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摘要:
针对高超声速飞行器再入滑翔段制导问题，提出一种基于粒子群优化-鲸鱼算法的在线制导策略。考虑其约束模型与交班条件，建立了过程约束与终端约束模型。为缩短轨迹生成时间，减少算法计算量，设计了一种能自动满足终端高度、路径角、航程约束的高度-剩余航程飞行剖面。基于阻力系数为常值的前提下，推导了满足航程约束的速度数值解。利用上述模型，设计了一种三参数寻优模型，实现对终端条件的控制。为优化过程约束，提出结合鲸鱼算法和粒子群优化算法的改进鲸鱼算法，克服了粒子群算法易早熟收敛的缺点，提高了求解效率，满足了飞行过程中热流率最小的目标。而后通过将航迹分段的方法，提出一种基于中间点的在线制导方法，对纵向剖面进行在线更新，从而满足终端约束。仿真结果表明，所提方法能高效率的求解最优飞行轨迹。
Abstract:In view of the guidance problem of the hypersonic vehicles in the glide-reentry segment, an online guidance strategy based on improved particle swarm optimization and whale algorithm was proposed. By considering its constraint model and shift conditions, a process constraint and terminal constraint model were established. To shorten the trajectory generation time and reduce the calculation amount of the algorithm, a height-range flight profile that could automatically meet the constraints of terminal height, path angle, and range was designed. Based on the premise that the drag coefficient is a constant value, a numerical solution of velocity that satisfied the range constraint was derived. Based on the above model, a three-parameter optimization model was designed to realize the control of the terminal conditions. To optimize the process constraints, an improved whale algorithm combining the whale algorithm and particle swarm optimization algorithm was proposed to overcome the shortcoming of precocious convergence of the particle swarm optimization algorithm, improve the solution efficiency, and minimize the heat flow rate during the flight. Then, through the method of segmenting the trajectory, an online guidance method based on the mid-point was proposed to update the longitudinal profile online to meet the terminal constraints. The simulation results show that the proposed method can efficiently solve the optimal flight trajectory.
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图 11 3种智能算法的热流率时间曲线
Figure 11. Heat flow rate-time curves of three intelligent algorithms
表 1 仿真初始条件
Table 1. Initial conditions of simulation
任务 初始位置/(°) 高度/km 速度/(m·s−1) 路径角/(°) 1 (E 90, N 50) 60|30 5500|1100 −1|−1 2 (E 90, N 50) 55|30 5250|950 0|−1 3 (E 90, N 45) 50|30 5000|800 −1|0 4 (E 90, N 45) 45|30 4750|650 0|0 
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表 2 仿真结果
Table 2. Simulation result
任务 $ \left| {\Delta V} \right|/({\text{m}} \cdot {\text{s}}^{-1}) $ $\left| {\Delta \gamma } \right|$/(°) $\left| {\Delta h} \right|/{\text{km}}$ $ \left| {\Delta {R_{\mathrm{L}}}} \right| / {\text{km}} $ 1 4.17 3.62×10−5 4.70×10−2 2.69 2 21.92 2.07×10−6 3.40×10−2 1.94 3 29.64 6.58×10−5 1.11×10−2 1.39 4 17.20 2.64×10−5 1.83×10−3 0.89
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表 3 终端约束相对误差
Table 3. Relative error of terminal constraint
任务 相对误差/% $\Delta V$ $\Delta \gamma $ $\Delta h $ $\Delta {R_{\mathrm{L}}} $ 1 0.38 0.0036 0.16 0.120 2 2.31 0.00021 0.11 0.086 3 3.71 0.0066 0.037 0.066 4 2.64 0.0026 0.0061 0.042
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表 4 3种智能算法的仿真结果
Table 4. Simulation results of three intelligent algorithms
算法 $ \left| {\Delta V} \right| / ({\text{m}} \cdot {\text{s}}^{-1}) $ $\left| {\Delta \gamma } \right| $/(°) $\left| {\Delta h} \right| /{\text{km}} $ $ \left| {\Delta {R_{\mathrm{L}}}} \right| /{\text{km}} $ PSO-WOA 16.28 1.48×10−6 1.21×10−3 0.56 WOA 35.43 1.66×10−6 2.36×10−2 0.98 PSO 11.41 1.17×10−5 2.15×10−2 1.23
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