Formation Control for Multiple Unmanned Surface Vehicles Under Large Transmission Delays: A Collision-free Algorithm With Motion Region Constraints
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摘要: 针对无人艇集群组网系统, 研究艇间数据传输存在长通信时延(时延不确定且长于通信触发间隔)限制的分布式编队控制问题. 在编队形成方面, 设计一种基于受限博弈理论的安全编队控制算法. 该算法提出采用不等式约束限制无人艇期望编队区域, 并采用等式约束确保最终编队精度, 能够在实现高编队精度的同时适配任意运动区域约束, 摆脱了传统方法无法实现指定区域内期望队形形成、最终编队位置严格依赖于编队初始位置以及仅适配特殊受限区域等问题. 在长通信时延方面, 设计一种基于历史触发信息记忆与加权补偿的艇间通信机制. 该机制能够通过所记忆的历史触发信息以及当前采样误差, 结合自身控制律设计相关性质, 有效估计并修正时延导致的艇间信息更新误差, 增强了所提算法在时延限制下的控制鲁棒性. 李雅普诺夫稳定性分析和仿真实验验证了所提算法的有效性.Abstract: For networked unmanned surface vehicles, we investigate the distributed formation control problem subject to large communication delays in inter-vehicle data transmission, where the delay is uncertain and longer than the communication triggering interval. For formation shaping, we develop a safe formation control algorithm based on constrained game theory. This algorithm employs inequality constraints to limit the desired formation region of unmanned surface vehicles and applies equality constraints to ensure the final formation accuracy, thus simultaneously achieving high formation accuracy and the adaptation of arbitrary motion region constraints. This algorithm overcomes the drawbacks of traditional methods, such as the inability to form the desired formation within a specified area, the strict dependence of the final formation position on the initial formation position, and the limitation of only being applicable to special restricted areas. For large transmission delays, an inter-vehicle communication mechanism based on historical triggering-information memory and weighted compensation is developed. By exploiting the memorized historical triggering information, the current sampling error, and the properties of the designed control command, such a mechanism can effectively estimate and compensate for information updating errors caused by large transmission delays, thereby enhancing system robustness under large delays. Lyapunov stability analysis and simulation results verify the effectiveness of the proposed algorithm.
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图 1 具备长通信时延鲁棒性的受限博弈集群控制算法框架
Fig. 1 Constrained game-based framework diagram for large delay-robust algorithm
图 3 无人艇集群相对距离演化(考虑不等式约束)
Fig. 3 Inter-vehicle distance evolution of the vehicle swarm (considering inequality constraints)
图 6 无人艇集群轨迹演化(复杂受限区域)
Fig. 6 Trajectory evolution of the unmanned surface vehicle swarm (complicated constrained area)
表 1 所提算法相关的控制参数增益
Table 1 Control parameter gains related to the proposed algorithm
Trule控制参数项 控制增益($ i \in {\cal{I}} $) 无人艇初始状态(单位: $ [ \text{m};\text{m};\text{rad} ] $) $ {{\boldsymbol{\eta}}_{1}}={{[ 18;16;{\pi }/{3}\; ]}} $, $ {{\boldsymbol{\eta}}_{2}}={{[ 0;30;{\pi }/{6}\; ]}} $, $ {{\boldsymbol{\eta}}_{3}}={{[ -24;9;-{\pi }/{2}\; ]}} $, $ {{\boldsymbol{\eta}}_{4}}={{[ 25;-18;-{\pi }/{6}\; ]}} $ 无人艇期望轨迹跟踪控制器 $ k_p = 10,\; \ k_d = 10 $ 分布式纳什均衡点搜索 $ k_1 = 10,\; \ k_2 = 3,\; \ k_3 = 1,\; \ k_4 = 1 $ 个体代价函数 $ \mu_{0i} = 0.01,\; \ \mu_{1i} = 1,\; \ \mu_{2i} = 0.3 $ 具备大时延鲁棒性的事件触发机制 $ D_i = 3,\; \ \tilde{\lambda}_i = 0.008,\; \ \gamma_{l_i,\; i} = 1,\; \ \tilde{\lambda}_{W_i} = 1.2,\; \ \bar{\rho}_i = 0.8 $ 期望编队构型设计 $ d_F = 5,\; \ \delta_i^{bias} = [\sin(2\pi i/N); \cos(2\pi i/N); 0] $ 海流干扰 波浪平均幅值$ 0.1\,\; \text{m} $, 海流速度$ 0.15\,\; \text{m/s} $, 海洋扰动方向$ 45^\circ $ 
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表 2 两种通信算法下性能指标对比
Table 2 Comparison of performance indicators under two distinct communication algorithms
性能指标 LDRSEC(21) CETC(67) 时延累积误差$ E_{d} $ 7 095.411 3 14 227.619 8 触发累积误差$ E_{t} $ 3 151.231 9 9 780.934 1 平均信息新鲜度$ {F}_{d} $ 0.339 8 3.818 1 平均触发次数$ N_{t} $ 350.25 52.00 平均触发间隔$ T_{ave} $ 0.428 1 2.921 6
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