Distance-based acyclic minimally persistent formations with non-steepest descent control

In this paper, we propose a control law to maneuver a group of mobile autonomous agents in the plane, where the information architecture among the agents is modeled by a directed graph. The objective is to achieve a prescribed formation shape by adjusting the inter-agent distances only, which is called the distance-based formation control. The proposed control law uses only relative position measurements so that each agent achieves its control objective in a decentralized manner. On the basis of the proposed control law, we analyze the convergence property of squared-distance errors. We first study a triangular formation and then extend the results of to acyclic minimally persistent formations having more than three agents. We also examine the formation including a moving leader. Numerical simulations and experiments with mobile robot platform are included.     

Finite-time formation of multiple agents based on multiple virtual leaders

The finite-time formation problem of multiple agents aims to find a control protocol to guarantee finite-time consensus, in which every agent can be in the right position and keep in the given formation configuration efficiently. However, it is hard to achieve a stable state if only by setting one virtual leader in multiple tasks system. This paper presents a formation controller design for a second-order multiple agents to address the finite-time formation problem. In the procedure, each agent has a virtual leader, and then a control law is designed so that the agents can keep pace with their virtual leaders in terms of speed and position. Accordingly, the controller can ensure that the relative positions among different agents and the trajectory of the whole formation can be specified in advance. Moreover, since the closed-loop system is finite-time stable, which implies that the required formation is attainable without a deviation in finite time. Finally, the stability analysis is proved by applying the graph theory, Lyapunov stability theory and homogeneous system theory. The effectiveness of the algorithm is demonstrated by numerical simulations.     

Discrete‐time global leader‐following consensus of a group of general linear systems using bounded controls

This paper deals with the problem of global leader‐following consensus of a group of discrete‐time general linear systems with bounded controls. For each follower agent in the group, we construct both a bounded state feedback control law and a bounded output feedback control law. The feedback laws for each input of an agent use a multi‐hop relay protocol, in which the agent obtains the information of other agents through multi‐hop paths in the communication network. The number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of real eigenvalues on the unit circle and the number of pairs of complex eigenvalues on the unit circle of the subsystem corresponding to the input, and the feedback gains are constructed from the adjacency matrix of the communication network. We show that these control laws achieve global leader‐following consensus when the communication topology among follower agents forms a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower agent. Copyright © 2017 John Wiley & Sons, Ltd.     

Formation Maneuvering and Target Interception for Multi‐Agent Systems via Rigid Graphs

In this paper, we introduce control laws for multi‐agent formation maneuvering and target interception problems. In the target interception problem, we consider that the target velocity is unknown. Using a single‐integrator agent model, the proposed controls consist of a formation acquisition term, dependent on the graph rigidity matrix, and a formation maneuvering or target interception term. The control laws are only a function of the relative position of agents in an infinitesimally and minimally rigid graph, and either the desired maneuvering velocity of the formation or the target's relative position to the leader. The target interception control includes a continuous dynamic estimation term to identify the unknown target velocity. A Lyapunov‐like stability analysis is used to prove that the control objectives are met.     

Formation Reorganization by Primitive Operations on Directed Graphs

In this paper, we study the construction and transformation of 2-D persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. Both notions are currently being used in various studies on coordination and control of autonomous multiagent formations. In the context of mobile autonomous agent formations, persistence characterizes the efficacy of a directed formation structure with unilateral distance constraints seeking to preserve the shape of the formation. Analogously to the powerful results about Henneberg sequences in minimal rigidity theory, we propose different types of directed graph operations allowing one to sequentially build any minimally persistent graph (i.e., persistent graph with a minimal number of edges for a given number of vertices), each intermediate graph being also minimally persistent. We also consider the more generic problem of obtaining one minimally persistent graph from another, which corresponds to the online reorganization of the sensing and control architecture of an autonomous agent formation. We prove that we can obtain any minimally persistent formation from any other one by a sequence of elementary local operations such that minimal persistence is preserved throughout the reorganization process. Finally, we briefly explore how such transformations can be performed in a decentralized way.     

3D Multi‐Agent Formation Control with Rigid Body Maneuvers

In this paper, we propose a control scheme for the formation maneuvering problem of multi‐agent systems where the team of agents can translate and rotate as a virtual rigid body in 3D. Using the single‐integrator model, we formulate the basic control law which is comprised of a formation acquisition term, function of the graph rigidity matrix, and a rigid body maneuvering term. The control is dependent on the relative position of agents that are connected in an infinitesimally and minimally rigid framework in addition to the desired rigid body motion of the formation. To facilitate the design of the rigid body maneuver, one agent in the convex hull of the formation serves as the reference point for the rotation component. A simulation study demonstrates the formation controller.     

利用方位角信息的移动机器人编队控制

本文以移动机器人为研究对象,仅利用方位角信息实现多智能体系统的编队控制.为实现大规模编队和队形的缩放控制,智能体被分为领航者、第1跟随者以及其余跟随者.首先,考虑智能体之间相对位置信息难以精确测量的情形,设计仅用方位角信息的估计算法获得准确的相对位置;然后,基于获得的相对位置信息设计第1跟随者的控制算法,使得第一跟随者与领航者之间的位置收敛到理想约束位置以控制整个队形的规模;接着,设计其余跟随者的控制算法使得各智能体之间的方位角达到理想约束角度,从而形成理想编队队形.最后通过数值和ROS仿真实验验证算法的有效性.     

Robust formation control of multiagent systems on the Lie group SE(3)

This paper addresses the robust formation control problem of multiple rigid bodies whose kinematics and dynamics evolve on the Lie group SE(3). First, it is assumed that all followers have access to the state information of a virtual leader. Then, a novel adaptive super‐twisting sliding mode control with an intrinsic proportional‐integral‐derivative sliding surface is proposed for the formation control problem of multiagent system using a virtual structure (VS) approach. The advantages of this control scheme are twofold: elimination of the chattering phenomenon without affecting the control performance and no requirement of prior knowledge about the upper bound of uncertainty/disturbance due to adaptive‐tuning law. Since the VS method is suffering from the disadvantages of centralized control, in the second step, considering a network as an undirected connected graph, we assume that only a few agents have access to the state information of the leader. Afterward, using the gradient of modified error function, a distributed adaptive velocity‐free consensus‐based formation control law is proposed where reduced‐order observers are introduced to remove the requirements of velocity measurements. Furthermore, to relax the requirement that all agents have access to the states of the leader, a distributed finite‐time super‐twisting sliding mode estimator is proposed to obtain an accurate estimation of the leader's states in a finite time for each agent. In both steps, the proposed control schemes are directly developed on the Lie group SE(3) to avoid singularity and ambiguities associated with the attitude representations. Numerical simulation results illustrated the effectiveness of the proposed control schemes.     

Semi‐global leader‐following consensus of multiple linear systems with position and rate limited actuators

This paper studies the semi‐global leader‐following consensus problem for a group of linear systems in the presence of both actuator position and rate saturation. Each follower agent in the group is described by a general linear system subject to simultaneous actuator position and rate saturation. For each follower agent, we construct both a linear state feedback control law and a linear output feedback control law by using low gain approach. We show that semi‐global leader‐following consensus can be achieved by using these control laws when the communication topology among follower agents is a connected undirected graph, and the leader is a neighbor of at least one follower. Simulation results illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

有向图中网络Euler-Lagrange系统无需相对速度信息的群一致性

在非对称有向图中,研究网络Euler-Lagrange系统的群一致性问题.每组内的智能体均为合作关系,而组间智能体则可以为合作关系或竞争关系.为了实现群一致性,假设组与组之间是无环连接的且系统有向图满足入度平衡条件.考虑到智能体间相对速度信息难以精确测量的实际情形,设计无需相对速度信息的分布式自适应控制算法,实现网络Euler-Lagrange系统的群一致性.最后通过仿真分析验证所设计算法的有效性.     

Formation‐containment control of networked collision‐free Lagrangian systems

The distributed formation‐containment (DFC) problem under a directed graph is addressed for networked Euler‐Lagrange systems. First, using a leader‐follower framework, the DFC problem is properly defined. For the leaders and the followers, respectively, a DFC control law is next proposed without using velocity information. Based on the artificial potential function, all the agents can achieve the control objective satisfactorily while avoiding collisions with others as well as the obstacles in the environment. By the Lyapunov stability theory, the boundedness of the error signals is guaranteed. Simulations are finally given to show the feasibility of this approach.     

Semi‐global output consensus of a group of linear systems in the presence of external disturbances and actuator saturation: An output regulation approach

This paper studies the problem of semi‐global leader‐following output consensus of a multi‐agent system. The output of each follower agent in the system, described by a same general linear system subject to external disturbances and actuator saturation, is to track the output of the leader, described by a linear system, which also generates disturbances as the exosystem does in the classical output regulation problem. Conditions on the agent dynamics are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the output consensus is achieved when the communication topology among the agents is a digraph containing no loop, and the leader is reachable from any follower agent. We also extend the results to the non‐identical disturbance case. In this case, conditions based on both the agent dynamics and the communication topology are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the leader‐following output consensus is achieved when the communication topology among the follower agents is a strongly connected and detailed balanced digraph, and the leader is a neighbor of at least one follower. In addition, under some further conditions on the agent dynamics, the control algorithm is adapted so as to achieve semi‐global leader‐following output consensus for a jointly connected undirected graph and the leader reachable from at least one follower. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive iterative learning control for coordination of second‐order multi‐agent systems

In this paper, an efficient framework is proposed to the consensus and formation control of distributed multi‐agent systems with second‐order dynamics and unknown time‐varying parameters, by means of an adaptive iterative learning control approach. Under the assumption that the acceleration of the leader is unknown to any follower agents, a new adaptive auxiliary control and the distributed adaptive iterative learning protocols are designed. Then, all follower agents track the leader uniformly on [0,T] for consensus problem and keep the desired distance from the leader and achieve velocity consensus uniformly on [0,T] for the formation problem, respectively. The distributed multi‐agent coordinations performance is analyzed based on the Lyapunov stability theory. Finally, simulation examples are given to illustrate the effectiveness of the proposed protocols in this paper.Copyright © 2013 John Wiley & Sons, Ltd.     

Circle formation control for multi-agent systems with a leader

In this paper, we focus on circle formation control of multi-agent systems (MAS) with a leader. The circle formation is achieved based on the lead-following and the artificial potential field method. A...     

Bearing-based formation manoeuvre control of nonholonomic multi-agent systems

ABSTRACT

This paper concerns on the bearing-based leader–follower formation manoeuvre control problem for two- (2D) and three-dimensional (3D) multi-agent systems with nonholonomic constraint. The target formation is defined by relative-bearing measurements, which, for example, can be obtained from onboard cameras. The contributions of this paper are twofold. Firstly, a distributed formation manoeuvre control law is proposed for 2D nonholonomic agents according to the inter-bearing measurement. The multi-agent systems can achieve the desired formation which is defined by the bearings information. The formation manoeuvre can be achieved by steering at least two leaders. Secondly, the control law is nontrivially extended to 3D nonholonomic multi-agents systems. The leader–follower formation tracking problem can also be solved by the proposed proportional-integral control scheme. Simulation results for 2D and 3D nonholonomic multi-agents systems are presented. Experiments that used ground mobile robots verify the effectiveness of the proposed control laws.     

Event‐triggered global leader‐following consensus of a group of neutrally stable linear systems subject to input saturation

This paper studies the global leader‐following consensus problem for a multiagent system using event‐triggered linear feedback control laws. The leader agent is described by a neutrally stable linear system and the follower agents are also described by a neutrally stable linear system but with saturating input. Both the state‐feedback case and the output‐feedback case are considered. In each case, an event‐triggered control law is constructed for each follower agent and an event‐triggering strategy is designed for updating these control laws. These event‐triggered control laws are shown to achieve global leader‐following consensus when the communication topology among the follower agents is strongly connected and detailed balanced and the leader is a neighbor of at least one follower agent. The Zeno behavior is excluded. The theoretical results are illustrated by simulation.     

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.     

Distance‐based control of formations with hybrid communication topology

In this paper, we focus on the control of multiagent formations with hybrid communication topology through a distance‐based approach. By saying hybrid topology, we mean that the communication topology contains both undirected and directed links, or the underlying graph of the formation contains both undirected and directed edges. A new type of graph, ie, hybrid graph, is introduced. We discuss the persistence of hybrid graphs and present the persistence verification strategy for hybrid graphs. It is proved that all the minimally persistent hybrid graphs can be obtained from persistent directed graphs by the operation of edge transformation. As the main result, it is shown that multiagent formations modeled by acyclic persistent hybrid graphs can be stabilized locally under distance‐based controllers.     

Semi‐global containment control for linear systems in the presence of actuator position and rate saturation

This paper studies the semi‐global containment control problem for a group of general linear systems in the presence of actuator position and rate saturation. Both a state feedback containment control algorithm and an output feedback containment algorithm are constructed for each follower agent in the system by using low gain approach. We show that the states of all follower agents will converge to the convex hull formed by the leader agents asymptotically under these control algorithms when the communication topology among follower agents is a connected undirected graph and each leader agent is a neighbor of at least one follower agent. Simulation results illustrate the theoretical results.     

Multi-robot formation control using distance and orientation

Formation control analyses the convergence of a group of mobile agents to predefined geometric patterns. In traditional approaches, it is assumed that each agent knows the exact position of certain members of the group with respect to a reference frame and the associated control laws are designed according to inter-robot relative positions. Designing a more decentralized scheme, this paper proposes a formation scheme, using Lyapunov techniques, considering that the local controllers of the agents can be equipped with distance and orientation sensors. The main result of the paper applies to certain distance-based potential functions with inter-robot collision avoidance and an arbitrary undirected formation graph. Also, the control law includes an integral-type control that eliminates the effects of the dead-zone of actuators in order to avoid the standard techniques of normalization. The control approach is analyzed for omnidirectional robots with numerical simulations and extended for unicycle-type robots with real-time experiments.