A method and system for fast planning of navigation path for stochastic flow field

Abstract

This application relates to the field of navigation planning technology, and particularly to a method and system for rapid navigation path planning in stochastic flow fields. The method includes: based on flow field ensemble forecast data, separating the deterministic and uncertain components of the stochastic flow field, constructing a median flow field and a perturbation flow field set for the stochastic flow field; using the median flow field to characterize the deterministic component of the stochastic flow field, and using the perturbation flow field set to characterize the uncertain component of the stochastic flow field; proposing a conservative adjustment strategy for navigation speed based on the median flow field and the perturbation flow field set; under the condition of conservative navigation speed, using an improved level set equation to evolve the reachable frontier clockwise from the navigation starting point until the reachable frontier reaches the navigation target point and stops evolving; after reaching the target point, performing a counter-clockwise backtracking of the reachable frontier to calculate the time-optimal trajectory under the conservative navigation speed adjustment strategy, and using this time-optimal trajectory as the navigation planning path in the stochastic flow field.

Description

Technical Field

[0001] This application relates to the field of navigation planning technology, and in particular to a method and system for rapid navigation path planning in stochastic flow fields. Background Technology

[0002] Stratospheric airships are near-space vehicles that fly in the weak or near-zero wind layer of the stratosphere, typically at altitudes above 18 kilometers. They are large, have high drag, low thrust, limited energy, and limited wind resistance, making them highly susceptible to environmental wind fields. In recent years, with the emergence of new materials, improved solar cell endurance, and significantly enhanced weather forecast accuracy, the long-term loiter capability of stratospheric airships has received increasing attention. Long-term flight of stratospheric airships in the stratosphere faces dynamic changes in the spatiotemporal wind field. Traditional flight path planning relies on deterministic wind field forecasts from atmospheric numerical weather prediction to provide effective flight paths. However, objectively, atmospheric changes and numerical weather prediction techniques contain randomness and uncertainty. Forecast errors decrease in accuracy as forecast lead time increases. Following a path planned using deterministic wind field forecasts may result in significant wind field deviations in practice, potentially leading to insufficient thrust to maintain the flight path or even rapid energy depletion and loss of control. Similarly, unmanned surface vessels (USVs) that navigate for extended periods in ocean currents also face the uncertainty or randomness of ocean current forecasts, have limited propulsion speed and energy, and are severely affected by ocean currents.

[0003] With the rapid development of ensemble forecasting technology, global or regional ensemble forecasting systems for atmospheric wind fields and ocean currents have been deployed in operational applications. These systems describe various stochastic possibilities in flow fields through multiple deterministic member forecast products. In atmospheric wind field forecasting, for example, my country's CMA forecasting system provides 15 members, the US National Oceanic and Atmospheric Administration's AIGEFS forecasting system has 31 members, the HGEFS forecasting system has 62 members, and the European Centre for Medium-Range Weather Forecasts (ECMWF)'s AIFS ENS forecasting system has 51 members. In ocean current ensemble forecasting, my country's CESM forecasting system has 20 members. Currently, how to utilize the vast amounts of data from these ensemble forecasting systems to provide rapid planning methods for navigation missions in stochastic flow field environments remains a challenge.

[0004] Navigation planning in stochastic flow fields typically faces challenges due to uncertainty, dynamism, and strong flow conditions. This is a 4-5 dimensional spatial search problem comprised of physical space (2-3 dimensions) or navigation speed (1 dimension) and direction (2-3 dimensions), as well as time (1 dimension) and flow field randomness (1 dimension). Its complexity increases exponentially with increasing dimensionality, leading to the curse of dimensionality; problems beyond 4 dimensions are generally very difficult to solve. A common approach is dimensionality reduction, such as ignoring the randomness and dynamism of the flow field, simplifying it to a static or quasi-static planning problem.

[0005] Traditional A* and D* algorithms, based on graph search, particle swarm optimization (PSO), ant colony optimization (ACO), genetic algorithm (GA), gray wolf optimization (GWO), and bat swarm optimization (BSO), are suitable for deterministic static and quasi-static flow fields, but struggle with dynamic, strong flow fields and even more so with environmental uncertainties. Rapid Exploration Random Tree (RRT) methods are suitable for deterministic static and dynamic flow fields, but suffer from excessively large search spaces, low efficiency, poor path smoothness, and the curse of dimensionality when combined with flow field uncertainties. The energy-time optimization level set method proposed by Doshi et al. constructs a multi-dimensional space of time, space, and energy for path planning, which can optimize navigation speed, but it involves enormous computation, poor real-time performance, and fails to address flow field uncertainties. The LS-PSO path planning method, combining level sets (LS) and particle swarm optimization (PSO), is also designed for deterministic dynamic flow fields, optimizing navigation speed to obtain the optimal path. However, it also involves large computations, and the addition of flow field randomness leads to the curse of dimensionality. In addition, some researchers have proposed various path planning methods based on reinforcement learning, but these methods are complex to implement, have poor interpretability, and pose certain security risks in application.

[0006] The current mainstream approach to path planning in stochastic flow fields involves sampling the stochastic flow field to form a flow field sample set, then using path planning methods for deterministic flow fields to plan a set of paths one by one. Finally, the performance of each path in each flow field sample is analyzed, considering metrics such as travel time and reachability, to select the optimal path. This is referred to as the set optimization method. For example, Deepk N et al. proposed a stochastic level set method based on dynamic orthogonal DO decomposition evolution to establish multiple time-optimal paths and proposed a path error metric under multiple flow fields for path analysis and optimization. Tong Wang et al. sampled based on an uncertain flow field parameterized model, solved the Boundary Value Problem (BVP) one by one to obtain a set of time-optimal paths, and after verification in multiple flow fields, selected the path with the minimum 95th percentile arrival time. However, these methods are computationally intensive, have poor real-time performance, and are difficult to apply in practice. Summary of the Invention

[0007] The purpose of this application is to overcome the above-mentioned deficiencies of the prior art, thereby providing a method and system for rapid navigation path planning in random flow fields.

[0008] To solve the above-mentioned technical problems, the technical solution of this application provides a method for rapid navigation path planning in stochastic flow fields, comprising: Step 1: Based on the flow field ensemble forecast data, separate the deterministic and uncertain parts of the random flow field, and construct the median flow field and the perturbation flow field ensemble of the random flow field. The median flow field is used to characterize the deterministic part of the random flow field, and the perturbation flow field ensemble is used to characterize the uncertain part of the random flow field. Step 2: Based on the median flow field and the disturbed flow field set, a conservative adjustment strategy for the sailing speed is adopted. Under the condition of conservative sailing speed, the improved level set equation is used to evolve the reachable front from the starting point of the sailing in a clockwise manner until the reachable front reaches the sailing target point and then the evolution stops. Step 3: After reaching the target point, perform reverse time backtracking on the reachable frontier to calculate the time-optimal trajectory under the conservative speed adjustment strategy, and use this time-optimal trajectory as the navigation planning path in the stochastic flow field.

[0009] As an improvement to the above technical solution, step 1 specifically includes: Step 1.1: Construct a flow field ensemble using the flow field data predicted by each member of the ensemble forecasting system: ; in, Indicates the first Samples of the flow field In spatial location and time The velocity vector of the flow field at that location; Indicates the first Each flow field sample corresponds to one member. , where m is the total number of members in the flow field ensemble prediction system. , For navigation space, It is the total number of spatial dimensions. , The maximum allowed time for the planned task; Step 1.2: According to spatiotemporal coordinates Statistical analysis of the flow field velocity vectors predicted by each member in each dimension of the flow field. upper boundary value and lower boundary value ,in, Represents the ordinal number of spatial dimensions. ; Step 1.3: Based on the aforementioned upper boundary value and lower boundary value Calculate the mean value of each component of the flow field The median of each component The median flow field that characterizes the deterministic part of a stochastic flow field ; Step 1.4: Based on the upper boundary value and lower boundary value Calculate the half-width of the uncertainty interval for each component of the flow field Based on the half-width of the uncertainty interval of each component Establish an upper approximate set of perturbation fields that characterize the uncertainties of the random flow field, as the perturbation flow field set. .

[0010] As an improvement to the above technical solution, in step 1.2, the upper boundary value for: ; lower boundary value for: ; in, =1,2 or 3 Represents the velocity vector of the flow field In the The components of the dimension, Indicates the first The sampled flow field in spacetime coordinates The velocity vector of the flow field; In step 1.3, the median of the i-th dimension component for: ; Median flow field for: ; in, It is the transpose symbol; In step 1.4, the half-width of the uncertain interval of the i-th component. for: ; Collection of perturbed flow fields for: ; in, In spacetime coordinates The perturbation flow field vector at that location. The first vector representing the perturbation flow field vector Dimensional components, each sampled flow field in spatiotemporal coordinates The perturbation flow field vector at the location satisfy .

[0011] As an improvement to the above technical solution, in step 1, if the flow field data predicted by each member of the ensemble forecasting system is lacking, and only a deterministically predicted flow field velocity vector exists... Then As the median flow field If the random flow field is a periodic flow field with a period of ; If the phase is unknown, then a time-invariant median field is established. Alternate median flow field The calculation formula is: ; The half-width vector of the disturbance interval is determined by either statistically predicting errors using historical flow field data or by setting errors based on expert experience. .

[0012] As an improvement to the above technical solution, in step 2, the improved level set equation is: ; in, In spacetime coordinates The signed distance scalar implicit function at the location, for The spatial gradient vector, yes The 2-norm, It is the result of correcting the spacetime coordinates using a conservative adjustment strategy for sailing speed. The propulsion speed at that location.

[0013] As an improvement to the above technical solution, the formula for setting the signed distance scalar implicit function at the initial time t=0 is as follows: = in, Let be the signed implicit function of the distance scalar at the initial time. This is the initial spatial position vector of the vehicle. The first of the initial spatial position vectors of the vehicle dimensional components, Spatial location The Dimensional components; Spatial gradient vector 2-norm for: ; Corrected in spacetime coordinates using a conservative speed adjustment strategy Propulsion speed at the location for: ; in, The design propulsion speed of the vehicle in the absence of flow field disturbance. This represents the retention amount of the sailing speed at the spacetime coordinate (x,t).

[0014] As an improvement to the above technical solution, the sailing speed retention amount Calculated using either the maximum projection method or the maximum length method, where the maximum projection method is denoted by N1 and the maximum length method by N2; where... Speed ​​retention calculated by the maximum projection method for: ; in, Spatial gradient vector The Dimensional components; Speed ​​retention calculated using the maximum length method for: ; in, Represents in spacetime coordinates The half-width vector of the disturbance interval at that location: ; in, This is the transpose symbol.

[0015] As an improvement to the above technical solution, in step 2, the evolution process of the reachable frontier includes: For navigation space A numerical computation grid is established, and the improved fundamental equations of the level set are solved using a numerical method for level sets, yielding a signed implicit function of the distance scalar. The value of (x,t); at time t, it satisfies The spatial locations (x,t)≤0 form the navigation reachable set at time t. ,satisfy },in, The position (x,t)=0 constitutes the reachable frontier. ,satisfy }; Real-time detection of navigation target points Signed distance scalar implicit function The value, if If the time is ≤0, the forward evolution of the reachable set ends, and the time at this point is the minimum travel arrival time. If reachable set For an empty set or evolved to If the target point has not been reached, the planning is deemed a failure.

[0016] As an improvement to the above technical solution, the specific formula for calculating the optimal time trajectory in step 3 is as follows: ; From minimum sailing arrival time Reverse time reversal can reach the frontier of the set, from the navigation target point The navigation trajectory was obtained by calculating up to t=0 using a step-by-step integration method. , as the time-optimal trajectory; in, It is the optimal navigation trajectory position at time t, 0≤t≤ ,and , Time of arrival The optimal navigation trajectory position at any given time. It is the median flow field at the optimal navigation trajectory point. It is the result of a conservative adjustment strategy for sailing speed in spacetime coordinates. The propulsion speed at that location, Is The spatial gradient vector at that location.

[0017] To achieve another objective of the present invention, the present invention also provides a rapid navigation path planning system for stochastic flow fields, comprising a flow field separation module, an reachable front evolution module, and a trajectory backtracking planning module, wherein, The flow field separation module is used to separate the deterministic and uncertain parts of the random flow field based on the flow field set forecast data, and to construct the median flow field and the perturbation flow field set of the random flow field. The median flow field represents the deterministic part of the random flow field, and the perturbation flow field set represents the uncertain part of the random flow field. The reachable front evolution module is used to adopt a conservative adjustment strategy for sailing speed based on the median flow field and the set of disturbed flow fields. Under the condition of conservative sailing speed, the improved level set equation is used to evolve the reachable front from the starting point of sailing in a clockwise manner until the reachable front reaches the target point of sailing and then stops evolving. The trajectory backtracking planning module is used to perform reverse time backtracking on the reachable front after reaching the target point, calculate the time-optimal trajectory under the conservative adjustment strategy of sailing speed, and use the time-optimal trajectory as the sailing planning path in the random flow field.

[0018] The advantages of this application are that the method and system for fast navigation path planning for random flow fields proposed in this invention adopts an approximate interval set to represent the uncertain disturbance part in the flow field, innovatively proposes a self-adjustment strategy for navigation speed and improves the basic equation of the level set. Through one forward evolution of the reachable front and one backward evolution backtracking, the optimized navigation trajectory can be obtained as the navigation path, which is simple and fast to calculate. Attached Figure Description

[0019] Figure 1 It is a separate random flow field Two-dimensional space ( ) Schematic diagram; Figure 2 A schematic diagram of the reachable frontier evolution in two-dimensional space; Figure 3 A schematic diagram illustrating the reverse-time backtracking method for finding the optimal trajectory to reach the frontier; Figure 4(a) shows the median flow field separated from the stratospheric wind field ensemble forecast at 3:00 on December 9, 2025, and the corresponding half-width of the zonal wind U-disturbance and the half-width of the meridional wind V-disturbance. Figure 4(b) shows the median flow field separated from the stratospheric wind field ensemble forecast at 9:00 on December 9, 2025, and the corresponding half-width of the zonal wind U-disturbance and the half-width of the meridional wind V-disturbance. Figure 4(c) shows the median flow field separated from the stratospheric wind field ensemble forecast at 15:00 on December 9, 2025, and the corresponding zonal wind U-disturbance half-width and meridional wind V-disturbance half-width. Figure 5(a) is a comparison of the paths to the first target point (#1) planned by various path planning methods; Figure 5(b) is a comparison of the paths planned to the second target point (#2) by various path planning methods; Figure 6(a) is a statistical chart showing the maximum peak speed and maximum energy consumption required for trajectory tracking navigation simulation of the paths to the first target point (#1) planned by each path planning method in 51 member flow fields; Figure 6(b) is a statistical chart showing the maximum peak speed and maximum energy consumption required for trajectory tracking navigation simulation of the paths to the second target point (#2) planned by each path planning method in 51 member flow fields; Figure 7(a) shows the navigation speed curve obtained by trajectory tracking navigation simulation of the path to the first target point (#1) planned by the planning strategy N1 of the present invention in each member flow field; Figure 7(b) shows the navigation speed curve obtained from the trajectory tracking navigation simulation of the path to the first target point (#1) planned by the planning strategy N2 of the present invention in each member flow field; Figure 7(c) shows the navigation speed curve obtained from the trajectory tracking simulation of the path from Median to the first target point (#1) in each member flow field based on the level set planning. Figure 8(a) shows the navigation speed curve obtained from the trajectory tracking navigation simulation of the path to the second target point (#2) planned by the planning strategy N1 of the present invention in each member flow field; Figure 8(b) shows the navigation speed curve obtained from the trajectory tracking navigation simulation of the path to the second target point (#2) planned by the planning strategy N2 of the present invention in each member flow field; Figure 8(c) shows the navigation speed curve obtained from the trajectory tracking simulation of the path from Median to the second target point (#2) in each member flow field based on the level set planning. Figure 9(a) shows some of the navigation speeds of the optimal path 1 planned by each member flow field when the trajectory tracking simulation is performed in other flow fields; Figure 9(b) shows a partial navigation speed diagram of the optimal path 21 planned by each member flow field when performing trajectory tracking simulation in other flow fields; Figure 9(c) shows some of the navigation speeds of the optimal path 51 in the flow field planning of each member when the trajectory tracking simulation is performed in other flow fields. Figure 10 This is a schematic diagram of a flow field sample around a cylinder. Figure 11 A comparison chart of navigation paths (#1 and #2) planned by various path planning methods from upstream to downstream two target points in a flow field around a cylinder; Figure 12 A comparison chart of navigation paths to two target points planned by various path planning methods in a transvortex field; Figure 13(a) is a statistical chart of the maximum speed and energy required for trajectory tracking and navigation simulation of the first target point (#1) from upstream to downstream in a flow field around a column, using various path planning methods. Figure 13(b) is a statistical chart of the maximum speed and energy required for trajectory tracking and navigation simulation of the second target point (#2) from upstream to downstream in a flow field with various path planning methods. Figure 14(a) shows the navigation speed curve of the planning strategy N1 of the present invention in the navigation simulation from upstream to downstream; Figure 14(b) shows the navigation speed curve of the planning strategy N2 of the present invention in the navigation simulation from upstream to downstream; Figure 14(c) shows the sailing speed curves of the optimal path in the median flow field during a navigation simulation from upstream to downstream. Figure 15 A flowchart of the method for rapid navigation path planning in stochastic flow fields provided by the present invention; Figure 16 A flowchart of step 1 of the rapid navigation path planning method; Figure 17 A flowchart for step 2 of the rapid navigation path planning method; Figure 18 This is a schematic diagram illustrating the forward evolution calculation of the reachable front in the flow field. Figure 19 A flowchart for step 3 of the rapid navigation path planning method; Figure 20 This is a schematic diagram of the backward backtracking calculation trajectory of the reachable front in the flow field. Detailed Implementation

[0020] The technical solutions provided in this application are further illustrated below with reference to the embodiments.

[0021] The purpose of this invention is to achieve rapid navigation path planning in stochastic flow field environments, effectively avoiding regions with high uncertainty in the flow field, reducing flow field disturbances and propulsion energy consumption during navigation, and featuring low computational complexity and ease of use. This invention can be used for navigation planning of stratospheric airships / aeriovans in stratospheric wind fields, and also for navigation planning of unmanned vessels in ocean currents.

[0022] Example 1 The fast navigation path planning method in random flow fields proposed in this embodiment, such as Figure 15 As shown, the method includes the following steps: First, construct the median flow field and the perturbed flow field set of the random flow field; then, construct a conservative navigation speed field using a conservative navigation speed adjustment strategy, and use an improved level set equation to evolve the reachable front forward in a clockwise direction from the starting point, stopping after reaching the target point; finally, perform a counterclockwise backtracking of the reachable front to calculate the time-optimal trajectory under the corresponding speed strategy, which serves as the path for navigation planning. The method of this embodiment will be described in detail below.

[0023] Step 1: Separate the deterministic and uncertain parts of the random flow field.

[0024] like Figure 16 As shown, the flow field ensemble is constructed using the member forecast flow fields of the ensemble forecast system. , This means that one sample of the flow field corresponds to one forecast member. It is the sampling sequence number. , where m is the total number of members in the ensemble forecast, It is spatial coordinates. , For navigation space, , For spatial dimensions, =1, 2, or 3 Represents the ordinal number of spatial dimensions. t is time. , The maximum time allowed for the planned task.

[0025] We construct median flow field and perturbed flow field using flow field ensembles, representing the deterministic and uncertain parts of the random flow field, respectively. First, for flow fields arranged according to spatiotemporal coordinates... Statistical analysis of the predicted flow field of each member each 2D flow field components upper boundary value and lower boundary value ,Right now (1) (2) in, Indicates the first The sampled flow field in spacetime coordinates The velocity vector of the flow field; The velocity vector of the flow field In the Dimensional components; Then, the mean values ​​of each component of the flow field are calculated according to the following formula. : (3) The half-width of the uncertainty interval for each component of the flow field is calculated using the following formula. : (4) in, Represents in spacetime coordinates First The half-width of the perturbation interval of the dimension; Mean values ​​of each dimension of the flow field The median flow field that makes up the predicted flow field The deterministic part used to characterize the predicted flow field: (5) in, Represents in spacetime coordinates The median flow field vector at a given location is derived from the median of the flow field components in each dimension. composition; The predicted flow fields of each member can be represented as a deterministic median field superimposed with a perturbation field: (6) in, Indicates the j-th sampled flow field in spacetime coordinates The perturbation flow field vector at a certain point reflects the random component of the flow field; Establish the upper approximate interval set of the perturbation field : (7) in, Represents in spacetime coordinates The upper approximate interval set of the perturbation field is used to characterize all possible flow field perturbations. In spacetime coordinates The perturbation flow field vector at that location, The first vector representing the perturbation flow field vector Dimensional components; have , The vector determines the width of the uncertainty interval of the perturbation field, which is also the boundary of the uncertainty: (8) in, Represents in spacetime coordinates The perturbation interval half-width vector at that location, This is the transpose symbol.

[0026] Figure 1 To separate random flow fields Two-dimensional space diagram ( ) diagram, that is =2.

[0027] If the random flow field lacks ensemble forecast data products, i.e., there is no flow field ensemble... However, there is only one deterministically predicted flow field velocity vector. Then As the median flow field The half-width vector of the perturbation field The settings can be configured more flexibly, and the following methods can be used: (a) Based on historical flow field data, statistically analyze the time ranges of each time interval in the uncertain interval according to equations (1-4). (b) Based on the historical flow field data, the maximum and minimum values ​​at each location and time are calculated according to equations (9~11) to obtain the range of uncertain intervals, which remains unchanged over time; (9) (10) (11) in, In spatial location First The upper boundary values ​​of the dimensional flow field components, In spatial location First The lower boundary value of the dimensional flow field component. Represented as spatial location First The perturbation interval half-width of the dimension.

[0028] Alternatively, take a multiple of the standard deviation of the flow field's historical time: , in, In spatial location Historical time i-dimensional flow field components The standard deviation, k>0. For a Gaussian distribution, usually... Choose 2 to 4.

[0029] (c) Based on the variation pattern of forecast error over time, set the spatial location Half-width vector of the disturbance interval where time is 0 And it increases over time; (d) Setting directly based on expert experience Even simplified to time invariance .

[0030] If the random flow field is periodic, with a period of... Since the phase is unknown, a time-invariant median field can be established as an alternative. :

[0031] in, The time-invariant median field of a periodic random flow field. Let be the period of the random flow field.

[0032] Step 2: As Figure 17 As shown, the reachability set front forward evolution is performed. Figure 18 The diagram illustrates the forward evolution calculation of the reachable front in a flow field (two-dimensional space, where the circles represent the initial navigation points and the star-shaped points represent the target points); the modified basic equations of the level set method are constructed as follows: (12) Figure 2 A schematic diagram of the evolution of the reachable frontier in two-dimensional space.

[0033] in, To predict the median vector field of the flow field, Let be a signed distance scalar implicit function, initially set at t=0: = (13) in, This is the initial spatial position vector of the vehicle. The first of the initial spatial position vectors of the vehicle dimensional components, Spatial location The dimensional components, implicit function Spatial gradient vector, for The dimensional components, It is the spatial gradient vector 2-norm: (14) in, It is the corrected version in spacetime coordinates The propulsion speed at a certain point is calculated using the following formula: (15) in, Let $\mathbf$ be the nominal speed of travel (the propulsion speed relative to the ambient flow field), which is the design propulsion speed of the vehicle under no flow field disturbance. Let $\mathbf$ be a scalar quantity. Spacetime coordinates Regarding the retention of sailing speed at a given location, this invention proposes two retention strategies: (a) Take the set of disturbance intervals Gradient of implicit function The projection of the maximum projection, or simply the maximum projection method, is denoted by N1 and is calculated as follows: (16) in, The speed reserve corresponding to the maximum projection method N1 is... It is the half width of the interval and The absolute value of the product.

[0034] (b) Take the set of disturbance intervals The maximum perturbation length, i.e., the half-width vector of the interval. The L2 norm of a vector, also known as the maximum length method, is denoted by N² and is calculated as follows: (17) in, This is the speed reserve corresponding to the maximum length method N2.

[0035] This invention designs two conservative strategies for sailing speed, as shown in equations (16) and (17), namely, at the nominal sailing speed... The plan reserves a portion of the propulsion speed to counteract uncertainties in the flow field, whereas conventional level-set methods typically use a fixed propulsion speed that evolves independently of position and time. The amount of propulsion speed reserved during planning varies with the uncertainty in the flow field. Make proactive adjustments. The larger the value, the greater the speed retention. The larger the speed, the greater the speed margin during navigation to cope with random flow field fluctuations, reducing the need for excessive propulsion speed for trajectory tracking.

[0036] In this step, the conventional numerical calculation method for level sets is used: according to the Hamilton-Jacobi equation (12), for A numerical computation grid is established in space to obtain... The numerical value of the implicit function. At time t, it satisfies... Spatial position composition The sailing time can reach the collection }, that is, starting from the initial point at time t. The area that can be reached by sailing at a given speed and strategy. yes The time capsule starts from the initial point The set of all reachable spatial locations; among which The location constitutes the reach frontier ,and The corresponding location is unreachable at that moment. The reach of time is at the forefront yes The boundary, characterization The farthest reachable position of the spacecraft at any given time.

[0037] To improve the success rate of navigation planning, it is recommended to use a higher nominal speed. The propulsion speed can be set according to the rated power of the aircraft, or the maximum propulsion speed corresponding to the safe power can be set according to the energy storage of the aircraft. Since the maximum length of the vector is not less than its projection in a certain direction, the N2 strategy reserves a larger speed than the N1 strategy, which is more conservative. As a result, its reachable front develops more slowly, and the time required to reach the target point is longer, which corresponds to a longer travel time. However, in principle, N2 can ensure that when tracking the actual navigation trajectory, its required propulsion speed will not exceed the nominal travel speed in the face of various flow field fluctuations.

[0038] In the evolution of reachable sets, the target point is continuously detected. Value, if its Then the forward evolution of the reachability set immediately ends. This moment is the minimum travel time to reach the destination given the travel speed and conservative strategy, denoted as . ,in, Indicates the target spatial position of the spacecraft; simultaneously, continuously detects the reachable set. If the value is zero, the planning is considered a failure. If it evolves to the scheduled task time... If the target point is not reached, it indicates that the plan has failed.

[0039] Step 3: As Figure 19 As shown, the optimal trajectory point is obtained by retrograde backtracking to the reachable front. Figure 20 The diagram illustrates the backward backtracking trajectory calculation in the reachable front in the flow field. According to equation (12), from... The inverse-time inversion at any given moment reaches the set front, and the following particle equation is used to calculate the velocity vector relative to the ground. From the target point The navigation trajectory can be obtained by starting with successive integration until t=0. : (18) in, yes The optimal flight path position at time t represents the planned position of the aircraft. The target spatial location at any given time. This represents the ground-based velocity vector at the optimal flight trajectory position. , , Minimum travel time The optimal navigation trajectory position at any given time. It is the median flow field vector at the trajectory point. It is the corrected version. The navigation speed at that location follows the same conservative speed strategy as in step 2, where... yes exist The gradient vector at the position.

[0040] Figure 3 A schematic diagram illustrating the reverse-time backtracking method for finding the optimal trajectory to reach the frontier.

[0041] By completing steps 1-3 above, the navigation path planning in the stochastic flow field is complete, and the resulting trajectory sequence points are obtained. As a planning path.

[0042] Navigation strategy in random flow field: In navigation in random flow fields, it is recommended to use a trajectory tracking method to execute the path planned by this method, that is, in time... Sailing at the planned location Above. The actual random flow field will be different from the median flow field. In order to achieve the ground speed of equation (18) The sailing speed needs to be adjusted based on the actual current velocity. This is because, according to equations (12, 16, 17), the sailing speed reserve during the planning process... Perturbation field width at specific location and time Correspondingly, for regions where larger disturbances in the flow field are more likely, the higher the pre-reserved propulsion speed of the vehicle and the shorter the spacing between the navigation trajectory points, which can be used to overcome the interference of the disturbance flow field. If the planned path is not executed according to the trajectory tracking method, the trajectory points may face a larger disturbance field due to the spatiotemporal coordinate offset during navigation, which may greatly exceed the pre-reserved navigation speed. This will not only increase navigation time and energy consumption, but may also cause the navigation to deviate from the planned path due to insufficient wind resistance propulsion capability.

[0043] Two examples are taken: the navigation planning of a stratospheric airship in a two-dimensional wind field of a 50 hPa pressure layer and the navigation planning of a vehicle in a random circumferential flow field.

[0044] Step S1: Based on the stratospheric airship's course, mission time, and area, acquire forecast data products provided by a flow field ensemble forecasting system (such as the European Centre for Medium-Range Weather Forecasts' AIFS ENS system), extract the 50 hPa pressure layer wind field data, and organize the flow field data of each member into... According to the flow field diagram described in step 1 and the relevant formulas, the mean flow field is calculated. and half-width of the perturbation flow field .

[0045] Step S2: Perform forward evolution of the reachability set front.

[0046] First, the two-dimensional space of the stratospheric airship's flight path. Discretization is performed using a Cartesian coordinate grid, with the grid interval set. The distance is 30 kilometers, determined based on the size of the route area. Number of grid points; Set the maximum time for the task. Divide the task duration into Segment, time step is For 0.5 hours, .

[0047] Then, according to Spatiotemporal grid, for , Temporal and spatial linear interpolation is performed to obtain the flow field data at the corresponding grid points.

[0048] Subsequently, the nominal speed was determined by the propulsion speed corresponding to the rated power of the aircraft. ,based on The spatiotemporal grid is used to perform forward numerical evolution calculations of the reachability front according to the flowchart in step 2. The spatial gradient of the grid points is calculated using the upwind Lax-Friedrichs scheme, and the time integration is performed using the second-order TVD Runge-Kutta method. The calculation is not limited to numerical grid points, and a time-space linear interpolation method is used. This is to facilitate determining whether the target point has been reached.

[0049] Step S3: Perform reverse-time backtracking along the reachable front to solve for the optimal trajectory point. Calculate the navigation trajectory point based on the flow field diagram described in Step 3 and related formulas. Not limited to numerical grid points, according to (18) , and The calculation is performed using a time-space linear interpolation method. It is based on the time step. The trajectory points are extracted to form the navigation path, and the starting point is used at t=0. Alternative To eliminate numerical bias.

[0050] (1) Example A: Stratospheric airship planning Taking the navigation planning of a stratospheric airship at a pressure altitude of 50 hPa in a region centered at N16° and E115° as an example, the navigation plan starts at 3:00 AM UTC on December 9, 2025, from northeast to southwest towards the target point. The wind field is predicted based on the ensemble of 51 members of the EC (Electronic Array for Geometry), with a time interval of 3 hours, a latitude and longitude resolution of 0.25°, and a rated propulsion speed of 10 m / s for the airship. This method is compared with conventional methods based on member wind field planning ensemble selection and level set planning (based on a single median flow field, ignoring random disturbances in the flow field, denoted as Median).

[0051] Figure 4(a) shows the median wind field separated from the stratospheric wind field ensemble forecast at 3:00 on December 9, 2025, and the corresponding half-width of the zonal wind U-disturbance and the half-width of the meridional wind V-disturbance. Figure 4(b) shows the median wind field separated from the stratospheric wind field ensemble forecast at 9:00 on December 9, 2025, and the corresponding zonal wind U-disturbance half-width and meridional wind V-disturbance half-width. Figure 4(c) shows the median wind field separated from the stratospheric wind field ensemble forecast at 15:00 on December 9, 2025, along with the corresponding zonal wind U-disturbance half-width and meridional wind V-disturbance half-width.

[0052] Figure 5(a) is a comparison of the paths to the first target point (#1) planned by various path planning methods; Figure 5(b) is a comparison of paths planned to the second target point (#2) by various path planning methods.

[0053] In terms of flight planning time, the ensemble optimization method requires several hours to plan and analyze the optimization for each member wind field separately, while the proposed method takes about 10 minutes, similar to the conventional level set planning method. Although the flight paths planned by the proposed method do not differ significantly in terms of spatial distribution, trajectory tracking simulations reveal that the proposed method results in lower maximum propulsion speed and energy consumption for the airship in various member wind fields (see Figures 6(a) and 6(b)). The N2 strategy only increases the flight time by about 2 hours, but significantly reduces the airship's propulsion speed by 2 m / s and maximum energy consumption by about 40%. In the navigation simulation, the required propulsion speeds for paths N1 and N2 are significantly smaller in fluctuation and peak value than those for the Median optimal path and the optimal paths for each member in the median flow field (see Figures 7(a) to 7(c) and 8(a) to 8(c)). In this case, the maximum propulsion speed of path N2 in the simulation is lower than the nominal propulsion speed (in principle, N2 can guarantee this speed, while N1 cannot). The maximum propulsion speed of method N1 may be slightly higher than the nominal propulsion speed. However, conventional path-based optimal paths for each member require a speed of at least 12 m / s to achieve trajectory tracking, which is 2 m / s higher than the nominal speed (see Figures 9(a) to 9(c)). This extra 2 m / s may exceed the vehicle's power limit, causing insufficient power or excessive energy consumption, thus leading to the risk of loss of control. The method N1 in this study effectively solves this problem.

[0054] Note: The trajectory tracking navigation simulation comparison adopts variable speed, that is, sailing at the planned position at the planned time point, and analyzing the required speed change and propulsion energy consumption.

[0055] Note: Energy consumption is calculated here. For the sake of simplicity, the energy consumption coefficient k is taken as 1 in the formula calculation. This refers to the actual time it takes for the vehicle to reach its target point.

[0056] (2) Example B: Navigation planning in a random flow field around a cylinder For example, in a river channel 80m wide with a 10m diameter cylinder in the middle, the flow velocity at the left inlet is 0.1m / s, and the Reynolds number Re=100. A numerical simulation of the flow field is performed using random initial field conditions to obtain 50 flow field samples around the cylinder, as shown in the figure below. The eddy period is approximately 500 seconds. Two navigation missions are planned, one from upstream to downstream and the other from one side, using a nominal navigation speed of 0.1m / s. Because the flow around the cylinder is periodic, the time-invariant median flow field is obtained after statistical analysis of 50 samples over 5000 seconds. Half-width field of flow field disturbance interval Used for path planning Figure 11 The maximum half-width of the medium-sized eddy current can reach 0.07, which is close to 70% of the nominal velocity.

[0057] Figure 10 This is a schematic diagram of a flow field sample around a cylinder, where the background represents the magnitude of the flow velocity.

[0058] In terms of navigation planning time, using the same computing platform, conventional ensemble optimization methods require several days to determine the planned path, while the proposed method and conventional level set planning methods take approximately 10 minutes. Regarding the spatial distribution of the planned path, the navigation path planned by the proposed method can significantly avoid areas with large fluctuations in the flow field, especially for navigation across eddy current regions. The proposed method, based on N1 and N2 strategies, actively bypasses areas with significant disturbances. In contrast, planning methods based on single flow field samples lack this feature, and most paths directly cross large disturbance areas, leading to strong flow field disturbances.

[0059] Figure 11 A comparison chart of navigation paths (#1 and #2) planned by various path planning methods from upstream to downstream two target points in a flow field around a cylinder; Figure 12 A comparison chart of navigation paths to two target points planned by various path planning methods in a transvortex field. Figure 12 The median vector field is the time-invariant median flow field. The background is flow field disturbance. Size (according to formula (11)).

[0060] The spatial differences in navigation paths planned by different methods from upstream to downstream are relatively small. However, when trajectory tracking navigation simulation is performed according to the planned path, the maximum peak navigation speed and energy consumption are significantly reduced, as shown in Figures 13(a) and 13(b). Navigation energy consumption can be reduced by about 50%, and the maximum speed is basically the nominal navigation speed of 0.1 m / s. The horizontal set plans multiple navigation paths for a single flow field sample. During simulation, the navigation speed is significantly greater than 0.1 m / s, which is 1.5-2 times the nominal speed, and remains so, as shown in Figure 14(c). This indicates that even with set optimization, there is still a greater demand for propulsion and energy, which may exceed the vehicle's capabilities.

[0061] Figure 13(a) is a statistical chart of the maximum speed and energy required for trajectory tracking navigation simulation of the first target point (#1) from upstream to downstream in a flow field with various path planning methods. Figure 13(b) is a statistical chart of the maximum speed and energy required for trajectory tracking navigation simulation of the second target point (#2) from upstream to downstream in a flow field with various path planning methods. The maximum peak speed and maximum energy consumption are statistically required.

[0062] Note: Energy consumption is calculated here. For the sake of simplicity, the coefficient k is set to 1 in the formula calculation.

[0063] Figure 14 shows the navigation speed curves in the navigation simulation from upstream to downstream second target point (#2) in each member flow field. Among them, Figure 14(a) shows the navigation speed curve of the planning strategy N1 of this method in the navigation simulation from upstream to downstream, Figure 14(b) shows the navigation speed curve of the planning strategy N2 of this method in the navigation simulation from upstream to downstream, and Figure 14(c) shows the navigation speed curve of the optimal path of the median flow field in the navigation simulation from upstream to downstream.

[0064] Example 2 This embodiment provides a rapid navigation path planning system for stochastic flow fields, used to implement the rapid navigation path planning method for stochastic flow fields in Embodiment 1. It includes a flow field separation module, an reachable front evolution module, and a trajectory backtracking planning module. The flow field separation module is used to separate the deterministic and uncertain parts of the random flow field based on the flow field set forecast data, and to construct the median flow field and the perturbation flow field set of the random flow field. The median flow field represents the deterministic part of the random flow field, and the perturbation flow field set represents the uncertain part of the random flow field. The reachable front evolution module is used to adopt a conservative adjustment strategy for sailing speed based on the median flow field and the set of disturbed flow fields. Under the condition of conservative sailing speed, the improved level set equation is used to evolve the reachable front from the starting point of sailing in a clockwise manner until the reachable front reaches the target point of sailing and then stops evolving. The trajectory backtracking planning module is used to perform reverse time backtracking on the reachable front after reaching the target point, calculate the time-optimal trajectory under the conservative adjustment strategy of sailing speed, and use the time-optimal trajectory as the sailing planning path in the random flow field.

[0065] Compared with the prior art, the present invention has the following advantages: (1) In the planning process, this invention decomposes the random flow field into a median flow field and a disturbance field, that is... use and This method efficiently characterizes both the deterministic and stochastic aspects of the flow field, reducing the required storage space by several times. For example, for a flow field with 50 members, the flow field data can be reduced to 2 / 50. This method also facilitates the incorporation of historical flow field statistics or expert knowledge. The median flow field and perturbation field can be simplified to time-invariant fields, further reducing the required storage space.

[0066] (2) This invention effectively reduces the dimensionality of the high-dimensional trajectory search problem. It adopts a velocity conservative strategy to simplify the search dimensions of sailing speed and randomness; it adopts the level set method to solve the trajectory points by backtracking, which simplifies the search of the sailing direction dimension. It simplifies the planning problem under random dynamic flow field into a specific spacetime reachable front evolution problem, realizes time-optimal path planning under the conservative strategy, significantly simplifies the problem complexity and improves the planning efficiency.

[0067] (3) The planning method of this invention only requires one forward and backward evolution of the level set, and the computational complexity increases linearly with the navigation mission time, making it highly practical. The computational complexity of conventional set selection methods increases exponentially with the number of flow field samples and the navigation mission time: for m flow field samples, m planning and m×m simulation analysis are required, and as the navigation planning mission time increases, the required computational resources are huge and the real-time performance is poor.

[0068] (4) This invention employs a conservative speed adjustment strategy during planning, including two methods: the maximum projection method (N1) and the maximum length method (N2), based on the specific flow field disturbance half-width (N2). The more likely a large disturbance in the flow field will occur, the greater the velocity will be retained. The benefits of this design are twofold: firstly, it allows for the control of the reachability front evolution process; regions with greater flow field disturbances develop the front more slowly, reaching the target later, and the final planned trajectory will try to bypass areas with large flow field disturbances; secondly, slowing down the reachability front evolution results in trajectory points with smaller unit step sizes, and the pre-reserved propulsion velocity is used to counteract the interference of the disturbed flow field, reducing the upper limit of propulsion velocity required for trajectory tracking.

[0069] (5) The N1 strategy for adjusting the sailing speed of the present invention accurately estimates the maximum impact of random flow field disturbances on the reachable front, provides an approximate fast estimate of the intersection of the reachable fronts of each flow field set, and can obtain a sailing path with a shorter sailing time; while the N2 strategy is more conservative, and in principle it can ensure that the propulsion speed is not greater than the nominal sailing propulsion speed when tracking the sailing trajectory.

[0070] (6) This invention realizes time-optimal navigation path planning under nominal propulsion speed and conservative strategy, which is easy to implement: the nominal propulsion speed can be the rated propulsion speed corresponding to the rated power of the aircraft, or the average propulsion speed can be calculated based on the safe power determined by the energy storage of the aircraft. If the maximum propulsion speed of the aircraft is directly used as the nominal propulsion speed, the N2 conservative strategy can be adopted to ensure that the actual propulsion has sufficient speed reserve to resist flow field disturbances.

[0071] (7) The navigation path planning method of this invention is carried out by trajectory tracking, and the actual navigation time and space position is as follows. It is definite, and the corresponding flow field disturbance boundary is determined by... Based on the velocity vector composition relationship, the range of actual propulsion speed variation during navigation will be definite and calculable, and the fluctuations in navigation arrival time, propulsion, and energy consumption will also be definite. This provides deterministic information support for navigation decisions in uncertain flow fields.

[0072] (8) This invention establishes a quantitative relationship between the influence of flow field uncertainty on navigation planning. Equations (12-17) show that: flow field uncertainty The larger the flow field uncertainty, the slower the reachable front develops, and the longer the required navigation time. The propulsion speed must counteract flow field uncertainty; the greater the uncertainty, the higher the required propulsion speed. Flow field uncertainty that consistently exceeds the propulsion capability can cause the reachable front to disappear, leading to planning failure. This also means that there is no definite reachable range in the flow field, posing a significant navigation risk. Therefore, ensuring safe navigation in stochastic flow fields requires, on the one hand, improving the accuracy of flow field prediction and reducing the range of uncertainty, and on the other hand, improving the propulsion capability of the vehicle.

[0073] This invention proposes a method and system for rapid navigation path planning in stochastic flow fields. It describes the stochastic flow field using a combination of median and disturbed flow fields. It innovatively proposes two conservative navigation speed strategies and improves the fundamental equations of the level set, obtaining the time-optimal navigation trajectory under the conservative strategies as the navigation path. The advantages of this approach include: From a technical perspective: (1) Good path planning effect This planning method, by simply characterizing the determinism and randomness of the flow field, can actively avoid regions with high uncertainty in the flow field (circumferential flow), effectively utilize the deterministic part of the flow field, and significantly reduce flow field fluctuations during navigation. In contrast, the path constructed by conventional ensemble optimization methods does not focus on avoiding uncertain regions.

[0074] (2) Fast planning and calculation speed This invention employs a highly efficient trajectory search method with reduced order, which is 2-3 orders of magnitude faster than conventional ensemble optimization methods. On the same computer, a 24-hour flight plan for a stratospheric airship can be completed in about ten minutes, while conventional ensemble optimization methods may require about a day for planning, analysis, and optimization.

[0075] (3) Saves navigation power and energy consumption This planning method recommends using trajectory tracking for navigation. Through relevant example tests and comparisons (see Example A and Example B), the navigation path planned by this method shows that the navigation propulsion speed and navigation energy consumption are significantly lower than those of the ensemble selection method in simulation.

[0076] From an economic perspective, this invention is particularly suitable for navigation missions with limited power and energy under uncertain and complex flow field conditions. It can improve the efficiency of stratospheric airships and marine unmanned surface vessels in performing missions, reduce fluctuations in navigation time, propulsion speed and energy consumption in uncertain flow fields, and help improve the scheduling and operation control level of the vehicle, thereby reducing operating costs. In addition, the power system and energy system indicators can be optimized during the design of the vehicle platform, reducing the platform weight and lowering the platform development cost.

[0077] From a social perspective, this invention can be combined with atmospheric wind field and ocean current field ensemble forecasting systems to provide determinism for navigation in uncertain flow fields, avoiding navigational loss of control caused by random changes in environmental flow fields, reducing navigational safety risks, and supporting automated applications of cross-regional, long-endurance stratospheric airships and marine unmanned surface vessels in fields such as rescue, environmental monitoring, and cross-regional logistics, demonstrating broad application prospects. This invention can also be used to support the construction of cluster scheduling and management systems for autonomous vehicles or public transportation management systems, laying a technological foundation for the development and safe utilization of my country's stratospheric and marine space. Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for fast navigation path planning in stochastic flow fields, comprising: Step 1: Based on the flow field ensemble forecast data, separate the deterministic and uncertain parts of the random flow field, and construct the median flow field and the perturbation flow field ensemble of the random flow field. The median flow field is used to characterize the deterministic part of the random flow field, and the perturbation flow field ensemble is used to characterize the uncertain part of the random flow field. Step 2: Based on the median flow field and the disturbed flow field set, a conservative adjustment strategy for the sailing speed is adopted. Under the condition of conservative sailing speed, the improved level set equation is used to evolve the reachable front from the starting point of the sailing in a clockwise manner until the reachable front reaches the sailing target point and then the evolution stops. Step 3: After reaching the target point, perform reverse time backtracking on the reachable frontier to calculate the time-optimal trajectory under the conservative speed adjustment strategy, and use this time-optimal trajectory as the navigation planning path in the stochastic flow field.

2. The method for rapid navigation path planning in stochastic flow fields according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Construct a flow field ensemble using the flow field data predicted by each member of the ensemble forecasting system: ; in, Indicates the first Samples of the flow field In spatial location and time The velocity vector of the flow field at that location; Indicates the first Each flow field sample corresponds to one member. , where m is the total number of members in the flow field ensemble prediction system. , For navigation space, It is the total number of spatial dimensions. , The maximum allowed time for the planned task; Step 1.2: According to spatiotemporal coordinates Statistical analysis of the flow field velocity vectors predicted by each member in each dimension of the flow field. upper boundary value and lower boundary value ,in, Represents the ordinal number of spatial dimensions. ; Step 1.3: Based on the aforementioned upper boundary value and lower boundary value Calculate the mean value of each component of the flow field The median of each component The median flow field that characterizes the deterministic part of a stochastic flow field ; Step 1.4: Based on the upper boundary value and lower boundary value Calculate the half-width of the uncertainty interval for each component of the flow field Based on the half-width of the uncertainty interval of each component Establish an upper approximate set of perturbation fields that characterize the uncertainties of the random flow field, as the perturbation flow field set. .

3. The method for rapid navigation path planning in stochastic flow fields according to claim 2, characterized in that, In step 1.2, the upper boundary value for: ； lower boundary value for: ； in, =1,2 or 3 Represents the velocity vector of the flow field In the The components of the dimension, Indicates the first The sampled flow field in spacetime coordinates The velocity vector of the flow field; In step 1.3, the median of the i-th dimension component for: ； Median flow field for: ； in, It is the transpose symbol; In step 1.4, the half-width of the uncertain interval of the i-th component. for: ； Collection of perturbed flow fields for: ； in, In spacetime coordinates The perturbation flow field vector at that location. The first vector representing the perturbation flow field vector Dimensional components, each sampled flow field in spatiotemporal coordinates The perturbation flow field vector at the location satisfy .

4. The method for rapid navigation path planning in stochastic flow fields according to claim 2, characterized in that, In step 1, if the flow field data predicted by each member of the ensemble forecasting system is lacking, and only a deterministic flow field velocity vector exists... Then As the median flow field ; If the random flow field is a periodic flow field with a period of... If the phase is unknown, then a time-invariant median field is established. Alternate median flow field The calculation formula is: ； The half-width vector of the disturbance interval is determined by either statistically predicting errors using historical flow field data or by setting errors based on expert experience. .

5. The method for rapid navigation path planning in stochastic flow fields according to claim 2, characterized in that, In step 2, the improved level set equation is: ； in, In spacetime coordinates The signed distance scalar implicit function at the location, for The spatial gradient vector, yes The 2-norm, It is the result of correcting the spacetime coordinates using a conservative adjustment strategy for sailing speed. The propulsion speed at that location.

6. The method for rapid navigation path planning in stochastic flow fields according to claim 5, characterized in that, The formula for setting the signed distance scalar implicit function at the initial time t=0 is as follows: = in, Let be the signed implicit function of the distance scalar at the initial time. This is the initial spatial position vector of the vehicle. The first of the initial spatial position vectors of the vehicle dimensional components, Spatial location The Dimensional components; Spatial gradient vector 2-norm for: ； Corrected in spacetime coordinates using a conservative speed adjustment strategy Propulsion speed at the location for: ； in, The design propulsion speed of the vehicle in the absence of flow field disturbance. This represents the retention amount of the sailing speed at the spacetime coordinate (x,t).

7. The method for rapid navigation path planning in stochastic flow fields according to claim 6, characterized in that, The speed retention Calculated using either the maximum projection method or the maximum length method, where the maximum projection method is denoted by N1 and the maximum length method by N2; where... Speed ​​retention calculated by the maximum projection method for: ； in, Spatial gradient vector The Dimensional components; Speed ​​retention calculated using the maximum length method for: ； in, Represents in spacetime coordinates The half-width vector of the disturbance interval at that location: ； in, This is the transpose symbol.

8. The method for rapid navigation path planning in stochastic flow fields according to claim 5, characterized in that, In step 2, the evolution process of the reachable front includes: For navigation space A numerical computation grid is established, and the improved fundamental equations of the level set are solved using a numerical method for level sets, yielding a signed implicit function of the distance scalar. The value of (x,t); at time t, it satisfies The spatial locations (x,t)≤0 form the navigation reachable set at time t. ,satisfy },in, The position (x,t)=0 constitutes the reachable frontier. ,satisfy }; Real-time detection of navigation target points Signed distance scalar implicit function The value, if If the time is ≤0, the forward evolution of the reachable set ends, and the time at this point is the minimum travel arrival time. If reachable set For an empty set or evolved to If the target point has not been reached, the planning is deemed a failure.

9. The method for rapid navigation path planning in stochastic flow fields according to claim 8, characterized in that, In step 3, the specific formula for calculating the optimal time trajectory in reverse time is as follows: ； From minimum sailing arrival time Reverse time reversal can reach the frontier of the set, from the navigation target point The navigation trajectory was obtained by calculating up to t=0 using a step-by-step integration method. , as the time-optimal trajectory; in, It is the optimal navigation trajectory position at time t, 0≤t≤ ,and , Time of arrival The optimal navigation trajectory position at any given time. It is the median flow field at the optimal navigation trajectory point. It is the result of a conservative adjustment strategy for sailing speed in spacetime coordinates. The propulsion speed at that location, Is The spatial gradient vector at that location.

10. A rapid navigation path planning system for stochastic flow fields, comprising a flow field separation module, an reachable front evolution module, and a trajectory backtracking planning module, wherein, The flow field separation module is used to separate the deterministic and uncertain parts of the random flow field based on the flow field set forecast data, and to construct the median flow field and the perturbation flow field set of the random flow field. The median flow field represents the deterministic part of the random flow field, and the perturbation flow field set represents the uncertain part of the random flow field. The reachable front evolution module is used to adopt a conservative adjustment strategy for sailing speed based on the median flow field and the set of disturbed flow fields. Under the condition of conservative sailing speed, the improved level set equation is used to evolve the reachable front from the starting point of sailing in a clockwise manner until the reachable front reaches the target point of sailing and then stops evolving. The trajectory backtracking planning module is used to perform reverse time backtracking on the reachable front after reaching the target point, calculate the time-optimal trajectory under the conservative adjustment strategy of sailing speed, and use the time-optimal trajectory as the sailing planning path in the random flow field.

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