A multi-objective optimal control trajectory optimization method for aircraft under wind influence
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摘要:
风影响下的四维航迹优化问题约束复杂，多目标四维航迹优化模型难以求解。基于最优控制方法研究固定水平航路下考虑风影响的航迹垂直剖面多目标优化问题的建模和求解。以飞行时间和飞行油耗最小化为双目标建立航迹最优控制模型；设计了梯形配点结合
ε -约束方法的模型求解方法，并针对按高度层飞行场景下的航迹优化提出两阶段求解方法；建立了四维航迹仿真模型用于对轨迹优化效果的仿真验证；选用长航线实际飞行计划数据作为算例进行算法性能分析，并区分自由高度飞行和按高度层飞行2种场景进行航迹优化效果验证。实验结果表明：所提模型和所提方法相比其他2种常用算法能获得更优的Pareto前沿解，按高度层飞行场景下采用所提方法能获得更优的前沿解；自由高度飞行和按高度层飞行2种场景下求得的前沿解中最小燃油耗航迹分别比飞行计划仿真航迹的油耗降低了6.33%和5.94%，最短飞行时间航迹分别比飞行计划仿真航迹的飞行时间降低了10.16%和10.01%。Abstract:The constraints of the 4D trajectory optimization problem under wind influence are complex, and the multi-objective 4D trajectory optimization model is difficult to solve. To this end, the modeling and solution of the multi-objective optimization problem of the vertical profile of the trajectory under a fixed horizontal flight path considering wind influence were studied based on the optimal control method. Firstly, the optimal trajectory control model was established with the objectives of minimizing flight time and flight fuel consumption. Then, a model solution method combining trapezoidal points with $\varepsilon \text{-} {\mathrm{constraint}} $ was designed, and a two-stage solution method was proposed especially for trajectory optimization under the flight scenario by altitude layer. Then, a 4D trajectory simulation model was established to verify the effect of trajectory optimization. Finally, the actual flight plan data of the long flight route was used as an example to analyze the performance of the algorithm, and two scenarios of flight at free altitude and flight by altitude layer were used to verify the effect of trajectory optimization. The experimental results show that the proposed model and algorithm can obtain better Pareto frontier solutions than the other two commonly used algorithms, and the two-stage solution method can obtain better frontier solutions in the flight scenario by altitude layer. In the frontier solutions obtained in the scenarios of flight at free altitude and flight by altitude layer, the lowest flight fuel consumption trajectories are reduced by 6.33% and 5.94%, respectively, compared with those of the flight plan simulation trajectories. The shortest flight time trajectory is 10.16% and 10.01% lower than that of the flight plan simulation trajectory.
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图 4 航迹仿真推演计算流程
Figure 4. Flow of calculation process of trajectory simulation derivation
图 9 KLM888航班航迹优化Pareto前沿解
Figure 9. Pareto frontier solution of trajectory optimization for flight KLM888
图 10 自由高度飞行最优航迹剖面对比
Figure 10. Comparison of optimal trajectory profiles for flight at free altitude
图 11 按高度层飞行最优航迹剖面对比
Figure 11. Comparison of optimal trajectory profiles for flight by altitude layer
表 1 3类算法性能对比
Table 1. Comparison of performance of three types of algorithms
算法 CM HV MID ε-约束 1 0.0109 13.1272 NSGA-Ⅱ 0 0.0050 107.5931 CI线性加权 0 0.0002 105.2507 
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表 2 高度层约束场景算法性能对比
Table 2. Comparison of performance of algorithms under altitude layer constraint
算法 CM HV MID 两阶段求解 1 0.0107 13.1608 直接求解（初始解1） 0 0.0013 33.6483 直接求解（初始解2） 0 0.0028 251.6432 直接求解（初始解3） 0 0.0014 32.5157
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表 3 KLM888航班四维航迹优化结果对比
Table 3. Comparison of 4D trajectory optimization results for flight KLM888
航迹 飞行时间/min 燃油消耗/kg 自由高度飞行最短飞行时间航迹 610 132 145 自由高度飞行最小燃油消耗航迹 669.5 111 396 按高度层飞行最短飞行时间航迹 611 127 197 按高度层飞行最小燃油消耗航迹 655.5 111 858 航班计划仿真航迹 679 118 920
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[1] LEE C. Transport and climate change: A review[J]. Journal of Transport Geography, 2007, 15(5): 354-367. doi: 10.1016/j.jtrangeo.2006.11.008 [2] TEOH L E, KHOO H L. Green air transport system: an overview of issues, strategies and challenges[J]. KSCE Journal of Civil Engineering, 2016, 20(3): 1040-1052. doi: 10.1007/s12205-016-1670-3 [3] HAGELAUER P, MORA-CAMINO F. A soft dynamic programming approach for on-line aircraft 4D-trajectory optimization[J]. European Journal of Operational Research, 1998, 107(1): 87-95. doi: 10.1016/S0377-2217(97)00221-X [4] RICHTER M, BITTNER M, RIECK M, et al. A non-cooperative bi-level optimal control problem formulation for noise minimal departure trajectories[C]//Proceedings of the 29th Congress of the International Council of the Aeronautical Sciences. St.Petersburg: ICAS, 2014: 7-12. [5] TIAN Y, HE X Q, XU Y, et al. 4D trajectory optimization of commercial flight for green civil aviation[J]. IEEE Access, 2020, 8: 62815-62829. doi: 10.1109/ACCESS.2020.2984488 [6] MURRIETA-MENDOZA A, BOTEZ R. Lateral navigation optimization considering winds and temperatures for fixed altitude cruise using dijsktra’s algorithm[C]//Proceedings of the ASME International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers. New York: ASME, 2014: 1-9. [7] 刘苑. 主干航路路径规划的仿真优化方法研究[D]. 天津: 中国民航大学, 2019: 41-43.LIU Y. Research on simulation optimization method for trunk route path planning[D]. Tianjin: Civil Aviation University of China, 2019: 41-43(in Chinese). [8] LEGRAND K, PUECHMOREL S, DELAHAYE D, et al. Robust aircraft optimal trajectory in the presence of wind[J]. IEEE Aerospace and Electronic Systems Magazine, 2018, 33(11): 30-38. doi: 10.1109/MAES.2018.170050 [9] GONZÁLEZ-ARRIBAS D, SOLER M, SANJURJO-RIVO M. Robust aircraft trajectory planning under wind uncertainty using optimal control[J]. Journal of Guidance, Control, and Dynamics, 2018, 41(3): 673-688. doi: 10.2514/1.G002928 [10] 吴丽娜, 王和平. 基于改进遗传算法的最快爬升航迹的优化分析[J]. 科学技术与工程, 2009, 9(10): 2669-2673.WU L N, WANG H P. Analysis of fastest climb trajectory optimal based on an improved genetic algorithms[J]. Science Technology and Engineering, 2009, 9(10): 2669-2673 (in Chinese). [11] GARDI A, SABATINI R, KISTAN T. Multiobjective 4D trajectory optimization for integrated avionics and air traffic management systems[J]. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(1): 170-181. doi: 10.1109/TAES.2018.2849238 [12] 杨磊, 李文博, 刘芳子, 等. 柔性空域结构下连续下降航迹多目标优化[J]. 航空学报, 2021, 42(2): 324157.YANG L, LI W B, LIU F Z, et al. Multi-objective optimization of continuous descending trajectories in flexible airspace[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(2): 324157 (in Chinese). [13] PISANI D, ZAMMIT MANGION D, SABATINI R. City-pair trajectory optimization in the presence of winds using the GATAC framework[C]// Proceedings of the AIAA Guidance, Navigation, and Control Conference. Reston: AIAA, 2013. [14] 谢华, 黎子弘, 杨磊, 等. 容量受限下城市对航班四维航迹优化[J]. 航空学报, 2022, 43(8): 325581.XIE H, LI Z H, YANG L, et al. Optimization of four-dimensional trajectory of city pair with limited capacity[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(8): 325581 (in Chinese). [15] BEN A S, ZONG P. 3D path planning, routing algorithms and routing protocols for unmanned air vehicles: A review[J]. Aircraft Engineering and Aerospace Technology, 2019, 91(9): 1245-1255. doi: 10.1108/AEAT-01-2019-0023 [16] SIDIBÉ S, BOTEZ R M. Trajectory optimization of FMS-CMA 9000 by dynamic programming[C]// 60th Aeronautics Conference and AGM. Toronto: Canadian Aeronautics and Space Institate, 2013: 1-3. [17] PATRÓN R S F, KESSACI A, BOTEZ R M. Horizontal flight trajectories optimisation for commercial aircraft through a flight management system[J]. The Aeronautical Journal, 2014, 118(1210): 1499-1518. doi: 10.1017/S0001924000010162 [18] BOUTTIER C, BABANDO O, GADAT S, et al. Adaptive simulated annealing with homogenization for aircraft trajectory optimization[C]//Operations Research Proceedings 2015. Berlin: Springer, 2017: 569-574. [19] MURRIETA-MENDOZA A, RUIZ H, BOTEZ R M, et al. Vertical reference flight trajectory optimization with the particle swarm optimisation[C]//Proceedings of the 36th IASTED International Conference on Modelling, Identification and Control. Innsbrunck: ACTA Press, 2017: 848. [20] CHAI R Q, SAVVARIS A, TSOURDOS A, et al. Overview of trajectory optimization techniques[M]// Design of Trajectory Optimization Approach for Space Maneuver Vehicle Skip Entry Problems. Berlin: Springer, 2019: 7-25. [21] SIMORGH A, SOLER M, GONZÁLEZ-ARRIBAS D, et al. A comprehensive survey on climate optimal aircraft trajectory planning[J]. Aerospace, 2022, 9(3): 146. doi: 10.3390/aerospace9030146 [22] SABATINI R, MOORE T, HILL C, et al. Trajectory optimisation for avionics-based GNSS integrity augmentation system[C]//Proceedings of the IEEE/AIAA 35th Digital Avionics Systems Conference. Piscataway: IEEE Press, 2016: 1-10. [23] DALMAU R, MELGOSA M, VILARDAGA S, et al. A fast and flexible aircraft trajectory predictor and optimiser for ATM research applications[C]//Proceedings of the 8th International Conference for Research in Air Transportation. Piscataway: IEEE Press, 2018: 1-8. [24] DALMAU R, PRATS X, BAXLEY B. Using broadcast wind observations to update the optimal descent trajectory in real-time[J]. Journal of Air Transportation, 2020, 28(3): 82-92. doi: 10.2514/1.D0174 [25] World Meteorological Organization. Guidelines on ensemble prediction systems and forecasting[M]. Switzerland: World Meteorological Organization, 2012: 1. -
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