Formations on directed cycles with bearing‐only measurements

This paper studies a bearing‐only–based formation control problem for a group of single‐integrator agents with directed cycle sensing topology. In a 2‐dimensional space, a necessary and sufficient condition for the set of desired bearing vectors to be feasible is derived. Then, we propose a bearing‐only control law for every agent and prove that the formation asymptotically converges to a formation specified by a set of feasible desired bearing vectors. Analysis of the equilibrium formations in the plane for a 3‐agent system and subsequent extension to an n‐agent system is provided. We further extend the analysis on directed triangular formation into a 3‐dimensional space. Finally, simulations validate the theoretical results.     

Autonomous scale control of multiagent formations with only shape constraints

This paper considers a novel problem of how to choose an appropriate geometry for a group of agents with only shape constraints but with a flexible scale. Instead of assigning the formation system with a specific geometry, here, the desired geometry is only characterized by its shape without any location, rotation, and most importantly, scale constraints. Optimal rigid transformation between two different geometries is discussed with especial focus on the scaling operation, and the cooperative performance of the system is evaluated by what we call the geometries' degrees of similarity with respect to the desired shape during the entire convergence process. The design of the scale when measuring the degree of similarity is discussed from constant value and time‐varying function perspectives, respectively. Fixed structured nonlinear control laws that are functions on the scale and the relative positions of agents are developed to guarantee the exponential convergence of the system to the assigned shape. Our research is originated from a three‐agent formation system and is further extended to multiple (n > 3) agents by defining a triangular complement graph. Simulations demonstrate that a formation system with the time‐varying scale function outperforms the one with an arbitrary constant scale, and the relationship between underlying topology and the system performance is further discussed according to the simulation observations. Moveover, the control scheme is applied to bearing‐only sensor–target localization to show its application potentials. Copyright © 2012 John Wiley & Sons, Ltd.     

Relative attitude formation control of multi‐agent systems

This paper investigates the relative attitude formation control problem for a group of rigid‐body agents using relative attitude information on SO(3). On the basis of the gradient of a potential function, a family of distributed angular velocity control laws, which differ in the sense of a geodesic distance dependent function, is proposed. With directed and switching interaction topologies, the desired relative attitude formation is showed to be achieved asymptotically provided that the topology is jointly quasi‐strongly connected. Moreover, several sufficient conditions for the desired formation to be achieved exponentially and almost globally are given. Additionally, numerical examples are provided to illustrate the effectiveness of the proposed distributed control laws. Copyright © 2017 John Wiley & Sons, Ltd.     

A backstepping design for directed formation control of three‐coleader agents in the plane

This paper deals with a directed formation control problem of three agents moving in the plane, where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbor, and each agent is described by a double integrator. Firstly, a directed formation control law based on the knowledge only of the neighbor's direction is designed by using the integrator backstepping technique, which can not only accomplish the desired triangle formation but also ensure that speeds of all agents converge to a common value without collision between each other during the motion. Then, with the purpose of relaxing and even overcoming the restriction of initial conditions of the agents owing to collision avoidance, we introduce the inter‐agent potential functions into the design. The convergence of the proposed control algorithms is proved by using tools from LaSalle's invariance principle. Simulation results are provided to illustrate the effectiveness of the control laws. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.     

Pursuit formations with dynamic control gains

The paper presents a coordinated motion control law of multiple autonomous agents based on the pursuit strategy with dynamical gains. In particular, we are interested in the control law with no communication between the agents, that is, the leader's moving velocity is not known by the follower robots. Each follower only utilizes its local measurement of relative position information to keep a desired distance and a desired bearing with its neighbors according to a fixed topology. The paper proposes a modified follower's control law, in which each follower pursues its neighbor along the line of sight rotated by a constant offset angle with a dynamic control gain. The offset angle is designed to attain the specific bearing and the dynamic control gain is introduced for the purpose of achieving the desired distance to its neighbor. Then, all the agents make the same motion to the leader's in a steady formation. It is shown that, for the case of uniform rectilinear motion, the group of mobile robots converges to the exact formation specified by the offset angles and the distances no matter what the leader's velocity is, whereas for the case of uniform circular motion, the group of agents converges to an approximation of the formation attained in the rectilinear motion case when the leader's turning radius is much greater than the desired distances between neighboring robots. The effectiveness of the proposed technique and the obtained analytical results are demonstrated in simulations. Copyright © 2011 John Wiley & Sons, Ltd.     

Formation shape control based on bearing rigidity

Distance measurements are not the only geometric quantities that can be used for multi-agent formation shape control. Bearing measurements can be used in conjunction with distances. This article employs bearing rigidity for mobile formations, which was developed for robot and sensor network localisation, so that bearings can be used for shape control in mobile formations. The first part of this article examines graph theoretical models for formation network analysis and control law design that are needed to maintain the shape of a formation in two-dimensional space, while the formation moves as a cohesive whole. Bearing-based shape control for a formation of mobile agents involves the design of distributed control laws that ensure the formation moves, so that bearing constraints maintain some desired values. The second part of this article focuses on the design of a distributed control scheme for nonholonomic agents to solve the bearing-based formation shape control problem. In particular, a control law using feedback linearisation is proposed based on shape variables. We simulate the shape control behaviour on differential drive agents for an exemplary bearing rigid formation using the results obtained in the first and second parts of this article.     

Distance‐based undirected formations of single‐integrator and double‐integrator modeled agents in n‐dimensional space

We study the local asymptotic stability of undirected formations of single‐integrator and double‐integrator modeled agents based on interagent distance control. First, we show that n‐dimensional undirected formations of single‐integrator modeled agents are locally asymptotically stable under a gradient control law. The stability analysis in this paper reveals that the local asymptotic stability does not require the infinitesimal rigidity of the formations. Second, on the basis of the topological equivalence of a dissipative Hamiltonian system and a gradient system, we show that the local asymptotic stability of undirected formations of double‐integrator modeled agents in n‐dimensional space is achieved under a gradient‐like control law. Simulation results support the validity of the stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Distributed formation control with relaxed motion requirements

Heterogeneous formation shape control with interagent bearing and distance constraints involves the design of a distributed control law that ensures the formation moves such that these interagent constraints are achieved and maintained. This paper looks at the design of a distributed control scheme to solve different formation shape control problems in an ambient two‐dimensional space with bearing, distance and mixed bearing and distance constraints. The proposed control law allows the agents in the formation to move in any direction on a half‐plane and guarantees that despite this freedom, the proposed shape control algorithm ensures convergence to a formation shape meeting the prescribed constraints. This work provides an interesting and novel contrast to much of the existing work in formation control where distance‐only constraints are typically maintained and where each agent's motion is typically restricted to follow a very particular path. A stability analysis is sketched, and a number of illustrative examples are also given. Copyright © 2014 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.     

Cooperative control for target-capturing task based on a cyclic pursuit strategy

This paper studies a methodology for group coordination and cooperative control of n agents to achieve a target-capturing task in 3D space. The proposed approach is based on a cyclic pursuit strategy, where agent i simply pursues agent i+1 modulo n. The distinctive features of the proposed method are as follows. First, no communication mechanism between agents is necessary and thus it is inherently a distributed control strategy. Also, it is a simple robust memoryless control scheme which has self-stability property. Finally, it guarantees a global convergence of all agents to the desired formation. Further, it is also guaranteed that no collision occurs. Simulation examples are given to illustrate the efficacy of the proposed method and the achievement of a desired pursuit pattern in 3D space.     

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.     

Formation stabilization and resizing based on the control of inter‐agent distances

We propose a control strategy that could steer the group of mobile agents in the plane to achieve a specified formation. The control law could be implemented in a fully decentralized manner so that each agent moves on their own local reference frame. Under the acyclic minimally persistent graph topology, each agent measures the relative displacements of neighboring agents and then adjusts the distances between them to achieve the desired formation. As well as achieving a fixed formation, we could resize the formation only by changing the leader edge, which connects the leader with the first‐follower in acyclic minimally persistent graph, without changing the structures of the control law. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Weighted predictor‐feedback formation control in local frames under time‐varying delays and switching topology

This article presents a novel control strategy based on predictor‐feedback delay compensation for multiagent systems to reach a prescribed target formation under unknown but bounded communication delays and switching communication topology. Both communication delays and network topology can be subjected to arbitrarily‐fast time variations. The key idea is to implement predictor‐feedback strategies using only relative measurements between agents expressed in each local agent's frame, with the aim to counteract the negative effect of time delays. Nevertheless, due to the decentralized nature of the control, the presence of time‐varying delays and switching communication topology, only partial delay compensation is possible. Despite this, we show that better performance can be achieved with our proposal with respect to nonpredictor control schemes by introducing a weighting factor for predictor‐feedback terms in the control law. Sufficient conditions based on Linear Matrix Inequalities for robust stability are also provided, which allow to easily design the controller parameters in order to maximize the speed of convergence. Finally, simulation results are provided to show the effectiveness of the proposed approach.     

Relative formation control of mobile agents for gradient climbing and target capturing

Cooperative controllers are designed to force a group of N mobile agents with limited communication using only relative position between the agents to form a desired formation structure. The centre of the formation structure is the mean position of all the agents. The agents are stabilised at desired positions with respect to the centre of the structure. The proposed controllers also preserve initial communication connectivity and guarantees no collisions between the agents. The control design is based on smooth step functions and potential functions. The proposed control design is applied to solve gradient climbing and target capturing problems in both two- and three-dimensional spaces. The gradient average of a distributed field in nature or artificially generated by a target is first estimated over a bounded region using the field measurement by the agents. The gradient average is then used as the reference velocity to guide the agents.     

Finite time distributed distance‐constrained shape stabilization and flocking control for d‐dimensional undirected rigid formations

Most of the existing results on distributed distance‐constrained rigid formation control establish asymptotic or exponential convergence. To further improve the convergence rate, we explain in this paper how to modify existing gradient controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to locally converge to a desired shape with finite settling time. We also show for undirected triangular formation shape control, if all the agents start with non‐collinear positions, then the formation will converge to the desired shape in finite time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

Consensus for formation control of multi‐agent systems

This study considers the formation problem for multi‐agent systems, which are described by the second‐order dynamics on nonlinear manifolds SE(2) and SE(3). In particular, the model of each agent contains information about its attitude. Using a consensus strategy, a control law is developed to guarantee that any desired formation can be achieved asymptotically under the conditions of complete or tree‐shaped communication topologies. Numerical simulations are presented to verify the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.