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.     

Distributed adaptive flocking of robotic fish system with a leader of bounded unknown input

A distributed leader-follower flocking problem of multiple robotic fish governed by extended second-order unicycles is studied in this paper. The multi-agent system consists of only one leader with pre-appointed and bounded speeds. A distributed flocking algorithm on the basis of the combination of consensus and attractive/repulsive functions is investigated, in which adaptive strategy is adopted to compute the weight of the velocity coupling strengths. The proposed control algorithm enables followers to asymptotically track the leader’s varying velocities and approach the equilibrium distances with their neighbors. Furthermore, the arbitrarily-shaped formation flocking problem of the system can also be solved by adding the information of a desired formation topology to the potential function term. Finally, simulations are carried out to verify the effectiveness of the proposed theoretical results.     

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.      

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.     

Flocking Algorithms in Networks with Directed Switching Velocity Interaction Topologies

This paper studies flocking algorithms for multi‐agent systems with directed switching velocity interaction topologies. It is assumed that the position information of each agent is available for agents within its neighborhood region of radius r, however, they communicate the velocity information between each other through unidirectional links modeled by a particular class of directed topologies. A new energy function is defined to analyze the global stability and a sufficient condition is derived for asymptotic flocking in the face of switching topologies. The proposed control strategy guarantees the achievement of desired formations, while avoiding collisions among agents. It also ensures velocity agreement under suitable conditions in a variety of real networks with greatly reduced velocity data exchange. Moreover, a leader‐follower framework is formulated for the described class of interaction topologies and it is shown that a more relaxed condition is required to achieve the desired performance. Finally, several simulations are performed to illustrate and confirm the theoretical results obtained.     

A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems

In this paper, a feedback control strategy that achieves convergence of a multi-agent system to a desired formation configuration is proposed for both the cases of agents with single integrator and nonholonomic unicycle-type kinematics. When inter-agent objectives that specify the desired formation cannot occur simultaneously in the state space the desired formation is infeasible. It is shown that under certain assumptions, formation infeasibility forces the agents’ velocity vectors to a common value at steady state. This provides a connection between formation infeasibility and flocking behavior for the multi-agent system. We finally also obtain an analytic expression of the common velocity vector in the case of formation infeasibility.     

Flocking of Multi‐Agents Following a Leader with Adaptive Protocol in a Noisy Environment

This paper investigates the flocking problem of multi‐agents following a leader with communication delays in a noisy environment. Based on potential fields and the LaSalle‐type theorem for stochastic differential delay equations, by introducing the adaptive protocol compensating for the desired velocity, a new neighbor‐based flocking protocol is proposed such that all the agents move with a virtual leader's velocity almost surely, and avoidance of collision between the agents is ensured. A numerical example is given to illustrate the effectiveness of the proposed methods.     

Fault-tolerant flocking for a group of autonomous mobile robots

Consider a system composed of mobile robots that move on the plane, each of which independently executing its own instance of an algorithm. Given a desired geometric pattern, the flocking problem consists in ensuring that the robots form this pattern and maintain it while moving together on the plane. In this paper, we explore flocking in the presence of faulty robots, where the desired pattern is a regular polygon. We propose a distributed fault tolerant flocking algorithm assuming a semi-synchronous model with a k-bounded scheduler, in the sense that no robot is activated no more than k times between any two consecutive activations of any other robot.The algorithm is composed of three parts: failure detector, ranking assignment, and flocking algorithm. The role of the rank assignment is to provide a persistent and unique ranking for the robots. The failure detector identifies the set of currently correct robots in the system. Finally, the flocking algorithm handles the movement and reconfiguration of the flock, while maintaining the desired shape. The difficulty of the problem comes from the combination of the three parts, together with the necessity to prevent collisions and allow the rotation of the flock. We formally prove the correctness of our proposed solution.     

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.     

Distributed Geodesic Control Laws for Flocking of Nonholonomic Agents

We study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions. By analyzing the velocity vectors of agents on a circle (for planar motion) or sphere (for 3-D motion), we develop a geodesic control law that minimizes a misalignment potential and results in velocity alignment and flocking. The proposed control laws are distributed and will provably result in flocking when the underlying proximity graph which represents the neighborhood relation among agents is connected. We further show that flocking is possible even when the topology of the proximity graph changes over time, so long as a weaker notion of joint connectivity is preserved     

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 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.     

Distributed tracking of a non-minimally rigid formation for multi-agent systems

The objective of this paper is to design distributed control algorithms for a multi-agent system such that a rigid formation can be achieved asymptotically and the agents can finally move with a desired velocity. In particular, it is assumed that the formation is not necessarily minimally rigid, and the desired velocity is available to only a subset of the agents. Estimators are constructed for the agents to estimate the desired velocity, which are further used to design the control inputs of the agents. The proposed control algorithms consist of a formation acquisition term which depends on a potential function and the rigidity matrix, and a velocity estimation term. To deal with non-minimal rigidity, the centre manifold theorem is exploited to prove the stability of the resulting system. Simulation results are also provided to show the effectiveness of the proposed control algorithms.     

Distributed leader‐follower flocking control

This paper presents a fuzzy based leader‐follower flocking system. To maintain the distance between robots, we use a fuzzy logic controller to design a “force function” which is related to the relative distance between neighbours. The “force function” is used to control velocity of robots. To prove stability of the flocking system, we build a Hamilton function which is kinetic energy of the flocking system. Utilizing the LaSalle's invariance principle, we prove that the system is stable. Specially, we develop a flocking controller in local form. By using the local controller, the robots in the flocking system only need to know local information (relative distances and relative angles between neighbours). To evaluate performance of the flocking system, we simulate the flocking system tracking trajectories with different shapes. The local flocking algorithm is tested with three Pioneer robots. We use the SICK laser scanner to measure the relative distances and relative angles between neighbours. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于自适应滑模的不确定Euler-Lagrange多智能体系统抗扰动蜂拥控制

针对具有参数不确定性和未知外部扰动的Euler-Lagrange多智能体系统,设计一种基于自适应滑模控制的分布式蜂拥算法.该算法使用自适应滑模控制和自适应控制律分别补偿未知的外部扰动与模型中可线性参数化回归的不确定项,从而在实现蜂拥控制的同时,避免智能体对外部扰动先验知识的要求.理论分析表明,在多智能体达成蜂拥的同时,算法保证滑模的自适应增益有界.此外,所提出的算法同时考虑虚拟领导者追踪与基于目标区域的跟踪问题,并给出碰撞避免的条件.最后,通过算例仿真验证所提出算法的有效性.     

Safe Autonomous Agent Formation Operations Via Obstacle Collision Avoidance

In this paper, we consider the problem of flocking and shape‐orientation control of multi‐agent systems with inter‐agent and obstacle collision avoidance. We first consider the problem of forcing a set of autonomous agents to form a desired formation shape and orientation while avoiding inter‐agent collision and collision with convex obstacles, and following a trajectory known to only one of the agents, namely the leader of the formation. Then we build upon the solution given to this problem and solve the problem of guaranteeing obstacle collision avoidance by changing the size and the orientation of the formation. Changing the size and the orientation of the formation is helpful when the agents want to go through a narrow passage while the existing size or orientation of the formation does not allow this. We also propose collision avoidance algorithms that temporarily change the shape of the formation to avoid collision with stationary or moving nonconvex obstacles. Simulation results are presented to show the performance of the proposed control laws.     

Pinning control of complex networked systems: A decade after and beyond

In practice, directly control every node in a dynamical networked system with a huge number of nodes might be impossible or unnecessary; therefore, pinning control is a desirable approach. This paper surveys advances in pinning control approaches to making a dynamical networked system have a desired behavior. For a network with fixed topology, we review the feasibility, stability and effectiveness of pinning control. We then focus on pinning-based consensus and flocking control of mobile multi-agent networked systems. One of the main challenges with consensus and flocking control is that the topology of the corresponding dynamical network is time-varying, which depends on the states of all the agents in the network. Looking forward to the next decade, we expect to have a much deeper understanding of the relationship between the effectiveness of pinning control and the structural properties of a complex network, which may result in better control of large scale networked systems.     

Fuzzy Policy Reinforcement Learning in Cooperative Multi-robot Systems

A multi-agent reinforcement learning algorithm with fuzzy policy is addressed in this paper. This algorithm is used to deal with some control problems in cooperative multi-robot systems. Specifically, a leader-follower robotic system and a flocking system are investigated. In the leader-follower robotic system, the leader robot tries to track a desired trajectory, while the follower robot tries to follow the reader to keep a formation. Two different fuzzy policies are developed for the leader and follower, respectively. In the flocking system, multiple robots adopt the same fuzzy policy to flock. Initial fuzzy policies are manually crafted for these cooperative behaviors. The proposed learning algorithm finely tunes the parameters of the fuzzy policies through the policy gradient approach to improve control performance. Our simulation results demonstrate that the control performance can be improved after the learning.     

Leader–follower flocking based on distributed event‐triggered hybrid control

In this paper, we proposed a new hybrid control algorithm to achieve leader–follower flocking in multi‐agent systems. In the algorithm, the position is transmitted continuously, whereas the velocity is utilized discretely, which is governed by a distributed event‐triggered mechanism, and the neighbors' velocity is not required to detect the event‐triggered condition for each agent. It is shown that stable flocking is achieved asymptotically while the connectivity of networks is preserved. A numerical example is provided to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

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.