﻿ 基于多智能体联盟的多机协同空战任务分配
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Task allocation in cooperative air combat based on multi-agent coalition
Diao Xinghua, Fang Yangwang, Xiao Bingsong, Mao Donghui
Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xi'an 710038, China
Abstract:Multi-agent coalition formation theory was used to analyze the task allocation of multi-aircraft against multi-target in net warfare combat. The process of cooperative air combat task allocating was just the process of coalition formatting. First, the whole striking task to all the targets was separated into a serious of subtasks, then the subtasks were decomposed to some task cells that can be executed by single platform. Second, the models of coalition reward, the ability cost and the communication spending were constructed based on the definition of the coalition characteristic function which was set as the object function of the air combat task allocation. Finally, particle swarm optimization was adopted in the form of binary matrix particle coding to generate the coalition, and the feasibility checking strategy of the particle was designed. Simulation studies were carried out to confirm the rationality and validity of the method in the cooperative air combat task allocation.
Key words: cooperative air combat     task allocation     multi-agent coalition     characteristic function     discrete particle swarm optimization algorithm

1 基于联盟的任务分配 1.1 联盟任务分解

 图 1 任务分解结构图 Fig. 1 Structure of task decomposition
1.2 协同作战联盟问题描述

1) 作战飞机普遍具有多目标攻击能力,能同时跟踪多个目标,也能够同时给多枚导弹提供中制导信息.即允许每个Agent同时加入多个联盟.

2) 联盟内Agent间的协同有两种情形:

① 协同完成同一个任务单元.如果单架飞机的能力达不到完成相应任务的能力需求,则作战飞机之间协同完成.如多架作战飞机协同跟踪一个目标,提高跟踪精度;或协同攻击一个目标,提高目标的毁伤概率.如果单架飞机的能力能够达到相应任务需求,则不协同.

② 协同完成不同的任务单元.如我机发射、他机制导的攻击方式.

1.3 作战平台能力分析

1.3.1 探测优势

1) 角度优势.

2) 距离优势.

3) 探测能力优势.

CR为单部雷达探测能力[14].对其进一步处理,使其取值处于[0, 1].

1.3.2 攻击优势

1) 角度优势.

2) 距离优势.

3) 能量优势.

4) 导弹攻击能力优势.

2 特征函数定义

2.1 联盟报酬

1) 目标的价值量vTk.

2) 对目标的毁伤能力pk.

2.2 能力成本

1) 付出的能力.

2) 各平台所受的威胁.

2.3 通信开销

Strk<0,两机间无法通信,故通信开销为∞.

2.4 联盟生成问题的数学模型

1)联盟j的协同探测能力须满足跟踪任务能力需求.

2)联盟j的协同攻击能力须满足联盟攻击能力需求.

3)第m架飞机最多同时跟踪的目标数量为NmMAX_DET.

4)第m架飞机所携带的导弹数量为NmMAX_ATC.

3 基于离散粒子群的联盟生成算法 3.1 离散粒子群优化

3.2 二进制矩阵编码

 图 2 二进制矩阵粒子编码 Fig. 2 Binary matrix particle coding
3.3 编码可行性检查 3.3.1 列 检 查

3.3.2 行 检 查

1) 随机选择一行进行检查,如果该行不需调整,则进入下一行,如需要调整,进入步骤2),如果所有行均处理完毕,则结束调整;

2) 如果第i行需要调整,则依次检查本行中元素1所在的列,将该位置的1置0,计算所在列剩余的所有能力能否完成任务,能则将该位置1置0,进入步骤4);否则保留1不变,继续对该行中其他位置的1元素进行置0的尝试;如果遍历该行所有1元素,该行仍承担过多任务,则进入步骤3);

3) 如果第i行的剩余1元素都不可置0,且超出了该行所能承担的最大任务量,需对该行做如下调整:

① 计算各1元素所在列对应的目标的威胁值,并排序;

② 将威胁值较低的目标所对应的多余的1元素置0;

③ 对置0的元素所在列按照3.3.1 节列检查的方法,进行调整,若该列所选0元素所在行的1元素达到或超出能力范围,则不将其置为1.

4) 更新ai所承担的任务量,满足约束转步骤1),不满足则转步骤2).

① 依次将各列中1元素所对应的能力排序;

② 将能力最小的1元素置0,计算剩余1元素能否完成联盟任务.能则将该位置1置0,并重复执行该步骤,直到剩余1元素不能完成联盟任务;不能则保留1不变,结束该列的调整,进入下一列. 3.4 协同作战联盟生成算法

1) 初始化.按照3.2节的方案随机生成S个粒子.每个粒子的随机生成值即为初始位置矢量xi,速度矢量Vi设为0;对每个粒子中的两个矩阵进行编码可行性检查,形成初始种群,计算每个个体的适应度,选择适应度最大的粒子的位置为Pg,每个粒子的当前位置为Pi.

2) 按式(33)、式(34)更新种群中每个粒子的速度矢量和位置矢量,产生新一代种群.对新种群进行可行性检查,计算新种群中粒子的适应度,更新PiPg.

3) 如果有某个粒子陷在Pg上不动,则随机初始化该粒子的位置,并进行编码可行性检查.

4) 如果达到最大迭代次数,结束进化,得到最优粒子的位置和适应度,否则转步骤2).

4 实验结果与分析

 图 3 红蓝双方态势图 Fig. 3 Situation of the red and blue sides

 Agent 探测能力 攻击能力 bD1 bD2 bD3 bD4 bD5 bD6 bD7 bA1 bA2 bA3 bA4 bA5 bA6 bA7 a1 0.851 0.808 0.760 0.715 0.681 0.642 0.618 0.224 0.201 0.160 0.129 0.114 0.101 0.103 a2 0.834 0.897 0.834 0.782 0.736 0.688 0.658 0.217 0.250 0.217 0.174 0.138 0.121 0.107 a3 0.756 0.810 0.869 0.876 0.810 0.750 0.709 0.149 0.186 0.232 0.229 0.197 0.148 0.129 a4 0.680 0.714 0.779 0.843 0.909 0.843 0.779 0.120 0.135 0.159 0.202 0.250 0.202 0.159 a5 0.617 0.638 0.690 0.728 0.806 0.887 0.882 0.098 0.108 0.127 0.134 0.170 0.220 0.225 dik 0.81 0.86 0.88 0.89 0.90 0.87 0.85 0.16 0.19 0.22 0.24 0.26 0.19 0.17

 图 4 实验进化曲线 Fig. 4 Experimental evolution curve

 Agent C1 C2 C3 C4 C5 C6 C7 t1D t1A t2D t2A t3D t3A t4D t4A t5D t5A t6D t6A t7D t7A a1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 a3 0 0 0 0 0 0 1 1 0 1 0 0 0 0 a4 0 0 0 0 1 0 1 1 1 1 0 0 0 0 a5 0 0 0 0 0 0 0 0 0 0 1 1 1 1

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#### 文章信息

Diao Xinghua, Fang Yangwang, Xiao Bingsong, Mao Donghui

Task allocation in cooperative air combat based on multi-agent coalition

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(9): 1268-1275.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0564