Low-altitude airspace path generation method based on space-time distribution field

Abstract

The invention relates to the technical field of low-altitude airspace flight path generation algorithms, and provides a space-time distribution field-based low-altitude airspace path generation algorithm, which aims at the complexity of a low-altitude airspace flight environment, performs self-adaptive division by using the idea of a layered airspace structure to construct an airspace three-dimensional grid model, and generates a space-time distribution field-based low-altitude airspace path generation algorithm. On this basis, a low-altitude airspace path generation algorithm based on a space-time distribution field is provided, and a Navier-Stokes equation is taken as a basis to comprehensively consider factors such as flight height, direction, collision avoidance, airspace resources and the like of each region to generate a flight path. A flight path generation algorithm is improved in the aspects of a layered airspace structure, a flight path generation mode, obstacles, safety interval constraint conditions and the like, and the solving quality of the Navier-Stokes equation and the Poisson equation for simulating the flowing of an incompressible ideal fluid in a two-dimensional space in the aspect of flight path generation is improved; and the requirements of balancing multiple targets such as airspace capacity, flight time and airspace resources in a low-altitude complex and dynamic flight environment are met.

Description

Technical Field:

[0001] The present invention relates to a method for generating high-density airspace paths in low-altitude airspace based on hydrodynamics; an adaptive flight corridor is constructed using the Navier-Stokes equation for the complex situations in each region of the low-altitude airspace structure, and it is a method for generating low-altitude flight paths that combines flight altitude, flight direction, collision avoidance, and spatio-temporal distribution fields. Background Art:

[0002] Low-altitude traffic relies on low-altitude airspace resources to ensure the safe and free flight of various types of manned and unmanned aircraft. However, the current allocation and management of airspace resources in China still basically remain in the state of independent use and non-dynamic control. Restricted by policies, the low-altitude airspace used for general aviation nationwide is less than 30% and is not networked and contiguous. The regional distribution is uneven, and most airports have relatively single functions, making it difficult to meet the diversified service needs. At the same time, the low-altitude traffic management method is still a continuation of the high-altitude management method, using manual scheduling and static scheduling methods, which are difficult to cope with the complex and dynamic flight environment in the low-altitude airspace and cannot balance multiple objectives such as airspace capacity, flight time, and airspace resources.

[0003] The current mainstream path planning algorithms (such as Rapidly-Exploring Random Trees and heuristic algorithms) have significant limitations in supporting the dynamic control of low-altitude traffic, further amplifying the above contradictions:

[0004] Among them, the Rapidly-Exploring Random Trees algorithm (RRT) expands a tree-like structure based on random sampling to quickly explore feasible paths in high-dimensional space. Each iteration randomly selects a target point, finds the nearest node from the current tree, and extends it in the target direction, avoiding obstacle areas. However, the paths generated by RRT are often redundant and tortuous and need post-processing for smoothing; and it is unable to fuse the dynamic changes in the airspace (such as temporary no-fly zones, sudden meteorological disturbances) in real time when generating paths.

[0005] Heuristic algorithms simulate the biological evolution process, use selection, crossover, and mutation operations to iteratively optimize the path population to adapt to multi-objective constraints (such as the shortest path, the lowest risk); they perform well in multi-objective optimization problems such as airspace corridor generation, but the defect of heuristic algorithms is that they face computational bottlenecks in complex airspaces. Taking the ant colony algorithm as an example, the complexity of its node traversal increases exponentially with the number of airspace grids. This directly leads to a lag in airspace resource allocation, and a large number of airspace units are forced to be in an "idle locked" state, further exacerbating the waste of 30% of the low-altitude utilization rate of resources. Summary of the Invention:

[0006] In view of the problems existing in the prior art, the present invention establishes a traffic model for low-altitude airspace air corridors in high-density obstacle areas such as cities. In order to maximize traffic throughput while ensuring a safe separation. For the three-dimensional urban spatial structure, the idea of a layered airspace structure is used to divide it into a finite number of two-dimensional spaces based on the vertical height and flight direction. By gridifying the plane to describe the occupancy state of the grid using elevation or point cloud data, and finally using the discrete Navier-Stokes equation and Poisson equation to solve the fluid velocity field and pressure field, simulating the flow of an incompressible ideal fluid in the two-dimensional space to generate streamlines; the streamlines safely wrap the buildings and obstacles in the grid, and define the streamline density and length based on the demand to generate a finite number of air corridors.

[0007] In order to achieve the above object, the technical solution of the present invention is as follows:

[0008] A method for generating a low-altitude airspace path based on a spatio-temporal distribution field, comprising the following steps:

[0009] Step 1: Divide the discrete layered airspace based on the vertical height

[0010] The low-altitude airspace is discretized into a finite number of M layers of planes, where each plane has a constant height h i (i = 1, 2,..., M) and a unified flight course angle interval;

[0011] By way of non-limiting example, the true course angle interval of the i-th layer plane is set as:

[0012]

[0013] Step 2: Determine the initial velocity field of the flight course in airspaces at different heights

[0014] Traverse all discrete planes and perform initialization:

[0015] Gridify the k-th layer plane with the current height of h k to generate an N×N grid area; if the obstacle height l in the elevation or point cloud data in the cell > h k , it means that the cell intersects with the obstacle and the cell is full, otherwise it means the cell is in a free state.

[0016] Initialize the velocity field ν = (u, v) to provide an iterative starting point for the Navier-Stokes equation, where u is the velocity in the x-axis direction and v is the velocity in the y-axis direction; u and v can be initialized to a certain constant value. The initialization of the velocity field v can determine the flight course angle of the airspace corridor in this layer; if the flow direction needs to be horizontally rotated by TH k , it can be achieved through the rotation matrix of formula (1-1).

[0017]

[0018] Step 3: Output the Navier - Stokes equation for velocity field calculation

[0019] The momentum conservation formula of the standard Navier - Stokes equation for two - dimensional incompressible fluids is shown in Equation (1 - 2):

[0020]

[0021] where \(v=(u, v)\) is the velocity field of the fluid, \(u\) is the velocity in the \(x\) - axis direction, \(v\) is the velocity in the \(y\) - axis direction, \(p\) is the fluid pressure field, and \(\rho\) is the fluid density (assumed to be 1). Here, the present invention does not consider the external force term \(f\) (such as external forces like gravity and surface tension) in the Navier - Stokes equation. Therefore, the velocity update formula based on the Navier - Stokes equation only contains three parts: the convection term the pressure gradient term and the diffusion term acting.

[0022] In order to solve numerically stably and calculate the three parts based on the time step, ensuring that each part can better approximate the true solution, especially in the case of incompressible fluids, it is necessary to discretize the Navier - Stokes equation.

[0023] The convection term represents the non - linear velocity term of the fluid in the plane, reflecting the self - change of the velocity field and involving the velocity components of \(u\) and \(v\):

[0024]

[0025] where \(n\) is the time step, and \(i, j\) represent the cell positions in the two - dimensional space.

[0026] The pressure gradient term is used to calculate the part of the velocity field that does not conform to the continuity equation. The pressure gradient term, which needs to be solved by iterating the Poisson equation, drives the correction of the velocity field. The velocity update for \(u\) is:

[0027]

[0028] The velocity update for \(v\) is:

[0029]

[0030] where \(p\) i,j is the pressure value at the grid point, \(\Delta t\) is the time step size, \(\Delta x\) and \(\Delta y\) are the grid spacings in the \(x\) and \(y\) directions respectively, and \(\rho\) is the fluid density.

[0031] The diffusion term is related to the viscosity coefficient of the fluid and describes the diffusion of the velocity field due to viscosity. The velocity update of the diffusion term is:

[0032]

[0033] Among them, μ is the dynamic viscosity coefficient of the fluid.

[0034] In summary, the updated formula for the velocity field of the discretized Navier-Stokes equation:

[0035]

[0036] Step 4: Calculate the Poisson equation to obtain the pressure field

[0037] As shown in equations (1-6) and (1-7), the updated formula for the velocity field of the discretized Navier-Stokes equation updates u and v through each time step iteration; and the premise of simulating the streamline in the present invention is the flow of an incompressible ideal fluid in a two-dimensional space. Therefore, the part where the velocity field needs to satisfy mass conservation (i.e., the continuity equation), in the case of an incompressible fluid, the continuity equation is:

[0038]

[0039] That is, the velocity field of the fluid must be divergence-free (i.e., no volume change). If the velocity field does not satisfy this condition, it needs to be corrected through the pressure term in the Navier-Stokes equation to make the mass of the fluid conserved. From the Navier-Stokes equation, the pressure equation is obtained through a divergence operation:

[0040]

[0041] That is, the pressure field p satisfies the Poisson equation. The right-hand side is the source term b from the non-linear term and the time-varying term of the velocity field. For numerical solution, the Poisson equation is discretized into a difference equation and discretized on a two-dimensional grid through the central difference method:

[0042]

[0043] Through an iterative process (usually using the Jacobi iterative method or the Gauss-Seidel iterative method), gradually approximate the final pressure field p;

[0044] Step 5: Calculate the source term of the Poisson equation

[0045] In the process of solving the pressure field using the Poisson equation in equation (1-10), it is necessary to calculate the source term b to ensure that the velocity field satisfies the mass conservation condition of the incompressible fluid (continuity equation) as shown in equation (1-8). Therefore, to solve the source term, the divergence of the momentum conservation equation of the Navier-Stokes equation is taken to obtain:

[0046]

[0047] Discretization (1 - 11) gives:

[0048]

[0049] Finally, by initializing the obstacle grid, fluid velocity field, and pressure field, update and calculate the discrete Navier - Stokes equations and Poisson equation to solve for the fluid velocity field and pressure field; repeat the above steps until the set number of iterations is reached, and generate an airspace corridor (streamline) based on the obtained velocity field.

[0050] Furthermore, in step two, when initializing the obstacle map, if a cell intersects with an obstacle, it means the cell is full; thus, the velocity field v in both directions of the obstacle cell is 0, and the generated streamline will not pass through the obstacle and its safety buffer area to achieve the purpose of collision avoidance.

[0051] It is also possible to set a certain safety buffer for the obstacle and the flight path, that is, set the grids around the obstacle cell as unavailable cells as well.

[0052] Furthermore, in step three, assuming a certain area is selected to generate N×N cells, then △x and △y should be 1 / N. At the same time, in actual generation experiments, when the dynamic viscosity coefficient μ of the fluid approaches 0, the generated streamline is smoother; thus, the time step △t should also be correspondingly reduced to ensure the stability of the calculation process.

[0053] Furthermore, in step four, the Poisson equation needs to set the boundary conditions of the pressure field to ensure physical consistency. For example: the pressure value at the right boundary of the pressure field is equal to the pressure in the second - last column, that is, assuming the pressure of the fluid at the right boundary is constant. The pressure value at the upper boundary is equal to the pressure value below it, that is, maintaining the continuity of the pressure. The pressure at the boundary is set to zero, which usually means that this boundary is in contact with the atmospheric pressure or other environmental boundary conditions.

[0054] In summary, the present invention conducts route planning for the low - altitude environment and aircraft characteristics, utilizes the idea of fluid mechanics, and designs an accurate and feasible air flight corridor in densely built - up areas such as cities. The fluid simulated by the Navier - Stokes equations can generate a high - density air corridor traffic model in a short time, maximizing the low - altitude traffic throughput while ensuring a safety buffer. At the same time, the idea of two - dimensional space modularization can effectively cope with the current irregular low - altitude airspace distribution state in China, improving the scalability of future low - altitude path generation and planning.

[0055] Beneficial effects

[0056] This article conducts route planning for the low-altitude environment and aircraft dynamics. Using the idea of fluid mechanics, it designs accurate and feasible aerial flight corridors in densely built-up areas such as cities. Different from traditional rule-based airspace management, this study dynamically generates corridors through the principles of fluid dynamics, which can adapt to changes in the urban environment and provide a theoretical basis for the real-time allocation of airspace resources. The fluid simulated by the Navier-Stokes equation can generate a high-density air corridor traffic model in a short time, maximizing the low-altitude traffic throughput while ensuring a safe separation. At the same time, the idea of two-dimensional space modularity can effectively address the current irregular low-altitude airspace distribution state, improving the scalability of future low-altitude path generation and planning, and enhancing the usability of the algorithm by using easily accessible elevation data. Description of the Drawings:

[0057] Figure 1 It is a schematic diagram of the hierarchical airspace structure based on vertical height and flight direction in an embodiment of the present invention;

[0058] Figure 2 It is a schematic diagram of the airspace path generated based on the Navier-Stokes equation in an embodiment of the present invention;

[0059] Figure 3 It is a flowchart of an algorithm for generating low-altitude airspace paths based on a spatio-temporal distribution field in the present invention. Detailed Embodiments:

[0060] The present invention will be further described below in conjunction with the drawings and embodiments.

[0061] Urban application cases mainly for logistics transportation, rescue, monitoring, and manned transportation have driven the global low-altitude aviation traffic system market. Although current low-altitude tasks are diverse, they must share the same urban sky and are restricted by the level of aircraft and management methods, resulting in low utilization of airspace resources. The present invention can effectively organize low-altitude traffic through a highly dense air corridor system and a complex low-altitude urban airspace landscape, minimizing or completely eliminating traffic conflicts. This novel spatial organization method can be combined with existing geofencing, airspace no-fly zones, and low-altitude traffic management solutions to maximize the transit traffic flow and support flight missions while ensuring safety.

[0062] Such as Figure 1 It is a schematic diagram of the hierarchical airspace structure based on vertical height and flight direction in an embodiment of the present invention;

[0063] Such as Figure 2 It is a schematic diagram of the airspace path generated based on the Navier-Stokes equation in an embodiment of the present invention;

[0064] Such as Figure 3This is a flowchart of a low-altitude airspace path generation algorithm based on the spatio-temporal distribution field for the present invention.

[0065] (1) Stereo space rasterization based on a hierarchical airspace structure

[0066] Low-altitude traffic requires an airspace system that can organize a large number of aircraft while ensuring a safe separation. Therefore, the present invention first divides the three-dimensional urban space into a hierarchical airspace structure based on the vertical height and flight direction, as Figure 1 shown, as a prerequisite for generating airspace flight paths.

[0067] 1. Taking Shanghai as an example, assume the available flight height of the city is H. If each layer of airspace is h, then the airspace is discretized into a finite number of M layers of planes, where each horizontal plane has a constant height h i = H / h (i = 1, 2,..., M). On this basis, a unified flight course angle is specified for each layer of airspace. Taking the true course angle as an example, the course angle intervals corresponding to different flight height layers are The purpose of the unified course angle of the hierarchical airspace is to effectively reduce the relative flight speed of the aircraft.

[0068] 2. Grid it into N×N cells based on the Shanghai elevation or point cloud data map. Assume the k-th layer of plane is selected for gridification, and the height is h k ; if the height l of the obstacle in the elevation or point cloud data > h k , it means that the cell intersects with the obstacle and the cell is full, otherwise it means the cell is in a free state; thus representing the obstacle map.

[0069] (2) Solving the urban space fluid velocity field based on the Navier-Stokes equation

[0070] After completing the grid modeling of the urban space elevation data, it is necessary to iteratively calculate the discrete Navier-Stokes equation and Poisson equation to solve the fluid velocity field and pressure field, and simulate the flow of an incompressible ideal fluid in a two-dimensional space.

[0071] 1. Initialize the velocity field v = (u, v) and the pressure field p; the initialization of the velocity field can determine the flight course angle of this layer. For example, if the flight corridor course of a certain layer is from due east to due west, the matrix u in the x-axis direction of the velocity field is set to all 1 (similarly for due west to due east). If the flight corridor course is from due north to due south, the matrix v in the y-axis direction of the velocity field is set to all 1 (similarly for due south to due north); for other angles, the velocity field is deflected accordingly. The pressure field can be initialized to all 0 and can also be adjusted according to actual needs.

[0072] 2. After determining the fluid flow direction, it is necessary to determine the fluid density, time step, and viscosity coefficient parameters to calculate the required flow field model through iterative loops. First, calculate the Poisson source term b according to Equation (1-12), substitute the source term into Equation (1-10), and iterate to calculate the pressure field p again; the boundary conditions of the pressure field need to be set in each loop to ensure the influence of the boundary conditions on the pressure field.

[0073] 3. Based on the calculations in the above steps, the velocity field v=(u, v) and the pressure field p can be obtained. Substitute them into the discrete Navier-Stokes equations of Equations (1-6) and (1-7) and iterate to obtain the final velocity field matrix; among them, the obstacle matrix should be substituted in each loop. If the cell is in an occupied state, the corresponding velocity field (u, v)=0; at the same time, expanding the occupied cells can also set the velocity fields of the surrounding positions to 0, indicating an increase in the safety interval between the airspace flight path and the obstacle. The obstacle matrix should be substituted in each iteration of the Navier-Stokes equations to ensure that the fluid does not flow into the obstacle and to ensure the influence of the obstacle on the flow field.

[0074] (III) Generating streamlines based on the fluid velocity field

[0075] Streamlines are a series of curves that satisfy Equation (1-13) in the flow field:

[0076]

[0077] Using numerical methods to solve the streamline equation based on the iteratively obtained velocity field, a common numerical method is to integrate the velocity field from the starting point based on the Euler method or the fourth-order Runge-Kutta method to obtain the streamlines, and then draw the streamlines in the given area, as Figure 2 shown. The starting point of the integration can be automatically selected or specified by the user. The streamlines will automatically avoid obstacles or be truncated according to the grid boundary and the size of the velocity field; therefore, if the obstacle avoidance accuracy or the dynamic smoothness of the streamlines is not as expected, the grid accuracy can be considered to be increased, that is, increase the value of N during meshing to generate denser cells; or interpolation can be performed on the velocity field without increasing the cell density to improve the smoothness of the streamlines.

[0078] The above description is only a description of the preferred embodiments of the present application and is not any limitation on the scope of the present application. Any change or modification made by any ordinary person skilled in the art according to the technical content disclosed above should be regarded as an equivalent effective embodiment and fall within the scope of the technical solution protection of the present application.

Claims

1. A method for generating a low-altitude airspace path based on a spatiotemporal distribution field, characterized in that: The following steps are involved: Step 1: Divide the airspace into discrete layers based on vertical height The low-altitude airspace is discretized into a finite number of M planes, each of which has a constant altitude h i (i=1,2,…,M) and a uniform flight heading angle interval; Step 2: Determine the flight heading at different altitudes and initialize the velocity field Iterate over all discrete planes and initialize them: For the current height h k The kth plane is gridded to generate an N×N grid area; if the elevation in the cell or the obstacle height in the point cloud data l>h k , it means that the cell intersects with the obstacle and the cell is full, otherwise it means that the cell is free; Initialize the velocity field ν = (u, v) to provide an iterative starting point for the Navier-Stokes equation, where u is the velocity in the x-axis direction and v is the velocity in the y-axis direction; u and v are initialized to a constant value; the initialization of the velocity field ν determines the flight heading angle of the airspace corridor at this layer; if the flow direction needs to be rotated horizontally TH k , through the formula (1-1) rotation matrix to achieve: Step 3: Output velocity field to calculate Navier-Stokes equations The momentum conservation formula of the standard Navier-Stokes equation in the case of two-dimensional incompressible fluid is shown in equation (1-2): Where p is the fluid pressure field and ρ is the fluid density. Without considering the external force term f in the Navier-Stokes equation, the velocity update formula based on the Navier-Stokes equation only contains three parts: the convection term Pressure gradient term and diffusion term The role of; The velocity field update formula of the discretized Navier-Stokes equation is: Step 4: Calculate Poisson's equation to obtain the pressure field The velocity field needs to satisfy the part of mass conservation (i.e., continuity equation). In the case of incompressible fluid, the continuity equation is: That is, the velocity field of the fluid must have a divergence of zero. If the velocity field does not meet this condition, it is necessary to correct it through the pressure term in the Navier-Stokes equation to conserve the mass of the fluid. From the Navier-Stokes equation, the pressure equation is obtained by taking the divergence operation: That is, the pressure field p satisfies the Poisson equation; the right half is the source term b, which comes from the nonlinear term and time-varying term of the velocity field; for numerical solution, the Poisson equation is discretized into a difference equation and discretized on a two-dimensional grid by the central difference method: Through the iterative process, the final pressure field p is gradually approached; Step 5: Calculate the source term of the Poisson equation In the process of solving the pressure field using the Poisson equation in equation (1-10), it is necessary to calculate the source term b to ensure that the velocity field satisfies the mass conservation condition (continuity equation) of the incompressible fluid as shown in equation (1-8); therefore, in order to solve the source term, it is necessary to take the divergence of the momentum conservation equation of the Navier-Stokes equation to obtain: Discretization (1-11) yields: Finally, by initializing the obstacle grid, fluid velocity field and pressure field, the discrete Navier-Stokes equations and Poisson equations are updated and calculated to solve the fluid velocity field and pressure field; the above steps are repeated until the set number of iterations is reached, and the airspace corridors, i.e., streamlines, are generated based on the obtained velocity field.

2. According to claim 1, a method for generating a low-altitude airspace path based on a spatiotemporal distribution field is characterized in that: The true heading angle interval of the i-th plane is set as:

3. According to the method for generating a low-altitude airspace path based on a spatiotemporal distribution field as claimed in claim 1, it is characterized in that: In step 2, when initializing the obstacle map, if a cell intersects with an obstacle, it means that the cell is full; the velocity field v in both directions of the obstacle cell is 0, and the generated streamline will not pass through the obstacle and its safe interval area to achieve the purpose of collision avoidance; A certain safety interval is set between obstacles and flight path generation, that is, the grids around the obstacle cells are also set as unavailable cells.

4. According to claim 1, a method for generating a low-altitude airspace path based on a spatiotemporal distribution field is characterized in that: In step 3, the discretized Navier-Stokes equations are as follows: The convection term represents the nonlinear velocity term of the fluid in the plane, reflecting the change of the velocity field itself, involving the velocity components of u and v: Where n is the time step, i and j represent the cell positions in two-dimensional space; The pressure gradient term is used to calculate the part of the velocity field that does not conform to the continuity equation; the pressure gradient term solved by iterative Poisson's equation drives the correction of the velocity field; The velocity update for u is: The velocity of v is updated as: Among them, p i,j is the pressure value at the grid point, △t is the time step, △x and △y are the spacing of the grid in and directions respectively, and ρ is the density of the fluid; The diffusion term is related to the viscosity coefficient of the fluid and describes the diffusion of the velocity field due to viscosity; the diffusion term velocity is updated as: Where μ is the dynamic viscosity coefficient of the fluid.

5. According to claim 4, a method for generating a low-altitude airspace path based on a spatiotemporal distribution field is characterized in that: In the step 3, it is assumed that a certain area is selected to generate N×N cells, then △x and △y are 1 / N; at the same time, in the actual generation experiment, when the dynamic viscosity coefficient μ of the fluid approaches 0, the generated streamlines are smoother; the time step △t is correspondingly reduced to ensure the stability of the calculation process.

6. According to claim 4, a method for generating a low-altitude airspace path based on a spatiotemporal distribution field is characterized in that: The Poisson equation described in step 4 is implemented by setting the boundary conditions of the pressure field to ensure physical consistency.

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