agents to form a designated formation while flocking within a constrained environment. We first propose a potential field based method to drive the agents to move in connection with their neighbors, and regulate their relative positions to achieve the specific formation. The communication topology is preserved during the motion. We then extend the method to flocking with environmental constraints. Stability properties are analyzed to guarantee that all agents eventually form the desired formation while flocking, and flock safely without collision with the environment boundary. We verify our algorithm through simulations on a group of agents performing maximum coverage flocking and traveling through an unknown constrained environment.     

具有干扰的多领航者系统的群集运动的快速收敛

针对具有多领航者网络化系统的离散时间群集运动问题,提出了一阶/二阶网络化系统的包容控制算法。运用现代控制理论、代数图论和线性矩阵不等式等分析工具对所提出的控制算法进行理论分析,得到了具有干扰的多领航者网络化系统在离散时间情况下有限时间内实现群集运动的收敛条件。最后,利用LMI工具箱数值仿真求得正定矩阵范围,进而确定线性系统的稳定性。系统仿真验证了所得结论的正确性。     

Attitude‐synchronization flocking of multiple 3‐dimensional nonholonomic agents without position measurement

This paper studies the attitude‐synchronization flocking problem for multiple 3‐dimensional nonholonomic agents. By analyzing the nonlinearity of the nonholonomic model and invoking the neighbor‐based design principle, we develop a distributed linear control protocol with the local information from each agent and its neighbors in proximity, especially, no position measurement is employed. Based on max‐min and Lyapunov stability theory, the proposed distributed control protocol can ensure the 3 flocking rules and attitude synchronization meanwhile, if collision avoidance and communication connectivity are guaranteed at the initial time. Additionally, numerical simulations are provided to verify the theoretical results.     

Flocking of multi-agent dynamical systems based on pseudo-leader mechanism

Flocking behavior of multiple agents can be widely observed in nature such as schooling fish and flocking birds. Recent literature has proposed the possibility that flocking can be achieved even with only a small fraction of informed agents with the desired position and velocity. However, it is still a challenging problem to determine which agents should be informed or have the ability to detect the desired information. This paper aims to address this problem. By combining the ideas of virtual force and pseudo-leader mechanism, where a pseudo-leader represents an informed agent who can detect the desired information, we propose a scheme for choosing pseudo-leaders in a multi-agent group, which can be applied to an unconnected or switching neighbor graph. Numerical examples are given to show the effectiveness of the methods presented in this paper.     

Flocking shape analysis of multi-agent systems

In this paper,we consider the shape control in flocking behavior of a multi-agent system with a virtual leader.Besides the traditional flocking control terms,which include a gradient-based term,a velocity consensus term and a navigational feed-back in general,a new piecewise smooth neighbor-based local controller is added to regulate the configuration to the desired flocking shape.All agent velocities approach the desired velocity asymptotically,while collisions among agents can be avoided.Furthermore,based...     

Flocking of multi‐agent dynamical systems with intermittent nonlinear velocity measurements

In this paper, the problem of flocking control in networks of multiple dynamical agents with intermittent nonlinear velocity measurements is studied. A new flocking algorithm is proposed to guarantee the states of the velocity variables of all the dynamical agents to converge to consensus while ensuring collision avoidance of the whole group, where each agent is assumed to obtain some nonlinear measurements of the relative velocity between itself and its neighbors only on a sequence of non‐overlapping time intervals. The results are then extended to the scenario of flocking with a nonlinearly dynamical virtual leader, where only a small fraction of agents are informed and each informed agent can obtain intermittent nonlinear measurements of the relative velocity between itself and the virtual leader. Theoretical analysis shows that the achieved flocking in systems with or without a virtual leader is robust against the time spans of the agent speed‐sensors. Finally, some numerical simulations are provided to illustrate the effectiveness of the new design. Copyright © 2011 John Wiley & Sons, Ltd.     

Flocking of Multi-agent Systems with Unknown Nonlinear Dynamics and Heterogeneous Virtual Leader

This paper investigates the flocking control of multi-agent systems with unknown nonlinear dynamics while the virtual leader information is heterogeneous. The uncertain nonlinearity in the virtual leader information is considered, and the weaker constraint on the velocity information measurements is assumed. In addition, a bounded assumption on the unknown nonlinear dynamics is also considered. It is weaker than the Lipschitz condition adopted in the most flocking control methods. To avoid fragmentation, we construct a new potential function based on the penalty idea when the initial network is disconnected. A dynamical control law including a adjust parameter is designed to achieve the stable flocking. It is proven that the velocities of all agents approach to consensus and no collision happens between the mobile agents. Finally, several simulations verify the effectiveness of the new design, and indicate that the proposed method has high convergence and the broader applicability in practical applications with more stringent restrictions.

     

等级制度下带有时变时滞的群集运动

主要研究了等级制度下带有时变时滞的群集运动。证明了在一定条件的等级制度下,当时间趋于无穷大时,智能体之间即使存在着时变的通信时滞,也能达到群集运动。最后,用数值仿真的例子来证明结论的有效性。     

Flocking control of a fleet of unmanned aerial vehicles

Current applications using single unmanned vehicle have been gradually extended to multiple ones due to their increased efficiency in mission accomplishment, expanded coverage areas and ranges, as well as enhanced system reliability. This paper presents a flocking control method with application to a fleet of unmanned quadrotor helicopters (UQHs). Three critical characteristics of formation keeping, collision avoidance, and velocity matching have been taken into account in the algorithm development to make it capable of accomplishing the desired objectives (like forest/pipeline surveillance) by safely and efficiently operating a group of UQHs. To achieve these, three layered system design philosophy is considered in this study. The first layer is the flocking controller which is designed based on the kinematics of UQH. The modified Cucker and Smale model is used for guaranteeing the convergence of UQHs to flocking, while a repelling force between each two UQHs is also added for ensuring a specified safety distance. The second layer is the motion controller which is devised based on the kinetics of UQH by employing the augmented state-feedback control approach to greatly minimize the steady-state error. The last layer is the UQH system along with its actuators. Two primary contributions have been made in this work: first, different from most of the existing works conducted on agents with double integrator dynamics, a new flocking control algorithm has been designed and implemented on a group of UQHs with nonlinear dynamics. Furthermore, the constraint of fixed neighbouring distance in formation has been relaxed expecting to significantly reduce the complexity caused by the increase of agents number and provide more flexibility to the formation control. Extensive numerical simulations on a group of UQH nonlinear models have been carried out to verify the effectiveness of the proposed method.