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摘要: 研究了船舶编队控制的特点，从船舶编队控制结构、编队路径规划、编队运动建模和编队运动控制4个方面分别对现状和方法进行分析；介绍了船舶编队控制原理，描述了船舶编队领导-跟随结构、虚拟结构、图论结构、基于行为结构的数学表示方法及应用场景；针对船舶编队路径规划，总结了编队环境建模、全局路径规划和局部避碰规划等最新方法及其特点，展示了基于粒子群优化算法的船舶编队局部避碰效果；针对船舶编队控制运动建模，构建了考虑干扰、控制时延和约束的船舶编队水动力模型，并将该模型在船舶编队过闸控制场景中进行了验证；针对船舶编队运动控制，归纳了典型集中式、分散式和分布式编队控制器特点，指出分布式编队控制器具有更好的鲁棒性和可扩展性，设计了基于分布式模型预测控制的编队航行控制器。研究结果表明：目前船舶编队控制技术瓶颈主要体现在有人/无人编队共融、岸端驾控为主的内河船舶编队控制、不确定干扰下的船舶编队控制、通信受限下船舶编队鲁棒控制、特殊水域船舶编队控制和船舶编队控制一致性等方面；在未来船舶编队发展中，应重点解决船舶编队分布式协同控制、船舶编队任务多元化控制、基于生物群体机制的船舶编队控制、特殊水域船舶编队控制、人工智能技术在船舶编队控制中的应用等问题。Abstract: The characteristics of ship formation control were studied, and its current situation and methods were analyzed from the aspects of the structure of ship formation control, formation path planning, formation motion modeling, and formation motion control. The principle of ship formation control was introduced, and the mathematical representation methods and application scenarios of leader-follower structure, virtual structure, graph theory structure, and behavior-based structure of ship formations were described. For the path planning of ship formations, the latest methods and characteristics of formation environment modeling, global path planning, and local collision avoidance planning were summarized, and the local collision avoidance effect of ship formations based on the particle swarm optimization algorithm was demonstrated. For the motion modeling of ship formation control, a hydrodynamic model of ship formations considering the disturbance, control delay, and constraints was built and verified in the contral scenario of a ship formation passing through the lock waterway. For the motion control of ship formations, the characteristics of typical centralized, decentralized, and distributed formation controllers were summarized. It was pointed out that the distributed formation controller had better robustness and scalability, and hence, a formation navigation controller based on the distributed model predictive control was designed. Analysis results show that the technical bottleneck of ship formation control is mainly reflected in the aspects such as the integration of manned/unmanned formations, inland ship formation control mainly based on shore-side driving and control, ship formation control under uncertain disturbances, robust ship formation control under communication constraints, ship formation control in special waters, and consistency of ship formation control. In the future development of ship formations, the following key problems should be addressed: distributed collaborative control of ship formations, diversified control of ship formation tasks, ship formation control based on the biological group mechanism, ship formation control in special waters, and application of artificial intelligence technology in ship formation control.
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图 4 有向图与无向图船舶编队结构
Figure 4. Directed graph and undirected graph based ship formation structures
图 9 基于粒子群优化的船舶编队避碰路径
Figure 9. Anti-collision path of ship formation based on particle swarm optimization
图 15 船舶编队分布式模型预测控制器设计
Figure 15. Design for distributed model predictive controller of ship formation
表 1 不同船舶编队控制结构特点
Table 1. Features of different ship formation control structures
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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表 2 不同全局路径规划算法对比
Table 2. Comparison of different global path planning algorithms
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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表 3 不同船舶编队运动控制方法对比
Table 3. Comparison of different ship formation control methods
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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