基于运动约束的无人机编队一致性优化算法

doi:10.12305/j.issn.1001-506X.2025.01.24

摘要/Abstract

摘要：

针对无人机运动约束下的编队任务研究标准二阶一致性控制算法的优化问题。首先, 结合编队信息, 基于虚拟结构法思想, 设计含虚拟参考点的二阶一致性编队控制算法, 使得编队收敛于指定队形, 解决标准二阶一致性控制算法的收敛状态与各无人机初值有关以及收敛位置趋于一致的问题, 得到编队渐近收敛的条件。其次, 引入饱和函数得到运动约束条件下的渐近收敛的二阶一致性编队控制算法, 设计无人机编队高度、航向、速度通道控制器。最后, 设计无人机编队队形集结仿真实验, 对比相同饱和函数不同一致性方法的编队控制算法、相同一致性方法不同饱和函数的编队控制算法, 验证了优化算法的有效性和快速性。

关键词: 无人机编队, 一致性编队控制算法, 虚拟参考点, 运动约束, 饱和函数

Abstract:

For formation tasks under unmanned aerial vehicle (UAV) motion constraints, optimization problem of standard second-order consensus control algorithm is studied. First of all, based on the formation information, the second-order consensus formation control algorithm with virtual reference point is designed, which makes the formation converge to the specified formation. The problem that the convergence state of the standard second-order consensus control algorithm is related to the initial value of each UAV and the convergence position tends to agree is solved. And the condition of asymptotic convergence of formation is obtained. Secondly, the saturation function is introduced to design the asymptotically converged second-order consensus formation control algorithm under the motion constraint, and then designed the UAV formation altitude, heading and velocity channel controller. Finally, simulation experiment of UAV formation assembly is designed to compare the formation control algorithm with different consensus methods of the same saturation function and the formation control algorithm with different saturation function of the same consensus method, and verify the effectiveness and speed of the optimization algorithm.

Key words: unmanned aerial vehicle (UAV) formation, consensus formation control algorithm, virtual reference point, motion constraint, saturation function

中图分类号:

V279

刘金鑫, 盛蔚, 张玉民. 基于运动约束的无人机编队一致性优化算法[J]. 系统工程与电子技术, 2025, 47(1): 230-243.

Jinxin LIU, Wei SHENG, Yumin ZHANG. Optimization algorithm for UAV formation consensus based on motion constraint[J]. Systems Engineering and Electronics, 2025, 47(1): 230-243.

图/表 13

图1

表1

图2

图3

表2

第120 s时编队内各无人机的实时状态"

仿真组别	编队内各无人机的实时位置/m	编队内各无人机的实时东向速度和北向速度/(m/s)	编队内各无人机的实时航向角/(°)
仿真(I)	$\left[\begin{array}{ccccc}394.375 & 394.165 & 394.181 & 394.339 & 394.630 \\ -11.490 & -11.4832 & -11.4712 & -11.4589 & -11.4508 \\ 5.00000 & 5.00000 & 4.99998 & 4.99999 & 4.99997\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccccc}3.56881 & 3.56688 & 3.56460 & 3.56213 & 3.56037 \\ -0.00341 & -0.00393 & -0.00479 & -0.00571 & -0.00628\end{array}\right]^{\mathrm{T}}$	$ [90.005 490.005490 .005490 .005490 .0054]^ \mathrm{T}$
仿真(II)	$\left[\begin{array}{llllll}371.476 & 371.263 & 371.225 & 371.324 & 371.567 \\7.40682 & 7.46003 & 7.52758 & 7.59523 & 7.64975 \\4.99996 & 4.999 91 & 4.99992 & 4.99992 & 4.99992\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccccc}3.55669 & 3.55826 & 3.55939 & 3.56078 & 3.56179 \\ -0.00037 & -0.00282 & -0.00588 & -0.00895 & -0.01146\end{array}\right]^{\text {T }}$	$[90.005 490.005490 .005490 .005490 .0054]^ \mathrm{T}$
仿真(Ⅲ)	$\left[\begin{array}{ccccc}479.654 & 484.683 & 474.705 & 489.701 & 469.793 \\-0.01728 & -4.99829 & -5.00132 & -9.98384 & -9.98558 \\5.00000 & 5.00000 & 5.00000 & 5.00000 & 4.99999\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccccc}3.99660 & 3.99647 & 3.99394 & 3.99501 & 3.99134 \\ 0.00087 & -0.00008 & 0.00007 & -0.00081 & -0.00073\end{array}\right]^{\mathrm{T}}$	$ [90.005 490.005490 .005490 .005490 .0054]^{\text {T }}$
仿真(Ⅳ)	$\left[\begin{array}{ccccc}479.650 & 484.628 & 474.666 & 489.626 & 469.690 \\ -0.01648 & -4.96923 & -4.94400 & -9.89885 & -9.87957 \\ 5.00001 & 5.00002 & 5.00001 & 5.00002 & 5.00001\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccccc}3.99630 & 3.99753 & 3.99649 & 3.99895 & 3.99665 \\ 0.00082 & -0.00155 & -0.00282 & -0.00509 & -0.00607\end{array}\right]^{\mathrm{T}}$	$[90.005 490.005490 .005490 .005490 .0054]^ \mathrm{T}$

表2

表3

第120 s时编队内各无人机实时状态与其理想状态的误差"

仿真组别	编队内各无人机的实时位置与其理想位置的误差/m	编队内各无人机的实时东向速度和北向速度与各自理想速度的误差/(m/s)	编队内各无人机实时航向角与其理想航向角误差/(°)
仿真(I)	$\left[\begin{array}{ccccc}-85.625 & -90.835 & -80.819 & -95.661 & -75.370 \\ -11.4906 & -6.4832 & -6.4712 & -1.4589 & -1.4508 \\ -0.00003 & -0.00007 & -0.00008 & -0.00008 & -0.00009\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lllllll}-0.43119 & -0.43312 & -0.43540 & -0.43787 & -0.43963 \\ -0.00341 & -0.00393 & -0.00479 & -0.00571 & -0.00628\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{llllll}0.0054 & 0.0054 & 0.0054 & 0.0054 & 0.0054\end{array}\right]^{ \mathrm{T}}$
仿真(II)	$\left[\begin{array}{ccccc}-108.524 & -113.737 & -103.775 & -118.676 & -98.443 \\ 7.4068 & 12.4600 & 12.5275 & 17.5951 & 17.6495 \\ -0.00004 & -0.00009 & -0.00008 & -0.00008 & -0.00008\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lllllll}-0.44331 & -0.44174 & -0.44061 & -0.439 & 22 & -0.438 21 \\ -0.00037 & -0.00282 & -0.00588 & -0.008 & 95 & -0.01146\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lllllll}0.0054 & 0.0054 & 0.0054 & 0.0054 & 0.0054\end{array}\right]^{ \mathrm{T}}$
仿真(Ⅲ)	$\left[\begin{array}{lllll}-0.346 & -0.317 & -0.295 & -0.299 & -0.207 \\ -0.0173 & 0.0017 & -0.0013 & 0.0161 & 0.0144 \\ 0.00000 & 0.00000 & 0.00000 & 0.00000 & 0.00001\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{cccccc}-0.00340 & -0.00353 & -0.00606 & -0.00499 & -0.00866 \\ 0.00087 & -0.00008 & 0.00007 & -0.00081 & -0.00073\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lllllll}0.0054 & 0.0054 & 0.0054 & 0.0054 & 0.0054\end{array}\right]^{\mathrm{T}}$
仿真(Ⅳ)	$\left[\begin{array}{ccccc}-0.350 & -0.372 & -0.334 & -0.374 & -0.310 \\ -0.0165 & 0.0307 & 0.0559 & 0.1010 & 0.1203 \\ 0.00001 & 0.00002 & 0.00001 & 0.00002 & 0.00001\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccccc}0.00370 & 0.00247 & 0.00351 & 0.00105 & 0.00335 \\ 0.00082 & -0.00155 & -0.00282 & -0.00509 & -0.00607\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lllllll}0.0054 & 0.0054 & 0.0054 & 0.0054 & 0.0054\end{array}\right]^{\mathrm{T}}$

表3

图4

图5

图6

图7

表4

表5

编队内各无人机在编队收敛时刻的实时状态"

仿真组别	编队收敛时间/s	编队收敛迭代次数	编队内各无人机的实时位置/m	编队内各无人机的实时东向速度和北向速度/(m/s)	编队内各无人机的实时航向角/(°)
仿真(V)	95.378 0	4 769	${\left[\begin{array}{ccccc}373.450 & 378.188 & 368.662 & 383.579 & 363.850 \\ -6.31151 & -11.2491 & -11.2398 & -16.1960 & -16.1933 \\ 5.00000 & 5.00000 & 4.99998 & 4.99999 & 4.99997\end{array}\right]^{\mathrm{T}}}$	${\left[\begin{array}{ccccc}3.99742 & 3.99594 & 3.98739 & 3.99064 & 3.97846 \\-0.00001 & -0.00314 & -0.00361 & -0.00581 & -0.00596\end{array}\right]^{\mathrm{T}}}$	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$
仿真(VI)	93.971 0	4 699	${\left[\begin{array}{ccccc}368.824 & 373.809 & 364.037 & 378.996 & 359.224 \\ -6.58404 & -11.5068 & -11.5031 & -16.4487 & -16.4540 \\ 5.00000 & 5.00000 & 4.99998 & 4.99999 & 4.99996\end{array}\right]^{\mathrm{T}}}$	${\left[\begin{array}{ccccc}3.99732 & 3.99542 & 3.98662 & 3.99000 & 3.97721 \\-0.00001 & -0.00388 & -0.00407 & -0.00680 & -0.06560\end{array}\right]^{\mathrm{T}}} $	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$
仿真(VII)	129.630	6 482	${\left[\begin{array}{ccccc}462.392 & 467.437 & 457.563 & 472.650 & 452.792 \\ -5.92220 & -10.9076 & -10.8975 & -15.8807 & -15.8724 \\ 5.00007 & 5.00006 & 5.00004 & 5.00003 & 5.00001\end{array}\right]^{\mathrm{T}}}$	${\left[\begin{array}{ccccc}3.96532 & 3.96408 & 3.95972 & 3.95811 & 3.95456 \\-0.00400 & -0.00463 & -0.00498 & -0.00566 & -0.00598\end{array}\right]^{\mathrm{T}}}$	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$
仿真(VIII)	201.530	10 077	${\left[\begin{array}{ccccc}789.185 & 794.202 & 784.208 & 798.714 & 779.504 \\ -3.26583 & -8.26583 & -8.26583 & -13.2658 & -13.2658 \\ 5.00000 & 5.00000 & 5.00000 & 4.99996 & 4.99905\end{array}\right]^{\mathrm{T}}}$	$ \left[\begin{array}{cccccccc}3.987 25 & 3.987 16 & 3.986 20 & 3.98440 & 3.90642 \\0.000 00 & 0.000 00 & 0.000 00 & 0.000 00&-0.00001\end{array}\right] ^{\mathrm{T}}$	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$

表5

表6

编队内各无人机在编队收敛时刻的实时状态与其理想状态的误差"

仿真组别	编队收敛时间/s	编队收敛迭代次数	编队内各无人机的实时位置与其理想位置的误差/m	编队内各无人机的实时东向速度和北向速度与各自理想速度的误差/(m/s)	编队内各无人机的实时航向角与其理想航向角的误差/(°)
仿真(V)	95.378 0	4 769	${\left[\begin{array}{ccccc}0.000 & -0.262 & -0.212 & -0.129 & -0.400 \\ 0.00000 & 0.0624 & -0.0717 & -0.1155 & -0.1182 \\ 0.00000 & 0.00000 & -0.00002 & -0.00001 & -0.00003\end{array}\right]^{\mathrm{T}}}$	$\left[\begin{array}{llllll}-0.00258 & -0.00406 & -0.01261 & -0.00936 & -0.02154 \\ -0.000 01 & -0.00314 & -0.00361 & -0.00581 & -0.00596\end{array}\right]^{\mathrm{T}}$	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$
仿真(VI)	93.971 0	4 699	${\left[\begin{array}{ccccc}0.00000 & -0.015 & 0.213 & 0.172 & 0.400 \\ 0.00000 & 0.0772 & 0.0809 & 0.1353 & 0.1300 \\ 0.00000 & 0.00000 & -0.00002 & -0.00001 & -0.00004\end{array}\right]^{\mathrm{T}}}$	$\left[\begin{array}{lllllll}-0.00268 & -0.00458 & -0.01338 & -0.01000 & -0.02279 \\ -0.000 01 & -0.00388 & -0.00407 & -0.00680 & -0.06560\end{array}\right]^{\mathrm{T}}$	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$
仿真(VII)	129.630	6 482	$\begin{gathered}{\left[\begin{array}{ccccc}0.000 & 0.045 & 0.171 & 0.258 & 0.400 \\ 0.00000 & 0.0146 & 0.0247 & 0.0415 & 0.0498 \\ 0.000 07 & 0.000 06 & 0.00004 &0.00003 & 0.00001\end{array}\right]^{\mathrm{T}}} \\\end{gathered}$	$\left[\begin{array}{lllllll}-0.03468 & -0.03592 & -0.040 28 & -0.04189 & -0.04544 \\ -0.00400 & -0.00463 & -0.00498 & -0.00566 & -0.00598\end{array}\right]^{\mathrm{T}}$	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$
仿真(VIII)	201.530	10 077	$ {\left[\begin{array}{ccccc}0.000 & 0.017 & 0.023 & -0.471 & 0.319 \\ 0.00000 & 0.00000 & 0.00000 & 0.0000 & 0.0000 \\ 0.000 00 & 0.00000 & 0.00000 & -0.00004 & 0.00095\end{array}\right]^{\mathrm{T}}}$	$ {\left[\begin{array}{ccccc}0.01275 & 0.01284 & 0.01380 & 0.0156 & 0.09358 \\ 0.000 00 & 0.00000 & 0.000 00 & 0.00000& -0.00001\end{array}\right]^{\mathrm{T}}}$	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$

表6

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仿真组别	收敛时间/s	迭代次数
仿真(I)	107.777	5 389
仿真(II)	109.798	5 490
仿真(III)	95.180	4 759
仿真(IV)	98.773	4 939

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