多智能体编队控制技术综述
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"这篇文档是《A survey of multi-agent formation control》的PDF版，由Kwang-Kyo Oha, Myoung-Chul Park和Hyo-Sung Ahn等人撰写，发表在2015年的《Automatica》期刊上。该文是一篇综述论文，深入探讨了多智能体系统的编队控制技术，包括基于位置、位移和距离的控制策略，并对相关研究进行了分类、总结和对比。关键词包括：编队控制、基于位置的控制、基于位移的控制和基于距离的控制。文章于2012年12月首次提交，2013年11月修订后再次提交，最终于2014年7月被接受，并在2014年10月28日在线发布。"
多智能体系统的编队控制是现代自动化和机器人学中的一个重要研究领域，它涉及多个自主实体如何协同工作以形成特定的几何形状或保持特定的距离关系。在这篇综述中，作者首先介绍了编队控制的基本概念，强调了智能体的感知能力和交互拓扑在控制策略设计中的关键作用。
基于位置的控制策略通常依赖每个智能体相对于预定参考点或相邻智能体的位置信息。这种策略常用于要求精确位置保持的场景，例如在军事编队、无人机集群或者自动化生产线中。然而，这种控制方法可能对传感器的精度要求较高，并且容易受到环境干扰的影响。
位移控制则关注智能体之间的相对位移，而不是绝对位置。这种方法允许智能体在不精确知道全局位置的情况下协同工作，更适用于局部信息交换的网络结构。它在环境感知和避障任务中表现出优势，因为智能体只需要关注与邻近个体的相对运动。
基于距离的控制是另一种常见的策略，它依赖于测量和维持智能体间的固定距离。这种方法对于保持稳定的间距和形状特别有用，常见于群体移动或分布式任务执行。然而，这种策略可能需要更复杂的反馈机制来处理动态变化的环境和个体间的相互影响。
作者在文中详细分析了这些控制策略的优缺点，以及它们在实际应用中的表现。他们还回顾了一些近期的研究进展，如动态编队、适应性控制以及在不确定性和通信约束下的控制方法。此外，论文还讨论了这些控制方案在解决其他问题上的应用，比如目标搜索、覆盖任务和协同感知。
《A survey of multi-agent formation control》为读者提供了一个全面的视角，理解多智能体系统编队控制的理论基础和最新发展，对从事相关研究和工程实践的专业人士具有很高的参考价值。
K.-K. Oh et al. / Automatica 53 (2015) 424–440 427
• Distance-based problem: In a distance-based control problem,
measurements y
i
contain only relative variables that can be
sensed with respect to local coordinate systems of the agents.
They do not contain any absolute and relative variables that
need to be sensed with respect to a global coordinate system.
The constraint (2) is usually given as
F(z) := [· · · ∥z
j
− z
i
∥ · · ·]
T
= F (z
∗
) (5)
for i, j = 1, . . . , N. The constraint (5) is invariant to combina-
tion of translation and rotation applied to z. Agents actively con-
trol [· · · ∥z
j
− z
i
∥ · · ·]
T
in this problem.
Note that the objective of the multi-agent system (1) in
Problem 3.1 is to achieve F (z) → F (z
∗
), which is not necessarily
z → z
∗
. The constraint (2) is different depending on problem
setups as discussed above. Suppose that z be the position vector
of the multi-agent system (1). Then the constraint (3) specifies the
desired positions with respect to the global coordinate system. The
constraints (4) and (5) are invariant to translation and combination
of translation and rotation, respectively, applied to the formation
of the agents. A constraint that is invariant to combination of
translation, rotation, and scaling of the formation of the agents is
found in angle-based formation control (Basiri, Bishop, & Jensfelt,
2010; Bishop, 2011b; Bishop, Shames, & Anderson, 2011). In angle-
based formation control, the constraint is given as F (z) := z = z
∗
,
where z
i
are subtended angles. Thus this constraint is invariant to
the combination of translation, rotation, and scaling applied to the
formation of agents.
We remark that consensus can be generally considered as a
special class of formation control. To see this, let z
∗
= 0 and
F(z) = [· · · (z
j
− z
i
)
T
· · ·]
T
for i, j = 1, . . . , N. Under this setup,
Problem 3.1 becomes a general output consensus problem, which
is called a rendezvous problem in formation control.
3.2. Classifications of formation control
Depending on problem setups, a variety of formation control
problems can be formulated. Though we categorize formation
control schemes into position-, displacement-, and distance-based
in this survey, the existing results may be classified based on other
criteria. In this subsection, we thus discuss several classifications.
According to whether or not desired formations are time-
varying, Ren and Cao (2010) have classified the formation control
problems as follows:
• Formation producing problems: The objective of agents is to
achieve a prescribed desired formation shape. In the literature,
these problems have been addressed through matrix theory
based approach, Lyapunov based approach, graph rigidity
approach, and receding horizon approach (Ren & Cao, 2010).
• Formation tracking problems: Reference trajectories for agents
are prescribed and the agents are controlled to track the
trajectories. These problems have been studied through matrix
theory based approach, potential function based approach,
Lyapunov based approach, and some other approaches (Ren &
Cao, 2010).
According to fundamental ideas in control schemes, Beard,
Lawton, and Hadaegh (2001) and Scharf et al. (2004) have classified
formation control into leader–follower, behavioral, and virtual
structure approaches:
• Leader–follower approach: At least one agent plays a role as a
leader and the rest of the agents are designated as followers. The
followers track the position of the leader with some prescribed
offsets while the leader tracks its desired trajectory.
• Behavioral approach: Several desired behaviors are prescribed
for agents in this approach. Such desired behaviors may include
cohesion, collision avoidance, obstacle avoidance, etc. This
approach is related to amorphous formation control described
below.
• Virtual structure approach: In this approach, the formation of
agents is considered as a single object, called a virtual structure.
The desired motion for the virtual structure is given. The desired
motions for the agents are determined from that of the virtual
structure.
Depending on whether or not desired formation shapes are
explicitly prescribed, one may also classify formation control
problems as follows:
• Morphous formation control: Desired formations are explicitly
specified by desired positions of agents, desired inter-agent
displacements, desired inter-agent distances, etc.
• Amorphous formation control: Without explicitly specified de-
sired formations, desired behaviors such as cohesion, collision
avoidance, etc., are given for agents. Amorphous formation con-
trol is related to behavioral approach discussed above.
4. 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 because the desired
formation can be achieved by position control of individual
agents. Interactions among the agents can be introduced
in position-based control for the purposes of enhancing
control performance or addressing additional objectives such
as formation shape keeping. The interaction graph of the agents
typically needs to be connected or have a spanning tree.
Research directions in position-based control are twofold in
the literature. First, interactions among agents are introduced to
enhance performance of formation control. Such interactions turn
out to be beneficial. Second, a global coordinator is introduced to
take feedback from agents and provide the agents with appropriate
coordination commands. This feedback coordination is beneficial if
the agents have limited actuation capabilities or they are subject to
disturbances.
Though the desired formation that is specified by the absolute
positions can be essentially achieved by position control of
individual agents, interactions among the agents may be beneficial.
To clarify this, we consider the following single-integrator modeled
agents, i.e.,
˙
p
i
= u
i
, where p
i
∈ R
n
and u
i
∈ R
n
denote the position
and control input of agent i with respect to a global coordinate
system for i = 1, . . . , N. Suppose that the objective of the agents
be to move from their initial positions to the desired ones while
controlling their formation shape. Let p
∗
∈ R
nN
be given. The
objective is to achieve p → p
∗
while satisfying p
j
− p
i
= p
∗
j
− p
∗
i
for i, j = 1, . . . , N during the movement. Assume that the agents
sense their absolute positions with respect to the global coordinate
system. Based on the assumption, we first consider the following
control law:
u
i
= k
p
(p
∗
i
− p
i
),
where k
p
> 0. Let e
p
:= p
∗
− p to obtain the error dynamics,
˙
e
p
= −k
p
e
p
, which shows exponential convergence of p to p
∗
.
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