A survey of multi-agent formation control

doi:10.1016/j.automatica.2014.10.022

Automatica

Volume 53, March 2015, Pages 424-440

https://doi.org/10.1016/j.automatica.2014.10.022 Get rights and content

Abstract

We present a survey of formation control of multi-agent systems. Focusing on the sensing capability and the interaction topology of agents, we categorize the existing results into position-, displacement-, and distance-based control. We then summarize problem formulations, discuss distinctions, and review recent results of the formation control schemes. Further we review some other results that do not fit into the categorization.

Introduction

A significant amount of research efforts have been focused on the control of multi-agent systems due to both their practical potential in various applications and theoretical challenges arising in coordination and control of them. Theoretical challenges mainly arise from controlling multi-agent systems based on partial and relative information without an intervention of a central controller.

Formation control, which is one of the most actively studied topics within the realm of multi-agent systems, generally aims to drive multiple agents to achieve prescribed constraints on their states. Depending on the sensing capability and the interaction topology of agents, a variety of formation control problems have been studied in the literature.

Excellent surveys of formation control of multi-agent systems are found in Anderson, Yu, Fidan, and Hendrickx (2008); Chen and Wang (2005); Mesbahi and Egerstedt (2010); Olfati-Saber, Fax, and Murray (2007); Ren, Beard, and Atkins (2005); Ren, Beard, and Atkins (2007); Ren and Cao (2010) and Scharf, Hadaegh, and Ploen (2004). However, Chen and Wang (2005); Mesbahi and Egerstedt (2010); Olfati-Saber et al. (2007); Ren, Beard, and Atkins (2005); Ren, Beard et al. (2007) and Ren and Cao (2010) have mainly focused on consensus based formation control. Some important results, particularly on inter-agent distance based formation control, have not been extensively reviewed in those surveys. Scharf et al. (2004) have presented a survey of spacecraft formation flying rather than an extensive survey of general multi-agent systems. An excellent introduction of inter-agent distance based formation control is found in Anderson et al. (2008); however, a considerable amount of studies have been conducted thereafter. Thus we believe that it is timely and helpful to present an extensive survey of formation control of multi-agent systems.

Due to the vast amount of the literature, it would be challenging to exhaustively review the existing results on formation control. Rather than an exhaustive review, we thus focus on the characterization of formation control schemes in terms of the sensing capability and the interaction topology of agents because we believe that both of them are linked to the essential features of multi-agent formation control.

The characterization of formation control schemes in terms of the sensing capability and the interaction topology naturally leads to the question of what variables are sensed and what variables are actively controlled by multi-agent systems to achieve their desired formation. The types of sensed variables specify the requirement on the sensing capability of individual agents. Meanwhile, the types of controlled variables are essentially connected to the interaction topology. Specifically, if positions of individual agents are actively controlled, the agents can move to their desired positions without interacting with each other. In the case that inter-agent distances are actively controlled, the formation of agents can be treated as a rigid body. Then the agents need to interact with each other to maintain their formation as a rigid body. In short, the types of controlled variables specify the best possible desired formation that can be achieved by agents, which in turn prescribes the requirement on the interaction topology of the agents.

Based on the aforementioned observation, we categorize the existing results on formation control into position-, displacement-, and distance-based according to types of sensed and controlled variables:

•
Position-based control: Agents sense their own positions with respect to a global coordinate system. They actively control their own positions to achieve the desired formation, which is prescribed by the desired positions with respect to the global coordinate system.
•
Displacement-based control: Agents actively control displacements of their neighboring agents to achieve the desired formation, which is specified by the desired displacements with respect to a global coordinate system under the assumption that each agent is able to sense relative positions of its neighboring agents with respect to the global coordinate system. This implies that the agents need to know the orientation of the global coordinate system. However, the agents require neither knowledge on the global coordinate system itself nor their positions with respect to the coordinate system.
•
Distance-based control: Inter-agent distances are actively controlled to achieve the desired formation, which is given by the desired inter-agent distances. Individual agents are assumed to be able to sense relative positions of their neighboring agents with respect to their own local coordinate systems. The orientations of local coordinate systems are not necessarily aligned with each other.

Note that the above categorization is useful in characterizing formation control schemes in terms of the requirement on the sensing capability and the interaction topology. As summarized in Table 1, position-based control is particularly beneficial in terms of the interaction topology though it requires agents to be equipped with more advanced sensors than the other approaches. Conversely, distance-based control is advantageous in terms of the sensing capability, but it requires more interactions among agents. Displacement-based control is moderate in terms of both sensing capability and interaction topology compared to the other approaches. Roughly speaking, this reveals a trade-off between the amount of interactions among agents and the requirement on the sensing capability of individual agents as illustrated in Fig. 1.

Though decentralization is one of important themes in multi-agent formation control, we avoid characterizing the existing results into centralized and decentralized due to the following two reasons. First, a formation control scheme may be classified into centralized or decentralized according to whether or not it requires a global coordinator²; however, such a categorization is not appropriate for an overview of various formation control schemes. Indeed, under this criterion, we find that most of formation control schemes found in the literature fall into decentralized control because they do not explicitly require a global coordinator. Second, meanings of decentralized formation control are not exactly the same in the literature and rather subjective. Thus a characterization in terms of decentralization may cause further confusion, which is not desirable.

On the other hand, the concepts of the terms, local and relative, which are often used for describing features of formation control schemes, can be clearly described based on the requirement on the sensing capability and the interaction topology. In the following, we attempt to sort out several concepts associated with the terms:

•
Relative: Every formation control scheme requires agents to sense variables such as positions and attitudes with respect to either local coordinate systems associated with individual agents or a global coordinate system associated with the multi-agent system. The term relative is usually taken to mean that a variable is sensed with respect to a local coordinate system, not a global one. Conversely, a variable that is sensed with respect to a global coordinate system is called absolute. One may associate relative with decentralized. In this respect, distance-based formation control can be considered more decentralized than position- and displacement-based control. However, such a characterization may cause confusion because decentralized has other meanings. Nevertheless, we emphasize that the concept of relative can be clearly described in terms of the sensing capability of individual agents.
•
Local: The term local can be understood in several ways. First, it can be associated with interactions among agents. A formation control scheme that requires agents to interact with all the other agents can be considered non-local. Otherwise, as it requires less interactions, it can be considered more local. This concept can be clearly described by the interaction topology. Second, local can be taken to mean that a variable is sensed with respect to a local coordinate system. That is, local means relative in terms of sensing of variables. In this case, the concept of local can be clearly described by the sensing topology. Finally, it involves with the non-existence of a global coordinator as mentioned above.

Based on the above discussions, once again, we try to avoid characterizing the existing results into centralized and decentralized because it may cause confusion. Rather than centralized and decentralized control, we categorize the existing results into position-, displacement-, and distance-based formation control. We then summarize problem formulations, discuss distinctions, and review recent results, particularly focusing on the sensing capability and the interaction topology. We believe that the categorization is useful for providing a clear overview of multi-agent formation control though it does not exhaustively cover the existing results. Since the categorization is not exhaustive, we additionally summarize some results that do not fit neatly into the categorization to make this survey more extensive. Specifically we review flocking, estimation based control, pure distance-based control, angle-based control, containment control, and cyclic pursuit.

The rest of this survey is organized as follows: In Section 2, we briefly review basic graph theory. In Section 3, we discuss various classifications of formation control. In Sections 4 Position-based formation control, 5 Displacement-based formation control, 6 Distance-based formation control, we discuss position-, displacement-, and distance-based formation control and review the existing results. Summary and discussions of issues are provided in Section 7. Some other results that do not fit into the categorization are reviewed in Section 8. Finally, concluding remarks and future works are provided in Section 9.

Section snippets

Notations

We denote the set of non-negative (respectively, positive) real numbers by ${\bar{R}}_{+}$ (respectively, $R_{+}$ ). Given a set $S$ , $| S |$ denotes the cardinality of $S$ . Given a real vector $x$ , $‖ x ‖$ denotes the Euclidean norm of $x$ . Given a matrix $A$ , $rank (A)$ denotes the rank of $A$ . We denote the $n$ -dimensional identity matrix by $I_{n}$ . Given two matrices $A$ and $B$ , $A \otimes B$ denotes the Kronecker product of the matrices. Given variables $x_{1}, \dots, x_{N}$ , we denote ${[x_{1}^{T} \dots x_{N}^{T}]}^{T}$ by $x$ if there is no confusion.

Graph theory

The interaction topology of a

A general formation control problem

We first formulate a formation control problem under a general problem setup. We then discuss distinctions of position-, displacement-, and distance-based formation control problems in terms of sensed and controlled variables and control objectives of agents.

Consider the following $N$ -agents: ${\begin{matrix} {\dot{x}}_{i} = f_{i} (x_{i}, u_{i}), \\ y_{i} = g_{i} (x_{1}, \dots, x_{N}), \\ z_{i} = h_{i} (x_{i}), \end{matrix} i = 1, \dots, N,$ where $x_{i} \in R^{n_{i}}$ , $u_{i} \in R^{p_{i}}$ , $y_{i} \in R^{q_{i}}$ , and $z_{i} \in R^{r}$ denote the state, measurement, and output of agent $i$ . Further $f_{i} : R^{n_{i}} \times R^{p_{i}} \to R^{n_{i}}$ , $g_{i} : R^{n_{1}} \times \dots \times R^{n_{N}} \to R^{q_{i}}$ , and $h_{i} : R^{n_{i}} \to R^{r}$ . Let $z^{*} \in R$

Position-based formation control

In this section, we review position-based formation control. A typical position-based formation control scheme imposes the following requirement on agents:

•
Sensing capability: The agents are required to commonly have a global coordinate system. They need to sense their absolute positions with respect to the global coordinate system.
•
Interaction topology: The desired formation is specified by the desired absolute positions for the agents. In this case, interactions are not necessarily required

Displacement-based formation control

We review displacement-based formation control in this section. A typical displacement-based formation control scheme imposes the following requirement on agents:

•
Sensing capability: The agents are required to have their own local coordinate systems, orientations of which are aligned to that of a global coordinate system. However, they do not necessarily know the origin of the global coordinate system. With respect to the local coordinate systems, the agents are required to sense relative

Distance-based formation control

In this section, we review distance-based formation control. In a typical distance-based formation control scheme, the following requirement is imposed on agents:

•
Sensing capability: The agents are required to carry their own local coordinate systems. The orientations of the coordinate systems need not to be aligned to each other. Further the agents do not need to have a common sense of orientation. The agents are required to sense relative positions of their neighbors, which implies existence

Summary and further issues

We reviewed the existing results by categorizing them into positions-, displacement-, and distance-based. The categorization clearly showed distinctions in the sensing capability, the interaction topology, and the control objective of agents as summarized in Table 1. Summary and discussions on further issues are provided in the following.

Flocking

It has been revealed that many collective behaviors discovered in various fields are indeed based on relatively simple interactions among individuals (Strogatz, 2003). Inspired by this, Reynolds (1987) has proposed an agent model based on the following three basic rules, known as Reynolds rules:

•
Cohesion: stay close to nearby neighbors;
•
Separation: avoid collisions with nearby neighbors;
•
Alignment: match velocity with nearby neighbors.

Many control laws have been proposed to achieve collective

Conclusion

In this paper, we presented a brief survey of multi-agent formation control. By categorizing the existing results into the position-, displacement-, and distance-based control, we discussed fundamental problem formulations and summarized distinctions between control schemes. This survey is far from an exhaustive literature review. Many important results might be missed in this paper though we expect that this survey provides a helpful overview of formation control.

Acknowledgments

The authors appreciate the editor, the associate editor, and the anonymous reviewers for their constructive comments and suggestions. The presentation of this survey paper has been significantly improved by their valuable comments and suggestions.

Kwang-Kyo Oh received the B.S. degree in mineral and petroleum engineering and the M.S. degree in electrical and computer engineering from Seoul National University, Seoul, Korea, in 1998 and 2001, respectively, and the Ph.D. degree in mechatronics from Gwangju Institute of Science and Technology, Gwangju, Korea, in 2013. He is currently with Korea Institute of Industrial Technology, Gwangju, Korea. He worked for Korea Aerospace Industries (2001–2003), Samsung Electronics (2003–2008), and LG

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Myoung-Chul Park received the B.S. degree in electronics engineering from Chungnam National University, Daejeon, Korea, in 2011, and the M.S. degree in information and mechatronics from Gwangju Institute of Science and Technology (GIST), Gwangju, Korea, in 2013. He is currently working toward the Ph.D. degree in mechatronics at GIST. His research interests include decentralized control of multi-agent systems and localization of sensor networks.

Hyo-Sung Ahn received the B.S. and M.S. degrees in astronomy from Yonsei University, Seoul, Korea, in 1998 and 2000, respectively, the M.S. degree in electrical engineering from the University of North Dakota, Grand Forks, in 2003, and the Ph.D. degree in electrical engineering from Utah State University, Logan, in 2006. Since July 2007, he has been with the School of Mechatronics, Gwangju Institute of Science and Technology (GIST), Gwangju, Korea. He is currently Associate Professor and Dasan Professor. Before joining GIST, he was a Senior Researcher with the Electronics and Telecommunications Research Institute, Daejeon, Korea. He is the author of the research monograph Iterative Learning Control: Robustness and Monotonic Convergence for Interval Systems (Springer-Verlag, 2007). His research interests include distributed control, learning control, network localization, and autonomous navigation systems.

^☆: This work was supported by the National Research Foundation of Korea (NRF) (No. NRF-2013R1A2A2A01067449). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Editor John Baillieul.

¹: Tel.: +82 62 715 2398; fax: +82 62 715 2384.

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Survey PaperA survey of multi-agent formation control☆

Abstract

Introduction

Section snippets

Notations

Graph theory

A general formation control problem

Position-based formation control

Displacement-based formation control

Distance-based formation control

Summary and further issues

Flocking

Conclusion

Acknowledgments

Systems & Control Letters

Journal of Mathematical Analysis and Applications

Systems & Control Letters

Systems & Control Letters

Automatica

Automatica

Automatica

Automatica

Automatica

Systems & Control Letters

Robotics and Autonomous Systems

Automatica

Automatica

Automatica

Automatica

Advances in Biophysics

Systems & Control Letters

Rigid graph control architectures for autonomous formations

IEEE Control Systems Magazine

A coordination architecture for spacecraft formation control

IEEE Transactions on Control Systems Technology

Maintaining a directed, triangular formation of mobile autonomous agents

Communications in Information and Systems

Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: Algorithms and experiments

IEEE Transactions on Control Systems Technology

Linear system theory and design

On the rendezvous problem for multiple nonholonomic agents

IEEE Transactions on Automatic Control

Connectedness preserving distributed swarm aggregation for multiple kinematic robots

IEEE Transactions on Robotics

Inverse agreement protocols with application to distributed multi-agent dispersion

IEEE Transactions on Automatic Control

Survey Paper
A survey of multi-agent formation control☆