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摘要:
针对无人机（UAV）在有障碍环境中编队形成和保持问题，提出了一种考虑系统约束的无参考轨迹的分布式模型预测控制(DMPC)算法。为处理模型预测控制(MPC)中存在的约束耦合和代价耦合，引入假设轨迹设计了低保守的相容性约束和无参考轨迹的代价函数，使算法可以分布式同步执行。基于速度障碍法设计终端约束，保证了终端域的安全，并给出了一个可行的终端控制输入。将代价函数作为Lyapunov函数，结合构造的稳定性约束，分析了算法的迭代可行性和系统稳定性。为兼顾实时性，在所提算法的基础上给出了一种能较好满足编队避障要求的非严格稳定的DMPC算法。通过数值仿真，验证了所提算法的有效性和优越性。
Abstract:To ensure and keep the formation of unmanned aerial vehicles (UAVs) facing obstacles, a distributed model predictive control (DMPC) algorithm without reference trajectory considering system constraints was proposed. Firstly, in order to deal with constraint coupling and cost coupling in model predictive control (MPC), the hypothetical trajectory was introduced to design low-conservative compatibility constraints and cost functions without reference trajectories so that the algorithm could be executed in a distributed manner synchronously. Secondly, the terminal constraints were designed based on the velocity obstacle method to ensure the security of the terminal domain, and a feasible terminal control input was given. Then, the cost function was taken as the Lyapunov function, and combined with the constructed stability constraints, the iterative feasibility and system stability of the algorithm were analyzed. In addition, to ensure real-time performance, based on the proposed algorithm, a non-strictly stable DMPC algorithm that could meet the requirements of formation obstacle avoidance was developed. Finally, the validity and superiority of the proposed algorithm were verified by numerical simulation.
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表 1 仿真参数
Table 1. Simulation parameters
参数 数值 参数 数值 $ {\lambda _{i{\text{,f}}}} $ 1 ${r_{{\text{margin-UAV}}}}$/m 0.1 $ {\lambda _{i{\text{,v}}}} $ 1 ${r_{{\text{obs}}}}$/m 0.25 $ {\lambda _{i{\text{,c}}}} $ 0.5 ${r_{{\text{margin-obs}}}}$/m 0.1 $ \Delta T $/s 0.5 ${\underline{v} _{ih}}$/（m·s−1） −1 $P$ 8 ${\bar v_{ih}}$/（m·s−1） 1 ${T_{{\text{max}}}}$/s 35 ${\underline{u} _{ih}}$/（m·s−2） −0.5 $ {{\boldsymbol{v}}_{{\text{ref}}}} $/（m·s−1） ${\left[ {\begin{array}{*{20}{c}} {0.5}&0 \end{array}} \right]^{\text{T}}}$ ${\bar u_{ih}}$/（m·s−2） 0.5 ${r_{{ - UAV}}}$/m 0.1 
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表 2 平均滚动优化时间对比
Table 2. Comparison of average receding horizon optimization time
N $\tau $/ms $\dfrac{\tau}{\Delta T} $/% 最小距离约束 超平面约束 最小距离约束 超平面约束 3 6.8 6.91 1.36 1.38 4 6.84 6.79 1.37 1.35 5 7.32 6.98 1.46 1.40 6 10.68 7.22 2.14 1.44 7 10.98 7.30 2.20 1.46 8 11.84 7.51 2.37 1.50 9 12.90 8.14 2.58 1.63 10 12.14 7.95 2.43 1.59
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