Distributed Collision Avoidance Tracking Control for Quadrotor Cooperative Suspension System Under Performance Constraints
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摘要: 针对存在未知扰动的多四旋翼无人机协同吊挂系统(Multi-quadrotor cooperative supension system, MQCSS), 提出一种具有避碰和性能约束的分布式自适应积分反步跟踪控制(Distributed adaptive integral backstepping tracking control, DAIBC)方法. 首先, 设计新型的有限时间性能函数和人工势函数分别用于处理负载的跟踪约束和四旋翼无人机(Quadrotor unmanned aerial vehicle, QUAV)之间的避碰问题. 然后, 构造一种积分型的辅助变量并结合动态面技术设计反步控制器, 实现四旋翼无人机的分布式编队运输负载. 同时, 将动态面技术与自适应调节机制相结合, 对系统存在的未知干扰进行抑制. 接着, 给出严格的Lyapunov稳定性分析, 证明闭环系统所有信号的最终一致有界. 最后, 通过数值对比仿真和实飞实验结果验证了所提方法的有效性.Abstract: This paper presents a distributed adaptive integral backstepping tracking control (DAIBC) method for a multi-quadrotor cooperative suspension system (MQCSS) under unknown disturbances. The proposed approach addresses both collision avoidance and performance constraints. Initially, a novel finite-time performance function and an artificial potential function are formulated to manage load tracking constraints and prevent collisions among quadrotors. An integral auxiliary variable is then introduced, and a backstepping controller is designed using dynamic surface technology to facilitate the distributed formation transport of quadrotors. Additionally, the dynamic surface technique is integrated with an adaptive adjustment mechanism to mitigate unknown disturbances within the system. A rigorous Lyapunov stability analysis demonstrates the ultimate uniform boundedness of all signals in the closed-loop system. Finally, the effectiveness of the proposed method is validated through numerical comparative simulations and real flight experiments.
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图 4 数值仿真: 负载跟踪误差的性能约束
Fig. 4 Numerical simulation: Performance constraint for load tracking error
图 5 数值仿真: QUAV分布式编队跟踪误差的2范数和QUAV之间的欧氏距离 $ ||d_{ij}|| $
Fig. 5 Numerical simulation: The 2-morm for QUAV distributed formation tracking errors and Euclidean distance $ ||d_{ij}|| $ between QUAVs
图 9 实验验证: 负载跟踪误差的性能约束
Fig. 9 Experimental verification: Performance constraint for load tracking error
图 10 实验验证: QUAV分布式编队跟踪误差的2范数
Fig. 10 Experimental verification: The 2-norm for QUAV distributed formation tracking errors
图 11 实验验证: QUAV之间的欧氏距离 $||d_{ij}||$
Fig. 11 Experimental verification: Euclidean distance $||d_{ij}||$ between QUAVs
图 12 实验验证: MQCSS的控制信号 $u_i$
Fig. 12 Experimental verification: Control signals $u_i$ for MQCSS
符号 定义 $ {{{P}}_i} = {\left[ {x_i,\;y_i,\;z_i} \right]^{\rm T}} $ 第$ i $架QUAV的位置 $ {{{P}}_L} = {\left[ {x_L,\;y_L,\;z_L} \right]^{\rm T}} $ 负载的位置 $ R_i $, $ R_L $ 第$ i $架QUAV和负载的旋转矩阵 $ q_i $ 第$ i $根连接杆的单位方向向量 $ r_i $ 负载质心到第$ i $个连接点的向量 $ m_{i} $, $ m_L $ 第$ i $架QUAV和负载的质量 $ J_L $ 负载的惯性矩阵 $ l_i $ 第$ i $根连接杆的长度 
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表 2 数值仿真结果的定量分析
Table 2 Quantitative analysis of numerical simulation results
控制方法 TBC TBC-TPF DAIBC-FTPF $ \Upsilon_{e_{L}} $ 0.1602 0.1136 0.0912 $ E $ $ 1.528\;3\times10^5 $ $ 1.527\;9\times10^5 $ $ 1.502\;9\times10^5 $
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表 3 模型参数、控制器参数、初始条件以及参考轨迹
Table 3 Model parameters, controller parameters, initial conditions, and reference trajectories
参数项 数值 模型参数 $ m_i=0.285\;({\rm kg}) $, $ m_L=0.245\;({\rm kg}), \;l_i=0.75\;({\rm m}) $, $ r_1=[0.75, \;0, \;0.1]^{\rm T}\;({\rm m}) $, $ r_2=[0, \;-0.75, \;0.1]^{\rm T}\;({\rm m}) $ $ r_3=[-0.75, \;0, \;0.1]^{\rm T}\;({\rm m}) $, $ r_4=[0, \;0.75.0.1]^{\rm T}\;({\rm m}) $, $ J_L={\rm diag}\{1.5, \;4.6, \;0.08\}10^{-2}\;({\rm kg\cdot m^2}) $ 控制器参数 $ T=5 $, $ a=[0.75, \;0.75, \;0.75, \;0.75, \;0.75, \;0.75]^{\rm T} $, $ \rho_{L0}=[0.5, \;0.5, \;0.5, \;0.25, \;0.25, \;0.25]^{\rm T} $ $ \rho_{L_\infty}=[0.1, \;0.1, \;0.1, \;0.1, \;0.1, \;0.1]^{\rm T} $, $ \Xi_{{\rm max}}=0.6 $, $ \Xi_{{\rm min}}=0.3 $, $ \sigma_{ij}=1 $, $ \beta_{id}^*=1 $ $ k_L={\rm diag}\{1, \;1, \;1, \;1, \;1, \;1\} $, $ \beta_L={\rm diag}\{1, \;1, \;1, \;1, \;1, \;1\} $, $ K_1={\rm diag}\{5, \;5, \;5, \;5, \;5, \;5\} $, $ K_2={\rm diag}\{10, \;10, \;10, \;10, \;10, \;10\} $ $ \gamma_{L}={\rm diag}\{0.1, \;0.1, \;0.1, \;0.1, \;0.1, \;0.1\} $, $ \gamma_{1i}=\gamma_{2i}={\rm diag}\{0.1, \;0.1, \;0.1\} $, $ \ell=0.01 $, $ \Upsilon_{L}=\Upsilon_{i}=1 $, $ \zeta_L=\zeta_i=2 $ $ k_i={\rm diag}\{1, \;1, \;1\} $, $ \beta_i={\rm diag}\{1, \;1, \;1\} $, $ K_{1i}={\rm diag}\{5, \;5, \;5\} $, $ K_{2i}={\rm diag}\{10, \;10, \;10\} $ 初始条件 $ P_{L}(0)=[1.25, \;0.25, \;0.25]^{\rm T}\;({\rm m}) $, $ \Theta_{L}(0)=[0, \;0, \;0]^{\rm T}\;({\rm rad}) $, $ P_{i}(0)=P_L(0)+r_i-l_i[0, \;0, \;-1]^{\rm T}\;({\rm m}) $ 参考轨迹 $ P_{Ldx}=1.5-0.15t\; ({\rm m}) $, $ P_{Ldy}=0\; ({\rm m}) $, $ P_{Ldz}=0.5\; ({\rm m}) $, $ \Theta_{Ld}=[0, \;0, \;0]^{\rm T}\;({\rm rad}) $
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