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摘要:
随着航空器自主保持间隔运行概念的逐渐发展，基于连续爬升运行(CCO)模式，可有效解决当前终端区内航空器离场路径固定单一所造成空域运行效率低问题。为此，提出一种基于人工势场-粒子群优化(APF-PSO)联合算法的终端区离场航空器自主路径规划方法。构建面向航空器自主运行模式的空域环境模型，对空域环境进行栅格化处理并计算各栅格的空域复杂度，限制离场航空器进入高复杂度栅格以保障运行安全；构建基于BADA数据库和减退力爬升模式的航空器爬升性能约束模型；应用APF-PSO联合算法进行路径规划，通过粒子群优化(PSO)算法广域搜索思想解决人工势场法（APF）固有的局部极值-目标不可达问题；使用贝塞尔曲线法优化该路径，引入滑动时间窗口理念优化航空器离场时刻；使用上海终端空域的实际结构和运行数据，应用所提方法进行仿真模拟。仿真结果表明：APF-PSO联合算法可有效生成航空器无冲突离场路径并规避繁忙空域，优化处理后的路径满足航空器爬升性能约束，且优于实际运行路径(路径长度减少23.78%，最大转弯率降低55.73%，最大爬升率降低9.94%)；离场航空器自主运行模式下的空中交通复杂性较当前运行模式更为均衡(栅格复杂度峰值降低3.92%)，可有效提升空域利用率。
Abstract:With the gradual development of the aircraft self-separation operation and the continuous climbing operation (CCO) mode, it can effectively solve the problem that the departure path of aircraft in the current terminal area is fixed and single, which leads to the low operational efficiency of airspace. Therefore, an autonomous path planning method based on artificial potential field-particle swarm optimization（APF-PSO） algorithm was proposed in this paper. To guarantee operation safety, the airspace environment was first rasterized, the aircraft autonomous operation mode was taken into consideration, and the airspace complexity of each grid was computed. This prevented departing aircraft from flying into high-complexity grids. The aircraft climbing performance constraint model was constructed based on the BADA database and reduced force climbing mode. Then the path planning was carried out by using the APF-PSO algorithm of artificial potential field（APF） and particle swarm optimization（PSO） algorithm, and the local extremum-target unreachable problem inherent in the artificial potential field method was solved by using the region search algorithm of particle swarm optimization. The Bessel curve method was used to optimize the path planning and the concept of sliding time window was introduced to optimize the departure time of aircraft. Finally, using the actual structure and operation data of Shanghai terminal airspace, the proposed method was applied to simulate. The simulation test results show that the APF-PSO algorithm can effectively generate the aircraft conflict-free departure path and avoid busy airspace. The optimized path satisfies the aircraft climbing performance constraints and is better than the actual path (path length reduced by 23.78%, maximum turning rate reduced by 55.73%, maximum climbing rate reduced by 9.94%). Additionally, the autonomous operation mode of departing aircraft results in a more balanced airspace operation condition than the actual operating mode (a reduction of 3.92% in peak grid complexity), which can significantly increase the airspace utilization rate.
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图 1 冲突规避栅格位置关系示意图
Figure 1. Schematic diagram of position relation of conflict avoidance grid
表 1 某型航空器基础参数
Table 1. Basic parameters of a certain aircraft type
参数 数值 参数 数值 机翼面积$ S $/m3 283.3 推力性能参数$ {C_{{\text{Tc}},3}} $ 0.419×1010 阻力性能参数$ {C_{D0,{\mathrm{CR}}}} $ 0.014 推力性能参数$ {C_{{\text{Tc}},5}} $ 0.0055 阻力性能参数$ {C_{D2,{\mathrm{CR}}}} $ 0.049 推力性能参数$ {C_{{\mathrm{red}}}} $ 0.10 推力性能参数$ {C_{{\text{Tc}},1}} $ 0.296×106 最大质量$ {m_{\max }} $/kg 181400 推力性能参数$ {C_{{\text{Tc}},2}} $ 0.509×105 最小质量$ {m_{\min }} $/kg 89900 
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表 2 某型航空器性能随高度变化数据
Table 2. A certain type of aircraft performance changes with height data
高度/m 最大爬升
推力/N航空器最大
速度/(km·h−1)最小转弯
半径/km最大爬升率/
(m·min−1)900 274783.56 351.88 3.69 799.92 1200 273142.29 416.70 5.18 974.45 1800 269866.11 503.74 7.57 1224.60 2400 266598.35 518.56 8.02 1175.16 3000 263339.04 535.23 8.54 1122.80 3600 260088.16 659.31 12.96 1111.16 4200 256845.72 677.83 13.70 1044.26 4800 253611.72 698.21 14.53 977.36 5400 250386.16 718.58 15.39 907.55 6000 247169.04 740.80 16.36 837.73
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表 3 APF-PSO联合算法参数定义及取值
Table 3. Parameters definition and values of APF-PSO algorithm
障碍物斥力
系数$ {k_{{\text{rep}}}} $斥力影响范围
$ {d_0} $(椭球距离)/kmPSO算法迭代
次数$ T $加速度
常数$ {c_1} $目标点引力
系数$ {k_{{\mathrm{att}}}} $位置系数参考椭球
距离$ {d_{{\mathrm{dtc}}}} $/km惯性
权重$ \omega $加速度
常数$ {c_2} $9 $ 2.5\sqrt 3 $ 100 2 1 $ 10\sqrt 3 $ 0.7 2
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表 4 离场航空器路径曲线性能对比
Table 4. Performance comparison of departing aircraft path curves
平均路径长度/km 平均最大转弯率/((°)·min−1) 平均最大爬升梯度/% 平均最大爬升率/(m·min−1) 实际运行
路径CCO规划
路径时刻
优化后实际运行
路径CCO规划
路径时刻
优化后实际运行
路径CCO规划
路径时刻
优化后实际运行
路径CCO规划
路径时刻
优化后241.45 184.04 180.75 55.50 24.57 24.71 9.44 9.47 9.06 901.13 811.55 809.88
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表 5 空域运行态势数据对比
Table 5. Comparison of airspace operational situation data
时间片 栅格复杂度峰值 高复杂度栅格占比/% 实际运行路径 CCO规划路径 离场时刻优化后路径 实际运行路径 CCO规划路径 离场时刻优化后路径 1 2.115 2.107 2.037 5.83 6.00 5.96 2 4.072 3.571 3.698 3.23 3.63 3.74 $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ 58 3.063 2.507 2.527 2.96 3.61 3.22 59 3.718 3.391 3.288 2.10 2.62 3.00
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表 6 算法性能对比统计
Table 6. Statistical of algorithms performance comparison
算法 路径规划成功率/% 运算时间/s 路径长度/km 最大转弯率/((°)·min−1) 最大爬升梯度/% 最大爬升率/(m·min−1) APF-PSO联合算法 100 4.42 184.04 24.57 9.47 811.55 APF算法 73.1 1.37 177.30 31.26 12.96 819.34 A*算法 96.2 3.61 183.73 26.10 12.17 846.58
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