Edge-grouped Communication Mechanism-based Game Formation Control for Unmanned Surface Vehicles
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摘要: 针对大规模网络化无人艇集群面临的通信资源受限、成员收益最大化问题, 提出一种基于边分组通信机制的博弈编队控制方案. 首先, 构造具有时变纳什均衡点的代价函数, 使编队成员能够通过动态博弈过程最大化自身收益, 并逐步形成期望的编队构型; 同时, 为每个成员设计分布式状态估计器, 以降低博弈过程对全局信息的依赖. 其次, 考虑大规模集群系统多边并发通信易导致信道拥塞、延迟、丢包等问题, 边分组通信机制将通信边划分成组, 并由各组自主生成相互交错的通信时间序列, 使各边通信错峰进行, 在各自的通信时刻避免竞争. 最后, 通过理论分析与数值仿真验证了所提控制方案的有效性与优越性.Abstract: To address the problems of limited communication resources and individual payoff maximization in large-scale networked unmanned surface vehicles swarm, this paper proposes a game formation control scheme based on edge-grouped communication mechanism. First, cost functions with time-varying Nash equilibrium points are constructed, enabling formation members to maximize their individual payoffs through a dynamic game process while gradually forming the desired formation configuration; Meanwhile, a distributed state estimator is designed for each member to reduce the game process's dependence on global information. Second, concurrent communications over multiple edges in large-scale swarms systems may lead to channel congestion, delays, and packet loss. In this context, an edge-grouped communication mechanism is introduced, where communication edges are divided into groups, and each group autonomously generates mutually interleaved communication time sequences, allowing communications to be scheduled in a time-staggered manner and thus avoiding contention at their respective communication instants. Finally, the effectiveness and superiority of the proposed control scheme are validated through theoretical analysis and numerical simulations.
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图 4 平均振幅为0.15 m的模拟浪面
Fig. 4 The simulated wave surface with an average amplitude of 0.15 m
图 12 边(2, 1)、(3, 1)、(4, 1)、(1, 2)、(3, 2)、(1, 3)的通信间隔
Fig. 12 Communication intervals of edges (2, 1)、(3, 1)、(4, 1)、(1, 2)、(3, 2)、(1, 3)、(2, 3)、(4, 3)、(1, 4)、(3, 4)
图 13 边(2, 3)、(4, 3)、(1, 4)、(3, 4)的通信间隔
Fig. 13 Communication intervals of edges (2, 3)、(4, 3)、(1, 4)、(3, 4)
表 1 本文方法与其他相关方法对比
Table 1 Comparison between the proposed method and other related methods.
状态 通信方式 优点 局限性 相关文献 静态编队 连续通信 信息交互充分, 便于实现纳什均衡搜索与协同控制 通信负担较大, 难以适应受限带宽条件, 不适用于真实海洋环境 [19−24] 动态编队 连续通信 及时跟踪时变编队参考, 控制精度高 依赖高频持续交互, 易造成通信延迟、丢包等情况 [25−28] 动态编队 周期性
事件触发降低节点计算与通信负担, 并可避免Zeno现象 统一检测周期易引发同步广播与信道竞争 [32] 动态编队 交错周期
事件触发降低节点计算与通信负担, 并可缓解同步触发导致的竞争问题 多智能体系统规模增大时可扩展性受限 [33−34] 动态编队 动态事件触发 触发条件自适应性较强, 有助于进一步节约通信资源 以节点或局部簇为对象, 对并发通信交互协调考虑不足 [35−36] 动态编队 边分组通信机制 降低节点计算与通信负担, 并可从通信边层面实现错峰交互, 减少信道竞争并提升可扩展性 需要进行通信边分组与时序设计 本文 
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表 2 核心符号说明
Table 2 Explanation of core symbols
符号 含义 无人艇参数 $ x_i $、$ y_i $ 第$ i $艘艇在地固坐标系中的质心位置 $ \psi_i $ 第$ i $艘艇的艏向角 $ u_i $、$ v_i $、$ r_i $ 第$ i $艘艇的纵荡、横荡和艏摇速度 $ m_{u,\; i} $、$ m_{v,\; i} $、$ m_{r,\; i} $ 第$ i $艘艇在对应方向上的惯性质量 $ \tau_{u,\; i} $、$ \tau_{r,\; i} $ 第$ i $艘艇的控制输入 $ d_{u,\; i} $、$ d_{v,\; i} $、$ d_{r,\; i} $ 第$ i $艘艇所受外部扰动 $ {{\boldsymbol{\eta}}_{\boldsymbol{i}}} $ 第$ i $艘艇坐标变换后的位置向量 $ {{\boldsymbol{\tau}}_{\boldsymbol{i}}} $ 第$ i $艘艇控制输入向量 算法与控制参数 $ \hat{k}_i $、$ k_{0i}\sim k_{8i} $ 各类控制增益, 均为正常数 $ \bar{k} $ 控制增益, 正常数 $ \alpha_i $ 双曲正切函数参数, 满足$ \alpha_i \gg 1 $ $ \xi_i $ 与未知项上界相关的常数 $ \hat{\xi}_i $ $ \xi_i $的估计值 $ \tilde{\xi}_i $ $ \xi_i $的估计误差, $ \tilde{\xi}_i=\xi_i-\hat{\xi}_i $ $ \kappa_1 $、$ \kappa_2 $、$ \kappa_3 $、$ K_4 $、$ K_9 $、$ \sigma $ 通信机制相关正常数, $ \sigma \in [0,\; 1) $ $ P $ 通信检测周期 $ \bar{N} $ 通信边总分组数量 博弈与编队参数 $ J_i $ 第$ i $艘艇的代价函数 $ {{\boldsymbol{\eta}}^{\bf{*}}} $ $ {{\boldsymbol{\eta}}} $对应的纳什均衡点 $ {{\boldsymbol{p}}_{\bf{0}}} $ 编队期望轨迹向量 $ {{\boldsymbol{\delta}}_{\boldsymbol{i}}} $ 第$ i $艘艇相对参考轨迹的位置偏移向量 $ \Delta $ 编队跟踪误差允许的小正常数 通信相关参数 $ {\hat{{\boldsymbol{\eta}}}_{\boldsymbol{i}}} $ 第$ i $艘艇位置$ {{\boldsymbol{\eta}}_{\boldsymbol{i}}} $的估计值 $ {\hat{{\boldsymbol{v}}}_{\boldsymbol{i}}} $ 第$ i $艘艇对期望速度$ {\dot{{\boldsymbol{\eta}}}_{\bf{0}}} $的估计值 $ {\bar{{\boldsymbol{\eta}}}_{\boldsymbol{i}}} $ 第$ i $艘艇的参考状态向量 $ {\hat{{\boldsymbol{\delta}}}_{{\boldsymbol{ij}}}} $ 第$ i $艘艇对第$ j $艘艇耦合误差的估计值 $ t_{l_{ik}}^{ik} $ 第$ k $艘艇向第$ i $艘艇进行通信的时刻 $ {{\boldsymbol{e}}_{{\bf{1}}{\boldsymbol{ik}}}}\sim {{\boldsymbol{e}}_{{\bf{8}}{\boldsymbol{ik}}}} $ 各类测量或观测误差向量 $ \gamma_i $ 通信指示变量, $ \gamma_i \in \{0,\; 1\} $ 图论相关参数 $ \mathcal{V} $ 图的节点集, 即无人艇集合 $ \mathcal{E} $ 图的边集, 即艇间通信链路集合 $ \mathcal{A} $ 图的邻接矩阵 $ \mathcal{L} $ 图的拉普拉斯矩阵 $ A_i $ 控制输入系数矩阵 $ \Lambda $、$ \beta $ 图论相关对角矩阵 仿真验证相关参数 $ B_{ij} $ 信道竞争率 $ l $ 径向基函数神经网络节点数量 $ b_i $、$ \mu_i $ 径向基函数神经网络高斯函数参数
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表 3 参数选择
Table 3 Parameter selections
种类 参数值$ (i\in {\cal{V}},\; (k,\; i)\in {\cal{E}}) $ 控制增益 $ {{\hat{k}}_{i}}=\bar{k}=10 $, $ {{k}_{0i}}={{k}_{1i}}=1 $, $ {{k}_{2i}}=0.5 $,
$ {{k}_{3i}}={{k}_{4i}}={{k}_{5i}}={{k}_{6i}}={{k}_{7i}}={{k}_{8i}}=25 $, $ {{K}_{9}}=0.01 $, $ {{\hat{\xi }}_{i}}(0)=3 $, $ \alpha =100 $, $ {{l}_{0}}=0.001 $通讯管理 $ {{\kappa }_{1}}=0.0001 $, $ {{\kappa }_{2}}=0.001 $, $ {{\kappa }_{3}}=1 $, $ \sigma =0.9 $, $ \bar{N}=3 $, $ P=0.006 $, $ {{\chi }_{ik}}(0)=100 $ 径向基神经网络 $ l=20 $, $ {{b}_{i}}=0.6 $, $ {{\boldsymbol{\mu}}_{i}}\in [-2,\; \ 6]\times [-2,\; \ 6]\times [-2,\; \ 2] $
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表 4 两种机制下的通信总数
Table 4 Total number of communications under two mechanisms
边 (2, 1) (3, 1) (4, 1) (1, 2) (3, 2) (1, 3) (2, 3) (4, 3) (1, 4) (3, 4) 总计 EGCM 15 365 17 656 14 282 18 557 17 656 18 557 13 837 14 282 18 557 17 656 166 405 NBPETCM 15 895 17 963 16 359 20 335 17 963 20 335 15 895 16 359 20 335 17 963 179 402
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表 5 参数选择
Table 5 Parameter selection
种类 参数值$ (i\in {\cal{V}},\; (k,\; i)\in {\cal{E}}) $ 控制增益 $ {{\hat{k}}_{i}}=\bar{k}=10 $, $ {{k}_{0i}}={{k}_{1i}}=1 $, $ {{k}_{2i}}=0.5 $, $ {{k}_{3i}}={{k}_{4i}}={{k}_{5i}}={{k}_{6i}}={{k}_{7i}}={{k}_{8i}}=25 $, $ {{K}_{9}}=0.01 $, $ {{\hat{\xi }}_{i}}(0)=3 $, $ \alpha =100 $, $ {{l}_{0}}=0.001 $ 通讯管理 $ {{\kappa }_{1}}=0.0001 $, $ {{\kappa }_{2}}=0.001 $, $ {{\kappa }_{3}}=1 $, $ \sigma =1 $, $ \bar{N}=3 $, $ P=0.008 $, $ {{\chi }_{ik}}(0)=1000 $ RBFNNs $ l=20 $, $ {{b}_{i}}=0.6 $, $ {{\boldsymbol{\mu}}_{i}}\in [-2,\; 6]\times [-2,\; 6]\times [-2,\; 2] $
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