考虑时间约束的近解析滑翔轨迹快速规划方法

doi:10.12382/bgxb.2023.0343

摘要/Abstract

摘要：

针对时间可控再入滑翔问题,提出一种基于阻力加速度-能量剖面的轨迹快速规划方法。该方法将滑翔轨迹规划问题分为纵向轨迹规划与侧向规划。在纵向轨迹规划部分,设计基于走廊边界双参数插值的多段光滑阻力加速度剖面,并给出终端当地弹道倾角约束的施加方法;重点推导考虑地球自转影响的时间、航程解析预测表达式,提升预测算法的快速性和精度,进而通过校正双剖面参数完成剖面设计,同时满足终端能量、航程、时间及当地弹道倾角约束。侧向规划则采用动态/静态航向角误差走廊方法,以实现禁飞区规避和终端航向调整;进一步引入考虑纵侧向运动耦合的目标航程及时间校正策略,完成考虑时间约束的3自由度滑翔轨迹生成。以美国通用飞行器CAV-H再入滑翔为例进行仿真,验证新方法的有效性、多任务适用性。验证结果表明:与现有时间解析预测方法相比,新的预测方法具有相当的计算效率和较高的计算精度优势;与现有基于标准剖面的方法相比,新规划方法具有较高的终端精度、计算效率以及较大的时间可调范围,亦可实现飞行能力边界的快速预示。

关键词: 滑翔轨迹规划, 时间约束, 阻力加速度剖面, 预测校正, 近解析, 能力边界预示

Abstract:

A rapid trajectory planning method based on drag acceleration-energy profile is proposed for the time controllable re-entry gliding. This method divides the gliding trajectory planning into longitudinal trajectory planning and lateral planning. In the longitudinal trajectory planning, a multi-segment smooth drag acceleration profile based on corridor boundary dual-parameter interpolation is designed, and a method for applying local path angle constraints at the terminal is provided. Then the analytical prediction expressions for time and range considering the influence of Earth rotation are derived, which improves the speed and accuracy of the prediction algorithm. The profile design is then completed by correcting the double profile parameters, while meeting the constraints of terminal energy, range, time, and local path angle. In the lateral planning, the dynamic/static heading angle error corridor method is used to avoid the no-fly zone and adjust the terminal heading, a target range and time correction strategy considering longitudinal and lateral motion coupling is further introduced, and a three-degrees-of-freedom gliding trajectory generation considering time constraints is completed. Finally, the effectiveness and multitasking applicability of the proposed method are verified by taking CAV-H re-entry gliding as an example for simulation. Compared with existing time analytical prediction methods, the proposed prediction method has significant computational efficiency and high computational accuracy. Compared with existing trajectory planning methods based on standard profiles, the proposed planning method has higher terminal accuracy, higher computational efficiency, and a larger time adjustable range, and can also achieve the rapid prediction of flight capability boundaries.

Key words: gliding trajectory planning, time constraint, drag acceleration profile, predictive correction, near analysis, capability boundary prediction

中图分类号:

V412.4

王培臣, 闫循良, 南汶江, 李新国. 考虑时间约束的近解析滑翔轨迹快速规划方法[J]. 兵工学报, 2024, 45(7): 2294-2305.

WANG Peichen, YAN Xunliang, NAN Wenjiang, LI Xinguo. A Rapid and Near Analytic Planning Method for Gliding Trajectory under Time Constraints[J]. Acta Armamentarii, 2024, 45(7): 2294-2305.

图/表 9

图1 D-E剖面示意图

Fig.1 D-E profile diagram

图2 3自由度轨迹生成算法流程图

Fig.2 Flow chart of 3-DOF trajectory generation algorithm

图3 飞行能力边界预示图

Fig.3 Predictive map of flight capability boundary

图4 航程、时间预测误差曲线

Fig.4 Predicted error curves of range and time

表1 仿真条件设置

Table 1 Simulation condition settings

算例	θ₀(°)	ϕ₀(°)	ψ₀(°)	$γ * f$ (°)	$t f *$ /s	$s f *$ /km
1	50	0	-70	-4.0	1010.0	4511.6
2	0	70	170	-2.0	1380.0	6659.6
3	0	70	170	-2.0	1560.0	6659.6
4	-60	20	100	-2.0	1690.0	7502.4
5	5	-70	0	-2.0	1960.0	8853.9

表1 仿真条件设置

Table 1 Simulation condition settings

算例	θ₀(°)	ϕ₀(°)	ψ₀(°)	$γ * f$ (°)	$t f *$ /s	$s f *$ /km
1	50	0	-70	-4.0	1010.0	4511.6
2	0	70	170	-2.0	1380.0	6659.6
3	0	70	170	-2.0	1560.0	6659.6
4	-60	20	100	-2.0	1690.0	7502.4
5	5	-70	0	-2.0	1960.0	8853.9

图5 不同约束条件对应的仿真结果曲线

Fig.5 Simulated result curves under different constraints

表2 不同仿真条件对应的终端结果

Table 2 Terminal parameters corresponding to different simulation conditions

算例	h_f/ km	v_f/ (m·s^-1)	s_togo,f/ km	γ_f/ (°)	Δt_f/ s	计算耗时/s
1	25.08	1999.12	50.03	-3.84	0.07	0.85
2	25.07	1999.62	50.43	-1.89	0.47	1.12
3	25.07	1999.72	50.22	-1.97	0.14	1.43
4	25.05	1999.62	50.23	-1.96	0.26	1.52
5	25.03	1998.02	50.29	-2.15	0.15	1.66

表3 禁飞区约束条件下不同算例对应的终端参数

Table 3 Terminal parameters corresponding to different computational examples under the constraints of no-fly zone

算例	h_f/ km	v_f/ (m·s^-1)	s_togo,f/ km	γ_f/ (°)	Δt_f/ s	计算耗时/s
1	25.05	1999.62	50.23	-1.96	0.26	1.52
2	25.06	1999.43	50.42	-1.96	0.38	1.61
3	25.07	1999.46	50.35	-1.94	0.35	1.46

图6 禁飞区约束条件下不同算例对应的仿真结果曲线

Fig.6 Simulated result curves corresponding to different computational examples under the constraints of no-fly zone

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