Re-entry trajectory planning for hypersonic morphing vehicles using penalty sequence convex programming
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摘要:
为实现高超声速飞行器由固定构型的单点最优向可变构型的全包线持续最优的跨越升级，设计了类乘波体变体飞行器布局与变后掠-变展长复合变形方案。在此基础上，针对高超声速变体飞行器再入轨迹规划问题求解难度大、规划耗时高的问题，提出了自适应信赖域更新的罚函数序列凸优化方法。采用对数凸化策略凸化路径约束，提高近似精度；引入虚拟控制，对动力学等式约束进行变量替换；定制二阶锥约束，并采用罚函数方法将其加入目标函数中，引导迭代结果向可行域逼近；设计自适应信赖域更新策略，加速序列凸优化算法收敛。仿真结果表明：相比于固定构型，高超变体飞行器增程16.63%，增程效果明显；相比于hp伪谱法，所提算法求解耗时降低了89.24%，具有更高的时效性。
Abstract:To realize continuous leapfrog upgrades of the hypersonic vehicle from single-point optimal fixed configuration to full envelope optimal of morphing configuration, a quasi-wave rider profile and composite deformation scheme morphing wingspan and sweep are designed. On this basis, to reduce the computational burdens of reentry trajectory planning, the adaptive trust-region-based penalty sequence convex programming method is proposed. To increase the approximate accuracy, the path restrictions are communicated using the logarithmic convexification technique. A virtual control is introduced to replace the dynamic equation constraints. Using the penalty function method, modify the second-order cone constraint and incorporate it into the objective function to direct the iterative results in order to approximate the feasible domain. An adaptive trust region updating strategy is designed to accelerate the convergence of the sequence convex optimization algorithm. As demonstrated by the simulation results, the hypersonic morphing vehicle's range extension is 16.63% when compared to the fixed configuration, and the ATP-SCP computing time is 89.24% less than when compared to the HP pseudospectral method.
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图 4 固定/可变构型状态变量对比
Figure 4. Comparison on state variables of fixed and morphing configuration
图 5 固定/可变构型路径约束对比
Figure 5. Comparison on path constraints of fixed and morphing configuration
图 6 固定/可变构型机翼变形量
Figure 6. Comparison on morphing variables of fixed and morphing configuration
图 7 hp伪谱法与ATP-SCP算法状态变量对比
Figure 7. Comparison on state variables of hp pseudospectrum and ATP-SCP algorithm
图 8 hp伪谱法与ATP-SCP算法路径约束对比
Figure 8. Comparison on path constraints of hp pseudospectrum and ATP-SCP algorithm
图 9 hp伪谱法与ATP-SCP算法变形量及对应控制变量对比
Figure 9. Comparison on morphing and control variables of hp pseudospectrum and ATP-SCP algorithm
表 1 升力系数、阻力系数和参考面积拟合精度
Table 1. RMSE of $ {{{C}}_{\rm{L}}} $, ${{{C}}_{\rm{D}}}$ and ${{S}}$
拟合精度指标 CL CD 参考面积/m2 RMSE 0.0096 0.0074 0.0195 
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表 2 高超声速变体飞行器参数
Table 2. Parameters of hypersonic morphing vehicle
飞行器性能参数 数值 质量m/kg 5500 固定外形参考翼面积S/m2 10.94 最大热流率${\dot Q_{{\mathrm{s}},\max }}$/(kW·m−2) 1500 热流相关系数$ {k_Q} $ $5 \times {10^{ - 8}}$ 最大动压${q_{\max }} $/kPa 38 最大过载${n_{\max }} $ 3g
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表 3 初末状态1
Table 3. Initial and final state 1
状态 射程x/km 海拔h/km 速度v/(m·s−1) 弹道倾角$\gamma $/(°) 内段翼后掠角${\chi _1}$/(°) 内段翼后后掠角${\chi _2}$ 展长$\xi $/m 初始状态 0 55 4950 −1 8 0 0.41 终端状态 30 2 000
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表 4 初末状态2
Table 4. Initial and final state 2
变量 射程x/km 海拔h/km 速度v/(m·s−1) 弹道倾角$\gamma $/(°) 攻角$\alpha $/(°) 内段翼后掠角${\chi _1}$/(°) 外段翼后后掠角${\chi _2}$ 前缘长度$\xi $/m 初始状态 0 61 5100 0 18 8 0 0.41 终端状态 30 12
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表 5 求解耗时与最优性对比
Table 5. Comparison of solving time and optimality
算法 求解耗时/s 最大射程/km ATP-SCP 4.10 3695.54 hp伪谱法 38.11 3747.67
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