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题 目 多无人机协同任务规划
摘 要:
本文研究了多无人机协同任务规划问题,结合无人机特性,建立了分层规
划模型,并使用改进的遗传算法显著提升了规划效率和精度,取得了如下成果:
问题一研究了无人机协同侦查任务规划。首先建立了分层规划模型,根据
敌方目标分布特性,以总滞留时间最少为目标,将任务分解为三层模型:(1)
目标群路线规划;(2)群内目标路线规划;(3)基于传感器性能的航迹优化。
将模型抽象为不确定数量的多起点开环多旅行商问题(MDO_MTSP),并使用
无性繁殖策略的多岛遗传算法,以较高的计算效率求得了最优的无人机数量、
路线以及航迹。还建立了全局规划模型,其结果与分层规划模型基本一致,两
者误差仅为 0.32%,分层规划模型结果在处理复杂模型时,不仅给出了更优解,
还在效率和资源占用方面远远优于全局规划模型。
问题二研究了带通信约束的无人机调度问题。在完全不增加滞留时间的情
况下,仅通过调整 FY-1 型无人机的起飞策略,根据问题一的路线将无人机间距
降到了最小值,使得通信中继无人机能尽可能多地同时为多架无人机保障通信,
降低了对 FY-2 型无人机的需求,并求出了 FY-2 型无人机的最少架次。
问题三研究了考虑目标威胁程度的无人机打击任务规划问题。应用本文提
出的分层规划思想,考虑敌方目标的特殊分布,参考匈牙利算法将任务分解为
三层模型:(1)雷达目标之间的路线规划;(2)打击雷达目标的航迹规划;(3)
打击非雷达目标的路线和航迹规划。将三层模型分别抽象为背包问题、带几何
约束的连续模型最优问题以及资源协同分配问题,分别使用了非线性内点法和
遗传算法对第二层模型进行求解,并分析了两种算法处理不同问题的性能,最
2
终通过建立资源矩阵和调度矩阵规划了第三层的路线和航迹。
问题四研究了多种威胁目标的无人机打击任务规划问题。基于问题三的结
论,进一步考虑两种雷达的威胁程度,将模型分解为四层:(1)远程雷达之间
的路线规划;(2)打击远程雷达的航迹规划;( 3)剩余普通雷达打击路线规划;
(4)无雷达目标打击路线规划。通过分层简化模型,在求解第三第四层路线时
直接使用问题三的算法得出了结果。
问题五研究了算法复杂度以及无人机参数对作战效能的影响。首先论证了
分层规划模型的科学性,详细分析了分层规划模型的算法的时间复杂度以及该
模型在应对复杂目标情况的优化性能,阐述了分层规划模型在效率、解的规模
以及灵活性方面对于全局优化模型的巨大优势。根据所建模型,讨论了无人机
各项参数对于优化结果的影响,给出了提高无人机作战能力的改进方案。
关键词:分层规划、全局规划、多岛遗传算法、威胁程度、时间复杂度
3
目录
一、问题重述 ··································································································· 4
二、模型假设 ··································································································· 5
三、符号说明 ··································································································· 6
四、问题一求解 ································································································ 6
4.1 问题分析 ····························································································· 6
4.2 模型建立 ····························································································· 8
4.2.1 第一层路线规划 ············································································ 8
4.2.2 第二层路线规划 ············································································ 9
4.2.3 第三层航迹规划 ··········································································· 10
4.3 侦查路线规划模型求解 ·········································································· 12
4.3.1 遗传算法的实现 ··········································································· 13
4.3.2 分层规划模型求解 ········································································ 14
4.3.3 全局规划模型求解 ········································································ 16
4.3.4 两种模型的对比 ··········································································· 18
五、问题二求解 ······························································································· 19
5.1 问题分析 ···························································································· 19
5.2 调度策略的调整 ··················································································· 19
5.3 FY-2 型无人机调度方案 ·········································································· 22
六、问题三求解 ······························································································· 22
6.1 问题分析 ···························································································· 22
6.1.1 打击单个雷达的滞留时间 ······························································· 23
6.1.2 打击多个雷达的滞留时间 ······························································· 24
6.2 目标打击三层规划模型 ·········································································· 25
6.2.1 第一层路线规划 ··········································································· 26
6.2.2 第二层航迹规划 ··········································································· 26
6.2.3 第三层路线和航迹规划 ·································································· 28
6.2.4 规划结果 ···················································································· 30
七、问题四求解 ······························································································· 32
7.1 问题分析 ···························································································· 32
7.2 远程雷达四层规划模型 ·········································································· 33
7.2.1 第一层路线规划 ··········································································· 33
7.2.2 第二层航迹规划 ··········································································· 34
7.2.3 第三层路线规划 ··········································································· 35
7.2.4 第四层路线和航迹规划 ·································································· 35
7.2.5 规划结果 ···················································································· 35
八、问题五 ····································································································· 36
8.1 分层规划模型的效率和复杂度分析 ··························································· 36
8.2 优化算法分析 ······················································································ 37
8.3 无人机参数分析 ··················································································· 37
参考文献 ········································································································ 39
附录 ·············································································································· 39
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4
多无人机协同任务规划
一、问题重述
无人机(Unmanned Aerial Vehicle,UAV)是一种具备自主飞行和独立执行
任务能力的新型作战平台,不仅能够执行军事侦察、监视、搜索、目标指向等
非攻击性任务,而且还能够执行对地攻击和目标轰炸等作战任务。随着无人机
技术的快速发展,越来越多的无人机将应用在未来战场。
某无人机作战部队现配属有 P01~P07 等 7 个无人机基地,各基地均配备一
定数量的 FY 系列无人机(各基地具体坐标、配备的无人机类型及数量见附件 1,
位置示意图见附件 2)。其中 FY-1 型无人机主要担任目标侦察和目标指示,FY-2
型无人机主要担任通信中继,FY-3 型无人机用于对地攻击。FY-1 型无人机的巡
航飞行速度为 200km/h,最长巡航时间为 10h,巡航飞行高度为 1500m;FY-2
型、FY-3 型无人机的巡航飞行速度为 300km/h,最长巡航时间为 8h,巡航飞行
高度为 5000m。受燃料限制,无人机在飞行过程中尽可能减少转弯、爬升、俯
冲等机动动作,一般来说,机动时消耗的燃料是巡航的 2~4 倍。最小转弯半径
70m。
FY-1 型无人机可加载 S-1、S-2、S-3 载荷。其中载荷 S-1 系成像传感器,
采用广域搜索模式对目标进行成像,传感器的成像带宽为 2km(附件 3 对成像
传感器工作原理提供了一个非常简洁的说明,对性能参数进行了一些限定,若
干简化亦有助于本赛题的讨论);载荷 S-2 系光学传感器,为达到一定的目标识
别精度,对地面目标拍照时要求距目标的距离不超过 7.5km,可瞬时完成拍照
任务;载荷 S-3 系目标指示器,为制导炸弹提供目标指示时要求距被攻击目标
的距离不超过 15km。由于各种技术条件的限制,该系列无人机每次只能加载
S-1、S-2、S-3 载荷中的一种。为保证侦察效果,对每一个目标需安排 S-1、S-2
两种不同载荷各自至少侦察一次,两种不同载荷对同一目标的侦察间隔时间不
超过 4 小时。
为保证执行侦察任务的无人机与地面控制中心的联系,需安排专门的 FY-2
型无人机担任通信中继任务,通信中继无人机与执行侦察任务的无人机的通信
距离限定在 50km 范围内。通信中继无人机正常工作状态下可随时保持与地面
控制中心的通信。
FY-3 型无人机可携带 6 枚 D-1 或 D-2 两种型号的炸弹。其中 D-1 炸弹系某
种类型的“灵巧”炸弹,采用抛投方式对地攻击,即投放后炸弹以飞机投弹时的
速度作抛物运动,当炸弹接近目标后,可主动寻的攻击待打击的目标,因此炸
弹落点位于目标中心 100m 范围内可视为有效击中目标。D-2 型炸弹在激光制导
模式下对地面目标进行攻击,其飞行速度为 200m/s,飞行方向总是指向目标。
攻击同一目标的 D-2 型炸弹在整个飞行过程中需一架 FY-1 型无人机加载载荷
S-3 进行全程引导,直到命中目标。由于某些技术上的限制,携带 D-2 型炸弹
的无人机在投掷炸弹时要求距目标 10km~30km,并且要求各制导炸弹的发射点
到目标点连线的大地投影不交叉(以保证弹道不交叉)。为达到一定的毁伤效果,
对每个目标(包括雷达站和远程搜索雷达)需成功投掷 10 枚 D-1 型炸弹,而对
同一目标投掷 2 枚 D-2 型炸弹即可达到相同的毁伤效果。
5
多架该型无人机在同时执行任务时可按照一定的编队飞行,但空中飞行时
两机相距要求 200m 以上。由于基地后勤技术保障的限制,同一基地的两架无
人机起飞时间间隔和降落回收的时间间隔要求在 3 分钟以上。无人机执行完任
务后需返回原基地。
根据任务要求,需完成侦察和打击的目标有 A01~A10 等 10 个目标群,每
个目标群包含数量不等的地面目标,每个目标群均配属有雷达站(目标以及各
目标群配署雷达的位置示意图见附件 2,具体坐标参数见附件 4),各目标群配
属雷达对 FY 型无人机的有效探测距离为 70km。
需要研究以下问题:
(1)一旦有侦察无人机进入防御方某一目标群配属雷达探测范围,防御方
10 个目标群的配属雷达均开机对空警戒和搜索目标,并会采取相应对策,包括
发射导弹对无人机进行摧毁等,因此侦察无人机滞留防御方雷达探测范围内时
间越长,被其摧毁的可能性就越大。现需为 FY-1 型无人机完成 10 个目标群(共
68 个目标)的侦察任务拟制最佳的路线和无人机调度策略(包括每架无人机起
飞基地、加载的载荷、起飞时间、航迹和侦察的目标),以保证侦察无人机滞留
防御方雷达有效探测范围内的时间总和最小。
(2)FY-1 型无人机对目标进行侦察时,须将侦察信息实时通过 FY-2 型无
人机传回地面控制中心。鉴于 50km 通信距离的限制,需安排多架 FY-2 型无人
机升空,以保证空中飞行的侦察无人机随时与 FY-2 型无人机的通信。FY-2 型
无人机可同时与多架在其有效通信范围的侦察无人机通信并转发信息。为完成
问题(1)的侦察任务,至少安排多少架次的 FY-2 型通信中继无人机?
(3)所有 FY-1 型无人机现已完成侦察任务并返回基地,均可加载载荷 S-3
用于为制导炸弹提供目标指示。现要求在 7 个小时内(从第一架攻击无人机进
入防御方雷达探测范围内起,到轰炸完最后一个目标止)完成对 10 个目标群所
有 68 个地面目标的火力打击任务,如何进行任务规划以保证攻击方的无人机滞
留防御方雷达有效探测范围内的时间总和最小?请给出具体的无人机任务规划
结果(包括每架无人机飞行路线、FY-3 型无人机携带炸弹的具体清单和攻击的
目标清单)。
(4)由相关信息渠道获知在 A02、A05、A09 周边可能还配置有三部远程
搜索雷达,该雷达对 FY 型无人机的有效作用距离是 200km。这三部雷达的工
作模式是相继开机工作,即只有首先开机的雷达遭到攻击后才开启第二部雷达,
同样只有第二部雷达被攻击后才开启第三部雷达。远程搜索雷达一旦开机工作,
攻击方无人机群即可获知信号并锁定目标,而后安排距其最近的无人机对其摧
毁。请基于防御方部署远程搜索雷达的情形重新考虑问题(3)。
(5)请对求解模型的算法的复杂度进行分析;并讨论如何有效地提高算法
的效率,以增强任务规划的时效性。基于你们小组构建的数学模型和对模型解
算的结果,讨论哪些技术参数的提高将显著提升无人机的作战能力?
二、模型假设
1、同一型号的无人机各项参数如速度、最长巡航时间等完全相同,忽略因
制造工艺产生的性能差异。
2、无人机在执行任务过程中没有损失,即无人机从起飞至返回基地降落,