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

Abstract

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

CLC Number:

V279

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.

Figures/Tables 13

Fig.1

Table 1

Fig.2

Fig.3

Table 2

Real-time status of each unmanned aerial vehicle in formation at the 120 s"

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)	$\left[\begin{array}{ccccc}479.650 & 484.628 & 474.666 & 489.626 & 469.690 \\ -0.01648 & -4.96923 & -4.94400 & -9.89885 & -9.87957 \\ 5.00001 & 5.00002 & 5.00001 & 5.00002 & 5.00001\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccccc}3.99630 & 3.99753 & 3.99649 & 3.99895 & 3.99665 \\ 0.00082 & -0.00155 & -0.00282 & -0.00509 & -0.00607\end{array}\right]^{\mathrm{T}}$	$[90.005 490.005490 .005490 .005490 .0054]^ \mathrm{T}$

Table 2

Table 3

Error between real-time state and its ideal state of each unmanned aerial vehicle in formation at the 120 s"

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)	$\left[\begin{array}{ccccc}-0.350 & -0.372 & -0.334 & -0.374 & -0.310 \\ -0.0165 & 0.0307 & 0.0559 & 0.1010 & 0.1203 \\ 0.00001 & 0.00002 & 0.00001 & 0.00002 & 0.00001\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{ccccc}0.00370 & 0.00247 & 0.00351 & 0.00105 & 0.00335 \\ 0.00082 & -0.00155 & -0.00282 & -0.00509 & -0.00607\end{array}\right]^{\mathrm{T}}$	$\left[\begin{array}{lllllll}0.0054 & 0.0054 & 0.0054 & 0.0054 & 0.0054\end{array}\right]^{\mathrm{T}}$

Table 3

Fig.4

Fig.5

Fig.6

Fig.7

Table 4

Table 5

Real-time state of each unmanned aerial vehicle in formation at the time of formation convergence"

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}}$	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$

Table 5

Table 6

Error between real-time state and its ideal state of each unmanned aerial vehicles in formation at the time of formation convergence"

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}}}$	$\begin{aligned}& {\left[\begin{array}{lll}90.0054 & 90.0054 & 90.0054\end{array}\right.} \\& 90.0054 \quad 90.0054]^{\mathrm{T}}\end{aligned}$

Table 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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Optimization algorithm for UAV formation consensus based on motion constraint

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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理想位置/m
仿真(V)	95.378 0	4 769	$\left[\begin{array}{ccccc}373.450 & 378.450 & 368.450 & 383.450 & 363.450 \\ -6.31151 & -11.3115 & -11.3115 & -16.3115 & -16.3115 \\ 5 & 5 & 5 & 5 & 5\end{array}\right]^{\mathrm{T}}$
仿真(VI)	93.971 0	4 699	$\left[\begin{array}{ccccc}368.824 & 373.824 & 363.824 & 378.824 & 358.824 \\ -6.58404 & -11.5840 & -11.5840 & -16.5840 & -16.5840 \\ 5 & 5 & 5 & 5 & 5\end{array}\right]^{\mathrm{T}}$
仿真(VII)	129.630	6 482	$\left[\begin{array}{ccccc}462.392 & 467.392 & 457.392 & 472.392 & 452.392 \\ -5.92220 & -10.9222 & -10.9222 & -15.9222 & -15.9222 \\ 5 & 5 & 5 & 5 & 5\end{array}\right]^{\mathrm{T}}$
仿真(VIII)	201.530	10 077	$\left[\begin{array}{ccccc}789.185 & 794.185 & 784.185 & 799.185 & 779.185 \\ -3.26583 & -8.26583 & -8.26583 & -13.2658 & -13.2658 \\ 5 & 5 & 5 & 5 & 5\end{array}\right]^{\mathrm{T}}$