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Communication Model-Task Pairing in Artificial Swarm Design
人工蜂群设计中的通信模型-任务配对

Musad Haque ( ( ^((){ }^{(}, Member, IEEE, Connor McGowan, Yifan Guo ® , Douglas Kirkpatrick,
Musad Haque ( ( ^((){ }^{(} , Member, IEEE, Connor McGowan, Yifan Guo ® , Douglas Kirkpatrick、and Julie A. Adams ⊕ ⊕ ^(o+){ }^{\oplus}, Senior Member, IEEE
和 Julie A. Adams ⊕ ⊕ ^(o+){ }^{\oplus} ，IEEE 高级会员

Abstract 摘要

Unraveling the nature of the communication model that governs which two individuals in a swarm interact with each other is an important line of inquiry in the collective behavior sciences. A number of models have been proposed in the biological swarm literature, with the leading models being the metric, topological, and visual models. The hypothesis evaluated in this letter is whether the choice of a communication model impacts the performance of a tasked artificial swarm. The biological models are used to design coordination algorithms for a simulated swarm, which are evaluated over a range of six swarm robotics tasks. Each task has an associated set of performance metrics that are used to evaluate how the communication models fare against each other. The general findings demonstrate that the communication model significantly affects the swarm’s performance for individual tasks, and this result implies that the communication model-task pairing is an important consideration when designing artificial swarms. Further analysis of each tasks’ performance metrics reveals instances in which pairwise considerations of model and one of the various experimental factors become relevant. The reported research demonstrates that the artificial swarm’s task performance can be increased through the careful selection of a communication model.
集体行为科学的一个重要研究方向是揭示控制蜂群中两个个体相互影响的通信模式的本质。生物群文献中提出了许多模型，其中主要的模型有度量模型、拓扑模型和视觉模型。这封信所评估的假设是，通讯模型的选择是否会影响人工蜂群的性能。生物模型被用于设计模拟蜂群的协调算法，并在六个蜂群机器人任务中进行评估。每个任务都有一组相关的性能指标，用于评估通信模型之间的相互影响。总体研究结果表明，通信模型会显著影响蜂群在单个任务中的表现，这一结果意味着在设计人工蜂群时，通信模型与任务的配对是一个重要的考虑因素。对各项任务性能指标的进一步分析表明，在某些情况下，模型与各种实验因素之一的配对考虑变得非常重要。报告中的研究表明，通过精心选择通信模型，可以提高人工蜂群的任务性能。

Index Terms-Swarms, biologically-inspired robots.

I. INTRODUCTION I.引言

NUMEROUS advantages are shared by animals that live in groups [1], which includes the “many-eyes effect” against predators and utilizing group hunting techniques during foraging. These benefits are attributed to the coordination amongst
群居动物有许多共同的优势[1]，其中包括对付捕食者的 "多眼效应 "以及在觅食过程中利用群体狩猎技术。这些优势归功于群居动物之间的协调[2]。
Manuscript received February 24, 2018; accepted June 7, 2018. Date of publication June 21, 2018; date of current version July 9, 2018. This letter was recommended for publication by Associate Editor B. Mazzolai and Editor Y. Sun upon evaluation of the reviewers’ comments. This work was supported by the U.S. Office of Naval Research under Award #N000141210987. (Corresponding author: Musad Haque.)
稿件收到时间：2018 年 2 月 24 日；接受时间：2018 年 6 月 7 日。发表日期2018年6月21日；当前版本日期2018年7月9日。经对审稿人意见进行评估，副主编 B. Mazzolai 和编辑 Y. Sun 建议发表此信。这项工作得到了美国海军研究办公室的支持，获奖编号为N000141210987。(通讯作者：Musad Haque）。
M. Haque is with the Space Exploration Sector, Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723 USA (e-mail: musad.haque@ jhuapl.edu).
M.Haque 是美国马里兰州劳雷尔 20723 约翰霍普金斯大学应用物理实验室太空探索部门的工作人员（电子邮件：musad.haque@ jhuapl.edu）。
C. McGowan and Y. Guo are with the Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37235 USA (e-mail: connor.r.mcgowan@vanderbilt.edu; yifan.guo@ vanderbilt.edu).
C.McGowan and Y. Guo are with the Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37235 USA (e-mail：connor.r.mcgowan@vanderbilt.edu; yifan.guo@ vanderbilt.edu).
D. Kirkpatrick is with the Department of Computer Science and Engineering, Michigan State University, East Lansing, MI 48824 USA (e-mail: kirkpa48@msu.edu).
D.柯克帕特里克现供职于密歇根州立大学计算机科学与工程系，地址：East Lansing, MI 48824 USA（电子邮件：kirkpa48@msu.edu）。
J. A. Adams is with the Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37235 USA, and also with the Department of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331 USA (e-mail: julie.a.adams @ oregonstate.edu).
A. Adams 是美国田纳西州纳什维尔市范德比尔特大学电气工程与计算机科学系（Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37235 USA）和美国俄勒冈州科瓦利斯市俄勒冈州立大学电气工程与计算机科学系（Department of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331 USA）的成员（电子邮件：julie.a.adams @ oregonstate.edu）。
This letter has supplemental downloadable multimedia material available at http://ieeexplore.ieee.org, provided by the authors. The Supplementary Materials contain videos showing preliminary efforts toward conducting experiments on Georgia Tech’s Robotarium. This material is 33.2 MB in size.
这封信有可下载的多媒体补充材料，可在http://ieeexplore.ieee.org下载，由作者提供。补充材料中的视频展示了在佐治亚理工学院机器人馆进行实验的初步努力。该材料大小为 33.2 MB。
Digital Object Identifier 10.1109/LRA.2018.2849562 group members. A high degree of coordination is displayed by some social animals during cooperative food retrieval [2], construction of living bridges [3], schooling [4], and flocking [5]. There is no central planner in these biological systems; instead, interactions based on locally-available information leads to such coordination [6].
数字对象标识符 10.1109/LRA.2018.2849562 群体成员。一些社会动物在合作获取食物[2]、建造生活桥梁[3]、就学[4]和成群结队[5]时表现出高度的协调性。在这些生物系统中没有中央计划者；相反，基于本地可用信息的互动导致了这种协调[6]。
Efforts to describe the rules that determine whether two individuals in a group are permitted to interact (i.e., the network topology that underpins communications) has resulted in numerous models being proposed in the biological swarm literature. The three predominant models are: the metric [7], the topological [5], and the visual models [4]. The swarm’s agents interact if they are within a critical distance of one another in the metric model; hence, this model is directly based on spatial proximity [7]. Ballerini et al.'s topological model [5] is similar in concept to the nearest neighbor rule ( k − N N ) ( k − N N ) (k-NN)(k-N N) [8], in that, it requires individuals to interact with a fixed number of nearest individuals. The visual model is based on sensory capabilities, where an individual only interacts with those within its field of view [4].
为了描述决定一个群体中两个个体是否可以互动的规则（即支持通信的网络拓扑结构），生物群文献中提出了许多模型。最主要的三种模型是：度量模型[7]、拓扑模型[5]和视觉模型[4]。在度量模型中，如果蜂群中的个体之间的距离在临界值之内，它们就会相互作用；因此，这种模型是直接基于空间接近性的[7]。Ballerini 等人的拓扑模型[5]在概念上类似于近邻规则 ( k − N N ) ( k − N N ) (k-NN)(k-N N) [8]，即要求个体与固定数量的最近个体相互作用。视觉模型基于感官能力，个体只与视野范围内的个体互动[4]。
Identifying the communication model that best describes a biological swarm is important to the science of collective behavior, as it provides insight into how information diffuses in a swarm [4]. The corresponding selection of those models is important to the science of autonomy, and is described as “one of the main challenges” in swarm robotics [9]. Biologically inspired artificial swarms derive characteristics such as decentralized control, scalability, and robustness to individual agent failures [10]; however, a survey [9] of human-swarm interaction notes that despite inheriting beneficial characteristics from their counterparts in nature, an ill-conceived communication model can lead to undesirable consequences. Kolling et al. [9] posit that erratic behavior from a poorly-assigned communication model increases the workload of a human operator interacting with the swarm.
确定最能描述生物群的通信模型对集体行为科学非常重要，因为它能让我们深入了解信息如何在生物群中扩散[4]。相应地选择这些模型对自主性科学非常重要，被称为蜂群机器人技术的 "主要挑战之一"[9]。受生物启发的人工蜂群具有分散控制、可扩展性和对单个代理故障的鲁棒性等特点[10]；然而，一项关于人类与蜂群互动的调查[9]指出，尽管从自然界中的对应物继承了有益的特点，但考虑不周的通信模式可能会导致不良后果。Kolling 等人[9]认为，分配不当的通信模型会导致不稳定的行为，从而增加与蜂群互动的人类操作员的工作量。
This manuscript’s findings demonstrate that the choice of a communication model - metric, topological, or visual - is an important swarm design consideration, since the communication model has a significant impact on an artificial swarm’s task performance. The focus is limited to the predominant models found in the biological swarm literature. Six tasks were analyzed: Search for Multiple Targets, Search for a Goal, Rally, Disperse, Avoid an Adversary, and Follow, and a breadth of performance metrics were recorded to judge the artificial swarm’s ability to conduct a task. No single communication model delivered the best performance across all the tasks. Further, agent and environmental parameters had meaningful interactions with the
本手稿的研究结果表明，通讯模型的选择--度量模型、拓扑模型或视觉模型--是蜂群设计的一个重要考虑因素，因为通讯模型对人工蜂群的任务性能有重大影响。研究重点仅限于生物蜂群文献中发现的主要模式。对六项任务进行了分析：通过记录各种性能指标来判断人工蜂群执行任务的能力。在所有任务中，没有一种通信模式能提供最佳性能。此外，代理参数和环境参数也与人工蜂群执行任务的能力产生了有意义的交互作用。
communication models in terms of performance. The results imply that the performance of a deployed artificial swarm is amplified through a task-based selection of a communication model. In addition, the choice of a communication model can be fine-tuned, given environmental and agent parameters, such as the swarm’s size. No prior research has conducted such an extensive analysis of the biologically inspired communication models within the context of artificial robotic swarm tasks.
通信模型的性能。结果表明，通过基于任务选择通信模式，部署的人工蜂群的性能得到了提升。此外，还可以根据环境和代理参数（如蜂群的大小）对通信模型的选择进行微调。之前的研究还没有在人工机器人蜂群任务的背景下对生物启发通信模型进行如此广泛的分析。
An understanding of the appropriate communication model to task specification has the potential to make it easier for a human operator to monitor and supervise an artificial swarm. A communication model that improves the swarms’ likelihood to complete a task will reduce the human’s workload associated with monitoring the task. Understanding the exact implications on human interaction is beyond the scope of this manuscript. Rather, the manuscript’s contribution focuses on factors related to the model-task pairings and the importance in their consideration for artificial swarm design.
了解适当的通信模型与任务规范，有可能使人类操作员更容易监控人工蜂群。一个能提高人工蜂群完成任务可能性的通信模式，将减少人类与监控任务相关的工作量。理解对人类互动的确切影响超出了本手稿的范围。相反，本手稿的重点在于与模型-任务配对相关的因素，以及考虑这些因素对人工蜂群设计的重要性。
The metric model is one of the earliest models developed to represent range-limited communication between biological swarm agents [11]-[13] and to capture sensor range constraints in the field of multi-robot systems [14], [15]. This model is used as a benchmark when comparing newer models [4], [5], [16]. The prior research comparing communication models can be classified based on research motivations: 1) Identify the model that accurately describes the network topology of a biological swarm (biology), 2) Understand model differences from their system-theoretic properties (physics), and 3) Determine the manipulability of models in terms of human-swarm interaction (robotics).
公制模型是最早开发的模型之一，用于表示生物群代理之间的通信距离限制[11]-[13]，以及捕捉多机器人系统领域的传感器距离限制[14]、[15]。在比较更新的模型 [4]、[5]、[16] 时，该模型被用作基准。之前比较通信模型的研究可根据研究动机进行分类：1）确定能准确描述生物群网络拓扑结构的模型（生物学）；2）从模型的系统理论特性了解模型的差异（物理学）；3）确定模型在人群互动方面的可操作性（机器人学）。
A field study of European starlings, Sturnus vulgaris, indicates that the swarm uses a topological, rather than a range limited model [5]. A simulation result as part of the study shows that a swarm using the topological model, compared to metric, decomposes into fewer groups and produces more cohesive swarms in response to a predator [5]. Strandburg-Peshkin et al. [4] introduced the visual model, and show that it best predicts golden shiners’, Notemigonus crysoleucas, response to stimuli. The model’s low clustering makes it fundamentally different from the metric and topological models, from a networktheoretic perspective.
对欧洲椋鸟（Sturnus vulgaris）的实地研究表明，椋鸟群使用的是拓扑模型，而不是范围限制模型[5]。作为研究一部分的模拟结果表明，使用拓扑模型的椋鸟群与使用度量模型的椋鸟群相比，在应对捕食者时分解成的群体更少，产生的椋鸟群更有凝聚力[5]。Strandburg-Peshkin 等人[4]引入了视觉模型，结果表明该模型能最好地预测金色歆鱼（Notemigonus crysoleucas）对刺激的反应。从网络理论的角度来看，该模型的低聚类特性使其与度量模型和拓扑模型有着本质区别。
Physics-based investigations of system-level properties of the topological and metric models found group orders [17], [18], the probability of reaching a consensus [19], rate of convergence of the consensus on agents’ headings [20], and the influence of the topological distance on a simulated swarm’s ability to reach a consensus in the presence of uncertainty [21]. Spears et al. [22] did not explicitly compare the three leading models in their “physicomimetic” simulated swarms, but compared swarm behaviors designed to be analogous to molecules in solid, liquid, and gas formations. This work was motivated by an unevaluated hypothesis that each swarm type (solid, liquid or gas) is particularly better suited than the other two in performing certain tasks.
对拓扑模型和度量模型的系统级特性进行的基于物理学的研究发现了群体阶数[17]、[18]、达成共识的概率[19]、对代理的方向达成共识的收敛速度[20]，以及拓扑距离对模拟蜂群在不确定情况下达成共识的能力的影响[21]。Spears 等人[22]没有明确比较他们的 "仿物理 "模拟蜂群中的三种主要模型，而是比较了设计成类似于固体、液体和气体形态中的分子的蜂群行为。这项工作的动机是一个未经评估的假设，即每种蜂群类型（固态、液态或气态）在执行某些任务时都比其他两种类型更适合。
Goodrich et al. [23] compare the topological and metric models in order to evaluate a human’s ability to control an artificial swarm by manipulating a leader agent that influences other swarm agents. Reportedly, a human operator can more easily manipulate a swarm using the topological model, and in general, swarms that have low inter-agent influences [24]. Other studies compare network topologies: De la Croix and Egerstedt [25], for instance, report on the ease with which a human operator can control a swarm whose communication network can either be a line, cycle, acyclic, or a complete graph. A single leader was controlled using a joystick. Multiple, dynamically assigned leaders were analyzed in networks, where agents were guaranteed to be 1-, 2-, or 3-hops from a leader [26]. The work can be interpreted as comparing select topological distances to a swarm leader.
Goodrich 等人[23]比较了拓扑模型和度量模型，以评估人类通过操纵影响其他蜂群代理的领导代理来控制人工蜂群的能力。据报道，使用拓扑模型，人类操作员可以更容易地操纵蜂群，一般来说，也更容易操纵代理间影响较小的蜂群[24]。其他研究对网络拓扑结构进行了比较：例如，De la Croix 和 Egerstedt[25]报告了人类操作员控制蜂群的难易程度，蜂群的通信网络可以是线状、循环、非循环或完整图。使用操纵杆控制单个领导者。在网络中对多个动态分配的领导者进行了分析，在这些网络中，保证代理与领导者的距离为 1、2 或 3 跳 [26]。这项工作可以理解为比较与蜂群首领的选定拓扑距离。
This manuscript’s evaluation is seemingly the first to compare biologically inspired communication models with respect to their performances over swarm robotics tasks.
本手稿的评估似乎是首次比较受生物启发的通信模型在蜂群机器人任务中的表现。

III. Coordination AlgorithMs
III.协调算法

The individual agents in a “small-scale” multi-robot systems are generally assumed to be capable of performing tasks on their own; for instance, consider the systems described by Mataric [27] and Burgard et al. [28]. Such systems benefit from the coordination amongst members, but such a characteristic is not a system-level requirement when agents are planning their own actions. However, a swarm, by definition, consists of “relatively incapable” units, and through simple interaction rules, a global system behavior emerges [29], [30].
一般认为，"小规模 "多机器人系统中的单个代理能够独立完成任务；例如，可以考虑 Mataric [27] 和 Burgard 等人 [28] 所描述的系统。这些系统得益于成员之间的协调，但当代理规划自己的行动时，这种特性并不是系统级的要求。然而，顾名思义，蜂群由 "能力相对较弱 "的单位组成，通过简单的交互规则，就能产生全局系统行为 [29], [30]。
Incapable swarm units are conceivably limited in their ability to execute intricate interaction rules. Therefore, the designed coordination algorithm defining the movement laws aims to remain simple. The agents, modeled as 2 D 2 D 2D2 D self-propelled particles, are controlled through updates to the velocity heading [31]-[33]. The agents are indexed 1 through N N NN, where N N NN is the swarm’s size. At time t t tt, agent i ∈ { 1 , … , N } i ∈ { 1 , … , N } i in{1,dots,N}i \in\{1, \ldots, N\} experiences a force given by:
可以想象，没有能力的蜂群单位执行复杂的交互规则的能力是有限的。因此，所设计的定义运动规律的协调算法旨在保持简单。通过更新速度航向[31]-[33]来控制被模拟为 2 D 2 D 2D2 D 自走粒子的代理。代理的索引为 1 到 N N NN ，其中 N N NN 是蜂群的大小。在时间 t t tt 时，代理体 i ∈ { 1 , … , N } i ∈ { 1 , … , N } i in{1,dots,N}i \in\{1, \ldots, N\} 受到的力为
F i ( t ) = F env , i ( t ) + F swarm , i ( t ) + F t a s k , i ( t ) F i ( t ) = F env  , i ( t ) + F swarm  , i ( t ) + F t a s k , i ( t ) F_(i)(t)=F_("env ",i)(t)+F_("swarm ",i)(t)+F_(task,i)(t)\mathbf{F}_{i}(t)=\mathbf{F}_{\text {env }, i}(t)+\mathbf{F}_{\text {swarm }, i}(t)+\mathbf{F}_{t a s k, i}(t)
where, F env , i ( t ) , F swarm , i ( t ) F env  , i ( t ) , F swarm  , i ( t ) F_("env ",i)(t),F_("swarm ",i)(t)\mathbf{F}_{\text {env }, i}(t), \mathbf{F}_{\text {swarm }, i}(t), and F task , i ( t ) F task  , i ( t ) F_("task ",i)(t)\mathbf{F}_{\text {task }, i}(t) are the forces due to the environmental factors, swarming, and the task at hand, respectively. Such a framework of accumulating forces to control a swarm has been used to analyze the effectiveness of providing haptic feedback to a human operator [34], [35]. F env,i ( t ) F env,i  ( t ) F_("env,i ")(t)\mathbf{F}_{\text {env,i }}(t) incorporates reactions to the environment, such as remaining within the bounds of the simulated world by “bouncing off” walls and avoiding obstacles. F task , i ( t ) F task  , i ( t ) F_("task ",i)(t)\mathbf{F}_{\text {task }, i}(t) depends on the task (Section IV-B), and is not designed to optimally solve the associated robotics task; rather, it is a simple task-related objective that contributes to the overall force acting on an agent. The reason for this design choice is to gain insight into what the overall swarm can achieve with little intelligence guiding the individual units.
其中， F env , i ( t ) , F swarm , i ( t ) F env  , i ( t ) , F swarm  , i ( t ) F_("env ",i)(t),F_("swarm ",i)(t)\mathbf{F}_{\text {env }, i}(t), \mathbf{F}_{\text {swarm }, i}(t) 和 F task , i ( t ) F task  , i ( t ) F_("task ",i)(t)\mathbf{F}_{\text {task }, i}(t) 分别为环境因素、蜂群和手头任务造成的力。这种累积力来控制蜂群的框架已被用于分析向人类操作员提供触觉反馈的有效性 [34], [35]。 F env,i ( t ) F env,i  ( t ) F_("env,i ")(t)\mathbf{F}_{\text {env,i }}(t) 包括对环境的反应，例如通过 "弹开 "墙壁和避开障碍物来保持在模拟世界的范围内。 F task , i ( t ) F task  , i ( t ) F_("task ",i)(t)\mathbf{F}_{\text {task }, i}(t) 取决于任务（第 IV-B 节），并不是为了优化解决相关的机器人任务而设计的；相反，它是一个与任务相关的简单目标，有助于增加作用在代理身上的总体力。之所以选择这样的设计，是为了深入了解在单个单元几乎没有智能指导的情况下，整个蜂群能够实现哪些目标。
F swarm , i ( t ) F swarm  , i ( t ) F_("swarm ",i)(t)\mathbf{F}_{\text {swarm }, i}(t) is constructed in a two-step process. The first step assigns “neighbors” to an agent. Then, agents swarm with their neighbors based on the widely-used repulsion-orientationattraction scheme [12], [13], [16], [31], [32], [36]-[38]. The choice of a communication model prescribes an agent’s neighbor set. A communication link from i i ii to agent j j jj, classifies agent j j jj as agent i i ii 's neighbor. N i ( t ) N i ( t ) N_(i)(t)\mathcal{N}_{i}(t) denotes the set of neighbors of i i ii at
F swarm , i ( t ) F swarm  , i ( t ) F_("swarm ",i)(t)\mathbf{F}_{\text {swarm }, i}(t) 分两步构建。第一步是为代理分配 "邻居"。然后，根据广泛使用的排斥-定向-吸引方案 [12], [13], [16], [31], [32], [36] - [38]，代理蜂拥与其邻居。通信模式的选择规定了代理的邻居集。从 i i ii 到代理 j j jj 的通信链路会将代理 j j jj 归类为代理 i i ii 的邻居。 N i ( t ) N i ( t ) N_(i)(t)\mathcal{N}_{i}(t) 表示 i i ii 的邻居集，位于
Fig. 1. The communication model—metric (dashed circle with radius d m e t d m e t d_(met)d_{m e t} ), topological ( n top n top  n_("top ")n_{\text {top }} lines), or visual (sector with radius d v i s d v i s d_(vis)d_{v i s} and ± ϕ ± ϕ +-phi\pm \phi from heading) — prescribes neighbors. Subsequently, agents interact with their neighbors through a repulsion-orientation-attraction scheme. (a) The focus agent (fill) is neighbors with agents 3,5 , and 6 when using the metric model. The agent’s neighbors using the topological model with n t o p = 4 n t o p = 4 n_(top)=4n_{t o p}=4 are agents 3 , 4 , 5 3 , 4 , 5 3,4,53,4,5, and 6 . The neighbors using the visual model are agents 3,4 , and 6 (agent 2 is occluded by 3, and agent 5 is in the blindspot). (b) There are two choices for each radius in the ( r r , r o , r a ) r r , r o , r a {:r_(r),r_(o),r_(a))\left.r_{r}, r_{o}, r_{a}\right) tuple, which leads to 2 3 2 3 2^(3)2^{3} possible configurations (see Table I). The inner-, middle, and outer-most zones represent the repulsion, orientation, and attraction zones, respectively, centered at the agent’s position.
图 1.通信模型--度量模型（半径为 d m e t d m e t d_(met)d_{m e t} 的虚线圆圈）、拓扑模型（ n top n top  n_("top ")n_{\text {top }} 线）或视觉模型（半径为 d v i s d v i s d_(vis)d_{v i s} 和 ± ϕ ± ϕ +-phi\pm \phi 的扇形线）--规定了邻居。随后，代理通过 "排斥-定向-吸引 "方案与其邻居互动。(a) 使用度量模型时，焦点代理（填充）与代理 3、5 和 6 相邻。使用拓扑模型 n t o p = 4 n t o p = 4 n_(top)=4n_{t o p}=4 时，该代理的邻居是代理 3 , 4 , 5 3 , 4 , 5 3,4,53,4,5 和 6。使用视觉模型时的邻居是代理 3、4 和 6（代理 2 被代理 3 遮挡，代理 5 处于盲区）。(b) ( r r , r o , r a ) r r , r o , r a {:r_(r),r_(o),r_(a))\left.r_{r}, r_{o}, r_{a}\right) 元组中的每个半径有两种选择，这导致 2 3 2 3 2^(3)2^{3} 可能的配置（见表 I）。最内侧、中间和最外侧的区域分别代表斥力区、定向区和吸引区，以代理的位置为中心。
time t t tt. The metric model is parameterized by a single distance measure, d m e t d m e t d_(met)d_{m e t}. All agents within a distance d m e t d m e t d_(met)d_{m e t} from agent i i ii are its neighbors. When using the topological model, N i ( t ) N i ( t ) N_(i)(t)\mathcal{N}_{i}(t) is the set containing the n t o p n t o p n_(top)n_{t o p} nearest agents from i i ii, where n t o p n t o p n_(top)n_{t o p} is referred to as the topological distance. The topological distance of Zebrafish, Danio rerio, is around five [39]; for starlings it is around seven [5]. The visual model prescribes neighbors based on three factors. Agent j j jj is agent i i ii 's neighbor, if the following conditions hold: 1) Agent j j jj is not in i i ii 's blindspot, 2) The two agents are less than a certain distance apart, and 3) There is a clear line-of-sight (occlusion is possible by another agent or object in the environment) [4]. An agent’s visual sensing is defined by a range d v i s d v i s d_(vis)d_{v i s} and an angle ± ϕ ± ϕ +-phi\pm \phi from its heading [32], [33], which is a geometric construction that can produce a blindspot (Fig. 1(a)).
时间 t t tt 。度量模型的参数为单一距离度量 d m e t d m e t d_(met)d_{m e t} 。与代理 i i ii 距离 d m e t d m e t d_(met)d_{m e t} 以内的所有代理都是它的邻居。使用拓扑模型时， N i ( t ) N i ( t ) N_(i)(t)\mathcal{N}_{i}(t) 是包含距离 i i ii 最近的 n t o p n t o p n_(top)n_{t o p} 代理的集合，其中 n t o p n t o p n_(top)n_{t o p} 被称为拓扑距离。斑马鱼（Danio rerio）的拓扑距离约为 5 [39]；椋鸟的拓扑距离约为 7 [5]。视觉模型根据三个因素来确定邻居。如果以下条件成立，则代理 j j jj 是代理 i i ii 的邻居：1) 代理商 j j jj 不在代理商 i i ii 的盲区内；2) 两个代理商之间的距离小于一定距离；3) 有清晰的视线（可能被环境中的其他代理商或物体遮挡）[4]。一个代理的视觉传感由其航向的范围 d v i s d v i s d_(vis)d_{v i s} 和角度 ± ϕ ± ϕ +-phi\pm \phi 所定义 [32]，[33]，这是一个可以产生盲区的几何结构（图 1(a)）。

IV. EXPERIMENTAL DESIGN IV.实验设计

A. Setup A.设置
The Processing development environment 1 1 ^(1){ }^{1} was used to conduct the experiments. This software primarily serves the
实验使用 Processing 开发环境 1 1 ^(1){ }^{1} 进行。该软件主要用于
TABLE I 表 I
FACTORS AND PARAMETERS COMMON ACROSs All TASKS
所有任务的共同因素和参数
Experimental Factor/Parameter
实验因素/参数		 Levels Explored/Value 探索的层面/价值
Communication model 交流模式 Metric, Topological, Visual
度量、拓扑、视觉
World 世界 500 pixels × 500 × 500 xx500\times 500 pixels
500 像素 × 500 × 500 xx500\times 500 像素
Agent (base, side, side ) ) ))
代理（基地、侧面、侧面 ) ) )) 		5 , 10.30 , 10.30 5 , 10.30 , 10.30 5,10.30,10.305,10.30,10.30 pixels  5 , 10.30 , 10.30 5 , 10.30 , 10.30 5,10.30,10.305,10.30,10.30 像素
Number of agents ( N ) ( N ) (N)(N)
代理数量 ( N ) ( N ) (N)(N) 		50 , 100 , 200 50 , 100 , 200 50,100,20050,100,200
Radius of repulsion ( r r ) r r (r_(r))\left(r_{r}\right)
斥力半径 ( r r ) r r (r_(r))\left(r_{r}\right) 		10,20 pixels 10,20 像素
Radius of orientation ( r o ) r o (r_(o))\left(r_{o}\right)
定向半径 ( r o ) r o (r_(o))\left(r_{o}\right) 		1.5 r r , 2.0 r r 1.5 r r , 2.0 r r 1.5r_(r),2.0r_(r)1.5 r_{r}, 2.0 r_{r}
Radius of attraction ( r a ) r a (r_(a))\left(r_{a}\right)
吸引力半径 ( r a ) r a (r_(a))\left(r_{a}\right) 		1.5 r o , 2.0 r o 1.5 r o , 2.0 r o 1.5r_(o),2.0r_(o)1.5 r_{o}, 2.0 r_{o}
Metric range ( d m e t ) d m e t (d_(met))\left(d_{m e t}\right) 公制范围 ( d m e t ) d m e t (d_(met))\left(d_{m e t}\right) r a r a r_(a)r_{a}
Topological distance ( n t o p ) n t o p (n_(top))\left(n_{t o p}\right)
拓扑距离 ( n t o p ) n t o p (n_(top))\left(n_{t o p}\right) 		5 , 6 , 7 , 8 5 , 6 , 7 , 8 5,6,7,85,6,7,8
Visual range ( d v i s ) d v i s (d_(vis))\left(d_{v i s}\right) 可视范围 ( d v i s ) d v i s (d_(vis))\left(d_{v i s}\right) 1 / 2 1 / 2 1//21 / 2 diagonal of the world
1 / 2 1 / 2 1//21 / 2 世界的对角线
Visual sensing sector ( ± ϕ ) ( ± ϕ ) (+-phi)( \pm \phi)
视觉传感部门 ( ± ϕ ) ( ± ϕ ) (+-phi)( \pm \phi) 		± 2 π / 3 ± 2 π / 3 +-2pi//3\pm 2 \pi / 3 rad from heading
± 2 π / 3 ± 2 π / 3 +-2pi//3\pm 2 \pi / 3 弧度从标题开始
Experimental Factor/Parameter Levels Explored/Value Communication model Metric, Topological, Visual World 500 pixels xx500 pixels Agent (base, side, side ) 5,10.30,10.30 pixels Number of agents (N) 50,100,200 Radius of repulsion (r_(r)) 10,20 pixels Radius of orientation (r_(o)) 1.5r_(r),2.0r_(r) Radius of attraction (r_(a)) 1.5r_(o),2.0r_(o) Metric range (d_(met)) r_(a) Topological distance (n_(top)) 5,6,7,8 Visual range (d_(vis)) 1//2 diagonal of the world Visual sensing sector (+-phi) +-2pi//3 rad from heading| Experimental Factor/Parameter | Levels Explored/Value | | :--- | :---: | | Communication model | Metric, Topological, Visual | | World | 500 pixels $\times 500$ pixels | | Agent (base, side, side $)$ | $5,10.30,10.30$ pixels | | Number of agents $(N)$ | $50,100,200$ | | Radius of repulsion $\left(r_{r}\right)$ | 10,20 pixels | | Radius of orientation $\left(r_{o}\right)$ | $1.5 r_{r}, 2.0 r_{r}$ | | Radius of attraction $\left(r_{a}\right)$ | $1.5 r_{o}, 2.0 r_{o}$ | | Metric range $\left(d_{m e t}\right)$ | $r_{a}$ | | Topological distance $\left(n_{t o p}\right)$ | $5,6,7,8$ | | Visual range $\left(d_{v i s}\right)$ | $1 / 2$ diagonal of the world | | Visual sensing sector $( \pm \phi)$ | $\pm 2 \pi / 3$ rad from heading |
visual arts and interactive media community, and lends itself to creating digital sketchbooks to program - and visualize swarms. The dimensions (in pixels) are provided in Table I. Across all tasks, the communication model was the experiment’s primary factor, with other factors being the number of agents ( N ) ( N ) (N)(N), and the radii of repulsion ( r r ) r r (r_(r))\left(r_{r}\right), orientation ( r o ) r o (r_(o))\left(r_{o}\right), and attraction ( r a ) r a (r_(a))\left(r_{a}\right). Some tasks utilized additional factors, which are specified in Section IV-B. A full factorial experiment was designed for a comprehensive analysis that reported the main effects of the model and the simple interactions between model and the additional factors.
它是视觉艺术和互动媒体界的一个重要组成部分，可用于创建数字草图本，对蜂群进行编程和可视化。表一提供了尺寸（像素）。在所有任务中，通信模型是实验的主要因素，其他因素包括代理数量 ( N ) ( N ) (N)(N) 、排斥半径 ( r r ) r r (r_(r))\left(r_{r}\right) 、定向半径 ( r o ) r o (r_(o))\left(r_{o}\right) 和吸引半径 ( r a ) r a (r_(a))\left(r_{a}\right) 。有些任务还使用了额外的因素，具体见第 IV-B 节。我们设计了一个全因子实验来进行综合分析，报告模型的主效应以及模型与附加因素之间的简单交互作用。
The biological swarm literature guides the parameter value selection of d met , n top , d v i s d met  , n top  , d v i s d_("met "),n_("top "),d_(vis)d_{\text {met }}, n_{\text {top }}, d_{v i s}, and ϕ . d met ϕ . d met  phi.d_("met ")\phi . d_{\text {met }} followed Couzin et al. [7]. d v i s d v i s d_(vis)d_{v i s} and ϕ ϕ phi\phi is close to what is observed in nature [4], [32]. Four levels of n top n top  n_("top ")n_{\text {top }} permitted variability [5], yet only n top = 7 n top  = 7 n_("top ")=7n_{\text {top }}=7 is reported for the topological model, without loss of generality. No difference in performance was found between the different levels of n t o p n t o p n_(top)n_{t o p} across all the tasks, and this characteristic of the model can be attributed to the existence of a critical topological distance n top ⋆ n top  ⋆ n_("top ")^(***)n_{\text {top }}^{\star}, beyond which the swarm’s performance does not vary [40]. This attempt to derive values from those reported in the biological swarm literature, adheres to the “descriptive agenda” of multi-agent learning [41], [42], where the goal is to model an underlying phenomenon from the social sciences.
生物群文献指导了 d met , n top , d v i s d met  , n top  , d v i s d_("met "),n_("top "),d_(vis)d_{\text {met }}, n_{\text {top }}, d_{v i s} 和 ϕ . d met ϕ . d met  phi.d_("met ")\phi . d_{\text {met }} 的参数值选择，并遵循了 Couzin 等人的研究[7]。 d v i s d v i s d_(vis)d_{v i s} 和 ϕ ϕ phi\phi 接近自然界的观测结果[4], [32]。四级 n top n top  n_("top ")n_{\text {top }} 允许变化[5]，但拓扑模型只报告了 n top = 7 n top  = 7 n_("top ")=7n_{\text {top }}=7 ，而没有损失一般性。在所有任务中， n t o p n t o p n_(top)n_{t o p} 的不同等级在性能上没有差异，该模型的这一特点可归因于存在一个临界拓扑距离 n top ⋆ n top  ⋆ n_("top ")^(***)n_{\text {top }}^{\star} ，超过该距离，蜂群的性能不会发生变化[40]。这种从生物群文献中得出数值的尝试，符合多代理学习的 "描述性议程"[41]，[42]，其目标是模拟社会科学中的基本现象。
F env,i ( t ) F env,i  ( t ) F_("env,i ")(t)\mathbf{F}_{\text {env,i }}(t) is responsible for reflecting agent i i ii off walls [43] by adding an offset to the current heading. Certainly, obstacles can be avoided more intelligently (using cones [44] or barrier certificates [45], for instance), but the reason to not employ such techniques is to allow the models to drive the coordination without the help of sophisticated maneuvers.
F env,i ( t ) F env,i  ( t ) F_("env,i ")(t)\mathbf{F}_{\text {env,i }}(t) 负责通过增加当前航向的偏移量，将代理 i i ii 从墙壁上反射出去[43]。当然，可以更智能地避开障碍物（例如使用锥形筒[44]或障碍物证书[45]），但不采用这些技术的原因是为了让模型在没有复杂操作的帮助下驱动协调。

B. Tasks B.任务

  1. Search for Multiple Targets: The swarm’s objective was to discover targets (Fig. 2). There were either 5, 10, or 20 targets ( N t ) N t (N_(t))\left(N_{t}\right), and the number of obstacles ( N o ) N o (N_(o))\left(N_{o}\right) was either 0 , 0.1 N 0 , 0.1 N 0,0.1 N0,0.1 N, or 0.2 N . F task,i ( t ) 0.2 N . F task,i  ( t ) 0.2 N.F_("task,i ")(t)0.2 N . \mathbf{F}_{\text {task,i }}(t) was 0 0 0\mathbf{0}; hence, no force required agents to search, let alone do so intelligently. This formulation investigated achievement through swarming alone, contained in an area, and while avoiding obstacles.
    搜索多个目标：蜂群的目标是发现目标（图 2）。目标 ( N t ) N t (N_(t))\left(N_{t}\right) 有 5 个、10 个或 20 个，障碍物 ( N o ) N o (N_(o))\left(N_{o}\right) 的数量为 0 , 0.1 N 0 , 0.1 N 0,0.1 N0,0.1 N 或 0.2 N . F task,i ( t ) 0.2 N . F task,i  ( t ) 0.2 N.F_("task,i ")(t)0.2 N . \mathbf{F}_{\text {task,i }}(t) 为 0 0 0\mathbf{0} ；因此，没有任何力量要求代理进行搜索，更不用说智能搜索了。这一表述考察了在一个区域内，在避开障碍物的情况下，仅通过蜂群的方式来实现搜索的情况。
  2. Search for a Goal: This task included a goal area that the swarm was required to locate. Once an agent located the goal, it communicated the location to its neighbors. F task , i ( t ) F task  , i ( t ) F_("task ",i)(t)\mathbf{F}_{\text {task }, i}(t) was enabled when an agent located the goal, which acted as an
    搜索目标：这项任务包括要求蜂群找到一个目标区域。一旦一个代理找到了目标，它就会将该位置告知其邻居。当一个代理找到目标时， F task , i ( t ) F task  , i ( t ) F_("task ",i)(t)\mathbf{F}_{\text {task }, i}(t) 就会启用，这就像一个
Fig. 2. Simulation screenshots of the various tasks. Each row consists of three figures and represents a specific task. The difference between a row’s figures is either the communication model being used or the time of the screenshot.
图 2.各种任务的模拟截图。每行由三个数字组成，代表一项具体任务。每行数字之间的差异是所使用的通信模型或截图的时间。
TABLE II 表 II
TRIALS AND ITERATIONS BY TASK
按任务进行试验和迭代
Task 任务 Factors per model 每个模型的系数 Trials 审判 Iterations per run 每次运行的迭代次数
Targets 目标 ( N , N o , N t , r r , r o , r a ) N , N o , N t , r r , r o , r a (N,N_(o),N_(t),r_(r),r_(o),r_(a))\left(N, N_{o}, N_{t}, r_{r}, r_{o}, r_{a}\right) 32400 1000
Goal 目标 ( N , N o , r r , r o , r a ) N , N o , r r , r o , r a (N,N_(o),r_(r),r_(o),r_(a))\left(N, N_{o}, r_{r}, r_{o}, r_{a}\right) 10800 1000
Rally 集结 ( N , p i , g , r r , r o , r a ) N , p i , g , r r , r o , r a (N,p_(i),g,r_(r),r_(o),r_(a))\left(N, p_{i}, g, r_{r}, r_{o}, r_{a}\right) 32400 750
Disperse 分散 ( N , N o , s , r r , r o , r a ) N , N o , s , r r , r o , r a (N,N_(o),s,r_(r),r_(o),r_(a))\left(N, N_{o}, s, r_{r}, r_{o}, r_{a}\right) 32400 200
Avoid 避免 ( N , r r , r o , r a ) N , r r , r o , r a (N,r_(r),r_(o),r_(a))\left(N, r_{r}, r_{o}, r_{a}\right) 3600 200
Follow 跟进 ( N , r r , r o , r a ) N , r r , r o , r a (N,r_(r),r_(o),r_(a))\left(N, r_{r}, r_{o}, r_{a}\right) 3600 2000
Task Factors per model Trials Iterations per run Targets (N,N_(o),N_(t),r_(r),r_(o),r_(a)) 32400 1000 Goal (N,N_(o),r_(r),r_(o),r_(a)) 10800 1000 Rally (N,p_(i),g,r_(r),r_(o),r_(a)) 32400 750 Disperse (N,N_(o),s,r_(r),r_(o),r_(a)) 32400 200 Avoid (N,r_(r),r_(o),r_(a)) 3600 200 Follow (N,r_(r),r_(o),r_(a)) 3600 2000| Task | Factors per model | Trials | Iterations per run | | :--- | :---: | ---: | ---: | | Targets | $\left(N, N_{o}, N_{t}, r_{r}, r_{o}, r_{a}\right)$ | 32400 | 1000 | | Goal | $\left(N, N_{o}, r_{r}, r_{o}, r_{a}\right)$ | 10800 | 1000 | | Rally | $\left(N, p_{i}, g, r_{r}, r_{o}, r_{a}\right)$ | 32400 | 750 | | Disperse | $\left(N, N_{o}, s, r_{r}, r_{o}, r_{a}\right)$ | 32400 | 200 | | Avoid | $\left(N, r_{r}, r_{o}, r_{a}\right)$ | 3600 | 200 | | Follow | $\left(N, r_{r}, r_{o}, r_{a}\right)$ | 3600 | 2000 |
attractor. Within the framework of (1), agents aware of the goal updated their headings by weighing the desire to travel to it and the desire to swarm [7], [23], [46].
吸引子。在（1）的框架内，意识到目标的代理通过权衡前往目标的愿望和成群结队的愿望来更新它们的航向[7], [23], [46]。
3) Rally: The objective was similar to the prior task, except some agents were aware of the goal (i.e., the rally point). Informed agents did not communicate this location to their neighbors. Each informed agent balanced its desire to abide by the swarming forces with a desire to move towards the rally point, similar to F t a s k , i ( t ) F t a s k , i ( t ) F_(task,i)(t)\mathbf{F}_{t a s k, i}(t) described in the prior task. The informed percentage ( p i ) p i (p_(i))\left(p_{i}\right) was 8 % , 16 % 8 % , 16 % 8%,16%8 \%, 16 \%, or 24 % 24 % 24%24 \% of N N NN. (A small fraction of the swarm acting as anonymous leaders has been shown to alter the group’s direction [7].) Agents were initialized into starting groups ( g ) ( g ) (g)(g) of 1,2 , or 4 .
3) 集合：目标与前一项任务类似，但有些代理知道目标（即集结点）。知情的代理并不会将这一地点告知其邻居。每个知情代理在遵守蜂群力量和向集结点移动的愿望之间保持平衡，这与之前任务中描述的 F t a s k , i ( t ) F t a s k , i ( t ) F_(task,i)(t)\mathbf{F}_{t a s k, i}(t) 类似。 ( p i ) p i (p_(i))\left(p_{i}\right) 的知情比例为 8 % , 16 % 8 % , 16 % 8%,16%8 \%, 16 \% ，或 N N NN 的 24 % 24 % 24%24 \% 。(事实证明，作为匿名领导者的一小部分蜂群可以改变群体的方向[7]）。代理被初始化为 1、2 或 4 的 ( g ) ( g ) (g)(g) 开始群组。
4) Disperse: This task required agents to scatter in the environment. Agents began the task placed around the center of the environment, and experienced a dispersing force, F t a s k , i ( t ) F t a s k , i ( t ) F_(task,i)(t)\mathbf{F}_{t a s k, i}(t), modeled by exerting a constant radial force away from the center. The force’s strength ( s ) ( s ) (s)(s), was set to either 45 % , 90 % 45 % , 90 % 45%,90%45 \%, 90 \%, and 135 % 135 % 135%135 \% of the swarming force.
4) 分散：这项任务要求代理在环境中分散。任务开始时，特工被放置在环境中心周围，并受到分散力 F t a s k , i ( t ) F t a s k , i ( t ) F_(task,i)(t)\mathbf{F}_{t a s k, i}(t) 的作用，该力是通过向中心施加一个恒定的径向力来模拟的。该力的强度 ( s ) ( s ) (s)(s) 被设置为蜂拥力的 45 % , 90 % 45 % , 90 % 45%,90%45 \%, 90 \% 和 135 % 135 % 135%135 \% 。
5) Avoid an Adversary: The swarm avoided a predatorlike agent, modeled with F t a s k , i ( t ) F t a s k , i ( t ) F_(task,i)(t)\mathbf{F}_{t a s k, i}(t) being a repulsive force exerted by the adversary. The swarm was initially aligned facing the predator. The predator (moving in a predefined path) was the same size as the agents (enlarged in Fig. 2) and occluded the visual communication between agents.
5) 避开对手：蜂群避开了一个类似捕食者的物体， F t a s k , i ( t ) F t a s k , i ( t ) F_(task,i)(t)\mathbf{F}_{t a s k, i}(t) 是对手施加的一种排斥力。蜂群最初对准捕食者。捕食者（按预定路径移动）与蜂群大小相同（图 2 中放大），并遮挡了蜂群之间的视觉通信。
6) Follow: The swarm followed a leader-like agent, modeled with F task,i F task,i  F_("task,i ")\mathbf{F}_{\text {task,i }} being an attractive force when the leader was an agent’s neighbor. The leader was the same size as the swarm agents (enlarged in Fig. 2), moved at the same speed, and randomly navigated the world.
6) 追随：蜂群跟随一个类似领导者的代理，当领导者是代理的邻居时， F task,i F task,i  F_("task,i ")\mathbf{F}_{\text {task,i }} 是一种吸引力。领导者与蜂群代理大小相同（在图 2 中放大），以相同的速度移动，并在世界中随机导航。

C. Trials C.审判

A trial was defined as a single simulation run for a given selection of factors. Twenty-five trials for each parameter selection were completed. The total number of trials per task is summarized in Table II. The Search for Multiple Targets task, for instance, had 5,400 metric, 5,400 visual, and 21,600 topological trials (due to the four levels of n t o p n t o p n_(top)n_{t o p} ).
一次试验的定义是对给定的因素选择进行一次模拟运行。每种参数选择完成 25 次试验。表 II 汇总了每项任务的试验总数。例如，"搜索多个目标 "任务有 5,400 次度量试验、5,400 次视觉试验和 21,600 次拓扑试验（由于 n t o p n t o p n_(top)n_{t o p} 有四个级别）。

D. Metrics D.衡量标准

The swarm’s performance was measured through the consideration of an array of metrics. The primary metrics are designed for the associated tasks, whereas the secondary metrics inform network characteristics and are common across all tasks. All secondary metrics are reported, but the analysis focuses on the ones that further provide evidence that swarm design needs to consider the communication model and task pairing in order to optimize the overall swarm performance.
蜂群的性能是通过一系列指标来衡量的。主要指标是针对相关任务设计的，而次要指标则反映了网络特性，并在所有任务中通用。我们报告了所有次要指标，但分析的重点是那些能进一步证明蜂群设计需要考虑通信模型和任务配对，以优化蜂群整体性能的指标。
The percent found ( P F ) ( P F ) (PF)(P F) measured the number of targets that have been discovered in the area.
发现的百分比 ( P F ) ( P F ) (PF)(P F) 衡量的是该区域已发现的目标数量。
The percent reached ( P R ) ( P R ) (PR)(P R) determined the fraction of the swarm that reached the goal. The latency ( L ) ( L ) (L)(L) represented the iterations required to transition from a state where at least one agent knew the goal’s location to all agents being aware.
到达百分比 ( P R ) ( P R ) (PR)(P R) 表示到达目标的蜂群比例。延迟 ( L ) ( L ) (L)(L) 表示从至少一个代理知道目标位置的状态过渡到所有代理都知道的状态所需的迭代次数。
Dispersion ( D ) ( D ) (D)(D) measured the percentage increase of the average agent-agent distance from the start to the end of a trial, which was one of the factors identified by Parrish et al. [48] to characterize the emergent properties of fish.
( D ) ( D ) (D)(D) 分散度衡量的是从试验开始到试验结束时代理与代理之间平均距离增加的百分比，这也是 Parrish 等人[48]确定的表征鱼类突发特性的因素之一。
Agent stickiness (AST K) represented the number of iterations an agent followed the leader, averaged over the swarm. The Swarm stickiness (SST K) was the iterations during which at least one agent was following the leader.
代理粘性（AST K）表示代理跟随领导者的迭代次数，是整个蜂群的平均值。蜂群粘性（SST K）是指至少有一个代理跟随领导者的迭代次数。
The number of connected components (NCC) was reported as an average over a trial’s duration. A connected component is defined as the largest collection of agents in which any two agents are either connected directly by a communication link or indirectly via neighbors [47]. The percent isolated components ( I ) ( I ) (I)(I) represented the fraction of the swarm that had no neighbors. The swarm clustering coefficient (SCC) was the average clustering coefficient over the swarm. The clustering coefficient in networks is the fraction of pairs of an agent’s neighbors that are neighbors with each other [47]. The asymmetric nature of links that resulted from the topological and visual models were ignored, following Strandburg-Peshkin et al.'s [4] treatment of directed links comparing different communication models for fish data. NCC, I I II, and S C C S C C SCCS C C represent the secondary metrics.
连接组件数 (NCC) 是以试验持续时间的平均值来报告的。连接组件的定义是，其中任何两个代理通过通信链路直接连接或通过邻居间接连接的最大代理集合[47]。孤立分量百分比 ( I ) ( I ) (I)(I) 表示没有邻居的蜂群分量。蜂群聚类系数（SCC）是蜂群的平均聚类系数。网络中的聚类系数是指一个代理的邻居中相互为邻的那部分[47]。按照 Strandburg-Peshkin 等人[4]对有向链接的处理方法，比较了鱼类数据的不同通信模型，拓扑模型和视觉模型产生的链接的非对称性质被忽略。NCC、 I I II 和 S C C S C C SCCS C C 代表二级指标。

V. RESULTS V.结果

A. Search for Multiple Targets
A.搜索多个目标

The topological model had the highest mean percent found (see Table III). An analysis of variance (ANOVA) showed that the effect of communication model on P F P F PFP F was significant ( F 8 , 5392 = 12 , 493.10 , p < 0.001 F 8 , 5392 = 12 , 493.10 , p < 0.001 F_(8,5392)=12,493.10,p < 0.001F_{8,5392}=12,493.10, p<0.001 ). Fisher’s LSD post-hoc test revealed that the three models had significantly different performances compared to each other. The communication model had significant interactions with r r ( F 2 , 5398 = 631.23 , p < 0.001 ) , r o r r F 2 , 5398 = 631.23 , p < 0.001 , r o r_(r)(F_(2,5398)=631.23,p < 0.001),r_(o)r_{r}\left(F_{2,5398}=631.23, p<0.001\right), r_{o} ( F 2 , 5398 = 160.75 , p < 0.001 ) F 2 , 5398 = 160.75 , p < 0.001 (F_(2,5398)=160.75,p < 0.001)\left(F_{2,5398}=160.75, p<0.001\right), and N o ( F 2 , 5398 = 228.48 , p < N o F 2 , 5398 = 228.48 , p < N_(o)(F_(2,5398)=228.48,p < :}N_{o}\left(F_{2,5398}=228.48, p<\right. 0.001 ). The visual model produced the lowest number of connected components. ANOVA found that the effect of model type was significant ( F 8 , 5392 = 7383.19 , p < 0.001 F 8 , 5392 = 7383.19 , p < 0.001 F_(8,5392)=7383.19,p < 0.001F_{8,5392}=7383.19, p<0.001 ), and the post-hoc analysis of the pairwise differences showed that the models were significantly different from each other. Metric at r r = 20 r r = 20 r_(r)=20r_{r}=20 yielded the lowest N C C N C C NCCN C C (Fig. 3(b)); otherwise, visual was the lowest across all N , r o N , r o N,r_(o)N, r_{o}, and r a r a r_(a)r_{a}.
拓扑模型的平均百分比最高（见表 III）。方差分析（ANOVA）表明，传播模式对 P F P F PFP F 的影响是显著的（ F 8 , 5392 = 12 , 493.10 , p < 0.001 F 8 , 5392 = 12 , 493.10 , p < 0.001 F_(8,5392)=12,493.10,p < 0.001F_{8,5392}=12,493.10, p<0.001 ）。费舍尔 LSD 事后检验表明，三种模式的表现有显著差异。沟通模式与 r r ( F 2 , 5398 = 631.23 , p < 0.001 ) , r o r r F 2 , 5398 = 631.23 , p < 0.001 , r o r_(r)(F_(2,5398)=631.23,p < 0.001),r_(o)r_{r}\left(F_{2,5398}=631.23, p<0.001\right), r_{o} ( F 2 , 5398 = 160.75 , p < 0.001 ) F 2 , 5398 = 160.75 , p < 0.001 (F_(2,5398)=160.75,p < 0.001)\left(F_{2,5398}=160.75, p<0.001\right) 和 N o ( F 2 , 5398 = 228.48 , p < N o F 2 , 5398 = 228.48 , p < N_(o)(F_(2,5398)=228.48,p < :}N_{o}\left(F_{2,5398}=228.48, p<\right. 有明显的交互作用（ r r ( F 2 , 5398 = 631.23 , p < 0.001 ) , r o r r F 2 , 5398 = 631.23 , p < 0.001 , r o r_(r)(F_(2,5398)=631.23,p < 0.001),r_(o)r_{r}\left(F_{2,5398}=631.23, p<0.001\right), r_{o} ( F 2 , 5398 = 160.75 , p < 0.001 ) F 2 , 5398 = 160.75 , p < 0.001 (F_(2,5398)=160.75,p < 0.001)\left(F_{2,5398}=160.75, p<0.001\right) 和 N o ( F 2 , 5398 = 228.48 , p < N o F 2 , 5398 = 228.48 , p < N_(o)(F_(2,5398)=228.48,p < :}N_{o}\left(F_{2,5398}=228.48, p<\right. 0.001 ）。视觉模型产生的连接组件数量最少。方差分析发现，模型类型的影响是显著的（ F 8 , 5392 = 7383.19 , p < 0.001 F 8 , 5392 = 7383.19 , p < 0.001 F_(8,5392)=7383.19,p < 0.001F_{8,5392}=7383.19, p<0.001 ），配对差异的事后分析表明，模型之间存在显著差异。 r r = 20 r r = 20 r_(r)=20r_{r}=20 处的度量值产生了最低的 N C C N C C NCCN C C （图 3(b)）；否则，视觉在所有 N , r o N , r o N,r_(o)N, r_{o} 和 r a r a r_(a)r_{a} 中都是最低的。

B. Search for a Goal
B.寻找目标

The overall mean percent reached was 35.95 ( S D = S D = SD=S D= 39.38). The topological and visual models produced means that were virtually identical (see Table III). ANOVA found that the model type had a significant impact on P R ( F 6 , 1794 P R F 6 , 1794 PR(F_(6,1794):}P R\left(F_{6,1794}\right. = 76.66 , p < 0.001 = 76.66 , p < 0.001 =76.66,p < 0.001=76.66, p<0.001 ). There was no significant difference between the visual and topological models. The mean P R P R PRP R was the
总平均到达率为 35.95 ( S D = S D = SD=S D= 39.38)。拓扑模型和视觉模型产生的平均值几乎相同（见表 III）。方差分析发现，模型类型对 P R ( F 6 , 1794 P R F 6 , 1794 PR(F_(6,1794):}P R\left(F_{6,1794}\right. = 76.66 , p < 0.001 = 76.66 , p < 0.001 =76.66,p < 0.001=76.66, p<0.001 有显著影响。）视觉模型和拓扑模型之间没有明显差异。 P R P R PRP R 的平均值是
TABLE III 表 III
DESCRIPTIVE Statistics (MEAN (SD)) FOR EACH TASK
描述性统计（均值（标差）每个任务
Fig. 3. The performances of the three communication models further visualized by the experiment’s additional factors.
图 3.通过实验的附加因素，三种通信模式的性能更加直观。
highest at N = 100 N = 100 N=100N=100 using topological and at N = 200 N = 200 N=200N=200 using the visual model (Fig. 3©). A significant difference in latency was found by an ANOVA between the models ( F 6 , 1794 = 440.77 F 6 , 1794 = 440.77 (F_(6,1794)=440.77:}\left(F_{6,1794}=440.77\right., p < 0.001 p < 0.001 p < 0.001p<0.001 ). L L LL for all three models were significantly different from each other in the post-hoc analysis. The mean swarm clustering coefficient was lowest in the visual model. The effect of model type on S C C S C C SCCS C C was significant ( F 6 , 1794 = 1810 , p < 0.001 ) F 6 , 1794 = 1810 , p < 0.001 (F_(6,1794)=1810,p < 0.001)\left(F_{6,1794}=1810, p<0.001\right). Post-hoc analysis revealed significant pairwise differences between the models. The interquartile ranges were typically tight (Fig. 3(d)).
使用拓扑模型时， N = 100 N = 100 N=100N=100 处的潜伏期最长，而使用视觉模型时， N = 200 N = 200 N=200N=200 处的潜伏期最长（图 3©）。通过对 ( F 6 , 1794 = 440.77 F 6 , 1794 = 440.77 (F_(6,1794)=440.77:}\left(F_{6,1794}=440.77\right. 、 p < 0.001 p < 0.001 p < 0.001p<0.001 和 L L LL 三个模型进行方差分析，发现它们的延迟时间有明显差异。）在事后分析中，所有三个模型的 L L LL 都有显著差异。视觉模型的蜂群聚类系数平均值最低。模型类型对 S C C S C C SCCS C C 的影响显著 ( F 6 , 1794 = 1810 , p < 0.001 ) F 6 , 1794 = 1810 , p < 0.001 (F_(6,1794)=1810,p < 0.001)\left(F_{6,1794}=1810, p<0.001\right) 。事后分析表明，模型之间存在明显的配对差异。四分位数间范围通常很窄（图 3(d)）。

C. Rally C.集会

The overall mean percent reached ( M = 81.40 , S D = 23.08 M = 81.40 , S D = 23.08 M=81.40,SD=23.08M=81.40, S D=23.08 ) was higher compared to the prior task. ANOVA showed that the model type had a significant effect on P R ( F 8 , 5392 = 1175.31 P R F 8 , 5392 = 1175.31 PR(F_(8,5392)=1175.31:}P R\left(F_{8,5392}=1175.31\right., p < 0.001 p < 0.001 p < 0.001p<0.001 ). Post-hoc analysis revealed that all three models’ performances were significantly different from one another. The mean P R P R PRP R was highest for the visual model. Model type significantly interacted with p i ( F 4 , 5396 = 90.93 , p < 0.001 ) p i F 4 , 5396 = 90.93 , p < 0.001 p_(i)(F_(4,5396)=90.93,p < 0.001)p_{i}\left(F_{4,5396}=90.93, p<0.001\right); however, the interaction with g g gg was not found to be significant (Fig. 3(e) and (f)).
与之前的任务相比，达到的总体平均百分比（ M = 81.40 , S D = 23.08 M = 81.40 , S D = 23.08 M=81.40,SD=23.08M=81.40, S D=23.08 ）更高。方差分析显示，模型类型对 P R ( F 8 , 5392 = 1175.31 P R F 8 , 5392 = 1175.31 PR(F_(8,5392)=1175.31:}P R\left(F_{8,5392}=1175.31\right. , p < 0.001 p < 0.001 p < 0.001p<0.001 ) 有显著影响。事后分析表明，三种模式的表现都有显著差异。视觉模型的 P R P R PRP R 平均值最高。模型类型与 p i ( F 4 , 5396 = 90.93 , p < 0.001 ) p i F 4 , 5396 = 90.93 , p < 0.001 p_(i)(F_(4,5396)=90.93,p < 0.001)p_{i}\left(F_{4,5396}=90.93, p<0.001\right) 有明显的交互作用；但与 g g gg 的交互作用不明显（图 3(e)和(f)）。

D. Disperse and Avoid an Adversary
D.分散和避开对手

The topological model had the highest dispersion for both tasks (see Table III). The effect of the model on D D DD was significant during the Disperse ( F 8 , 5392 = 9232.53 , p < 0.001 ) F 8 , 5392 = 9232.53 , p < 0.001 (F_(8,5392)=9232.53,p < 0.001)\left(F_{8,5392}=9232.53, p<0.001\right) and Avoid tasks ( F 4 , 596 = 492.82 , p < 0.001 F 4 , 596 = 492.82 , p < 0.001 F_(4,596)=492.82,p < 0.001F_{4,596}=492.82, p<0.001 ). The model by s s ss interactions were found to be significant for the Disperse task ( F 8 , 5392 = 996.64 , p < 0.001 ) F 8 , 5392 = 996.64 , p < 0.001 (F_(8,5392)=996.64,p < 0.001)\left(F_{8,5392}=996.64, p<0.001\right). The topological model at the lowest s s ss and the visual model at the highest s s ss had similar means (Fig. 3(g)). There were significant interactions between model and N N NN for the Disperse ( F 8 , 5392 = 1112.47 , p < 0.001 ) F 8 , 5392 = 1112.47 , p < 0.001 (F_(8,5392)=1112.47,p < 0.001)\left(F_{8,5392}=1112.47, p<0.001\right) and Avoid ( F 4 , 596 = 118.32 , p < 0.001 F 4 , 596 = 118.32 , p < 0.001 F_(4,596)=118.32,p < 0.001F_{4,596}=118.32, p<0.001 ) tasks. Generally during Disperse, D D DD increased in N N NN, but the opposite occurred in Avoid (Fig. 3(i)). The model’s effect on number of connected components was significant for both the Disperse ( F 8 , 5392 = 4224.10 , p < 0.001 ) F 8 , 5392 = 4224.10 , p < 0.001 (F_(8,5392)=4224.10,p < 0.001)\left(F_{8,5392}=4224.10, p<0.001\right) and Avoid ( F 4 , 596 = 1638.76 , p < 0.001 ) F 4 , 596 = 1638.76 , p < 0.001 (F_(4,596)=1638.76,p < 0.001)\left(F_{4,596}=1638.76, p<0.001\right) tasks. The metric and visual models had comparable N C C N C C NCCN C C at r r = 20 r r = 20 r_(r)=20r_{r}=20 for both tasks (Fig. 3(h) and (j)).
在这两项任务中，拓扑模型的离散度最高（见表 III）。模型对 D D DD 的影响在分散任务 ( F 8 , 5392 = 9232.53 , p < 0.001 ) F 8 , 5392 = 9232.53 , p < 0.001 (F_(8,5392)=9232.53,p < 0.001)\left(F_{8,5392}=9232.53, p<0.001\right) 和回避任务（ F 4 , 596 = 492.82 , p < 0.001 F 4 , 596 = 492.82 , p < 0.001 F_(4,596)=492.82,p < 0.001F_{4,596}=492.82, p<0.001 ）中显著。模型与 s s ss 的交互作用在分散任务 ( F 8 , 5392 = 996.64 , p < 0.001 ) F 8 , 5392 = 996.64 , p < 0.001 (F_(8,5392)=996.64,p < 0.001)\left(F_{8,5392}=996.64, p<0.001\right) 中显著。最低 s s ss 的拓扑模型和最高 s s ss 的视觉模型具有相似的平均值（图 3(g)）。在 "分散" ( F 8 , 5392 = 1112.47 , p < 0.001 ) F 8 , 5392 = 1112.47 , p < 0.001 (F_(8,5392)=1112.47,p < 0.001)\left(F_{8,5392}=1112.47, p<0.001\right) 和 "回避"（ F 4 , 596 = 118.32 , p < 0.001 F 4 , 596 = 118.32 , p < 0.001 F_(4,596)=118.32,p < 0.001F_{4,596}=118.32, p<0.001 ）任务中，模型和 N N NN 之间存在明显的交互作用。一般来说，在 "分散 "任务中， D D DD 会随着 N N NN 的增加而增加，但在 "回避 "任务中情况正好相反（图 3(i)）。在 "分散" ( F 8 , 5392 = 4224.10 , p < 0.001 ) F 8 , 5392 = 4224.10 , p < 0.001 (F_(8,5392)=4224.10,p < 0.001)\left(F_{8,5392}=4224.10, p<0.001\right) 和 "回避" ( F 4 , 596 = 1638.76 , p < 0.001 ) F 4 , 596 = 1638.76 , p < 0.001 (F_(4,596)=1638.76,p < 0.001)\left(F_{4,596}=1638.76, p<0.001\right) 任务中，模型对连接成分数量的影响都很显著。在这两项任务中，度量模型和视觉模型在 r r = 20 r r = 20 r_(r)=20r_{r}=20 时的 N C C N C C NCCN C C 具有可比性（图 3(h) 和 (j)）。

E. Follow E.遵循

The effect of model type on swarm stickiness was significant ( F 4 , 596 = 26.89 , p < 0.001 F 4 , 596 = 26.89 , p < 0.001 F_(4,596)=26.89,p < 0.001F_{4,596}=26.89, p<0.001 ), and the visual model’s SST K K KK was the highest. The metric model produced the lowest SST K K KK for most N most N most N\operatorname{most} N (Fig. 3(k)), except at N = 200 N = 200 N=200N=200, where it had comparable performance to the visual model. The metric model had the highest agent stickiness. ANOVA revealed that model type had a significant impact on AST K ( F 4 , 596 = 925.26 , p < 0.001 ) AST K F 4 , 596 = 925.26 , p < 0.001 AST K(F_(4,596)=925.26,p < 0.001)\operatorname{AST} K\left(F_{4,596}=925.26, p<0.001\right), and a post-hoc analysis revealed significant pairwise differences between the models. AST K K KK decreased in N N NN for all models (Fig. 3(1)).
模型类型对蜂群粘性的影响是显著的（ F 4 , 596 = 26.89 , p < 0.001 F 4 , 596 = 26.89 , p < 0.001 F_(4,596)=26.89,p < 0.001F_{4,596}=26.89, p<0.001 ），视觉模型的 SST K K KK 最高。在 most N most N most N\operatorname{most} N 时，公因子模型产生的 SST K K KK 最低（图 3(k)），但在 N = 200 N = 200 N=200N=200 时除外，其性能与视觉模型相当。度量模型的代理粘性最高。方差分析显示，模型类型对 AST K ( F 4 , 596 = 925.26 , p < 0.001 ) AST K F 4 , 596 = 925.26 , p < 0.001 AST K(F_(4,596)=925.26,p < 0.001)\operatorname{AST} K\left(F_{4,596}=925.26, p<0.001\right) 有显著影响，事后分析显示模型之间存在显著的配对差异。在所有模型中，AST K K KK 在 N N NN 中都有所下降（图 3(1)）。
Across all the tasks, the metric model produced the highest S C C S C C SCCS C C, whereas visual produced the lowest. The metric model had the highest I I II for all tasks, while the topological model by definition had an I I II of 0 . The topological model produced the highest NCC for the first three tasks, whereas the metric model produced the highest for the last three tasks.
在所有任务中，度量模型产生的 S C C S C C SCCS C C 最高，而视觉模型产生的 S C C S C C SCCS C C 最低。在所有任务中，度量模型的 I I II 最高，而拓扑模型的 I I II 则为 0。拓扑模型在前三个任务中产生的 NCC 最高，而度量模型在后三个任务中产生的 NCC 最高。

VI. DISCUSSION AND CONCLUSION
VI.讨论和结论

The presented research focuses on a general hypothesis that the selection of a communication model impacts a swarm’s task performance. Six swarm robotics tasks were investigated for the three most predominant communication models found in the biological swarm literature. The primary finding is that different tasks benefit from different models, and as such, the task by communication model pairing is an important dimension in the effective design of swarms.
本文研究的重点是一个一般性假设，即通信模式的选择会影响蜂群的任务表现。针对生物群文献中发现的三种最主要的通信模式，研究了六项生物群机器人任务。主要发现是不同的任务受益于不同的模型，因此，任务与通信模型的配对是有效设计蜂群的一个重要方面。
No single model outperformed the others across all the tasks; however, some general trends emerged within the limited task design considerations. The visual model was beneficial in tasks that required the swarm to move to a particular area, and the tasks that had this transport-like flavor were the Search for a Goal and Rally tasks. The topological model was better at enduring a force directed toward the swarm, as is the case with the Disperse and Avoid tasks.
在所有任务中，没有一种模式的表现优于其他模式；不过，在有限的任务设计考虑范围内，出现了一些总体趋势。在需要蜂群移动到特定区域的任务中，视觉模型更有优势，而具有类似运输功能的任务是 "寻找目标 "和 "集结 "任务。拓扑模型则更能承受向蜂群施加的力，"分散 "和 "避开 "任务就是这种情况。
The visual model, with its potentially long communication links was better able to keep the swarm together. This tendency also led to the model fairing poorly when exploring the environment during the Search for Multiple Targets task.
视觉模型的通信线路可能较长，因此能够更好地将蜂群保持在一起。在 "搜索多个目标 "任务中，这种趋势也导致该模型在探索环境时表现不佳。
Agents favorably oriented and not occluded had a higher chance of establishing long-range links using the visual model and were more likely to receive the goal’s location (Search for a Goal) or be influenced (Rally) by an informed agent. These links acted as “short-cuts” [49] for information transfer; yet despite this advantage, at the lowest and highest r a r a r_(a)r_{a}, the metric model produced similar and lower L L LL.
使用视觉模型时，定向良好且未被遮挡的代理有更高的机会建立长距离联系，并且更有可能获得目标位置（搜索目标）或受到知情代理的影响（集结）。这些链接就像信息传递的 "捷径"[49]；然而，尽管有这种优势，在 r a r a r_(a)r_{a} 最低和最高的情况下，度量模型产生的 L L LL 相似且更低。
The topological model is the better choice for the Avoid an Adversary task, as the model produced the highest dispersion, low connected components, and no isolated components. A design limitation was the use of a single adversary moving in a pre-defined motion, rather than a (coordinated) attack.
在 "避免对手 "任务中，拓扑模型是较好的选择，因为该模型产生的分散度最高，连接组件较少，而且没有孤立组件。设计上的一个限制因素是，使用的是按预定运动方式移动的单个对手，而不是（协调的）攻击。
Swarm agents in frontal positions influenced agents behind them to follow the Follow task’s leader, in a cascading effect, when using the visual model. The leader was lost multiple times during a trial, a drawback of the model. The metric model is a better choice for persistent tracking (and if tracking by a small fraction of the swarm is tolerable).
在使用视觉模型时，处于前方位置的蜂群会影响其后方的蜂群，使其跟随 "跟随任务 "的领导者，从而产生连带效应。在一次试验中，领导者多次丢失，这是该模型的一个缺点。度量模型是持续跟踪的更好选择（如果可以容忍一小部分虫群进行跟踪）。
A general limitation of the overall evaluation is the focus on individual tasks. Additional analysis over task combinations is required to fully support the general hypothesis. Providing theoretical results, beyond hypothesis testing, allows for the findings to be generalizable over cases not considered here. However, the presented results provide the preliminary evidence that support the general hypothesis.
整体评估的一个普遍局限性是侧重于单个任务。要完全支持一般假设，还需要对任务组合进行更多分析。除了假设检验之外，提供理论结果还能使研究结果普遍适用于本文未考虑的情况。不过，本文介绍的结果提供了支持一般假设的初步证据。
The implemented model parameter values provides connections to the biological literature. For instance, Couzin et al. [32] showed that r r r r r_(r)r_{r} does not affect transitions between different swarm movement patterns. Rather, the relative sizes of r o / r r r o / r r r_(o)//r_(r)r_{o} / r_{r}, and r a / r o r a / r o r_(a)//r_(o)r_{a} / r_{o} produce the transitions: a torus for a low r o / r r r o / r r r_(o)//r_(r)r_{o} / r_{r} and a relatively high r a / r o r a / r o r_(a)//r_(o)r_{a} / r_{o} ratio, for instance. Presented results for the Search for a Goal task conform to the r r r r r_(r)r_{r} finding. The duration of this task resulted in trials that demonstrated movement patterns, and the performance was not impacted by the choice in r r r r r_(r)r_{r}. A mapping of movement types to performance was beyond the scope of this work.
实施的模型参数值提供了与生物文献的联系。例如，Couzin 等人[32] 的研究表明， r r r r r_(r)r_{r} 并不影响不同蜂群运动模式之间的转换。相反， r o / r r r o / r r r_(o)//r_(r)r_{o} / r_{r} 和 r a / r o r a / r o r_(a)//r_(o)r_{a} / r_{o} 的相对大小会产生过渡：例如，低 r o / r r r o / r r r_(o)//r_(r)r_{o} / r_{r} 和相对较高的 r a / r o r a / r o r_(a)//r_(o)r_{a} / r_{o} 比率会产生一个环形。"寻找目标 "任务的结果符合 r r r r r_(r)r_{r} 的结论。这项任务的持续时间导致了能够展示运动模式的试验，而 r r r r r_(r)r_{r} 中的选择对成绩没有影响。运动类型与成绩之间的映射关系超出了本研究的范围。
The scope of the reported research did not follow the socalled prescriptive agenda [41], [42], where the values of the model parameters are free design choices. This line of inquiry will become necessary when specific platforms attempt to adopt the models (e.g., the vision-equipped s-bots [50]). The metric model can be realized with omni-directional antennas, as well as infrared LEDs [51]: two significantly different ranges. The topological model can be implemented using band-limited channels [23], but band-limited platforms, such as the r-one [52], impose constraints on the realizable n top n top  n_("top ")n_{\text {top }}.
所报告的研究范围并不遵循所谓的规范性议程[41]、[42]，即模型参数值是自由的设计选择。当特定平台试图采用这些模型时（例如，配备视觉设备的 s-bots [50]），就有必要进行这方面的研究。度量模型可通过全向天线和红外线 LED 实现[51]：这是两种截然不同的范围。拓扑模型可使用带限信道 [23] 实现，但带限平台（如 r-one [52]）对可实现的 n top n top  n_("top ")n_{\text {top }} 施加了限制。
Future work includes conducting experiments on a multirobot platform (see Supplementary Materials for the preliminary efforts using the Robotarium, available: robotarium. org). Two immediate challenges of this transition have been identified. First, the visual model depends on the agents’ geometry, so re-interpretation must account for the platform. The second challenge pertains to the testbed’s built-in safe guards related to collision avoidance. They interfere with the repulsion zones, and the plan is to formally fold avoidance algorithms into the repulsion zone.
未来的工作包括在多机器人平台上进行实验（使用机器人馆进行的初步工作见补充材料，网址：robotarium. org）。在这一转变过程中，我们发现了两个紧迫的挑战。首先，视觉模型取决于代理的几何形状，因此重新解释必须考虑到平台。第二个挑战与测试平台内置的防碰撞安全保护有关。它们会干扰斥力区，因此计划将避撞算法正式纳入斥力区。

ACKNOWLEDGMENT 致谢

The authors thank Ovunc Tuzel and Electa A. Baker.
作者感谢 Ovunc Tuzel 和 Electa A. Baker。

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