A data-driven robust optimization method and device for low-altitude air route planning and a medium
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-27
- Publication Date
- 2026-08-11
AI Technical Summary
本发明提供了一种数据驱动鲁棒优化的低空航路规划方法，首先将低空公共航路规划空域划分为若干个空域网格单元，并获取每个空域网格单元在历史各时间段的历史风险程度值，为后续的数据驱动和鲁棒优化提供标准化的数据基础；然后采用数据驱动方式分别构建每一空域网格单元满足预设风险阈值的风险不确定性集合，既能反映风险波动规律，又满足安全概率要求，为后续风险概率约束提供了合理的参数边界；还构建了包含目标函数和若干约束的目标规划模型，将离散化的低空公共航路规划问题转化为了网络流优化问题，再将风险不确定性集合嵌入机会约束进行鲁棒优化，实现了将风险概率约束转换为易于计算的线性确定性约束，消除了对精确已知概率分布的依赖，还保留了风险不确定性集合中的上限信息；最后对优化后的目标规划模型进行求解，得到从待规划航路起点到待规划航路终点的最优低空公共航路；也即，本发明在无需精确概率分布的前提下，动态实现了安全、可靠且低成本的低空公共航路规划。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of low-altitude flight path planning technology, and in particular to a data-driven robust optimization method, device and medium for low-altitude flight path planning. Background Technology
[0002] Low-altitude public airway planning is a crucial means of ensuring the safe and efficient operation of low-altitude aircraft such as drones. The planning process requires careful management of various safety risks, primarily including dynamically variable risks such as population density risk, weather condition risk, and electromagnetic environment risk. Currently, mainstream low-altitude airway planning methods typically employ deterministic estimates of each risk factor, using a fixed risk value to characterize the severity of risk in a given area and planning airways based on this fixed value. However, this method fails to reflect the dynamic fluctuations in risk, leading to uncontrollable safety risks in actual operation of the planned airways. For example, in cases of sudden deterioration in weather conditions or a momentary increase in population density, the safety margin of the airways may be insufficient.
[0003] To address risk uncertainty, some studies have introduced opportunity constraint methods. These methods characterize risk severity at a set confidence level, requiring that the probability of a risk exceeding a safety threshold not exceed a preset value. While theoretically well-suited to the practical needs of risk management in low-altitude air routes, opportunity constraint methods have a key limitation: solving for opportunity constraints typically relies on precisely known probability distributions of risk factors. In actual low-altitude operational environments, due to the complexity and variability of risk factors and the limited availability of historical observation data, precise probability distributions are often difficult to obtain or verify, making traditional opportunity constraint methods difficult to apply directly.
[0004] Therefore, there is an urgent need for a low-altitude public airway planning method that can effectively overcome risk uncertainty and ensure airway safety and reliability even when the probability distribution is unknown. Summary of the Invention
[0005] To address the aforementioned technical problems, this invention provides a data-driven robust optimization method, device, and medium for low-altitude route planning. By constructing a risk uncertainty set of airspace grid cells through a data-driven method and embedding opportunity constraints for robust transformation, safe, reliable, and low-cost low-altitude public route planning is dynamically achieved without requiring precise probability distributions.
[0006] According to a first aspect of the present invention, a data-driven robust optimization method for low-altitude route planning is provided, comprising the following steps: S1 divides the airspace for low-altitude public airway planning into several uniformly scaled airspace grid units and obtains the historical risk level values of each airspace grid unit in different historical time periods.
[0007] S2, based on several historical risk level values of each spatial grid cell, uses a data-driven approach to construct a risk uncertainty set for each spatial grid cell that satisfies a preset risk threshold.
[0008] S3, map each airspace grid cell to a network node, and map the adjacency relationship between adjacent network nodes to edges in the network, to construct a target planning model based on network flow; the target planning model aims to minimize the total route distance and includes origin-end point flow constraints, edge capacity constraints, anti-loop constraints, risk probability constraints based on each airspace grid cell, and flow conservation constraints for each network node except for the origin and end point of the route to be planned.
[0009] S4 embeds the set of risk uncertainties into the risk probability constraints, so that the original probabilistic risk probability constraints are transformed into linear deterministic constraints with the maximum value in the set of risk uncertainties as the coefficient after robust optimization, and the goal programming model is updated.
[0010] S5 uses a preset optimization solver to solve the target planning model, and obtains and outputs the optimal low-altitude public route from the starting point to the ending point of the route to be planned.
[0011] According to a second aspect of the present invention, a non-transitory computer-readable storage medium is provided, wherein at least one instruction or at least one program is stored therein, the at least one instruction or the at least one program being loaded and executed by a processor to implement the above-described data-driven robust optimization low-altitude route planning method.
[0012] According to a third aspect of the present invention, an electronic device is provided, including a processor and the aforementioned non-transitory computer-readable storage medium.
[0013] The present invention has at least the following beneficial effects: This invention provides a data-driven robust optimization method for low-altitude airway planning. First, the airspace for low-altitude public airway planning is divided into several airspace grid cells, and the historical risk level values of each airspace grid cell in different historical time periods are obtained, providing a standardized data foundation for subsequent data-driven and robust optimization. Then, a risk uncertainty set satisfying a preset risk threshold is constructed for each airspace grid cell using a data-driven approach. This set reflects both risk fluctuation patterns and safety probability requirements, providing reasonable parameter boundaries for subsequent risk probability constraints. Furthermore, a target planning model containing an objective function and several constraints is constructed, transforming the discretized low-altitude public airway planning problem into a network flow optimization problem. The risk uncertainty set is then embedded with chance constraints for robust optimization, converting risk probability constraints into easily computed linear deterministic constraints. This eliminates the dependence on precisely known probability distributions while retaining the upper limit information in the risk uncertainty set. Finally, the optimized target planning model is solved to obtain the optimal low-altitude public airway from the starting point to the ending point of the planned airway. In other words, this invention dynamically achieves safe, reliable, and low-cost low-altitude public airway planning without requiring precise probability distributions. Attached Figure Description
[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0015] Figure 1 A flowchart of a data-driven robust optimization low-altitude route planning method provided in an embodiment of the present invention. Detailed Implementation
[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0017] This invention provides a data-driven, robust optimization method for low-altitude route planning, such as... Figure 1 As shown, the method includes the following steps: S1 divides the airspace for low-altitude public airway planning into several uniformly scaled airspace grid units and obtains the historical risk level values of each airspace grid unit for different historical time periods. In other words, in practical implementation, the airspace for low-altitude public airway planning is divided into seamless, non-overlapping, and uniformly scaled grids. Those skilled in the art can set the total historical time period according to actual needs and divide it into several time periods of equal length.
[0018] Specifically, obtaining the historical risk level value of each spatial grid cell in different historical time periods includes: S101, acquire historical observation data of various risk factors corresponding to each airspace grid unit within the low-altitude public airway planning airspace; the various risk factors include two categories: deterministic risk factors and random risk factors, wherein random risk factors are dynamically recorded at equal time intervals.
[0019] Among them, deterministic risk factors refer to risk factors that can be regarded as fixed values, such as terrain slope, fixed building location, and other risk factors that do not change or change very slowly over time, requiring only one measurement; random risk factors refer to risk factors that change dynamically over time and have uncertainty, such as wind speed, rainfall, and other risk factors. Because they change rapidly, continuous observation is required to capture their fluctuation patterns. Therefore, this embodiment adopts a dynamic recording method with equal time intervals.
[0020] S102, for each airspace grid cell, based on the pre-constructed low-altitude public airway risk assessment index system and the preset weights of each risk assessment index, the historical risk level value of each airspace grid cell in each historical time period is obtained by weighted summation; the historical time periods correspond to the equal time intervals.
[0021] For example, for wind speed, a random risk factor, the corresponding assessment index is the wind speed risk level, which includes no risk level, low risk level, medium risk level, and high risk level. These assessment indexes are mapped to a level value between 0 and 1 as the risk assessment value. For fixed building location, a deterministic risk factor, the corresponding assessment indexes include building height and building density. By presetting the maximum building height and the total area of the airspace grid cells containing the building, the risk assessment values for building height and building density are obtained by normalization.
[0022] The above-mentioned approach, by introducing deterministic and stochastic risk factors, takes into account both static environmental characteristics and dynamic risk changes, and achieves reliable quantification of the risk level of airspace grid units. Furthermore, by recording at equal time intervals, it can capture the dynamic changes of each airspace grid unit over time, providing a standardized data foundation for subsequent data-driven and robust optimization. This allows for the generation of robust routes even without precise probability distributions.
[0023] S2, based on several historical risk level values of each spatial grid cell, uses a data-driven approach to construct a risk uncertainty set for each spatial grid cell that satisfies a preset risk threshold.
[0024] Specifically, the step of constructing a risk uncertainty set for each spatial grid cell using a data-driven approach, satisfying a preset risk threshold, includes: S201, for each spatial grid cell, use several historical risk level values of that spatial grid cell as the original sample set.
[0025] S202 initializes the number of self-sampling attempts N, the significance level α, and the maximum probability ε that the risk score can exceed the preset risk score upper limit; this can be understood as requiring that the probability of the risk score not exceeding the preset risk score upper limit is not less than (1-ε). Those skilled in the art can set ε according to actual needs, for example, 10%.
[0026] S203, draw a random sample set with replacement from the original sample set, and calculate the (1-ε) quantile of each random sample set as the risk threshold estimate of the random sample set itself, and obtain a total of N risk threshold estimates; that is, after sorting the M historical risk level values from smallest to largest, select the (1-ε)% value as the risk threshold estimate of the random sample set.
[0027] It can be understood as: the statistic of any random sample set , where r m Let t be the m-th value in the random sample set. I() represents the indicator function, which takes the value 1 when the inequality in parentheses is true and 0 when it is false. The purpose of this formula is to take the smallest t as the risk threshold estimate, which is the value corresponding to the (1-ε)th quantile, so that there are (1-ε)×M historical risk level values that do not exceed the risk threshold estimate.
[0028] S204, rearrange the N risk threshold estimates in ascending order, and take the N×(1-α)th risk threshold estimate as the preset risk threshold to obtain the risk uncertainty set of the spatial grid cell that satisfies the preset risk threshold; that is, take the preset risk threshold as the maximum value to obtain the set of historical risk level values that do not exceed the preset risk threshold.
[0029] This can be understood as follows: the significance level is α, which means that there is a probability of misjudgment risk of α. For example, when α is 5%, the probability that the true risk score exceeds the preset risk threshold is not more than 5%. Similarly, the probability that the true risk score does not exceed the preset risk threshold is 95%. Therefore, after sorting the N risk threshold estimates from smallest to largest, the N×(1-α)th risk threshold estimate is taken as the preset risk threshold, and several risk threshold estimates that do not exceed the preset risk threshold are combined into a risk uncertainty set.
[0030] The above-mentioned data-driven approach extracts the risk fluctuation range of each airspace grid cell from historical risk level values, which can quantify the uncertainty characteristics of risk without relying on precise prior probability distributions. This ensures that the obtained preset risk thresholds have statistical confidence, thereby constructing a risk uncertainty set that can both reflect the risk fluctuation pattern and meet the safety probability requirements. This provides reasonable parameter boundaries for subsequent risk probability constraints, enabling route planning to cope with dynamically changing environments.
[0031] S3 maps each spatial grid cell to a network node, and maps the adjacency relationship between adjacent network nodes to edges in the network, thus constructing a target planning model based on network flow; this can be understood as connecting adjacent network nodes to obtain edges in the network.
[0032] Specifically, the target planning model aims to minimize the total route distance and includes origin-end point flow constraints, edge capacity constraints, loop prevention constraints, risk probability constraints based on each airspace grid cell, and flow conservation constraints for each network node except for the origin and end point of the route to be planned.
[0033] Specifically, the flow conservation constraint of the network node means that the number of directed edges entering the network node is equal to the number of directed edges leaving the network node itself.
[0034] The origin and destination flow constraints refer to the fact that the number of directed edges starting from the origin of the planned route and the number of directed edges entering the destination of the planned route are both 1.
[0035] The edge capacity constraint means that each directed edge can be used at most once by the route to be planned.
[0036] The anti-loop constraint means that each network node can be entered at most once by the route to be planned.
[0037] Furthermore, the risk probability constraint is expressed as follows: P(r ij ×f ij ≤R)≥(1-ε), (i,j)∈E, where P() represents probability, (i,j) represents the directed edge between adjacent network nodes i and j, E is the set of directed edges, and r ij Let f be the random risk score for (i,j). ij Let f be the decision variable, and R be the preset risk threshold; where f is the threshold when (i, j) is selected into the route. ij The value is 1, and the value is 0 otherwise.
[0038] This can be understood as follows: The risk probability constraint means that for any directed edge, if that directed edge is selected by the route to be planned, then the probability that the risk score of that directed edge does not exceed a preset risk threshold is not less than (1-ε), that is, r ij It is an unknown random variable.
[0039] Specifically, the objective function for minimizing the total route distance is expressed as follows: Where Z represents the total route distance, and L ij Let be the distance value between (i, j).
[0040] The above-mentioned approach, based on the risk uncertainty set constructed from historical data, employs opportunity constraints to ensure that the probability of risk exceeding the limit is lower than the preset risk threshold, enabling the planned route to proactively avoid high-risk periods or areas and reduce the probability of flight accidents. Furthermore, an objective function and multiple constraints are added to ensure that the distance from the starting point to the destination is minimized under the condition of satisfying multiple constraints. This step transforms the discretized low-altitude public route planning problem into a network flow optimization problem in graph theory, thereby ensuring the continuity, uniqueness, acyclicity, and safety controllability of the planned route.
[0041] S4 embeds the set of risk uncertainties into the risk probability constraints, so that the original probabilistic risk probability constraints are transformed into linear deterministic constraints with the maximum value in the set of risk uncertainties as the coefficient after robust optimization, and the goal programming model is updated.
[0042] It's important to note that robust optimization is an optimization method for handling uncertain problems, aiming to obtain feasible and robust solutions under all possible parameter variations. Unlike stochastic optimization, robust optimization does not rely on the probability distribution of uncertain parameters, but rather describes all possible parameter values by defining a set of uncertain parameters.
[0043] Specifically, by embedding the set of risk uncertainties into the risk probability constraints, we obtain: , where g ij This represents any historical risk level value in the risk uncertainty set of the spatial grid cell corresponding to network node j.
[0044] After robust optimization, it is equivalently transformed into a linear expression of the risk constraint, that is, the linear deterministic constraint is expressed as follows: ,in, This is the upper limit of the risk uncertainty set of the spatial grid cell corresponding to the network node j at endpoint (i,j). It can be understood as: taking the maximum value in the risk uncertainty set corresponding to a directed edge as the worst-case risk score for that directed edge, requiring that the product of this worst-case risk score and the decision variable does not exceed a preset risk threshold.
[0045] The above-mentioned robust optimization processing strategy transforms the probabilistic chance constraints that are difficult to solve directly into easily computed linear deterministic constraints, eliminating the dependence on precise probability distributions. The transformed constraints retain the upper limit information in the risk uncertainty set, ensuring that the route can still meet safety requirements when facing the most unfavorable risk fluctuations, thereby improving the robustness and actual flyability of the planned route.
[0046] S5 uses a preset optimization solver to solve the target planning model, and obtains and outputs the optimal low-altitude public route from the starting point to the ending point of the route to be planned.
[0047] Specifically, the S5 steps include the following: S501, the objective function and constraints in the goal programming model are modeled using integer linear programming, and together they are constructed into an integer linear programming model; it can be understood as: the objective function and the constraints together constitute an integer linear programming model, where the decision variables are integers of 0-1, and the constraint matrix is a sparse matrix, that is, each network node is only connected to its neighboring nodes.
[0048] S502 inputs an integer linear programming model into a preset optimization solver, and solves for the 0-1 integer solutions of the decision variables using a branch and bound algorithm or a cutting plane algorithm, outputting the optimal low-altitude common route corresponding to the optimal solution; it can be understood as: finding the combination of decision variables that minimizes the objective function Z under the premise of satisfying all constraints; that is, based on the set of directed edges corresponding to the found combination of decision variables, traversing from the starting point to the ending point in the order of network node connection to obtain a complete sequence of airspace grid cells.
[0049] Specifically, the preset optimization solver can be an open-source solver such as Gurobi, CPLEX, or SCIP that can implement branch and bound algorithms or cutting plane algorithms.
[0050] Furthermore, the branch and bound algorithm finds the optimal solution by recursively decomposing the problem into subproblems and pruning branches that cannot produce the optimal solution; the cutting plane algorithm tightens the feasible region of the linear relaxation problem by continuously adding effective inequalities, eventually obtaining the optimal solution. Those skilled in the art are familiar with the specific implementation methods of the branch and bound algorithm or the cutting plane algorithm, and will not elaborate further here.
[0051] In a specific scenario, if the preset optimization solver cannot find the global optimal solution within a reasonable time, a time limit can be set, and the current optimal feasible solution can be output as the optimal low-altitude common route.
[0052] As described above, by unifying the objective function and all constraints into an integer linear programming model, the route planning problem is transformed into a mathematical form that can be directly processed by a preset optimization solver. Under the premise of satisfying all safety and topological constraints, the optimal low-altitude public route with the minimum total distance can be efficiently solved, ensuring the global optimality and practicality of the planning results, and providing a safe and economical path solution for actual low-altitude flights.
[0053] Embodiments of the present invention also provide a non-transitory computer-readable storage medium that can be disposed in an electronic device to store at least one instruction or at least one program related to implementing a method in the method embodiments, wherein the at least one instruction or the at least one program is loaded and executed by the processor to implement the data-driven robust optimization low-altitude route planning method provided in the above embodiments.
[0054] Embodiments of the present invention also provide an electronic device, including a processor and the aforementioned non-transitory computer-readable storage medium.
[0055] While specific embodiments of the invention have been described in detail by way of example, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of the invention. It should also be understood that various modifications can be made to the embodiments without departing from the scope and spirit of the invention. The scope of the invention is defined by the appended claims.
Claims
1. A data-driven robust optimization approach for low-altitude route planning, characterized in that, The method includes the following steps: S1 divides the airspace for low-altitude public airway planning into several uniformly scaled airspace grid units and obtains the historical risk level value of each airspace grid unit in different historical time periods. S2, based on several historical risk level values of each spatial grid cell, a risk uncertainty set that satisfies a preset risk threshold is constructed for each spatial grid cell using a data-driven approach; S3, map each airspace grid cell to a network node, and map the adjacency relationship between adjacent network nodes to edges in the network, to construct a target planning model based on network flow; the target planning model aims to minimize the total route distance and includes origin and destination flow constraints, edge capacity constraints, anti-loop constraints, risk probability constraints based on each airspace grid cell, and flow conservation constraints for each network node except for the origin and destination of the route to be planned; S4. Embed the risk uncertainty set into the risk probability constraint, so that the original probabilistic risk probability constraint is transformed into a linear deterministic constraint with the maximum value in the risk uncertainty set as the coefficient after robust optimization, and the goal programming model is updated. S5 uses a preset optimization solver to solve the target planning model, and obtains and outputs the optimal low-altitude public route from the starting point to the ending point of the route to be planned.
2. The data-driven robust optimization method for low-altitude route planning according to claim 1, wherein, In step S1, obtaining the historical risk level value of each spatial grid cell in different historical time periods includes: S101, acquire historical observation data of various risk factors corresponding to each airspace grid unit within the low-altitude public airway planning airspace; the various risk factors include two categories: deterministic risk factors and random risk factors, wherein random risk factors are dynamically recorded at equal time intervals; S102, for each airspace grid cell, based on the pre-constructed low-altitude public airway risk assessment index system and the preset weights of each risk assessment index, the historical risk level value of each airspace grid cell in each historical time period is obtained by weighted summation; the historical time periods correspond to the equal time intervals.
3. The data-driven robust optimization approach for low-altitude route planning according to claim 1, wherein, In step S2, the step of constructing a risk uncertainty set for each spatial grid cell that satisfies a preset risk threshold using a data-driven approach includes: S201, For each spatial grid cell, use several historical risk level values of that spatial grid cell as the original sample set; S202, initialize the number of self-sampling attempts N, the significance level α, and the maximum probability ε that the risk score is allowed to exceed the preset risk score limit; S203, draw a random sample set with replacement from the original sample set and calculate the (1-ε) quantile of each random sample set as the risk threshold estimate of the random sample set itself, and obtain a total of N risk threshold estimates. S204, rearrange the N risk threshold estimates in ascending order, and take the N×(1-α)th risk threshold estimate as the preset risk threshold to obtain the risk uncertainty set of the spatial grid cell that satisfies the preset risk threshold.
4. The data-driven robust optimization method for low-altitude route planning according to claim 3, wherein, The risk probability constraint is expressed as follows: P(r ij ×f ij ≤R)≥(1-ε), (i,j)∈E, wherein P() represents a probability, (i,j) represents a directed edge between adjacent network node i and network node j, E is a directed edge set, r ij is a random risk score of (i,j), f ij is a decision variable, and R is the preset risk threshold; wherein f ij is 1 when (i,j) is selected into the route, and is 0 otherwise.
5. The data-driven robust optimization method for low-altitude route planning according to claim 1, wherein, The flow conservation constraint of the network node means that the number of directed edges entering the network node is equal to the number of directed edges leaving the network node itself. The origin and destination flow constraints refer to the fact that the number of directed edges starting from the origin of the planned route and the number of directed edges entering the destination of the planned route are both 1. The edge capacity constraint means that each directed edge can be used at most once by the route to be planned; The anti-loop constraint means that each network node can be entered at most once by the route to be planned.
6. The data-driven robust optimization low-altitude route planning method according to claim 4, characterized in that, The objective function for minimizing the total route distance is expressed as follows: wherein Z represents a total distance value of the route, L ij is the distance value for (i, j).
7. The data-driven robust optimization method for low-altitude route planning according to claim 4, wherein, In step S4, the linear deterministic constraint is expressed as follows: wherein, an upper bound value of the set of risk uncertainties of the spatial grid cell corresponding to the network node j that is the endpoint of (i,j).
8. The data-driven robust optimization method for low-altitude route planning according to claim 1, wherein, The S5 steps include the following: S501, the objective function and constraints in the goal programming model are modeled using integer linear programming, and together they are constructed into an integer linear programming model; S502 inputs the integer linear programming model into the preset optimization solver, solves the 0-1 integer solutions of the decision variables through the branch and bound algorithm or the cutting plane algorithm, and outputs the optimal low-altitude public route corresponding to the optimal solution.
9. A non-transitory computer-readable storage medium, wherein the storage medium stores at least one instruction or at least one program segment, characterized in that, The at least one instruction or the at least one program segment is loaded and executed by the processor to implement the data-driven robust optimization low-altitude route planning method as described in any one of claims 1-8.
10. An electronic device, characterized in that, Includes a processor and the non-transitory computer-readable storage medium as described in claim 9.