| Citation: | LIU Chen-guang, HE Zhi-bo, CHU Xiu-min, WU Wen-xiang, LI Song-long, XIE Shuo. Overview on ship formation control[J]. Journal of Traffic and Transportation Engineering, 2022, 22(4): 10-27. doi: 10.19818/j.cnki.1671-1637.2022.04.002
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Compared with other forms of motion formation control, the particularity of ship formation control is mainly reflected in the following aspects: 1) The navigation environment of ship formation is complex and varied, and it is simultaneously affected by factors such as wind, waves, currents, and limited water areas[19]Due to the characteristics of high inertia, underactuation, and control delay in ship maneuvering, the difficulty of ship formation path planning, formation control, and path control is greater; 3) The problem of reliable control of ship formations under communication limitations or failures caused by navigation environments is significant[20]The ship formation navigation system mainly includes subsystems such as environmental perception, situational awareness, and formation control. Among them, the ship formation control subsystem mainly implements functions such as task allocation, formation organization and transformation, formation collision avoidance planning, formation motion modeling, and formation collaborative control, which are the basis for realizing ship formation navigation.
Formation control structure, also known as formation control method in some literature, mainly refers to the form of formation construction and operation. At present, typical ship formation structures include leader follower structure, virtual structure, behavior based structure, graph theory based structure, artificial potential field structure, composite structure, etc.
The leader follower structure uses one ship in the formation as the leading ship and the other ships as follower ships. By planning the navigation trajectory of the leading ship, the follower ships track the trajectory of the leading ship at a desired angle and distance through specific control laws. A typical leader follower structure based on line of sight navigation isFigure 2As shown[26].Figure 2Two coordinate systems are defined in the document: one is an inertial coordinate systemxoOoyo, that is, taking a fixed point on the surface of the Earth as the originOoTo the north isxoThe axis is in the positive direction, and the positive east direction isyoAxis positive direction; The other is a shipiAttached coordinate systemx(b, i)O(b, i), y(b, i), i.e. by shipiThe center is the originO(b, i), ShipiThe longitudinal section from the stern to the bow direction isx(b, i)Axis positive direction, shipiThe direction perpendicular to the mid longitudinal plane pointing to the starboard side isy(b, i)Axis positive direction.Figure 2In the middle, shipsiFor navigation ships, vesselsjAnd shipsj+1 is to follow the ship. shipiWith shipsjTarget tracking distancedi, jTracking angle with the targetΦi, jDefined as
| {di,j=√x2(b,i),j+y2(b,i),jΦi,j=arctan(y(b,i),jx(b,i),j) | (1) |
In the formula:x(b, i), jandy(b, i), jFor ships respectivelyjOn board the shipiThe horizontal and vertical coordinates in the attached coordinate system.
shipjAnd shipsj+1. Track the target status separately（di, j, Φi, j）And（di, j+1, Φi, j+1）Realize formation navigation control, and also achieve formation transformation by changing the target state.
Encarnacao et al[27]By using unmanned surface vessels as leaders and underwater vehicles as followers, the coordinated control of trajectory and path tracking for two ships has been achieved; Considering that the leader follower structure may cause the entire formation to collapse in the event of a leader malfunction or unknown status, Pereira et al[28]The cooperative navigation method was proposed, which means that the follower is simultaneously influenced by both the leader and other followers, reducing the reliance on the leader alone; Li Yun and others[29]Divide the ship formation control process into two stages: leader follower and follower follower, in order to compensate for the shortcomings of centralized control in a single leader follower structure. Selecting a virtual leader in the formation can also overcome the problems of one-way information flow and lack of feedback in the traditional leader follower structure[30-33]In order to enhance the stability and reliability of ship formation control and reduce reliance on the leader, some scholars have proposed a leader follower structure where followers only follow their own former counterparts. This structure provides a foundation for implementing distributed computing for formation control[34]The leader follower structure is simple and easy to implement, but the leader and follower are independent of each other, making it difficult to obtain follower tracking feedback.
Virtual structure treats the entire formation as a rigid body, with each individual in the formation being a relatively fixed point within the rigid body. When the formation moves in the form of a rigid body, the individual tracks its relative position within the rigid body as the target[35]After the formation of the ship formation is established, each ship has its corresponding reference point, such asFigure 3As shown. In the picture{x1, x2...} is the state vector of each vessel in the fleet. By designing a formation controller, the formation state can be controlled by{x1, x2...} Migration to{x'1, x'2...}.
The current methods for resolving behavioral conflicts mainly include behavior inhibition method, weighted average method, fuzzy logic method, and zero space method. Among them, the zero space method is widely adopted because it can partially or completely complete low priority tasks while completing high priority tasks.
Formation control based on behavioral structure is usually executed according to behavioral rules, which is difficult to quantitatively analyze from a mathematical perspective, leading to problems such as unpredictable formation behavior and low stability of formation control.
In recent years, the artificial potential field formation structure has also been applied in intelligent agent formation control[49]The basic principle is to establish different potential fields to control the movement of formation objects. Introducing an artificial potential field structure with a virtual leader, such asFigure 5As shown[50]The dashed line in the figure represents the effect of potential field forces. The virtual navigation ship maintains the ships in the formation near it through the gravitational field, and the ships in the formation maintain a safe distance through mutual repulsion field. The artificial potential field structure algorithm is concise and flexible, but it can easily cause the formation to fall into local minima.
| 编队控制结构 | 优点 | 缺点 | 文献 |
| 领导-跟随结构 | 简单，易实现 | 领航者与跟随者之间相互独立，难以获得跟随者的跟踪反馈 | [26]~[33] |
| 虚拟结构 | 可将编队误差作为反馈引入控制器，具有较好的控制稳定性和全局收敛性 | 编队灵活性和自适应性较弱，不适用于复杂队形控制 | [12]、[35]~[39] |
| 基于行为结构 | 可将复杂编队任务进行分解，自适应能力强 | 编队不同对象行为可能存在冲突，难以从数学角度进行定量分析，编队控制稳定性不高 | [40]~[45] |
| 图论结构 | 可描述复杂的编队结构，有利于解决大规模编队控制问题 | 实际应用时复杂性较高 | [46]~[48] |
| 势场结构 | 算法简明，灵活性高 | 易陷入局部最小点，势场配置随机性较强 | [49]~[50] |
| 组合结构 | 可发挥不同编队结构的优势 | 增加了编队控制的复杂度和不确定性 | [51]~[52] |
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(1) Binary method. The binarization method is the simplest way to model environments, which only requires converting map information into a logical matrix. In the map matrix, 1 represents the passable area and 0 represents the impassable area. For the convenience of expression, map matrices are usually displayed as binary images, such asFigure 8 (a)As shown, the black polygonal area represents obstacles, and the blank area represents passable areas. Fast random tree and other algorithms rely on binary maps[53].
(2) Visual visualization method. Visual representation is a common method for constructing graphical models[54]The visual map method forms a line of sight map by connecting the edges of vertices that are visible to each other. If there are no obstacles between the two connection points, they are considered visibleFigure 8 (b)As shown.
(4) Grid method. Grid method is a commonly used graphic model, including honeycomb grid, triangular grid, square grid, etc. Among them, honeycomb grid is often used in some common game map building modules, while square grid is more commonly used in daily use, such asFigure 8 (d)As shown.
Global path planning for ship formation is to provide feasible paths from the starting point to the endpoint for ship formation. From the perspective of computational principles, global path planning algorithms can be divided into two types: heuristic search algorithms and optimization algorithms. The heuristic search algorithm mainly covers A-Star (A)*）Algorithm[56]Fast Marching (FM) algorithm[57]Rapid exploring Random Tree (RRT) algorithm[58]Wait; Optimization algorithms mainly include genetic algorithms[59]Simulated Annealing Algorithm[60]Ant colony optimization algorithm[61]Particle Swarm Optimization Algorithm[62]Tianniu Xu Search Algorithm[63]Wait.
| 算法名称 | 计算时间 | 是否总能找到最优路径 | 轨迹平滑度 | 缺陷和优势 |
| FM算法 | 较慢 | 否 | 平滑 | 使用简单、响应速度快，生成路径足够光滑且连续，但是生成路径离障碍物较近，缺乏安全性 |
| A*算法 | 较慢 | 是 | 不平滑 | 在面对多栅格地图的时候全局规划耗时长，且生成轨迹不平滑，但优势是总能找到最优路径 |
| RRT算法 | 较慢 | 否 | 不平滑 | 适用于求解复杂障碍空间路径规划问题，但是较小的搜索步长会极大增加计算时间，较大的搜索步长则可能无法求解，且RRT算法生成路径不是最优路径 |
| 优化算法 | 快 | 否 | 平滑 | 能够直接生成平滑轨迹，便于实现轨迹跟随，且在面对一些操纵性约束、避碰规则约束时更容易实现，缺点是容易陷入局部最优，而忽视全局最优解 |
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The potential field method was used as the modeling method for the formation environment, and the particle swarm optimization algorithm was utilized to achieve the local collision avoidance path of the ship formation. The local collision avoidance path of the formation is as follows:Figure 9As shown.
In summary, there are various ways for ship formation path planning, from map modeling to global path planning and local collision avoidance. Choosing different combinations of methods can effectively solve problems in different scenarios. If the grid method is used to model the global path planning map, the global path planning algorithm should choose A*Algorithms are beneficial in reducing computational complexity when searching for the optimal path; Using the potential field method in local collision avoidance map modeling can more intuitively and conveniently describe the degree of danger of obstacles, making it easier to achieve formation collision avoidance, etc; Reinforcement learning has better collision avoidance performance when dealing with known water bodies.
causeNA ship formation composed of ships is defined asF=(V1, V2, …, VN）Set up the vesseliPosition vectorηido
| ηi=(xo,i,yo,i,ψi)T | (2) |
Velocity vectorνido
| vi=(vx,i,vy,i,ri)T | (3) |
In the formula:xo, i、yo, iFor shipsiPosition in the inertial coordinate system;ψiFor shipsiThe bow of the ship;vx, i、vy, i、riFor ships respectivelyiThe forward velocity, lateral velocity, and yaw rate in the attached coordinate system.
| {˙xo,i=vx,icos(ψi)−vy,isin(ψi)˙yo,i=vx,isin(ψi)+vy,icos(ψi)˙ψi=ri | (4) |
| \boldsymbol{M}_i \dot{\boldsymbol{v}}_i=-\boldsymbol{C}_i\left(\boldsymbol{v}_i\right) \boldsymbol{v}_i-\boldsymbol{D}_i\left(\boldsymbol{v}_i\right) \boldsymbol{v}_i+{\mathit{\pmb{τ}}}_i+{\mathit{\pmb{τ}}}_{\mathrm{d}, i} | (5) |
| \boldsymbol{x}_i=\left(\boldsymbol{\eta}_i^{\mathrm{T}}, \boldsymbol{v}_i^{\mathrm{T}}\right)^{\mathrm{T}} |
Ship formation statusXdo
| \boldsymbol{X}=\left(\boldsymbol{x}_1, \boldsymbol{x}_2, \cdots, \boldsymbol{x}_{\mathrm{N}}\right)^{\mathrm{T}} |
Considering the significant impact of control saturation and time delay on ship formation motion control[79-80]On the one hand, it is necessary to constrain the movement of ship formations, and on the other hand, delay needs to be considered in the motion model.
The constraints on ship formation motion include formation control input constraints and state constraints. shipiThe input constraint can be represented as
| \left[\begin{array}{c} \tau_{x, i, \min } \\ \tau_{y, i, \min } \\ \tau_{r, i, \min } \end{array}\right] \leqslant {\mathit{\pmb{τ}}}_i \leqslant\left[\begin{array}{c} \tau_{x, i, \max } \\ \tau_{y, i, \max } \\ \tau_{r, i, \max } \end{array}\right] | (6) |
In the formula:τx, i, min、τx, i, max、τy, i, min、τy, i, max、τr, i, minandτr, i, maxFor ships respectivelyiThe minimum and maximum values of forward displacement, lateral displacement, and yaw rate.
| \begin{aligned} &v_{i, \min } \leqslant v_i \leqslant v_{i, \max } \\ &v_i=\sqrt{v_{x, i}^2+v_{y, i}^2} \end{aligned} | (7) |
In the formula:vi, minandvi, maxFor ships respectivelyiThe minimum and maximum allowable speeds.
The ship requires a time interval from the issuance of control input instructions to their executionTThis can lead to an increase in overshoot of the control system, a decrease in control accuracy, but usually control delayTSmall in size, with limited impact on control performance. Sometimes, in order to achieve more precise control effects, control delay is also considered in the formation model (5)
| \boldsymbol{M}_i \dot{\boldsymbol{v}}_i=-\boldsymbol{C}_i\left(\boldsymbol{v}_i\right) \boldsymbol{v}_i-\boldsymbol{D}_i\left(\boldsymbol{v}_i\right) \boldsymbol{v}_i+\boldsymbol{\tau}_i(t-T)+\boldsymbol{\tau}_{\mathrm{d}, i} | (8) |
| \boldsymbol{X}_{\mathrm{F}}=\left(\boldsymbol{X}^{\mathrm{T}}, \boldsymbol{X}_{\mathrm{c}}^{\mathrm{T}}\right)^{\mathrm{T}} | (9) |
Using the "Container" ship in the Marine Systems Simulator of MATLAB toolbox as the object, the constructed ship formation motion model was used to achieve the coordinated control of ship formation through a 5-level lock. The changes in ship speed, bow direction, and lateral spacing during the formation navigation control were as follows:Figure 11As shown.
The types of ship formation motion control can be divided into centralized formation motion controller, decentralized formation motion controller, and distributed formation motion controller[81].
The entire ship formation control system has only one centralized formation motion controller, which can control all ships in the formation. The controller structure is as followsFigure 12As shown[82]In the pictureui、uj、xi、xjandyi、yjFor ships respectivelyi、jThe controller output vector, state vector, and controller input vector. The centralized formation control method is simple and easy to implement, but it requires high system robustness. Once the centralized controller fails, it will affect the safety of the entire formation navigation.
The distributed formation motion controller also decomposes the entire ship formation motion controller into multiple independent subsystems, each of which is controlled by a local controller, but the local controllers are interrelated and share information with each other. Its control structure is as followsFigure 14As shown. Compared with centralized control, distributed control shares the computational pressure, and the failure of any ship generally does not cause the collapse of the entire formation system, making it more robust. Compared with decentralized control, distributed control can achieve overall optimization through cooperation between local controllers. In addition, the distributed formation motion control method also has the advantages of strong scalability and high reliability.
| 方法 | 优点 | 缺点 |
| PID | 实现简单，不依赖船舶编队运动模型 | 难以处理时滞、强惯性系统控制问题 |
| 滑模控制 | 响应快速，对参数变化和扰动不灵敏 | 难以消除抖振问题 |
| 反步法 | 使控制律设计过程结构化，能保证闭环系统的稳定性 | 难以构造李雅普诺夫函数 |
| 智能控制 | 能处理复杂的非线性、干扰、不确定性、时变等控制问题 | 难以定义控制目标以及从理论上分析控制鲁棒性和稳定性 |
| 模糊控制 | 能充分发挥专家经验在控制中的作用，通过控制规则描述系统变量的关系，处理非线性、时变问题较强 | 控制目标定义不明确 |
| 自抗扰控制 | 不依赖系统模型，通过设置过渡过程能有效解决超调与快速性之间的矛盾 | 对控制器参数敏感，且不大适用于解决多输入多输出控制问题 |
| 反馈线性化 | 使控制问题简化 | 非线性控制律比较复杂，对模型精度要求比较高 |
| 有限时间控制 | 能从理论上保证系统控制的快速收敛性 | 难以构造李雅普诺夫函数 |
| 最优控制 | 能处理约束以及显示定义控制目标 | 对模型精度要求比较高，难以处理不确定性干扰对控制的影响 |
| 模型预测控制 | 能显式处理多变量约束以及不确定性干扰对控制的影响 | 非线性优化问题求解速率较慢，有时难以满足实时性需求 |
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Table 3When applying the formation motion control method to ship formation motion control, it is necessary to design corresponding types of ship formation controller deployment, such as distributed, decentralized, centralized, etc. Taking into account the requirements for ship formation motion control, this paper proposes the Distributed Model Predictive Control (DMPC) method[93]It is a typical distributed ship formation control method, which has been successfully applied to object covered robot formations[94]Aircraft formation[95]Vehicle formation[96]In fields such as ship formation. In terms of ship formation control, Chen et al[97-98]A distributed collaborative model predictive control method for ship formation was proposed, which achieved collaborative control of mixed formation of autonomous and manually operated ships; Zheng et al[99]A distributed collaborative model predictive control method was used to achieve collision avoidance control for automatic guided ship formations on water. To achieve multi ship formation navigation control, a multi ship formation navigation optimization problem was constructed based on the model predictive control method with multiple constraints set. The Alternative Direction Method of Multipliers (ADMM) was used to achieve distributed and efficient computing.
Based on the idea of distributed formation control, the principle of distributed model predictive controller for ship formation is as follows:Figure 15As shown. Specifically, the ship formation control targets are assigned to each vessel through the formation structure, and the specific tasks and target paths of each vessel are obtained; Constructing a multi-objective optimization problem for ship formation considering multiple constraints such as speed, input, and spacing, utilizing ADMM and DMPC to achieve distributed solution of the problem, and ensuring the coordination and convergence of ship formation navigation.
Looking at the research results both domestically and internationally, the current focus is on controlling ship formations in open waters, with a particular emphasis on issues such as maintaining ship formations, avoiding collisions, and tracking formation paths. However, there is a lack of research on issues such as the integration of manned/unmanned ships in ship formations, remote control, uncertain interference, limited communication, and special water areas. The specific manifestations are as follows.
In some special water areas, such as polar waters, ship lock waters, etc., the conditions for ship formation navigation in water areas are significantly different from those in open water areas. For example, the sailing speed of ships in the approach channel and chamber waters of ship locks is usually required to be less than 2 m · s-1And located in restricted waters, its motion model needs to consider factors such as low speed, shore wall effect, shallow water effect, and close distance between ships, which increases the difficulty of ship formation navigation control. Considering that the motion mechanism of ships in ice and restricted waters is still not clear enough, and the navigation strategy, navigation control, risk control and other issues during formation navigation still need to be studied, it is urgent to solve the problems of analyzing the characteristics of ship formation navigation in special waters, controlling the speed and distance under tight formation conditions, and identifying and controlling the risks of formation navigation.
(1) Distributed collaborative control of ship formation
Target encirclement and target coverage are not controlled by a single geometric shape, but rather a special formation control method aimed at encircling and covering targets, which has been applied in multi-agent system control. The target encirclement and coverage of ship formations have broad application prospects in military, emergency search and rescue, underwater detection and other fields. However, there is currently little research on this topic, and the targets of ship formation encirclement and coverage may be multiple dynamic targets, such as enemy ship encirclement, underwater obstacle target coverage, etc. Therefore, future ship formation control tasks not only include traditional tasks such as path tracking, obstacle avoidance, and formation transformation, but also need to develop towards diversified tasks such as target encirclement and coverage.
(4) Special water area vessel formation control
The low efficiency and high safety risks of ship navigation in restricted waters (such as lock waters, bridge area waters, etc.) have become important factors restricting the improvement of inland waterway transportation capacity. Taking the ship formation passing through the lock as an example, currently multiple ships are widely used to enter and exit the lock chamber in sequence, greatly reducing the space utilization of ships in the lock water area (mainly including the approach channel, navigation wall, lock chamber, etc.). Synchronized gate crossing formation control of ships can greatly improve the efficiency and safety of ship entry and exit gates. The three-dimensional effect of multi ship formation gate crossing is as followsFigure 16As shown. At present, there is an urgent need to solve technical problems such as modeling the behavior of ship formations passing through gates, modeling the motion of restricted water areas, and multi-objective distributed optimization control. In order to ensure the safety and economy of ships sailing in polar regions, formation navigation is usually adopted[106]Formation navigation can not only reduce the risk of single ship navigation, but also improve the economy of the entire ship formation navigation. With the gradual commercialization of the Arctic shipping route, future ship fleet navigation in polar waters has broad application prospects.
(5) Application of Artificial Intelligence Technology in Ship Formation Control
(2) As a branch of multi-agent control, research on ship formation control is still in the theoretical method research stage compared to aircraft formation control, vehicle formation control, and robot formation control. The testing and application of ship formation navigation in real scenarios have not been extensively carried out.
(3) The integration of manned/unmanned ship formations, robust and consistent control of formations in complex navigation environments, control of ship formations in special water areas, and control of ship formations under communication limitations all urgently need to be addressed.
(4) Distributed computing, artificial intelligence, biomimetic technology, advanced sensing technology, and high bandwidth low latency communication technology provide important technical support for the realization of future ship formations, and new development opportunities have emerged for ship formation navigation.
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| 编队控制结构 | 优点 | 缺点 | 文献 |
| 领导-跟随结构 | 简单，易实现 | 领航者与跟随者之间相互独立，难以获得跟随者的跟踪反馈 | [26]~[33] |
| 虚拟结构 | 可将编队误差作为反馈引入控制器，具有较好的控制稳定性和全局收敛性 | 编队灵活性和自适应性较弱，不适用于复杂队形控制 | [12]、[35]~[39] |
| 基于行为结构 | 可将复杂编队任务进行分解，自适应能力强 | 编队不同对象行为可能存在冲突，难以从数学角度进行定量分析，编队控制稳定性不高 | [40]~[45] |
| 图论结构 | 可描述复杂的编队结构，有利于解决大规模编队控制问题 | 实际应用时复杂性较高 | [46]~[48] |
| 势场结构 | 算法简明，灵活性高 | 易陷入局部最小点，势场配置随机性较强 | [49]~[50] |
| 组合结构 | 可发挥不同编队结构的优势 | 增加了编队控制的复杂度和不确定性 | [51]~[52] |
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CSV
| 算法名称 | 计算时间 | 是否总能找到最优路径 | 轨迹平滑度 | 缺陷和优势 |
| FM算法 | 较慢 | 否 | 平滑 | 使用简单、响应速度快，生成路径足够光滑且连续，但是生成路径离障碍物较近，缺乏安全性 |
| A*算法 | 较慢 | 是 | 不平滑 | 在面对多栅格地图的时候全局规划耗时长，且生成轨迹不平滑，但优势是总能找到最优路径 |
| RRT算法 | 较慢 | 否 | 不平滑 | 适用于求解复杂障碍空间路径规划问题，但是较小的搜索步长会极大增加计算时间，较大的搜索步长则可能无法求解，且RRT算法生成路径不是最优路径 |
| 优化算法 | 快 | 否 | 平滑 | 能够直接生成平滑轨迹，便于实现轨迹跟随，且在面对一些操纵性约束、避碰规则约束时更容易实现，缺点是容易陷入局部最优，而忽视全局最优解 |
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CSV
| 方法 | 优点 | 缺点 |
| PID | 实现简单，不依赖船舶编队运动模型 | 难以处理时滞、强惯性系统控制问题 |
| 滑模控制 | 响应快速，对参数变化和扰动不灵敏 | 难以消除抖振问题 |
| 反步法 | 使控制律设计过程结构化，能保证闭环系统的稳定性 | 难以构造李雅普诺夫函数 |
| 智能控制 | 能处理复杂的非线性、干扰、不确定性、时变等控制问题 | 难以定义控制目标以及从理论上分析控制鲁棒性和稳定性 |
| 模糊控制 | 能充分发挥专家经验在控制中的作用，通过控制规则描述系统变量的关系，处理非线性、时变问题较强 | 控制目标定义不明确 |
| 自抗扰控制 | 不依赖系统模型，通过设置过渡过程能有效解决超调与快速性之间的矛盾 | 对控制器参数敏感，且不大适用于解决多输入多输出控制问题 |
| 反馈线性化 | 使控制问题简化 | 非线性控制律比较复杂，对模型精度要求比较高 |
| 有限时间控制 | 能从理论上保证系统控制的快速收敛性 | 难以构造李雅普诺夫函数 |
| 最优控制 | 能处理约束以及显示定义控制目标 | 对模型精度要求比较高，难以处理不确定性干扰对控制的影响 |
| 模型预测控制 | 能显式处理多变量约束以及不确定性干扰对控制的影响 | 非线性优化问题求解速率较慢，有时难以满足实时性需求 |
DownLoad:
CSV
| 编队控制结构 | 优点 | 缺点 | 文献 |
| 领导-跟随结构 | 简单，易实现 | 领航者与跟随者之间相互独立，难以获得跟随者的跟踪反馈 | [26]~[33] |
| 虚拟结构 | 可将编队误差作为反馈引入控制器，具有较好的控制稳定性和全局收敛性 | 编队灵活性和自适应性较弱，不适用于复杂队形控制 | [12]、[35]~[39] |
| 基于行为结构 | 可将复杂编队任务进行分解，自适应能力强 | 编队不同对象行为可能存在冲突，难以从数学角度进行定量分析，编队控制稳定性不高 | [40]~[45] |
| 图论结构 | 可描述复杂的编队结构，有利于解决大规模编队控制问题 | 实际应用时复杂性较高 | [46]~[48] |
| 势场结构 | 算法简明，灵活性高 | 易陷入局部最小点，势场配置随机性较强 | [49]~[50] |
| 组合结构 | 可发挥不同编队结构的优势 | 增加了编队控制的复杂度和不确定性 | [51]~[52] |
| 算法名称 | 计算时间 | 是否总能找到最优路径 | 轨迹平滑度 | 缺陷和优势 |
| FM算法 | 较慢 | 否 | 平滑 | 使用简单、响应速度快，生成路径足够光滑且连续，但是生成路径离障碍物较近，缺乏安全性 |
| A*算法 | 较慢 | 是 | 不平滑 | 在面对多栅格地图的时候全局规划耗时长，且生成轨迹不平滑，但优势是总能找到最优路径 |
| RRT算法 | 较慢 | 否 | 不平滑 | 适用于求解复杂障碍空间路径规划问题，但是较小的搜索步长会极大增加计算时间，较大的搜索步长则可能无法求解，且RRT算法生成路径不是最优路径 |
| 优化算法 | 快 | 否 | 平滑 | 能够直接生成平滑轨迹，便于实现轨迹跟随，且在面对一些操纵性约束、避碰规则约束时更容易实现，缺点是容易陷入局部最优，而忽视全局最优解 |
| 方法 | 优点 | 缺点 |
| PID | 实现简单，不依赖船舶编队运动模型 | 难以处理时滞、强惯性系统控制问题 |
| 滑模控制 | 响应快速，对参数变化和扰动不灵敏 | 难以消除抖振问题 |
| 反步法 | 使控制律设计过程结构化，能保证闭环系统的稳定性 | 难以构造李雅普诺夫函数 |
| 智能控制 | 能处理复杂的非线性、干扰、不确定性、时变等控制问题 | 难以定义控制目标以及从理论上分析控制鲁棒性和稳定性 |
| 模糊控制 | 能充分发挥专家经验在控制中的作用，通过控制规则描述系统变量的关系，处理非线性、时变问题较强 | 控制目标定义不明确 |
| 自抗扰控制 | 不依赖系统模型，通过设置过渡过程能有效解决超调与快速性之间的矛盾 | 对控制器参数敏感，且不大适用于解决多输入多输出控制问题 |
| 反馈线性化 | 使控制问题简化 | 非线性控制律比较复杂，对模型精度要求比较高 |
| 有限时间控制 | 能从理论上保证系统控制的快速收敛性 | 难以构造李雅普诺夫函数 |
| 最优控制 | 能处理约束以及显示定义控制目标 | 对模型精度要求比较高，难以处理不确定性干扰对控制的影响 |
| 模型预测控制 | 能显式处理多变量约束以及不确定性干扰对控制的影响 | 非线性优化问题求解速率较慢，有时难以满足实时性需求 |
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