WO2022194310A1 - 一种航班飞行轨迹多目标动态规划方法 - Google Patents

一种航班飞行轨迹多目标动态规划方法 Download PDF

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WO2022194310A1
WO2022194310A1 PCT/CN2022/097768 CN2022097768W WO2022194310A1 WO 2022194310 A1 WO2022194310 A1 WO 2022194310A1 CN 2022097768 W CN2022097768 W CN 2022097768W WO 2022194310 A1 WO2022194310 A1 WO 2022194310A1
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flight
waypoint
state
segment
decision
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French (fr)
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杨尚文
付胜豪
蒋璐
黄吉波
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中国电子科技集团公司第二十八研究所
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Priority to US17/813,171 priority Critical patent/US11663921B2/en
Publication of WO2022194310A1 publication Critical patent/WO2022194310A1/zh

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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G5/00—Traffic control systems for aircraft, e.g. air-traffic control [ATC]
    • G08G5/003—Flight plan management
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G5/00—Traffic control systems for aircraft, e.g. air-traffic control [ATC]
    • G08G5/003—Flight plan management
    • G08G5/0034—Assembly of a flight plan
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/40—Business processes related to the transportation industry
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G5/00—Traffic control systems for aircraft, e.g. air-traffic control [ATC]
    • G08G5/003—Flight plan management
    • G08G5/0039—Modification of a flight plan

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  • the invention belongs to the field of air traffic management, and in particular relates to a multi-objective dynamic planning method for flight trajectories which can be applied to air traffic control and air traffic flow management.
  • Trajectory planning in air traffic management generally optimizes flight trajectories with certain goals according to airspace structure, aircraft performance, flight restrictions and other conditions.
  • the main methods include trajectory planning based on airspace grids, trajectory planning based on restricted area geometry, and fixed Trajectory planning of waypoints, trajectory planning based on standard approach and departure procedures, trajectory planning based on free flight, etc.
  • Most of the existing researches aim at shortening the voyage and flight time, reducing flight conflicts, etc., but less consideration is given to factors such as altitude changes and air waiting, and trajectory planning is difficult to meet the requirements of four-dimensional trajectory management; in addition, trajectory planning is mostly used in unmanned aerial vehicles.
  • Aircraft management is less used in control automation systems and air traffic flow management systems.
  • Dynamic programming is an effective method to solve the optimization problem of multi-stage decision-making process, and it has good application effect in optimal path, resource allocation and other problems.
  • the flight trajectory of the flight is divided into several stages, and the dynamic programming method is used to optimize the decision-making of each stage to quickly form a trajectory planning decision-making sequence.
  • the dynamic programming method is used to optimize the decision-making of each stage to quickly form a trajectory planning decision-making sequence.
  • the technical problem to be solved by the present invention is: according to the conditions such as the route network structure, the length of the flight segment, the altitude configuration of each flight segment, the flow control and other information in the available airspace of the flight, the fuel consumption is the least and the flight time is the shortest.
  • the minimum number of altitude changes is the goal, establish a multi-objective dynamic programming model of flight trajectory, reshape the route network structure in the available airspace of the flight according to the needs of the solution, design the algorithm for solving the multi-objective dynamic programming model of the flight trajectory, and realize a single trajectory
  • the rapid generation of planning strategies can reasonably arrange flight routes and altitudes for flights, and provide auxiliary decision-making for scientifically formulating flight plans and improving the efficiency of diversion.
  • the present invention discloses a multi-objective dynamic planning method for flight trajectories, which includes the following steps:
  • Step 1 Obtain information such as route network structure, flight segment length, altitude configuration of each flight segment, and flow control in the available airspace of the flight;
  • Step 2 Establish a multi-objective dynamic programming model of flight trajectory
  • Step 3 Design the algorithm for solving the multi-objective dynamic programming model of flight trajectory
  • Step 4 Use the algorithm designed in Step 3 to solve the multi-objective dynamic programming model of the flight trajectory established in Step 2, and form multiple strategies for multi-stage decision-making of the flight trajectory.
  • the step 2 includes:
  • Step 2.1 Construct stage variables, state variables, and state transition equations
  • Step 2.2 Establish basic equations with the goal of minimum fuel consumption
  • Step 2.3 Establish the basic equation with the goal of the shortest flight time
  • Step 2.4 Establish basic equations with the goal of minimizing the number of altitude changes.
  • step 2.1 the stage variables, state variables, and state transition equations are constructed, which are expressed as:
  • the state variable sk represents the waypoint at the beginning of phase k
  • P k i represents the waypoint in the available airspace of the flight
  • At least one element in Sk is the immediate previous waypoint of any element in Sk+1 and there is a unique segment connection
  • all elements in Sk +1 have corresponding elements in Sk
  • this element is Sk
  • the immediate preceding waypoint of the element of +a and there is a unique flight segment connection set a-1 virtual waypoints evenly distributed by distance on the flight segment, and divide the flight segment into a flight segments.
  • the altitude configuration of the segment is still the same as that of the flight segment, and each virtual waypoint belongs to the corresponding state
  • step 2.2 aiming at the minimum fuel consumption, the basic equation is established as:
  • D k ( sk , uk ) represents the length of the flight segment between the state sk waypoint and the next stage sk+1 waypoint after the decision uk is adopted
  • C k l ( sk , uk ) Represents the fuel consumption per unit time at the lth level of the flight segment between the state sk waypoint and the next stage sk +1 waypoint after the decision uk is adopted
  • L k is the number of flight segments between the state sk waypoint and the next stage sk +1 waypoint after the decision uk is adopted
  • v represents the average ground speed of the flight
  • f k (s k ) represents the optimal indicator function.
  • step 2.3 aiming at the shortest flight time, the basic equation is established as:
  • T k ( sk , uk ) represents the air waiting time required by the next stage sk+1 waypoint flow control after the state sk waypoint adopts the decision uk .
  • step 2.4 aiming at the minimum number of changes in the height level, the basic equation is established as:
  • H k (s k , u k ) represents the height difference between the state sk waypoint using the decision uk and the decision u k -1 in the previous stage, the same height is 0, and the different height is 0 1.
  • the step 3 includes:
  • each flight segment starting from the waypoint P k+1 j has a total of L k+1 j levels, and L k i -1 virtual waypoints P k are generated for the waypoint P k i i , generate L k+1 j -1 virtual waypoints P k+1 j for the waypoint P k+1 j , each original and virtual waypoint P k i and each original and virtual waypoint P k i
  • There are flight segments between points P k+1 j each flight segment has the same distance and air waiting time required by flow control as the original flight segment, and there is only one altitude, the same original or virtual flight segment.
  • the flight segment between the waypoint P k i and the original or virtual waypoint P k+1 j has the same level;
  • Step 3.2 Normalize and weight each target to form a dimensionless single target, and establish the basic equation as:
  • G() represents the normalization function, so that each target value is in the same order of magnitude, and ⁇ 1 , ⁇ 2 , and ⁇ 3 respectively represent the weight of each target;
  • Step 3.3 Constantly change the weight of each objective to form different weight combinations, and use the reverse order method of dynamic programming to solve the single objective basic equation established in step 3.2.
  • FIG. 1 is a flow chart of the method of the present invention.
  • FIG. 2 is a schematic diagram of the route network structure for dynamic planning of flight trajectories.
  • FIG. 3 is a flow chart of a specific embodiment of the present invention.
  • Figure 4 is a schematic diagram of the reshaped route network structure for dynamic planning of flight trajectory.
  • a multi-objective dynamic planning method for flight flight trajectory includes the following steps:
  • step (3) Use the algorithm designed in step (3) to solve the multi-objective dynamic programming model of flight trajectory established in step (2), and form a variety of strategies for multi-stage decision-making of flight trajectory.
  • the route network structure in the available airspace during the flight has various flight segment combinations as optional trajectories.
  • Each flight segment may have multiple altitude layers.
  • Some waypoints implement flow control due to flight deployment and other reasons. To make the flight passing through the waypoint generate a certain air waiting time, it is necessary to optimize the selection of flight segments to achieve the best trajectory planning.
  • the present invention discloses a multi-objective dynamic planning method for flight flight trajectory.
  • the specific implementation process is shown in FIG. 3 and includes the following steps:
  • Step 1 Obtain information such as route network structure, flight segment length, level configuration of each flight segment, and flow control in the available airspace of the flight;
  • Step 2 Construct stage variables, state variables, and state transition equations
  • Step 3 Establish basic equations with the goal of minimum fuel consumption
  • Step 4 Establish the basic equation with the shortest flight time as the goal
  • Step 5 Establish the basic equation with the goal of minimizing the number of altitude changes
  • Step 6 Design the algorithm for solving the multi-objective dynamic programming model of flight trajectory
  • Step 7 Use the algorithm designed in Step 6 to solve the multi-objective dynamic programming model of the flight trajectory established in Step 2, Step 3, Step 4, and Step 5, and form multiple strategies for multi-stage decision-making of the flight trajectory.
  • step 2 the stage variables, state variables, and state transition equations are constructed, which are expressed as:
  • the state variable sk represents the waypoint at the beginning of stage k
  • P k i represents the available airspace of the flight
  • the waypoint of , at least one element in Sk is the immediately preceding waypoint of any element in Sk+1 and there is a unique segment connection, all elements of Sk+1 have corresponding elements in Sk , the The element is the immediately preceding waypoint of any element in Sk+1 and there is a unique segment connection; as shown in Figure 2, for any two non-adjacent state variables sk and sk+a (a ⁇ 2) , if there is an immediate preceding waypoint whose element is the element of Sk+a in Sk and there is a unique flight segment connection, then set a-1 virtual waypoints evenly distributed by distance on this flight segment, and this flight segment Divided into a flight segment, the altitude configuration of each flight segment is still the same as that of the flight
  • step 3 aiming at the minimum fuel consumption, the basic equation is established as:
  • D k ( sk , uk ) represents the length of the flight segment between the state sk waypoint and the next stage sk+1 waypoint after the decision uk is adopted
  • C k l ( sk , uk ) Represents the fuel consumption per unit time at the lth level of the flight segment between the state sk waypoint and the next stage sk +1 waypoint after the decision uk is adopted
  • L k is the number of flight segments between the state sk waypoint and the next stage sk +1 waypoint after the decision uk is adopted
  • v represents the average ground speed of the flight
  • f k (s k ) represents the optimal indicator function.
  • step 4 aiming at the shortest flight time, the basic equation is established as:
  • T k ( sk , uk ) represents the air-holding time required by the flow control of the next stage sk +1 waypoint after the state sk waypoint adopts the decision uk.
  • step 5 aiming at the minimum number of changes in the height level, the basic equation is established as:
  • H k (s k , u k ) represents the height difference between the state sk waypoint using the decision uk and the decision u k -1 in the previous stage, the same height is 0, and the different height is 0 1.
  • the algorithm for solving the multi-objective dynamic programming model of the flight trajectory in step 6 includes:
  • each flight segment starting from the waypoint P k+1 j has a total of L k+1 j levels, and L k i -1 virtual waypoints P k are generated for the waypoint P k i i , generate L k+1 j -1 virtual waypoints P k+1 j for the waypoint P k+1 j , each original and virtual waypoint P k i and each original and virtual waypoint P k i
  • There are flight segments between points P k+1 j each flight segment has the same distance and air waiting time required by flow control as the original flight segment, and there is only one altitude, the same original or virtual flight segment.
  • the flight segment between the waypoint P k i and the original or virtual waypoint P k+1 j has the same altitude, as shown in Figure 4, taking the waypoints P 1 1 and P 2 1 as examples;
  • Step 6.2 Normalize and weight each target to form a dimensionless single target, and establish the basic equation as:
  • G() represents the normalization function, so that each target value is in the same order of magnitude, and ⁇ 1 , ⁇ 2 , and ⁇ 3 respectively represent the weight of each target;
  • Step 6.3 Constantly change the weight of each objective to form different weight combinations, and use the inverse order method of dynamic programming to solve the single objective basic equation established in step 6.2.
  • the modeling process of the invention is simple and easy to implement, easy to solve and realize, and is suitable for the development of control automation systems and air traffic flow management system tools.
  • the present invention provides a multi-objective dynamic planning method for flight trajectories.
  • the above are only the preferred embodiments of the present invention. Said that, on the premise of not departing from the principles of the present invention, several improvements and modifications can also be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.
  • Each component that is not specified in this embodiment can be implemented by existing technology.

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Abstract

本发明公开了一种航班飞行轨迹多目标动态规划方法，属于空中交通管理领域。该方法首先获取航班可用空域内的航路网络结构、航段长度、各航段的高度层配置、流量控制等信息，然后以燃油消耗最少、飞行时间最短、高度层变更次数最少为目标建立航班飞行轨迹多目标动态规划模型，进而设计航班飞行轨迹多目标动态规划模型的求解算法，最后求解模型，形成航班飞行轨迹多阶段决策的多种策略。本发明为空中交通管制、空中交通流量管理提供了技术依据。

Description

一种航班飞行轨迹多目标动态规划方法 技术领域
本发明属于空中交通管理领域，特别涉及一种可应用于空中交通管制、空中交通流量管理的航班飞行轨迹多目标动态规划方法。
背景技术
空中交通管理中的轨迹规划一般根据空域结构、航空器性能、飞行限制等条件，以一定目标优化飞行轨迹，主要方法包括基于空域网格的轨迹规划、基于受限区几何形状的轨迹规划、基于固定航路点的轨迹规划、基于标准进离场程序的轨迹规划、基于自由飞行的轨迹规划等。现有研究大多以缩短航程和飞行时间、减少飞行冲突等为目标，对高度层变化、空中等待等因素考虑较少，轨迹规划难以满足四维轨迹管理的要求；此外，轨迹规划多应用于无人机管理，在管制自动化系统、空中交通流量管理系统中应用较少。动态规划是解决多阶段决策过程最优化问题的有效方法，在最优路径、资源分配等问题中有良好的应用效果。根据空域结构、飞行过程将航班飞行轨迹划分为若干阶段，采用动态规划方法优化每一阶段的决策，快速形成轨迹规划决策序列。目前尚缺少一种面向四维轨迹管理的航班飞行轨迹多目标动态规划实现方法。
发明内容
发明目的：本发明要解决的技术问题是：根据航班可用空域内的航路网络结构、航段长度、各航段的高度层配置、流量控制等信息等条件，分别以燃油消耗最少、飞行时间最短、高度层变更次数最少为目标，建立航班飞行轨迹多目标动态规划模型，根据求解需要重塑航班可用空域内的航路网络结构，设计航班飞行轨迹多目标动态规划模型的求解算法，实现单次轨迹规划策略的快速生成，为航班合理安排飞行航路和高度层，为科学制定飞行计划、提高改航效率提供辅助决策。
为了解决上述技术问题，本发明公开了一种航班飞行轨迹多目标动态规划方法，包括如下步骤：
步骤1：获取航班可用空域内的航路网络结构、航段长度、各航段的高度层配置、流量控制等信息；
步骤2：建立航班飞行轨迹多目标动态规划模型；
步骤3：设计航班飞行轨迹多目标动态规划模型的求解算法；
步骤4：采用步骤3设计的算法求解步骤2建立的航班飞行轨迹多目标动态规划模型，形成航班飞行轨迹多阶段决策的多种策略。
所述步骤2包括：
步骤2.1：构建阶段变量、状态变量、状态转移方程；
步骤2.2：以燃油消耗最少为目标建立基本方程；
步骤2.3：以飞行时间最短为目标建立基本方程；
步骤2.4：以高度层变更次数最少为目标建立基本方程。
步骤2.1中构建阶段变量、状态变量、状态转移方程，表示为：
阶段变量k＝1,2,3,…,N，N是从可用空域进入点至退出点的各航路所包含航段的最大数量，可用空域进入点和退出点均唯一且不相同；
状态变量s k表示阶段k开始时的航路点，状态变量s k的状态集合S k＝{P k i}(i＝1,2,…)，P k i表示航班可用空域内的航路点，S k中至少有一个元素是S k+1中任一元素的紧前航路点且存在唯一航段连接，S k+1的全部元素均在S k中有对应的元素，该元素是S k+1中任一元素的紧前航路点且存在唯一航段连接；对于任意两个不相邻的状态变量s k和s k+a(a≥2)，若S k中存在元素是S k+a的元素的紧前航路点且存在唯一航段连接，则在该航段上设置a-1个按距离平均分布的虚拟航路点，将该航段划分成a个航段，每个航段的高度层配置仍与该航段相同，每个虚拟航路点分别归属相应的状态集合；
状态转移方程为s k+1＝u k(s k)，u k(s k)表示第k阶段当状态为s k时的决策变量。
步骤2.2中以燃油消耗最少为目标，建立基本方程为：
Figure PCTCN2022097768-appb-000001
其中，D k(s k,u k)表示状态s k航路点与采用决策u k后的下一阶段s k+1航路点之间的航段长度，C k l(s k,u k)表示航班在状态s k航路点与采用决策u k后的下一阶段s k+1航路点之间的航段的第l个高度层的单位时间燃油消耗量，1≤l≤L k，L k为状态s k航路点与采用决策u k后的下一阶段s k+1航路点之间的航段的高度层数量；v表示航班的平均地速，f k(s k) 表示最优指标函数。
步骤2.3中以飞行时间最短为目标，建立基本方程为：
Figure PCTCN2022097768-appb-000002
其中，T k(s k,u k)表示状态s k航路点采用决策u k后的下一阶段s k+1航路点流量控制所要求的空中等待时间。
步骤2.4中以高度层变更次数最少为目标，建立基本方程为：
Figure PCTCN2022097768-appb-000003
其中，H k(s k,u k)表示状态s k航路点采用决策u k与上一阶段的决策u k-1的高度层差异，高度层相同取值为0，高度层不同取值为1。
所述步骤3包括：
步骤3.1：根据求解需要重塑航班可用空域内的航路网络结构，状态变量s k的状态集合S k＝{P k i}(i＝1,2,…)中的任一航路点P k i与下一阶段s k+1的状态集合S k+1＝{P k+1 j}(j＝1,2,…)中的航路点P k+1 j之间存在航段，该航段有L k i个高度层，以航路点P k+1 j为起点的航段共有L k+1 j个高度层，针对航路点P k i生成L k i-1个虚拟的航路点P k i，针对航路点P k+1 j生成L k+1 j-1个虚拟的航路点P k+1 j，每个原有和虚拟的航路点P k i与每个原有和虚拟的航路点P k+1 j之间均产生航段，每个航段具有与原航段相同的距离和流量控制所要求的空中等待时间，有且仅有一个高度层，同一个原有或虚拟的航路点P k i与原有或虚拟的航路点P k+1 j之间的航段具有相同的高度层；
步骤3.2：将各目标归一化加权形成无量纲的单目标，建立基本方程为：
Figure PCTCN2022097768-appb-000004
其中，G()表示归一化函数，使各目标值处于同一数量级，ω 1、ω 2、ω 3分别表示各目标的权重；
步骤3.3：不断改变各目标权重，形成不同的权重组合，采用动态规划的逆序法求 解步骤3.2建立的单目标基本方程。
有益效果：
1、为基于轨迹运行模式下的航班精细化轨迹规划或改航规划提供了一种实现方法；
2、为管制自动化系统、空中交通流量管理系统中的轨迹管理等软件研制提供技术支撑。
附图说明
下面结合附图和具体实施方式对本发明做更进一步的具体说明，本发明的上述和/或其他方面的优点将会变得更加清楚。
图1为本发明的方法流程图。
图2为航班飞行轨迹动态规划的航路网络结构示意图。
图3为本发明的具体实施方式流程图。
图4为航班飞行轨迹动态规划的重塑航路网络结构示意图。
具体实施方式
下面将结合附图，对本发明的实施例进行描述。
如图1所示，一种航班飞行轨迹多目标动态规划方法，包括如下步骤：
(1)获取航班可用空域内的航路网络结构、航段长度、各航段的高度层配置、流量控制等信息；
(2)建立航班飞行轨迹多目标动态规划模型；
(3)设计航班飞行轨迹多目标动态规划模型的求解算法；
(4)采用步骤(3)设计的算法求解步骤(2)建立的航班飞行轨迹多目标动态规划模型，形成航班飞行轨迹多阶段决策的多种策略。
如图2所示，航班飞行过程中可用空域内的航路网络结构存在多种航段组合作为可选轨迹，各航段可能存在多个高度层，部分航路点因飞行调配等原因实施流量控制，使经过该航路点的航班产生一定的空中等待时间，需优化选择航段，实现最佳轨迹规划。
本发明公开了一种航班飞行轨迹多目标动态规划方法，具体实施流程如图3所示，包括如下步骤：
步骤1：获取航班可用空域内的航路网络结构、航段长度、各航段的高度层配置、 流量控制等信息；
步骤2：构建阶段变量、状态变量、状态转移方程；
步骤3：以燃油消耗最少为目标建立基本方程；
步骤4：以飞行时间最短为目标建立基本方程；
步骤5：以高度层变更次数最少为目标建立基本方程；
步骤6：设计航班飞行轨迹多目标动态规划模型的求解算法；
步骤7：采用步骤6设计的算法求解步骤2、步骤3、步骤4、步骤5建立的航班飞行轨迹多目标动态规划模型，形成航班飞行轨迹多阶段决策的多种策略。
步骤2中构建阶段变量、状态变量、状态转移方程，表示为：
阶段变量k＝1,2,3,…,N，N是从可用空域进入点至退出点的各航路所包含航段的最大数量，可用空域进入点和退出点均唯一且不相同；
状态变量s k表示阶段k开始时的航路点，状态变量s k的状态集合S k＝{P k i}(i为自然数，i＝1,2,…)，P k i表示航班可用空域内的航路点，S k中至少有一个元素是S k+1中任一元素的紧前航路点且存在唯一航段连接，S k+1的全部元素均在S k中有对应的元素，该元素是S k+1中任一元素的紧前航路点且存在唯一航段连接；如图2所示，对于任意两个不相邻的状态变量s k和s k+a(a≥2)，若S k中存在元素是S k+a的元素的紧前航路点且存在唯一航段连接，则在该航段上设置a-1个按距离平均分布的虚拟航路点，将该航段划分成a个航段，每个航段的高度层配置仍与该航段相同，每个虚拟航路点分别归属相应的状态集合；
状态转移方程为s k+1＝u k(s k)，u k(s k)表示第k阶段当状态为s k时的决策变量。
步骤3中以燃油消耗最少为目标，建立基本方程为：
Figure PCTCN2022097768-appb-000005
其中，D k(s k,u k)表示状态s k航路点与采用决策u k后的下一阶段s k+1航路点之间的航段长度，C k l(s k,u k)表示航班在状态s k航路点与采用决策u k后的下一阶段s k+1航路点之间的航段的第l个高度层的单位时间燃油消耗量，1≤l≤L k，L k为状态s k航路点与采用决 策u k后的下一阶段s k+1航路点之间的航段的高度层数量；v表示航班的平均地速，f k(s k)表示最优指标函数。
步骤4中以飞行时间最短为目标，建立基本方程为：
Figure PCTCN2022097768-appb-000006
其中，T k(s k,u k)表示状态s k航路点采用决策u k后的下一阶段s k+1航路点流量控制所要求的空中等待时间。
步骤5中以高度层变更次数最少为目标，建立基本方程为：
Figure PCTCN2022097768-appb-000007
其中，H k(s k,u k)表示状态s k航路点采用决策u k与上一阶段的决策u k-1的高度层差异，高度层相同取值为0，高度层不同取值为1。
步骤6中航班飞行轨迹多目标动态规划模型的求解算法包括：
步骤6.1：根据求解需要重塑航班可用空域内的航路网络结构，状态变量s k的状态集合S k＝{P k i}(i＝1,2,…)中的任一航路点P k i与下一阶段s k+1的状态集合S k+1＝{P k+1 j}(j＝1,2,…)中的航路点P k+1 j之间存在航段，该航段有L k i个高度层，以航路点P k+1 j为起点的航段共有L k+1 j个高度层，针对航路点P k i生成L k i-1个虚拟的航路点P k i，针对航路点P k+1 j生成L k+1 j-1个虚拟的航路点P k+1 j，每个原有和虚拟的航路点P k i与每个原有和虚拟的航路点P k+1 j之间均产生航段，每个航段具有与原航段相同的距离和流量控制所要求的空中等待时间，有且仅有一个高度层，同一个原有或虚拟的航路点P k i与原有或虚拟的航路点P k+1 j之间的航段具有相同的高度层，如图4所示，以航路点P 1 1和P 2 1为示例；
步骤6.2：将各目标归一化加权形成无量纲的单目标，建立基本方程为：
Figure PCTCN2022097768-appb-000008
其中，G()表示归一化函数，使各目标值处于同一数量级，ω 1、ω 2、ω 3分别表示各 目标的权重；
步骤6.3：不断改变各目标权重，形成不同的权重组合，采用动态规划的逆序法求解步骤6.2建立的单目标基本方程。
本发明建模过程简便易行，易于求解实现，适合应用于管制自动化系统、空中交通流量管理系统工具的开发。
本发明提供了一种航班飞行轨迹多目标动态规划方法，具体实现该技术方案的方法和途径很多，以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。本实施方式中未明确的各组成部分均可用现有技术加以实现。

Claims (7)

  1. 一种航班飞行轨迹多目标动态规划方法，其特征在于，包括如下步骤：
    步骤1：获取航班可用空域内的航路网络结构、航段长度、各航段的高度层配置和流量控制信息；
    步骤2：建立航班飞行轨迹多目标动态规划模型；
    步骤3：设计航班飞行轨迹多目标动态规划模型的求解算法；
    步骤4：采用步骤3设计的算法求解步骤2建立的航班飞行轨迹多目标动态规划模型，形成航班飞行轨迹多阶段决策的多种策略。
  2. 根据权利要求1所述的一种航班飞行轨迹多目标动态规划方法，其特征在于，所述步骤2包括：
    步骤2.1：构建阶段变量、状态变量、状态转移方程；
    步骤2.2：以燃油消耗最少为目标建立基本方程；
    步骤2.3：以飞行时间最短为目标建立基本方程；
    步骤2.4：以高度层变更次数最少为目标建立基本方程。
  3. 根据权利要求2所述的一种航班飞行轨迹多目标动态规划方法，其特征在于，步骤2.1中构建阶段变量、状态变量、状态转移方程，表示为：
    阶段变量k＝1,2,3,…,N，N是从可用空域进入点至退出点的各航路所包含航段的最大数量，可用空域进入点和退出点均唯一且不相同；
    状态变量s k表示阶段k开始时的航路点，状态变量s k的状态集合S k＝{P k i}(i＝1,2,…)，P k i表示航班可用空域内的航路点，S k中至少有一个元素是S k+1中任一元素的紧前航路点且存在唯一航段连接，S k+1的全部元素均在S k中有对应的元素，该元素是S k+1中任一元素的紧前航路点且存在唯一航段连接；对于任意两个不相邻的状态变量s k和s k+a(a≥2)，若S k中存在元素是S k+a的元素的紧前航路点且存在唯一航段连接，则在该航段上设置a-1个按距离平均分布的虚拟航路点，将该航段划分成a个航段，每个航段的高度层配置仍与该航段相同，每个虚拟航路点分别归属相应的状态集合；
    状态转移方程为s k+1＝u k(s k)，u k(s k)表示第k阶段当状态为s k时的决策变量。
  4. 根据权利要求2所述的一种航班飞行轨迹多目标动态规划方法，其特征在于，步骤2.2中以燃油消耗最少为目标，建立基本方程为：
    Figure PCTCN2022097768-appb-100001
    其中，D k(s k,u k)表示状态s k航路点与采用决策u k后的下一阶段s k+1航路点之间的航段长度，C k l(s k,u k)表示航班在状态s k航路点与采用决策u k后的下一阶段s k+1航路点之间的航段的第l个高度层的单位时间燃油消耗量，1≤l≤L k，L k为状态s k航路点与采用决策u k后的下一阶段s k+1航路点之间的航段的高度层数量；v表示航班的平均地速，f k(s k)表示最优指标函数。
  5. 根据权利要求2所述的一种航班飞行轨迹多目标动态规划方法，其特征在于，步骤2.3中以飞行时间最短为目标，建立基本方程为：
    Figure PCTCN2022097768-appb-100002
    其中，T k(s k,u k)表示状态s k航路点采用决策u k后的下一阶段s k+1航路点流量控制所要求的空中等待时间。
  6. 根据权利要求2所述的一种航班飞行轨迹多目标动态规划方法，其特征在于，
    步骤2.4中以高度层变更次数最少为目标，建立基本方程为：
    Figure PCTCN2022097768-appb-100003
    其中，H k(s k,u k)表示状态s k航路点采用决策u k与上一阶段的决策u k-1的高度层差异，高度层相同取值为0，高度层不同取值为1。
  7. 根据权利要求6所述的一种航班飞行轨迹多目标动态规划方法，其特征在于，所述步骤3包括：
    步骤3.1：根据求解需要重塑航班可用空域内的航路网络结构，状态变量s k的状态集合S k＝{P k i}(i＝1,2,…)中的任一航路点P k i与下一阶段s k+1的状态集合S k+1＝{P k+1 j}(j＝1,2,…)中的航路点P k+1 j之间存在航段，该航段有L k i个高度层，以航路点P k+1 j为起点的航段共有L k+1 j个高度层，针对航路点P k i生成L k i-1个虚拟的航路点P k i，针对航路点P k+1 j生成L k+1 j-1个虚拟的航路点P k+1 j，每个原有和虚拟的航路点P k i与每个原有和 虚拟的航路点P k+1 j之间均产生航段，每个航段具有与原航段相同的距离和流量控制所要求的空中等待时间，有且仅有一个高度层，同一个原有或虚拟的航路点P k i与原有或虚拟的航路点P k+1 j之间的航段具有相同的高度层；
    步骤3.2：将各目标归一化加权形成无量纲的单目标，建立基本方程为：
    Figure PCTCN2022097768-appb-100004
    其中，G()表示归一化函数，使各目标值处于同一数量级，ω 1、ω 2、ω 3分别表示各目标的权重；
    步骤3.3：不断改变各目标权重，形成不同的权重组合，采用动态规划的逆序法求解步骤3.2建立的单目标基本方程。
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