Interception Mission Planning of USV Swarms for Normally Distributed Targets: Deployment Design, Scheme Implementation and Probability Calculation
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摘要: 移动目标出现的时空信息不确定性为水面无人艇(USV)集群拦截带来巨大挑战. 针对出现位置服从正态分布、出现时间服从均匀分布的水面移动目标, 开展USV集群对这类移动目标的拦截任务筹划研究. 首先, 在USV集群的布阵设计阶段, 结合目标出现位置的正态分布特性, 提出USV集群“非均匀”布阵设计方案, 生成与目标出现位置的正态分布特性相匹配的优化拦截线; 其次, 分别通过预设时间控制、领导者—跟随者控制等关键技术, 实现USV集群入阵、定速跟踪以及协同撤收, 三者共同完成USV集群对移动目标的拦截控制; 最后, 根据正态分布概率密度函数特性, 给出该拦截方案下USV集群对该类移动目标拦截概率的解析表达式. 研究表明, 该方案能显著应对目标出现的时空不确定性, 显著提升了对该类移动目标的拦截效能.Abstract: The spatiotemporal information uncertainty associated with emerging mobile targets presents a significant challenge for interception by unmanned surface vessel (USV) swarms. This paper addresses the problem of intercepting a surface mobile target whose emergence location follows a normal distribution and emergence time follows a uniform distribution. During the deployment design phase, a novel “non-uniform” deployment design scheme of the USV swarms is first introduced, generating an optimized interception line that matches the normal distribution characteristic of the target＇s location. The scheme then integrates prescribed-time and leader-following control laws to manage the entire interception cycle: Swarm deployment into formation, constant-speed tracking, and coordinated withdrawal. Finally, leveraging the properties of the normal distribution probability density function, an analytical expression for the interception probability under the proposed scheme is derived. Simulation studies demonstrate that the proposed scheme effectively counters the spatiotemporal uncertainty of target emergence and markedly enhances interception performance.
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Key words:
- normally distributed targets /
- USV swarms /
- target interception /
- swarm deployment /
- USV control
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图 4 第$ i $艘USV在$ t_p=30 $s时各个变量的收敛轨迹示意图
Fig. 4 Schematic diagram of the convergence trajectories of the state variables for the $ i $-th USV at the prescribed time $ t_p=30 $s
图 5 在控制算法(11)和(14)作用下, USV集群位置的连续仿真时间快照
Fig. 5 The successive simulation time snapshots of the positions of the USV swarm under control algorithms(11) and (14)
图 9 USV集群与移动目标的相对运动示意图
Fig. 9 Schematic diagram of the relative motion between the USV swarm and the moving target
图 10 第$ i $艘USV完成一次完整往返巡逻的相对探测区域
Fig. 10 The relative detection area of the $ i $-th USV completing one full round-trip patrol
图 11 拦截概率式(31)的仿真验证
Fig. 11 Verification on the interception probability given in (31)
图 12 非均匀布阵、均匀布阵和随机布阵下的拦截概率
Fig. 12 Interception probability under non-uniform, uniform and random deployment
表 1 USV动力学参数
Table 1 Dynamic parameters of USV
参数 符号 数值 单位 纵荡一阶阻尼 $ X_u $ −0.72 kg/s 纵荡二阶阻尼 $ X_{u|u|} $ −1.62 kg/m 横漂一阶阻尼 $ Y_v $ −0.86 kg/s 横漂二阶阻尼 $ Y_{v\left|v\right|} $ −56.30 kg/m 艏摇角一阶阻尼 $ N_r $ −1.90 kg·m2/s 艏摇角二阶阻尼 $ N_{r|r|} $ −6.40 kg·m2 
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表 2 各USV巡逻一周到达起始入阵点位的时刻(s)
Table 2 The time when each USV returns to its starting point after one patrol cycle(s)
第1次 第2次 第3次 USV1 $ t_0 = 30 $ s $ t_1 = 101.4 $ s $ t_2 = 172.8 $ s USV2 $ t_0 = 30 $ s $ t_1 = 101.4 $ s $ t_2 = 172.8 $ s USV3 $ t_0 = 30 $ s $ t_1 = 101.4 $ s $ t_2 = 172.8 $ s USV4 $ t_0 = 30 $ s $ t_1 = 101.4 $ s $ t_2 = 172.8 $ s
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