Near-space vehicle trajectory optimization based on control vector parameterization
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摘要:
针对计算制导场景下临近空间飞行器的在线轨迹优化问题，提出了一种基于实际动力学方程控制向量参数化的轨迹优化方法。通过翻转Radau伪谱离散非线性动力学方程，建立了含初始和终端状态约束的轨迹优化问题。通过参数化控制向量，将各离散点处控制量的优化问题转化为几个参数向量的优化问题，简化了计算过程，并提升了计算效率。此外，针对参数幅值约束，融合凸规划技术提出了一种基于控制向量参数化的轨迹优化方法。考虑到中制导任务对终端飞行时间不敏感，将优化问题的自变量从时间转换为航程，进一步缩短了计算时间。仿真结果表明，所提方法能够有效满足计算制导中高精度高效率轨迹优化的任务需求。
Abstract:For online trajectory optimization of the near-space vehicle in computational guidance, a trajectory optimization method based on actual dynamic equations is proposed via control vector parameterization. Firstly, a trajectory optimization problem with initial and terminal state constraints is developed by discretizing the nonlinear dynamic equations using the flipped-Radau pseudospectral approach. Secondly, control vector parameterization reduces complexity and boosts computational efficiency by converting the optimization problem for control quantities at each discrete point into an optimization problem for multiple parameter vectors. Thirdly, to deal with parameter amplitude constraints, a trajectory optimization method based on convex programming techniques is proposed via control vector parameterization. Finally, given that the midcourse guidance mission is insensitive to terminal flight time, the optimization problem is transformed from being time-dependent to downrange-dependent, thereby further reducing the computational time. Simulation results demonstrate that the proposed method satisfies the high-efficiency and high-precision requirements for trajectory optimization in computational guidance.
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图 12 4种方法的航程-高度-侧向位置曲线
Figure 12. Curves of downrange, altitude, and lateral position for 4 methods
图 14 4种方法的航程-侧向位置曲线
Figure 14. Curves of lateral position with downrange for 4 methods
图 20 航程-高度-侧向位置曲线（初始状态摄动）
Figure 20. Curves of downrange, altitude, and lateral position (initial state perturbations)
图 21 时间-航迹角曲线（初始状态摄动）
Figure 21. Curves of flight-angle with time (initial state perturbations)
图 22 时间-航向角曲线（初始状态摄动）
Figure 22. Curves of heading angle with time (initial state perturbations)
图 23 时间-法向过载曲线（初始状态摄动）
Figure 23. Curves of normal overload with time (initial state perturbations)
图 24 时间-侧向过载曲线（初始状态摄动）
Figure 24. Curves of lateral overload with time (initial state perturbations)
图 25 航程-高度-侧向位置曲线（模型摄动）
Figure 25. Curves of downrange, altitude, and lateral position (model perturbations)
表 1 初始和终端状态约束
Table 1. Initial and terminal state constraints
状态
约束速度/
(m·s−1)航迹角/
(°)航向角/
(°)航程/
km高度/
km侧向
位置/km初始 1 870 2 −40 0 32 0 终端 1 647 −5 −48 35 31 35 
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表 2 终端状态误差
Table 2. Terminal state errors
终端状态方法 速度误差/(m·s−1) 航迹角误差/(°) 航向角误差/(°) 航程误差/m 高度误差/m 侧向位置误差/m DCHU-SC (84) −2.90×10−3 −4.90×10−5 −2.60×10−4 0.52 0.14 0.46 MPSC (3 000) 0.10 −5.43×10−4 1.96×10−3 −0.41 −1.34 −0.10 MPSC (84) −7.11 0.05 0.24 −76.23 −52.18 26.95 GPOPS(84) −0.02 −4.32×10−6 −4.18×10−6 0.54 0.10 0.54 SCP (84) 0.02 0.02 0.03 16.25 2.12 3.26
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