文献笔记 - A Survey on Aerial Swarm Robotics

总结了空中集群机器人的特点：

3-D Flow and Swarm Autonomy:   Motion planning and con trol methods for aerial swarms rely on autonomously generated 3-D traffic flows that do not have fixed edges or roads. Real time flight control and swarm operation must also take into account high-fidelity six-degree-of-freedom (6-DOF) flight dy namicmodels,trafficvariations,weather,andothertime-varying operational conditions found in crowded urban environments.

Scalability Through Hierarchy and Multimodality: 

Hierarchical approaches are pervasive in both the machine learning and con trol fields for dealing with complexity and high dimensionality (e.g., hierarchical task networks [11], hierarchical tree or lattice networks employed in sequential game theory [12], and sin gular perturbation theory [13], [14]). They are also especially well-suited for aerial robots due to the inherent diversity of time scales in the system.

II. MODELS,STABILITY AND CONTROLLABILITY OF SWARMS

A. Types of Multiagent Systems

In a team, the behavior and strategies of each individual agent seek to explicitly maximize a local objective.

在一个团队中，每个个体的行为和策略都试图明确地最大化一个局部目标。

In contrast to a team, a formation almost always consists of cooperative interactions, and the relationship between the states of the agents is well-defined for objectives such as energy efficiency (e.g., flocks of birds in an aerodynamically optimum V-formation [17]).

与团队相比，编队几乎总是由合作相互作用组成，对于能源效率等目标，代理人状态之间的关系是明确的（例如，处于空气动力学最佳V编队中的鸟群[17]）。

A swarm generally refers to a group of sim ilar agents that displays emergent behavior arising from local interactions among the agents

群体通常是指一组相似的智能体，它们表现出由智能体之间的局部交互引起的新行为

B. Models for Swarm Dynamical Systems

关于集群飞行下的流体可视化

关于队形保持

这张图里的方程其实描述的是无人机集群协同控制的核心原理，核心思想是让每个无人机根据邻居的位置/状态调整自己，最终实现整体一致或编队稳定。我来拆解一下关键点，尽量用通俗的语言解释：

一、方程核心含义

方程表达式：

x˙i​=j∈Ni​∑​wij​(xj​−xi​)

• ​物理意义：每个无人机 i 的状态变化（比如位置或速度）取决于它和邻居无人机 j 的状态差异。
• ​符号解释：
  • xi​：无人机 i 的状态（如位置坐标）。
  • x˙i​：状态随时间的变化率（如速度）。
  • Ni​：无人机 i 的邻居集合（通过传感器或通信能感知到的其他无人机）。
  • wij​：权重（表示对邻居 j 的信任程度或通信强度）。

举个栗子🌰：
假设无人机 i 发现自己右边的邻居 j 离自己太远（即 xj​−xi​>0），它会加速向右移动（x˙i​>0），反之则减速。通过这种局部调整，整个集群会逐渐趋于一致（比如保持相同速度或间距）。

二、拉普拉斯矩阵（Laplacian Matrix）

方程可以写成矩阵形式：

x˙=−Lx

其中 L 是拉普拉斯矩阵，它的作用是描述无人机之间的连接关系：

• ​矩阵构造：
  • 对角线元素 Lii​=∑j​wij​（所有邻居权重之和）。
  • 非对角线元素 Lij​=−wij​（如果 j 是 i 的邻居，否则为0）。
• ​关键性质：L1n​=0，即所有无人机状态相同时（x=c1n​），状态不再变化（x˙=0），系统达到稳态。

物理意义：拉普拉斯矩阵把局部交互规则转化为全局动力学行为，比如收敛到一致状态或形成特定编队。

三、通信拓扑与时间变化

1. ​固定拓扑（L 是常数矩阵）​：
   无人机之间的通信关系固定（比如始终与固定几个邻居通信）。此时系统收敛性取决于 L 的特征值（需满足稳定性条件）。

2. ​动态拓扑（L(t) 随时间变化）​：
   通信关系可能因障碍物、信号中断等变化（比如邻居集合 Ni​(t) 随时间改变）。此时需要分析时变系统的稳定性。

四、与无人机集群的关联

1. ​编队控制：
   通过调整权重 wij​ 和通信拓扑，可以让无人机集群形成特定队形（如三角形、雁阵）。例如，权重大的邻居对当前无人机影响更大。

2. ​避障与一致性：
   如果某个无人机检测到障碍物，可以通过临时改变邻居集合 Ni​ 或权重 wij​ 实现避障，同时保持整体稳定。

3. ​收敛性分析：
   通过拉普拉斯矩阵的特征值（如第二小特征值代表收敛速度），可以判断集群能否达成一致，或需要多长时间达成。

还有对于任务分区域的算法

核心思想

这段描述的是如何将复杂环境划分成多个“功能区域”​​（functional bins），并基于这些区域设计无人机集群的任务分配和路径规划策略。类似快递分拣仓库划分不同区域，每个区域只能容纳有限机器人。

​关键概念拆解

1. ​Functional Bins（功能区域）​

• ​定义：将任务环境划分为多个逻辑区域（例如：战区中的关键据点、仓库中的货架区、城市中的充电站）。
• ​作用：
  • 每个区域（bin）有最大容量限制（比如区域1最多容纳3架无人机，区域2最多容纳5架）。
  • 简化路径规划和任务分配的复杂度（只需关注区域间的转移，而非具体坐标）。

举个栗子🌰：
假设战场被划分为5个据点（bins），每个据点最多停放2架无人机（容量限制）。现在有10架无人机需要分配到这些据点执行任务。

C. Physics-Based Models for Robotic Agents

集群系统的欧拉-拉格朗日方程：

符号解释与物理意义

1. ​广义状态 qi​

• ​定义：描述机器人i位姿的广义坐标，可以是：
  • 机械臂的关节角度（如θ1​,θ2​,...）
  • 无人机的位置+姿态（如x,y,z,ϕ,θ,ψ）
  • 轮式机器人的轮子转角+车身位置
• ​举例🌰：
  四旋翼无人机的qi​=[x,y,z,ϕ,θ,ψ]T（位置+欧拉角）。

2. ​惯性矩阵 Mi​(qi​)

• ​物理意义：描述机器人在当前位姿下的“惯性”（质量分布+转动惯量）。
  • 类似牛顿定律中的质量m，但扩展到高维（矩阵形式）。
• ​举例🌰：
  机械臂伸展时，末端惯性大（Mi​对角元素大）；收缩时惯性小。

3. ​科里奥利力与离心力项 Ci​(qi​,q˙​i​)q˙​i​

• ​物理意义：由机器人运动产生的“虚拟力”：
  • ​离心力​（旋转时向外甩的力，如旋转的摩天轮）
  • ​科里奥利力​（非惯性系中的偏转力，如北半球的台风旋转方向）
• ​举例🌰：
  无人机快速横滚（ϕ˙​大）时，会产生离心力，需电机额外出力补偿。

4. ​重力项 gi​(qi​)

• ​物理意义：重力对机器人的作用（如机械臂下垂趋势）。
  • 与位姿相关（例如机械臂抬高时重力势能大）。
• ​举例🌰：
  起重机吊起重物时，重力项gi​向下，需要电机提供反向力矩。

5. ​外部力矩 τi​

• ​定义：控制输入（如电机力矩、推力）和外部耦合力的总和。
  • 包含两部分：
    1. ​自身控制输入：电机/执行器提供的力或力矩。
    2. ​邻居耦合项：来自其他机器人j∈Ni​的影响（如集群协同中的交互力）。
• ​公式右侧：
  τi​(qi​,q˙​i​,qd​,qj∈Ni​​,q˙​j∈Ni​​)
  • qd​：期望轨迹（如目标位置/姿态）
  • qj∈Ni​​：邻居机器人的状态（用于协同控制）

公式的直观理解

左边是机器人的“运动阻力”，右边是“驱动力”，两者平衡时方程成立：

惯性力 + 离心力 + 重力=电机出力 + 邻居交互力

举个栗子🌰：
想象你骑自行车：

• ​惯性矩阵Mi​：车+人的质量越大，加速越难。
• ​离心力项Ci​：转弯时感觉被甩向外侧。
• ​重力项gi​：上坡时需要额外用力。
• ​外部力矩τi​：你踩踏板的力 + 同伴推你的力（协同控制）。

与集群控制的关系

1. ​耦合项：邻居状态qj∈Ni​​通过τi​影响当前机器人，类似之前提到的拉普拉斯矩阵中的邻居交互。
2. ​一致性目标：若所有机器人收敛到相同状态（qi​=qd​且q˙​i​=0），系统达到平衡。

总结

这个方程是机器人动力学的核心模型，它告诉你：

1. ​机器人如何运动​（左边描述运动惯性、离心效应、重力）。
2. ​需要施加多少力​（右边包括控制输入和邻居影响）。
3. ​如何设计控制器：通过调整τi​中的控制项（如PID或协同算法），让机器人跟踪期望轨迹qd​或与邻居同步。

如果有具体应用场景（比如无人机编队或机械臂控制），可以进一步解释如何设计τi​！ 🚀

好的！我来用两个无人机的例子，分别展示它们完全独立和刚性链接时的动力学方程展开，并结合图中的公式(5)进行解释。

​1. 完全独立的两架无人机

假设：

• 无人机1和无人机2之间无物理连接和通信耦合，各自独立跟踪期望轨迹 qd​(t)。
• 每架无人机的动力学方程互不影响，耦合项为零。

​动力学方程展开（公式(5)）​

对每架无人机 i=1,2：

Mi​(qi​)q¨​i​+Ci​(qi​,q˙​i​)q˙​i​+gi​(qi​)=τicontrol​

• ​参数说明：
  • qi​∈Rn：无人机i的广义状态（如位置+姿态）。
  • τicontrol​：仅包含自身控制输入（如电机推力/力矩）。
  • ​无耦合项：τi​中不包含邻居状态 qj​ 或 q˙​j​。

​控制输入设计

假设使用PD控制器跟踪期望轨迹 qd​(t)：

τicontrol​=−Kp​(qi​−qd​)−Kd​(q˙​i​−q˙​d​)

• Kp​,Kd​：比例和微分增益矩阵。
• ​物理意义：无人机仅根据自身与期望轨迹的误差调整推力。

​举例🌰

假设无人机在二维平面运动，状态为 qi​=[xi​,yi​]T（位置）：

• ​惯性矩阵：Mi​=[mi​0​0mi​​]（质量矩阵）。
• ​科里奥利力：若忽略空气阻力，Ci​=0。
• ​重力：平面运动时 gi​=0。
• ​方程简化为：mi​[x¨i​y¨​i​​]=−Kp​[xi​−xd​yi​−yd​​]−Kd​[x˙i​−x˙d​y˙​i​−y˙​d​​]每架无人机独立跟踪目标轨迹，互不影响。

​2. 刚性链接的两架无人机

假设：

• 无人机1和2通过刚性杆连接（类似双足机器人的双腿），形成协同系统。
• 两架无人机的状态通过耦合项相互影响。

​动力学方程展开（公式(5)）​

对无人机i=1：

M1​(q1​)q¨​1​+C1​(q1​,q˙​1​)q˙​1​+g1​(q1​)=τ1control​+τ1coupling​(q1​,q2​)

对无人机i=2：

M2​(q2​)q¨​2​+C2​(q2​,q˙​2​)q˙​2​+g2​(q2​)=τ2control​+τ2coupling​(q2​,q1​)

• ​耦合项 τicoupling​：来自刚性连接的相互作用力（如杆的拉力/力矩）。

​耦合项设计

假设使用线性扩散耦合​（类似拉普拉斯矩阵）：

τ1coupling​=−k(q1​−q2​),τ2coupling​=−k(q2​−q1​)

• k：耦合强度（类似弹簧刚度）。
• ​物理意义：两无人机倾向于保持相对位置一致（类似用弹簧连接）。

​举例🌰

假设两无人机通过刚性杆在二维平面运动：

• ​广义状态：q1​=[x1​,y1​]T, q2​=[x2​,y2​]T。
• ​刚性杆约束：两无人机间距固定（∣∣q1​−q2​∣∣=L），但这里用弹性耦合近似表示。
• ​耦合项：τ1coupling​=−k[x1​−x2​y1​−y2​​],τ2coupling​=−k[x2​−x1​y2​−y1​​]
• ​完整方程​（以无人机1为例）：m1​[x¨1​y¨​1​​]=−Kp​[x1​−xd​y1​−yd​​]−Kd​[x˙1​−x˙d​y˙​1​−y˙​d​​]−k[x1​−x2​y1​−y2​​]无人机1的推力需同时抵抗自身轨迹误差和来自无人机2的拉力。

​对比总结

​物理直觉

1. ​完全独立：无人机之间没有“弹簧”连接，各自为战。
2. ​刚性链接：无人机之间通过“弹簧”产生拉力，迫使它们同步运动。若一架偏离，另一架会通过耦合项将其拉回。

这种耦合机制正是集群协同控制的核心：通过设计耦合项（类似拉普拉斯矩阵），实现自组织编队或一致性。

如果需要更具体的参数数值或仿真代码，可以进一步补充细节！ 🚁

D. Synchronization With Leader Following

To control a swarm, it is useful at times to define a physi cal or virtual leader that the rest of swarm agents then follow (see Fig. 2). The motion of the leader can be given apriori or controlled directly by separate dynamics. Alternatively, a desired trajectory (i.e., the path of a virtual leader) can be com puted using optimal control or motion planning algorithms (see Section III).

E. Leader Selection and Sensor Placemen

When the dynamics of the aerial swarm agents are identical, controllability from agivensetofleadernodes(equivalently,ob servability from a given set of sensors) depends on the topology of the graph as well as the individual edge weights. A system defined on a graph is said to be structurally controllable when it is controllable for almost all edge weights, and strongly struc tural controllable when it is controllable for all edge weights.

F. Synchronization and Hierarchical Stability for Swarms

群的同步性和层次稳定性

Consider (4) with diffusive couplings. It is well-known that the matrix L gives rise to a stable system under the following conditions on the underlying graph: 1) Undirected time-invariant graph: the graph is con nected [56]. 2) Directed time-invariant graph: consensus to the average value if and only if the graph is balanced and weakly con nected [57]. Existence of a rooted tree guarantees consen sus, though not necessarily to the average value [58]. 3) Time-varying undirected/directed graph: satisfies a gen eralized strong connectivity condition [58, Propositions 1 and 2], [59]

考虑（4）扩散耦合。众所周知，在基础图上，矩阵L在以下条件下会产生一个稳定的系统：
1） 无向时不变图：图是连通的[56]。
2） 有向时不变图：当且仅当图是平衡且弱连接时，对平均值的共识[57]。有根树的存在保证了共识，尽管不一定达到平均值[58]。
3） 时变无向/有向图：满足广义强连通性条件[58，命题1和2]，[59]

III. CONTROL OF SWARMS IN 3-D WORLDS

集群适合的任务包括分散感知 搜救 稀疏分离图像 

可以分为两大类 一个是环境有待探索的（覆盖 建图） 一个是环境只是在完成其他任务时被经过和利用的（穿越障碍）

A. Trajectory Generation and Motion Planning for Swarms

Trajectories generated independently of the task assignment al gorithmcanbethoughtofinthesamelightastraditionaloptimal motion planning or boundary value problems

Popular random ized algorithms, such as PRM [81], rapidly exploring random tree (RRT) [82], and RRT*[83],maynotbeeffective forobtain ing optimal and safe flight of multiple 6-DOF aerial robots; not only cantheynoteffectively handle 6-DOFnonlinear dynamics, but they also use a finite set of primitives predicated on asymp totic optimality without using higher fidelity dynamic models, which could preclude a large set of otherwise flyable trajec tories in a high-dimensional space.

The rapid advancement in computing capacity combined with algorithmic improvements has enabled the development of tools that are capable of solv ing constrained optimization problems in real-time, which can better provide explicit or approximate solutions to an optimal control problem of the form

Direct optimal control approaches [25], [85] [87] cast the dynamics into equality constraints between the states in successive time steps for optimization (e.g., iterative linearization of dynamics in sequential convex programming (SCP) [25], [87]).

直接最优控制方法[25]，[85][87]将动力学转化为连续时间步长中状态之间的等式约束，以进行优化（例如，序列凸规划（SCP）中动力学的迭代线性化[25]，[77]）。

Alternately, the control design can be separated from optimal trajectory design by treating the optimized state trajectory for each robot, obtained from (7), as a desired trajec tory for the tracking controller [25], [28], [87], [93], [94]. This approach has the benefit of setting up the control design problem in the traditional input-tracking or model reference setting with guaranteed closed-loop stability. It is particularly suitable for robotic systems, such as aerial robots, whose physical models are complex but well-understood from the point of view of con trol design. Alternately, control laws designed without virtual leaders typically consist of a sum of terms that represent the multiple objectives: trajectory-following, coordination with neigh bors, and collision-avoidance. As explained above, trajectory following laws can be derived readily using a physical model of the robots. Terms for coordination and collision-avoidance require sensing and communication with other agents in the formation.

或者，通过将从（7）中获得的每个机器人的优化状态轨迹视为跟踪控制器[25]、[28]、[87]、[93]、[94]的期望轨迹，可以将控制设计与最优轨迹设计分开。这种方法的优点是在传统的输入跟踪或模型参考设置中建立控制设计问题，并保证闭环稳定性。它特别适用于机器人系统，如空中机器人，其物理模型复杂，但从控制设计的角度来看很容易理解。或者，在没有虚拟领导者的情况下设计的控制律通常由一系列表示多个目标的术语组成：轨迹跟踪、与邻居的协调和碰撞避免。如上所述，使用机器人的物理模型可以很容易地推导出轨迹跟踪定律。协调和避免碰撞的术语要求与编队中的其他代理进行感应和通信。

Trajectory generation occasionally requires a hierarchical “model-based” approach when motion requirements stem from specific tasks that the swarm needs to perform, or from needing to deal with exigencies. For instance, cooperative construction [98], [99] requires formation-like motion as well as special ized low-level motions for stabilizing and manipulating objects. In such cases, physics-based models for manipulation can be solved to find a relative motion plan for the robots, while aglobal path plan can be constructed using any of the well-known path planning algorithms [98].

当运动需求源于群体需要执行的特定任务或需要应对紧急情况时，轨迹生成偶尔需要一种分层的“基于模型”的方法。例如，协同构造[98]、[99]需要类似编队的运动以及特殊的低级运动来稳定和操纵物体。在这种情况下，可以求解基于物理的操纵模型，为机器人找到相对运动计划，而全局路径计划可以使用任何众所周知的路径规划算法构建[98]。

Specialized controllers must be designed to allow aerial robots flying in an energy-efficient formation to deal with ac tuator failures in individual aircraft and enable them to hold their formation [100]. These controllers benefit from aerody namic models that help estimate the influence of neighboring aircraft on the controllability of a given aircraft. As pointed out in Section II-B, aerial swarms differ from ground-based robots in that the individual aircraft are coupled aerodynamically, due to the flow induced by one vehicle affecting its neighbors. The team may also generate trajectories that account for these aero dynamic effects and plan trajectories that minimize disturbance [101]. Alternately, the team can reconstruct the wake profile, as demonstrated in [102], although it requires that the aircraft per form cross-track motion to ensure the stability of the estimator.

必须设计专门的控制器，使以节能编队飞行的空中机器人能够处理个别飞机的执行器故障，并使其能够保持编队[100]。这些控制器受益于空气动力学模型，该模型有助于估计相邻飞机对给定飞机可控性的影响。正如第II-B节所指出的，空中无人机群与地面机器人的不同之处在于，由于一辆车引起的流动会影响其邻居，因此每架飞机在空气动力学上是相互耦合的。该团队还可以生成考虑这些空气动力学效应的轨迹，并计划将干扰降至最低的轨迹[101]。或者，该团队可以重建尾流剖面，如[102]所示，尽管它要求飞机每种形式的交叉轨迹运动以确保估计器的稳定性。

Looking at constraints beyond collision avoidance and dynamic feasibility, one key factor with UAVs is their lim ited battery life. To extend the mission life, a cooperative team of ground vehicles may be used as mobile recharging stations [103]. The UAVs then plan paths to ensure that they are able to accomplish their missions while maintaining power.

考虑到防撞和动态可行性之外的限制，无人机的一个关键因素是其有限的电池寿命。为了延长任务寿命，地面车辆的合作团队可以用作移动充电站[103]。然后，无人机规划路径，以确保它们能够在保持动力的同时完成任务。

B. Simultaneous Planning With Distributed Assignment

In a homogeneous swarm of robots, it does not matter which agent completes a given task. This fact may be exploited to do simultaneous task assignment and trajectory planning for teams of 100’s of agents in a centralized or decentralized formula tion [80]. This decentralized formulation is suboptimal com pared to the centralized solution, but it is still complete. For example, simultaneous optimal assignment and trajectory plan ning computes an optimal terminal point constraint of (7) for shape reconfiguration control [25], [87].

在同质的机器人群体中，哪个代理完成给定的任务并不重要。这一事实可以被利用，以集中或分散的形式为100人的代理团队同时进行任务分配和轨迹规划[80]。与集中式解决方案相比，这种分散的公式是次优的，但它仍然是完整的。例如，同时进行最优分配和轨迹规划可以计算出形状重构控制的最优终点约束（7）[25]，[87]。

A special case of assignment is cooperative pursuit, wherein multiple pursuers seek a single target. A pursuit strategy and conditions for a successful pursuit in a bounded domain were determined in [104]. The conditions for a successful pursuit link the relative speeds of the pursuers and the evader, the turning radius of the pursuer (assuming an arbitrarily agile evader),and the total number of pursuers. More realistic, physics-based scenar ios have been investigated in the context of missile interception, wherein multiple defensive missiles are used to intercept one or more incoming (target) missiles, which are assumed to use a standard optimal guidance and evasion law. Estimating the states and guidance laws of the target missiles is a significant challenge, compounded by the fact that the time delay involved in estimating the states can have a severely adverse effect on the pursuit [105]. In [106], cooperative estimation of the target states (compared to each missile using solely its own estimates) was shown to improve the likelihood of success significantly. Information sharing between the missiles can also be used to directly tune their navigation law, as demonstrated in [107], to achieve a synchronized hit on the target.

一种特殊的任务是合作追捕，其中多个追捕者寻找单个目标。[104]中确定了在有界域内成功追击的追击策略和条件。成功追捕的条件包括追捕者和躲避者的相对速度、追捕者的转弯半径（假设是一个任意敏捷的躲避者）和追捕者的总数。在导弹拦截的背景下，已经研究了更现实的基于物理的场景，其中使用多枚防御导弹拦截一枚或多枚来袭（目标）导弹，假设这些导弹使用标准的最佳制导和规避法则。估计目标导弹的状态和制导规律是一项重大挑战，而估计状态所涉及的时间延迟可能会对追击产生严重不利影响[105]。在[106]中，目标状态的合作估计（与每枚导弹仅使用自己的估计相比）被证明可以显著提高成功的可能性。导弹之间的信息共享也可用于直接调整其导航规律，如[107]所示，以实现对目标的同步打击。

A scenario related to cooperative pursuit is that of multiple UAVs tracking a single target. From the point of view of trajec tory generation, it is of interest to consider scenarios wherein the environment is populated with no-go areas and with ter rain features that may sporadically occlude the pursuers’ view of the target, such as a typical urban neighborhood. In order to facilitate the generation of trajectories that minimize occlu sion, it is beneficial to develop adequate models of the sensors, such as gimbaled cameras, that are used to track the target. The constraints of the tracking system can then be added to the dy namic limitations of each UAV to generate guidance laws for the complete team of UAVs [108].

与合作追踪相关的场景是多架无人机跟踪单个目标。从轨迹生成的角度来看，考虑环境中没有禁区和可能偶尔遮挡追捕者对目标的视线的大雨特征的情况是有意义的，例如典型的城市社区。为了便于生成最小化遮挡的轨迹，开发用于跟踪目标的传感器（如万向架相机）的适当模型是有益的。然后，跟踪系统的约束可以添加到每架无人机的动力学限制中，为整个无人机团队生成制导律[108]。

The simplest task assignment problem is the following static, symmetric problem: given a set of n agents, n bins, and a ma trix of rewards P ∈ Rn×n (or, equivalently, a matrix of costs C ∈Rn×n),wherePi,j (resp. Ci,j) denotes the reward derived (resp. cost incurred) by agent i from being assigned to bin j and Pi,j = −∞(resp. Ci,j = ∞) denotes an infeasible assign ment, determine the map A : i→ j = A(i) which assigns to each agent a unique bin while maximizing the collective reward i Pi,A(i) (resp. minimizing the equivalent collective cost). Parallel or distributed algorithms to solve target assignment in clude manyvariants of distributed auction algorithms [16], [25], [109]–[111] and decentralized hierarchical strategies [112] that approximate true optimality of Kuhn’s centralized Hungarian method. As an illustration of the computational complexity of auction algorithms, the number of computations required for the distributed algorithm from [16] to converge is O(Δn2), where Δis the diameter of the communication graph underlying the network of agents participating in the auction.

An elementary auction algorithm is illustrated in Algorithm1. This algorithm is centralized, and requires a central register where information about the bids and assignments is maintained. Incontrast,distribute dalgorithms distribute computation as well as communication among the agents. Forinstance,the algorithm in [25] adjusts the number of targets based on the number of agents available at aspecific stage.This is accomplished through bidding, rather than a consensus-like process, which is useful in large swarms with agents that may drop out spontaneously. This distributed target assignment can be solved simultaneously to provide goal states of real-time optimal trajectory generation, thereby, effectively solving (7) [25], [80], [113].

算法1中说明了一种基本的拍卖算法。该算法是集中式的，需要一个中央寄存器来维护有关投标和分配的信息。相比之下，分布式算法在代理之间分配计算和通信。例如，[25]中的算法根据特定阶段可用的代理数量调整目标数量。这是通过竞标来实现的，而不是一个类似共识的过程，这在大量可能自发退出的代理人中很有用。这种分布式目标分配可以同时求解，以提供实时最优轨迹生成的目标状态，从而有效地求解（7）[25]、[80]、[113]。

An equivalent geometric problem involves partitioning a physical volume into portions that are then assigned to each agent inside the volume. A well-known result is that the optimal partition corresponds to the generation of Voronoi cells using a suitable metric function [114]. This approach was introduced in [114] for sensor coverage, and generalized in [115] and [116] to cover learning (of the task distribution) and decentralized information sharing.

一个等效的几何问题涉及将物理体积划分为多个部分，然后将这些部分分配给体积内的每个代理。一个众所周知的结果是，最佳分割对应于使用合适的度量函数生成Voronoi单元[114]。这种方法在[114]中被引入用于传感器覆盖，并在[115]和[116]中得到推广，以涵盖（任务分配的）学习和分散的信息共享。

Assignment can be obtained as the solution to an optimal transport problem [117] when the transition between bins is modeled in a probabilistic framework through homogeneous Markov matrices. An improved approach has been proposed in [23] using time-inhomogeneous Markov chains that allow for the inclusion of feedback terms, thereby, solving both bin-to-bin swarm shape control and stochastic target assignment.

当在概率框架中通过齐次马尔可夫矩阵对仓之间的转换进行建模时，可以获得分配作为最优传输问题的解决方案[117]。[23]中提出了一种改进的方法，该方法使用时间非齐次马尔可夫链，允许包含反馈项，从而解决了仓到仓群形状控制和随机目标分配问题。

C. Collision Avoidance and Collision-Free Motions

The problem of collision avoidance becomes particularly challenging in swarms because the obstacles encountered by a robot include other members of its swarm, and collision avoid ance has to factor in the need to maximize the performance of the swarm(e.g.,avoidincreasing thetimetocompleteanassign ment). The most intuitive techniques for avoiding collisions are speedadjustment[118]andsequentially replanning thetrajecto ries [87] without changing the assignment in an optimal control framework (7). In particular, mixed-integer linear programming has been successfully derived for optimal collision-free mo tions and applied to mobile robots, spacecraft, and UAVs [85], [86], [119]. More recently, SCP has been used to approximate collision-free regions by incrementally drawing hyperplanes and has been demonstrated in simulation and experiments on swarms [25], [87]. The conservatism of hyperplane-based con vexification of collision-free regions has been relaxed by ex panding convex spherical regions along graph-based primitive paths in [120]. An alternate approach to replanning just the tra jectories involves reassigning the goals as shown in [80]. The reassignment is purely local and need not affect the criteria used for the assignment in the first place.

在群体中，避免碰撞的问题变得特别具有挑战性，因为机器人遇到的障碍物包括其群体的其他成员，避免碰撞必须考虑到最大限度地提高群体性能的需要（例如，避免增加二次完成的设计）。避免碰撞的最直观的技术是速度调整[118]和在不改变最优控制框架中的分配的情况下依次重新规划项目[87]（7）。特别是，混合整数线性规划已成功推导出最佳无碰撞运动，并应用于移动机器人、航天器和无人机[85]、[86]、[119]。最近，SCP已被用于通过增量绘制超平面来近似无碰撞区域，并在蜂群的模拟和实验中得到了证明[25]，[87]。在[120]中，通过沿基于图的基元路径展开凸球面区域，放宽了基于超平面的无碰撞区域协扰的保守性。仅重新规划项目的另一种方法是重新分配目标，如[80]所示。重新分配纯粹是本地的，不需要影响最初用于分配的标准。

Amore direct approach to collision avoidance in swarms in volves the use of artificial potential fields [121]–[124] or barrier functions [125], [126]. It must be noted that Reynolds’ model (1) also includes the gradient of a potential function. Potential f ields are computationally easy to implement for the purpose of collision avoidance, but not necessarily for path planning. Furthermore, artificial potential fields directly couple the dy namics of the individual robots and this can adversely affect the stability of the swarm if the communication topology is not selected properly. Connectivity is not enough to guarantee sta bility in directed graphs (see Section II-F). An approach similar to potential fields involves using the gradient of a Lyapunov function, which implicitly takes into account the possibility of collisions. Such control laws have been constructed using a dif ferential game approach [127], [128] and simultaneously solve a greedy optimization problem. The difficulty lies in solving the optimal control problem in the presence of nonlinearities and local communication.

在群体中避免碰撞的直接方法包括使用人工势场[121]-[124]或屏障函数[125]，[126]。必须注意的是，Reynolds模型（1）还包括势函数的梯度。潜在场在计算上易于实现，以避免碰撞，但不一定用于路径规划。此外，人工势场直接耦合了单个机器人的动力学，如果通信拓扑选择不当，这可能会对群体的稳定性产生不利影响。连通性不足以保证有向图中的稳定性（见第II-F节）。一种类似于势场的方法涉及使用李雅普诺夫函数的梯度，该函数隐含地考虑了碰撞的可能性。这种控制律是使用微分博弈方法[127]、[128]构建的，同时解决了贪婪优化问题。难点在于解决存在非线性和局部通信的最优控制问题。

D. Aerial Manipulation

Aerial robotic swarms have the ability to transport objects in two ways, where each individual robot is capable of carrying an object or where multiple robots are required to lift a single object. Ineitherscenario,theobjectmaybesuspendedviacables attached to the robots [129]–[133] or may be rigidly attached to the robots [134]–[138]. UAVs that are rigidly attached to the objects use a variety of grippers, including friction-based [134], penetration-based [135], or magnetic [137].

空中机器人群能够以两种方式运输物体，其中每个单独的机器人能够携带一个物体，或者需要多个机器人来提升一个物体。在任何情况下，物体都可能是附着在机器人上的悬浮物[129]-[133]，也可能是刚性附着在机器人身上的[134]-[138]。刚性附着在物体上的无人机使用各种夹具，包括基于摩擦的[134]、基于穿透的[135]或磁性的[137]。

When each individual robot is capable of grasping an object, having a swarm of robots allows a large number of objects to be moved more quickly. This can be used for tasks, such as package delivery [133], [138] and construction [134].

当每个单独的机器人都能够抓取一个物体时，拥有一群机器人可以更快地移动大量物体。这可用于任务，如包裹递送[133]、[138]和施工[134]。

When multiple robots are required to move a single object, small teams of robots may be used to cooperatively transport a single object [129]–[132], [135]–[137]. This task requires some type of communication between the robots. This is typically done in an explicit manner, but can also be done implicitly by sensing the internal forces of the robots acting onthetransported object [132]. The swarm also seeks to minimize these internal forces, as these represent wasted energy usage [136].

当需要多个机器人来移动单个物体时，可以使用小团队的机器人来协同运输单个物体[129]-[132]，[135]-[137]。这项任务需要机器人之间进行某种类型的通信。这通常是以显式方式完成的，但也可以通过感测机器人作用于运输物体的内力来隐式完成[132]。蜂群还试图将这些内力最小化，因为这些内力代表了浪费的能源使用[136]。

E. External Control of Aerial Swarms

External control of swarms refers to one of the following two situations:

1) The swarm is assigned objectives in real time by an exter nal user, especially a human operator.

2) Some or all members of the swarm interact with an adver sary or a hostile agent which, in turn, is within a human user’s control.

蜂群的外部控制是指以下两种情况之一：
1） 群体由外部用户，特别是人类操作员实时分配目标。
2） 群体中的一些或所有成员与一个攻击者或敌对代理进行交互，而这反过来又在人类用户的控制范围内。

At the simplest level,a human teleoperator sends motion commands to the swarm.

In order to reduce the cognitive load on the operator, it is desirable to minimize the number of inputs that the operator must provide and manage. To this end, it is possi ble to control the bulk motion of the swarm by guiding a single virtual leader and controlling the size and shape of the swarm with respect to this virtual leader [139], [140]. An alternative to using a virtual leader is to use the virtual rigid body framework, developed and demonstrated in [141] and [142]. The human could also issue a command in a language that the swarm is de signed to understand. This is no different conceptually from the usual setting of an autonomous swarm, since it involves the hu man acting essentially outside the algorithmic loop. It has been argued that humans are able to guide a swarm better using a dy namic set of leaders [143], as compared to manipulating a fixed leader. There is also evidence which suggests that human oper ators can adapt their handling of (virtual) leaders to guide large swarms through obstacle-rich environments in a better manner than built-in, standard flocking rules [144]. The next level of sophistication involves the human issuing commands using nat ural language, while still staying outside the algorithmic loop that controls the swarm. Here, the challenge is the one of in ferring a specific command from the operator’s verbiage [145]. The highest explored level of sophistication is using computer to infer humanintent. Here, the humanisverymuchapartofthe algorithmic loop: the algorithm that controls the swarm actively seeks input from the human about its performance. Kim and Coleman [146] proposes a framework to extend this idea to a team of robotic agents (including UAVs).

在最简单的层面上，人类远程操作员向蜂群发送运动命令。
为了减少操作员的认知负荷，最好尽量减少操作员必须提供和管理的输入数量。为此，可以通过引导单个虚拟领导者并控制群体相对于该虚拟领导者的大小和形状来控制群体的整体运动[139]，[140]。使用虚拟领导者的另一种方法是使用[141]和[142]中开发和演示的虚拟刚体框架。人类还可以用群体设计为能够理解的语言发出命令。这在概念上与自主群体的通常设置没有什么不同，因为它涉及胡人在算法循环之外的行为。有人认为，与操纵固定的领导者相比，人类能够使用动态的领导者集更好地引导群体[143]。还有证据表明，人类操作员可以调整他们对（虚拟）领导者的处理，以比内置的标准群集规则更好的方式引导大型群集通过障碍物丰富的环境[144]。下一个复杂程度涉及人类使用自然语言发出命令，同时仍处于控制蜂群的算法循环之外。在这里，挑战在于从操作员的措辞中传递特定的命令[145]。探索的最高复杂程度是使用计算机推断人类内容。在这里，人类很可能是算法循环的一部分：控制群体的算法主动寻求人类对其性能的输入。Kim和Coleman[146]提出了一个框架，将这一想法扩展到机器人代理团队（包括无人机）。

The concept of adversarial control addresses the case where there is no direct way of tapping into a swarm’s command and control algorithm.

对抗性控制的概念解决了无法直接利用群体指挥和控制算法的情况。

An example of adversarial control is the family containment and herding strategies modeled after dolphins [21], sheep-dogs [147]–[152] and birds of prey used to herd a flock of birds [153]. Paranjape et al. [153] examined the use of arobotic UAV,possibly one built to resemble a bird of prey like a falcon, to herd flocks of birds away from sensitive areas like airports and solar farms.The UAV interacts with the flockby engaging birds located on the boundary of the flock.The herding algorithm makes use of the flock’s inherent tendency to maintain a cohesive structure to reduce the number of robotic agents required to achieve herding. The perturbation in the velocity of the birds on the boundary of the flock diffuses through the swarm and causes the flock to alter its heading and speed. It has been shownin[153]that asingle robotic agent suffices to herd a flock of birds, while related work [150] suggests that the quality of the herding can be improved substantially by using multiple UAVs.

对抗性控制的一个例子是模仿海豚[21]、牧羊犬[147]-[152]和用于放牧鸟类的猛禽[153]的家庭控制和放牧策略。Paranjape等人[153]研究了使用arobotic无人机（可能是一种类似猎鹰等猛禽的无人机）将成群的鸟类从机场和太阳能农场等敏感地区驱赶出去。无人机与位于鸟群边界的鸟群互动。羊群算法利用羊群保持内聚结构的固有倾向来减少实现羊群所需的机器人代理数量。鸟群边界上鸟类速度的扰动通过鸟群扩散，导致鸟群改变其航向和速度。[153]已经表明，一个机器人代理足以放牧一群鸟，而相关工作[150]表明，使用多架无人机可以大大提高放牧质量。

One particular problem of interest in the context of adver sarial control is inferring the model underlying the swarm’s motion. If the model is known, together with the response of the swarm to an adversary, it would be possible to not just design optimal strategies to divert or control the swarm, but also de rive guarantees on the performance of such strategies. In [153], experimental data was used to identify a model, based on [154] and [155], for the response of a flock of birds to a UAV located within a certain range of the flock. The approach adopted in [153] works for flocks whose response to perturbations is based on a static, deterministic law. When the response takes a more strategic, dynamic form, it is necessary to use learning-based techniques that expressly account for this behavior [156], [157]. A filter-based technique lies midway between the two sets of aforementioned approaches.Consider the case of missiles where it is known that a target missile follows one of a well-defined set of navigation laws at all times. The exact law and its pa rameters are unknown. Such problems can be solved efficiently using a bank of filters to determine the most likely model, as demonstrated in [158].

在对流控制的背景下，一个特别有趣的问题是推断群体运动背后的模型。如果已知该模型以及蜂群对对手的反应，不仅可以设计最优策略来转移或控制蜂群，还可以保证这些策略的性能。在[153]中，基于[154]和[155]，使用实验数据确定了一个模型，用于描述一群鸟对位于其一定范围内的无人机的反应。[153]中采用的方法适用于对扰动的响应基于静态确定性定律的羊群。当反应采取更具战略性、动态的形式时，有必要使用基于学习的技术来明确解释这种行为[156]，[157]。基于滤波器的技术位于上述两组方法之间。考虑导弹的情况，已知目标导弹始终遵循一套明确的导航规律之一。确切的规律及其参数尚不清楚。如[158]所示，使用一组过滤器来确定最可能的模型可以有效地解决这些问题。

IV. AERIAL DISTRIBUTED SENSING,MONITORING, AND COOPERATIVE MAPPING

A. Target Search and Tracking

1) Single, Dynamic Target Estimation:

2) Estimation of Multiple Targets of Known Number:

3) Multiple Targets of Unknown Number:

As mentioned above, when the number of targets is unknown, the search prob lem becomes much more difficult and the team must always ex plore the entire environment in order to complete the task. The standard method used to solve this task is to utilize a quadtree representation to adaptively refine the environment in areas that are likely to contain targets [167]–[169].

如上所述，当目标数量未知时，搜索问题变得更加困难，团队必须始终探索整个环境才能完成任务。用于解决此任务的标准方法是利用四叉树表示来自适应地优化可能包含目标的区域中的环境[167]-[169]。

Perhaps the mostchallenging target search and tracking prob lem is when the number of targets is unknown and dynamically changes over time, e.g., due to targets entering and leaving the area of interest. The tool most commonly used in this scenario is the PHDfilter [170], which allows the team to simultaneously estimate the number of targets and the dynamic state of each target. This has been used by a small team of fixed-wing UAVs to track vehicles on roadways using an information-based tech nique [172] and by a large team of multirotor UAVs to track ground robots using a Voronoi-based controller [173].

也许最具挑战性的目标搜索和跟踪问题是目标数量未知且随时间动态变化的情况，例如，由于目标进入和离开感兴趣的区域。在这种情况下最常用的工具是PHDfilter[170]，它允许团队同时估计目标的数量和每个目标的动态。一小群固定翼无人机使用基于信息的技术跟踪道路上的车辆[172]，一大群多旋翼无人机使用沃罗诺伊控制器跟踪地面机器人[173]。

B. Surveillance and Monitoring

Target tracking, as the name implies, takes a target-centric approach. The alternative is to take an area-centered approach, where the team of robots focuses on covering an area of interest.

A是关注对象（跟踪/抓捕）  B是关注区域 （监视区域）

1) Persistent Monitoring:

2) Surveillance:

The primary distinction between persistent monitoring and surveillance is that in surveillance there is no hard requirement that each area be visited with a certain fre quency.

C. Cooperative Aerial Mapping

In contrast to surveillance and monitoring tasks, where the goal is to only observe the environment, mapping is the pro cess of acquiring a globally consistent representation of an environment.

1) Visual Sparse Mapping: Visual sparse representation consists of points and lines, which are extracted and tracked from images.

2) Visual Dense Mapping:Dense mapping systems describe the environment using a dense collection of points or planes.

3) Lidar-Based Mapping:

V. TECHNOLOGY FOR SWARMING

A. Platforms

B. Vehicle Power Management

C. Pose and State Estimation

1) Pose Estimation Using External Sensors:

real-time kinematic (RTK) GPS, optical motion capture systems, and ultrawideband (UWB)

2) Pose Estimation Using On-board Sensors:

cameras, lidars, and inertial measurement units (IMUs).

D. Communication Infrastructure

Bluetooth, UWB,orstandardWi-Fi

Researchers are looking into possible alternatives that demonstrate low latency, high reliability, and high bandwidth, such as URLLC [227].

VI. CONCLUSION AND FUTURE WORK

In the near future, our airspace will be populated by swarms of aerial robots, performing complex tasks that would be impos sible for a single vehicle. This papers reviews work that could provide the fundamental algorithmic, analytic, perceptive, and technological building blocks necessary to realize this future. The research issues discussed in this survey paper span hierar chical integration of swarm synchronization control with safe trajectory optimization and assignment, and cooperative estima tion and control with perception in the loop, offering the readers a broad perspective on aerial swarm robotics.

在不久的将来，我们的空域将布满成群的空中机器人，执行单个飞行器无法完成的复杂任务。本文回顾了可以提供实现这一未来所需的基本算法、分析、感知和技术构建块的工作。本文讨论的研究问题涵盖了群同步控制与安全轨迹优化和分配的分层集成，以及具有感知的协同估计和控制，为读者提供了对空中群机器人的广阔视野。

In addition, we emphasize the importance of the three-way tradeoff between computational efficiency, stability and robust ness, and optimal system performance. To truly address this tradeoff, we argue that it is imperative to advance beyond meth ods that are currently being used in autonomous drones and general swarm robotics in order to realize long-term autonomy of aerial swarm systems.

此外，我们强调了计算效率、稳定性和鲁棒性与最优系统性能之间三方权衡的重要性。为了真正解决这一权衡问题，我们认为，必须超越目前用于自主无人机和通用群体机器人的方法，以实现空中群体系统的长期自主。

One important area of further study is to develop learning and decision-making architectures that will endow swarms of aerial robots with high levels of autonomy and flexibility. We argue that such architectures will ultimately lead to reduced risk and cost as well as long-term autonomous operations. To be successful, any such architecture must provide the framework for reasoning about the wide-ranging nature of uncertainties and modeling errors, ranging from known unknowns (e.g., sensor and actuator noise) to unknown unknowns (e.g., wind disturbance, hardware failures). All of these impact the safety and robustness of algo rithms and system-level functions of swarm behaviors. Further more, computation and communication within a swarm must be fast enough toensure stability under model changes andmission specifications at the various timescales and bandwidths within the system.

进一步研究的一个重要领域是开发学习和决策架构，使成群的空中机器人具有高度的自主性和灵活性。我们认为，这种架构最终将降低风险和成本，并实现长期自主运营。为了取得成功，任何这样的架构都必须提供一个框架，用于推理不确定性和建模误差的广泛性质，从已知的未知量（如传感器和执行器噪声）到未知的未知值（如风干扰、硬件故障）。所有这些都会影响算法的安全性和鲁棒性以及群体行为的系统级功能。此外，群内的计算和通信必须足够快，以确保在系统内各种时间尺度和带宽的模型变化和任务规范下的稳定性。

For aerial swarm systems with highly uncertain environmen tal models, the role of high-level planning, decision making, and classification in flight in conjunction with low-level swarm con trol and estimation systems can be characterized mathematically through the properties of stability, convergence, and robustness. Various aspects of the swarm decision-making, control, and es timation should come in different timescales and hierarchical levels to exploit scalability and computational efficiency. An example of such characterization on stability would be a mathematical theorem correlating desired models and parameters to be updated online as well as their update or learning rates, to func tions of various system features, such as sampling rate, swarm control law update rate, bandwidth of dynamics and communi cation, dimensions of dynamic systems, and properties of envi ronmental uncertainties. This should also provide a guideline as to gauge how efficient and robust a particular swarm algorithm or system-level architecture is at achieving autonomy in aerial swarms. For example, distributed optimal planning (e.g., [25], [87]) requires robots to share their optimal solutions with their neighbors, up to a certain time horizon. Adding simultaneous target or task allocation to this problem further increases the required size of communicated information. It would be bene f icial to combine such methods with online adaptation methods that can forecast the neighbors’ future behavior and would, in turn, effectively reduce communication requirements. The key idea is again combining formal mathematical analysis with the hierarchical and multimodal decomposition discussed earlier. Another important area is to establish rigorous methodologies for fault detection, isolation, and recovery to handle various po tential faults occurring at subsystem levels, individual system levels, and swarm levels.

对于具有高度不确定环境模型的空中群体系统，高级规划、决策和分类在飞行中的作用以及低级群体控制和估计系统可以通过稳定性、收敛性和鲁棒性的特性进行数学表征。群体决策、控制和估计的各个方面应该采用不同的时间尺度和层次结构，以利用可扩展性和计算效率。这种稳定性特征的一个例子是一个数学定理，该定理将所需的模型和参数及其更新或学习速率与各种系统特征的函数相关联，如采样率、群控制律更新率、动力学和通信带宽、动态系统的维度以及环境不确定性的性质。这也应该提供一个指导方针，以衡量特定的群体算法或系统级架构在实现空中群体自治方面的效率和鲁棒性。例如，分布式最优规划（例如[25]，[87]）要求机器人在一定的时间范围内与邻居共享其最优解。将同时的目标或任务分配添加到这个问题中会进一步增加所需的通信信息大小。将这些方法与在线适应方法相结合将是有益的，在线适应方法可以预测邻居的未来行为，从而有效地降低通信需求。关键思想再次是将形式数学分析与前面讨论的分层和多模态分解相结合。另一个重要领域是建立严格的故障检测、隔离和恢复方法，以处理在子系统级别、单个系统级别和群级别发生的各种潜在故障。

As swarms are deployed to a greater extent for aggressive or agile autonomous missions, it will become necessary to cre ate the means to exert some form of adversarial control on swarms. Such counter-swarm techniques can also be used for civilian purposes, such as maintaining law and order and herd ing birds and animals away from environmental hazards, such as floods or wildfires. The work reported in Section III-E is a good starting point for these techniques. Key open questions include the type of maneuvers that need to be performed to rapidly estimate a swarm’s location and intent; assess an aerial swarm’s internal dynamics; identify the task and role assign ment within a given swarm; and identify the primary leader and sensing nodes. The next level of questions pertain to identify ing ways of defeating these types of probing maneuvers from an adversarial swarm, which is a direct analogue of the usual minimax paradigm for games. It is interesting to note the simi larities exhibited in the case of social networks, which suggests that an adoption of the tools from that literature may provide early breakthroughs for counter-swarm development. Yet, even by adopting well-established tools from the theory of social networks and games, an important and significant challenge at both levels is identifying the role of the aerial vehicle dynamics in enabling, and defeating, the probing operations. A cleverly executed set of maneuvers could help identify, and equally pro vide deceptive leads about, a swarm’s intent, organization and capabilities.

随着蜂群在更大程度上被部署用于攻击性或敏捷的自主任务，有必要创造对蜂群施加某种形式的对抗性控制的手段。这种反蜂群技术也可用于民用目的，例如维护法律和秩序，以及驱赶鸟类和动物远离洪水或野火等环境危害。第III-E节中报告的工作是这些技术的良好起点。关键的未决问题包括需要执行的机动类型，以快速估计蜂群的位置和意图；评估空中蜂群的内部动态；确定给定群体内的任务和角色分配；并识别主要领导者和感测节点。下一级问题涉及确定如何从对抗性群体中击败这些类型的探测机动，这是游戏中常见的极小极大范式的直接模拟。值得注意的是，社交网络中表现出的相似性表明，采用该文献中的工具可能会为反群体发展提供早期突破。然而，即使采用社交网络和游戏理论中成熟的工具，两个层面的一个重要而重大的挑战是确定飞行器动力学在实现和击败探测行动中的作用。一组巧妙执行的机动可以帮助识别群体的意图、组织和能力，并同样提供欺骗性的线索。

In summary,manyopen problems and research issues in aerial swarm robotics involve the characterization of the interdepen dencies between the properties of swarm vehicle dynamics, the properties of uncertainties, and different swarm learning/control methods employed.Only by understanding these inter dependencies, either through careful system identification or integrated system design, can fully autonomous aerial swarms be proven to operate in complex, real-world environments.

总之，空中群体机器人技术中的许多悬而未决的问题和研究问题涉及群体车辆动力学特性、不确定性特性和所采用的不同群体学习/控制方法之间相互依赖关系的表征。只有通过仔细的系统识别或集成系统设计来理解这些相互依赖关系，才能证明完全自主的空中无人机群可以在复杂的现实环境中运行。

总结：