水下机器人分布式编队控制：自适应SOM神经网络方法

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"这篇论文提出了一种自适应自组织映射(SOM)神经网络方法，用于水下机器人(AUVs)的分布式编队控制。该方法允许一组AUV在保持编队形状的同时移动到预设路径上的目标位置，并考虑了工作负载平衡和能源效率。此外，编队还能够避开障碍物并根据需要改变形状。" 在现代海洋探索和科学研究中，自主水下机器人(AUVs)的编队控制是至关重要的技术。论文“An Adaptive SOM Neural Network Method for Distributed Formation Control of a Group of AUVs”探讨了如何利用自适应自组织神经网络实现这一目标。SOM神经网络是一种无监督学习算法，它能够自组织地将输入数据映射到一个二维结构上，形成所谓的“地图”。在本文中，作者 Xin Li 和 Daqi Zhu 提出的方法中，每个AUV的控制器只使用自身的信息以及有限的邻居AUV的信息，实现了控制律的分布式设计。这样可以减少通信开销，提高系统的鲁棒性和可靠性。编队控制策略基于自我组织的竞争计算，同时考虑了工作负载平衡，确保所有AUV在完成任务的同时能有效地分配能量。论文进一步阐述了如何通过这种控制策略使AUV编队能够在预定轨迹上按照期望的编队形状达到目标位置。在遇到障碍时，编队能够灵活地调整其形状以避开障碍物，体现了编队的动态适应性。此外，这种分布式领导者-跟随者结构使得整个系统更加稳定，因为领导AUV可以引导其他成员，而每个成员只需关注与其相邻的AUV。论文内容深入探讨了自适应SOM网络的具体实现细节，包括网络训练过程、邻域关系的定义、以及如何根据环境变化实时调整控制策略。通过仿真和可能的实验验证，作者证明了该方法的有效性和实用性，为水下机器人编队控制提供了新的理论和技术支持。这篇论文为水下机器人编队控制提供了一个创新的解决方案，结合了机器学习和分布式控制理论，有望在海洋探测、海底作业等领域得到广泛应用。这种方法不仅提高了AUV编队的自主性，还确保了任务的高效执行和系统的稳定性。

8262 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 10, OCTOBER 2018

Fig. 1. Plan view of a tr i angular formation example with three randomly

distributed AUVs.

reduction of the total traveling cost and the workload balance of

every single AUV are taken into consideration.

B. Thinking in SOM

The SOM neural network method was ﬁrst introduced by T.

Kohonen in the 1980s and extended later [32]–[34]. It is based

on the idea that there is a special order of processing units in

the mammalian brain. Each unit is dedicated to a speciﬁc task

and each group of neurons is sensitive to a particular type of

input signal. The units are determined by parameters that can be

changed in certain processes to produce meaningful organiza-

tions. This algorithm soon became a valuable tool and was used

to solve many kinds of problems. In recent years, this method

has been applied to solve task assignment problems and control

of multirobot systems [35]–[38].

In this paper, we develop an SOM-based approach that could

be applied to the formation-control problems by improving the

previous SOM method. The idea comes from the similar char-

acteristics and phenomena between a multi-AUV system and an

SOM network. First, a multi-AUV formation system is the same

as a self-organizing system that only changes its inner structure.

Second, the SOM algorithm has the competitive, cooperative,

and self-organizing characteristics that are attractive for a multi-

AUV system. Thus, the SOM network could be adapted to an

unordered team of AUVs to automatically achieve the desig-

nated locations with cooperation and competition. The AUV

formation could be achieved in this way. By the formation-

tracking strategy, the movement and tracking of the formation

is also realized. In this paper, we propose an improved workload

function, which makes sure that the traveling length of a single

AUV is balanced within a limited range.

An SOM-based neural network model is shown in Fig. 2(a),

and the mapping relationship is shown in Fig. 2(b). The proposed

algorithm could be executed within a reasonable computation

time, emphasizing on workload balance for each AUV in the

team. At the initial state, there are J AUVs randomly distributed

in the workspace, where J ∈ N

. L points are set at the key

positions of the expected formation shape. For instance, there

are three points to form a triangle as Fig. 1 illustrates, so that we

Fig. 2. Structure of SOM Neural Network. (a) The structure (T

: coordi-

nates of the lth point; R

: coordinates of AUV at a certain time instant).

(b) Mapping relationship of the two layers.

obtain L =3. In this way, the SOM model has two layers of neu-

rons. The ﬁrst layer is the input layer including L neurons, where

L ∈ N

. These neurons represent the Cartesian coordinates of

the points in the 3-D workspace. T is a 3 × L matrix that de-

notes the coordinates of the target points as input neurons. Each

input neuron has three parameters (x

) according to the

coordinates of its corresponding point, where l =1, 2,...,L.

All the coordinates of the points form the input data set. The

second layer is the output layer. Neurons in the output layer

represent the coordinates of the AUVs and the corresponding

path for each AUV. Each neuron of the output layer is fully con-

nected to the neurons of the input layer. There are K neurons to

establish an optimal path for each AUV, where K ∈ N

, so that

there are K × L neurons in all. The connection weight of each

output neuron, i.e., the weight W

=(x, y, z) of that neuron,

is given by a 1 × 3 weight vector, which is initialized as the

coordinates of the initial AUV position. The network is initial-

ized with the weight vector R

= W

=(w

jkx

jky

jkz

where j =1, 2,...,J and k =1, 2,...,K. R

changes with

during every computation iteration. After the iterations, we

obtain a 3 × J × K matrix R that denotes the coordinates of the

output neurons, i.e., the trajectories of t he AUVs. The input data

set is given sequentially to the network in a random order during

the iterations, i.e., targets’ coordinates are inputted to the net-

work one by one until the last target. This input strategy with the

random order of the input data results in the robustness of the al-

gorithm and reduces its dependence on initial workspace conﬁg-

uration. During this process of formation, the visiting sequence

of the points by AUVs is gradually worked out, and the points

would attract output neurons to form a formation for the AUVs.

The iterations end until all of the AUVs reach the points. In

order to assure that each point in the formation gets an AUV, we

set L = J in the algorithm. Note that the relationship between

L and J are deﬁned by the algorithm, which means the corre-

spondence between AUVs and the target points are not ﬁxed.

III. M

AIN ALGORITHM

In order to further explain how the SOM method is applied

on formation control of a multiple AUV system, mathematical

models and formulas with some discussions are given in this

section.

Notations and deﬁnitions: for a vector ω ∈ R

, the norm |·|

is deﬁned as |ω| = |ω|



i =1

|ω

)

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