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摘要:
针对欠驱动多无人机包含控制中个体无人机无法获取全局信息，并受到未知外部扰动，难以快速收敛的问题，提出一种基于动态尺度观测器的欠驱动多无人机分布式固定时间控制策略。设计分布式固定时间观测器，使各无人机在大部分个体无法获取目标状态条件下能快速估计出完成包含任务所需空间状态；提出一种基于浸入与不变理论的有限时间动态尺度观测器，能快速准确地估计各无人机所受外部扰动；设计非奇异分布式固定时间控制器，利用局部信息实现了欠驱动多无人机系统的快速立体包含控制。所提控制策略使系统的收敛时间上界不受初始状态影响，只取决于信息传递阵特征值和控制器参数。通过理论证明和仿真实验验证了所设计控制器的优越性。
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关键词:
- 欠驱动多无人机系统 /
- 有限时间动态尺度观测器 /
- 浸入与不变 /
- 固定时间控制 /
- 立体包含控制
Abstract:To address the problem that individual unmanned aerial vehicle (UAV) in under-actuated multi-UAV inclusion control cannot obtain global information and is subject to unknown external perturbations, making it difficult to converge quickly, this paper proposed a distributed fixed-time control strategy for under-actuated UAVs based on a dynamic scale observer. Firstly, a distributed fixed-time observer was designed to enable each UAV to quickly estimate the space state required to complete the contained mission when most UAVs fail to obtain the target state. Secondly, a finite-time dynamic scale observer based on immersion and invariance theory was proposed to quickly and accurately estimate the external perturbations to each UAV. Finally, a non-singular distributed fixed-time controller was designed to achieve the fast stereoscopic inclusion control of an under-actuated multi-UAV system by using local information. With the proposed control strategy, the upper bound on the convergence time of the system was independent of the initial state and depended only on the eigenvalues of the information transfer array and the controller parameters. The superiority of the designed controller was verified by theoretical demonstration and simulation experiments.
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图 2 欠驱动多无人机系统编队-包含控制框架
Figure 2. Under-actuated multi-UAV formation inclusion control framework
图 12 第一架无人机各位置子系统扰动估计误差
Figure 12. Perturbation estimation error of subsystem of first UAV at different positions
图 13 第一架无人机各姿态子系统扰动估计误差
Figure 13. Perturbation estimation error of each attitude subsystem of first UAV
图 14 不同类型干扰下扰动观测误差对比
Figure 14. Comparison of perturbation observation errors under different types of perturbations
图 16 不同监督因子对动态尺度误差的影响
Figure 16. Effect of different supervision factors on dynamic scale error
图 17 不同监督因子对动态尺度因子的影响
Figure 17. Effect of different supervision factors on dynamic scale factor
图 18 不同控制器跟踪轨迹对比
Figure 18. Comparison of trajectory tracking of different controllers
图 19 不同控制器轨迹跟踪误差对比
Figure 19. Comparison of trajectory tracking errors of different controllers
表 1 无人机物理参数
Table 1. Physical parameters of each UAV
参数 数值 \参数 数值 mu /kg 2.00 lu/m 0.20 kx/(N·s·rad−1) 0.01 kθ/(N·s·rad−1) 0.01 ky/(N·s·rad−1) 0.01 kφ/(N·s·rad−1) 0.01 kz/(N·s·rad−1) 0.01 kψ/(N·s·rad−1) 0.01 Ix/(N·s2·rad−2) 1.75 Iy/(N·s2·rad−2) 1.75 Iz/(N·s2·rad−2) 3.50 g/(m·s−2) 10.00 
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表 2 外部包围层无人机包含矢量
Table 2. Inclusion vector of UAV in external layer
lli(t) 包含矢量/m ll1(t) [1+0.353 5δ(t) 1.707−0.353 5δ(t) δ(t)]T ll2(t) [−1−0.353 5δ(t) 1.707−0.353 5δ(t) δ(t)]T ll3(t) [−1−0.353 5δ(t) −1.707+0.353 5δ(t) δ(t)]T ll4(t) [1+0.353 5δ(t) −1.707+0.353 5δ(t) δ(t)]T ll5(t) [1.707−0.353 5δ(t) 1+0.353 5δ(t) −δ(t)]T ll6(t) [−1.707+0.353 5δ(t) 1+0.353 5δ(t) −δ(t)]T ll7(t) [−1.707+0.353 5δ(t) −1−0.353 5δ(t) −δ(t)]T ll8(t) [1.707−0.353 5δ(t) −1−0.353 5δ(t) −δ(t)]T
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表 3 无人机各子系统所受外部扰动模型
Table 3. External perturbation to each UAV
dij(t) 扰动/(N·m) di1(t) 2sin(0.1πt) di2(t) 4(1−e−t) di3(t) 2 di4(t) 3(tanh(t)+e−t) di5(t) 5tanh(t) di6(t) 2cos(3t)+2sin(0.5πt)
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表 4 控制器参数
Table 4. Controller parameters
参数 数值 参数 数值 T1 0.6 Tf 2.00 p1 0.9 p2 0.25 q1 1.9 q2 1.75 ll/lf 2.0 λ 2.00 k3 1.1 k4 1.00 k5 1.5 k71 1.5 k72 2.0 k8 1.00 k9 1.1 k10 1.00 m 0.3 α 5.00 γ 2.0 Δ 0.01
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表 5 不同类型干扰下扰动观测效果
Table 5. Observation effect of different perturbations
扰动/(N·m) T/s dRMSE 本文方法 I&I方法 本文方法 I&I方法 5 0.06 0.61 0.368 8 0.590 1 5cost 0.05 ∞ 0.029 6 0.060 6 5−5coste0.05t 0.03 ∞ 0.011 3 0.117 7
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表 6 观测器和控制器收敛效果对比
Table 6. Comparison of observer and controller convergence effects
控制效果 T/s dRMSE 本文方法 FTSMO方法 本文方法 FTSMO方法 分布式观测器 0.41 3.34 0.013 0.214 控制器 1.28 2.62 0.041 0.100
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