A low-altitude airspace path generation method based on a space-time distribution field

Abstract

The application relates to the technical field of flight path generation algorithms of low-altitude airspace, and provides a low-altitude airspace path generation algorithm based on a space-time distribution field, which is adaptive to the complexity of the low-altitude airspace flight environment, uses the idea of a layered airspace structure to adaptively divide and construct an airspace three-dimensional grid model, and on the basis, proposes the low-altitude airspace path generation algorithm based on the space-time distribution field, which generates the flight path by comprehensively considering the flight height, direction, collision avoidance and airspace resources and other factors of each region based on the Navier-Stokes equation. The flight path generation algorithm is improved in the aspects of the layered airspace structure, the flight path generation mode and the obstacle and safety interval constraint conditions, the solving quality of the Navier-Stokes equation and the Poisson equation simulating the flow of the incompressible ideal fluid in the two-dimensional space is improved for the flight path generation, and the flight path generation algorithm is more in line with the needs of balancing the airspace capacity, the flight time and the airspace resources and other multiple targets under the low-altitude complex and dynamic flight environment.

Description

TECHNICAL FIELD

[0001] The application relates to a high-density airspace path generation method based on fluid mechanics in low-altitude airspace; a flight corridor is adaptively constructed using a Navier-Stokes equation for the complex conditions of each region in a low-altitude airspace structure, and is a low-altitude flight path generation method that combines flight height, flight direction, collision avoidance and a space-time distribution field. BACKGROUND

[0002] Low-altitude traffic needs to rely on low-altitude airspace resources to ensure the safe and free flight of various types of manned and unmanned aircraft. However, the current airspace resource allocation and management in China still basically remains in the state of independent use and non-dynamic control. Less than 30% of the low-altitude airspace is used nationwide due to policy constraints, and the low-altitude airspace is not connected and distributed unevenly. Most airports have single functions and cannot meet the diversified service demand. At the same time, the low-altitude traffic management mode is still a continuation of the high-altitude management mode, and the use of manual scheduling and static scheduling methods cannot cope with the complex and dynamic flight environment in the low-altitude airspace, and cannot balance the airspace capacity, flight time and airspace resources and other multiple targets.

[0003] The current mainstream path planning algorithm (such as the rapid exploration random tree and heuristic algorithm) has significant limitations in supporting dynamic control of low-altitude traffic, further exacerbating the above-mentioned contradictions:

[0004] Among them, the rapid exploration random tree algorithm (RRT) is based on random sampling to expand the tree structure and quickly explore the feasible path in high-dimensional space. In each iteration, a target point is randomly selected, the nearest node in the current tree is found, and the target direction is extended to avoid the obstacle region. However, the path generated by RRT is often redundant and winding, and needs to be smoothed after processing. Moreover, the path generated cannot be fused with the dynamic changes of the airspace (such as temporary flight restricted areas and sudden weather disturbances) in real time.

[0005] The heuristic algorithm simulates the biological evolution process, uses selection, crossover and mutation operations to iteratively optimize the path population, and adapts to multiple target constraints (such as the shortest path and the lowest risk). In the airspace corridor generation, this kind of multi-objective optimization problem performs well, but the heuristic algorithm has the defect of computational bottleneck in complex airspace. Taking the ant colony algorithm as an example, the node traversal complexity 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 the "idle and locked" state, further exacerbating the waste of 30% of the low-altitude resource utilization rate. SUMMARY

[0006] To solve the problems in the prior art, the application establishes a low-altitude airspace air corridor traffic model for high-density obstacle areas such as cities. In order to maximize the traffic throughput under the premise of ensuring the safety interval, the three-dimensional urban space structure is divided into a limited number of two-dimensional spaces based on the vertical height and the flight direction by using the idea of hierarchical airspace structure, the plane is gridded to describe the occupancy state of the grid by using the elevation or point cloud data, and finally the fluid velocity field and pressure field are solved by using the discrete Navier-Stokes equation and Poisson equation to simulate the flow of incompressible ideal fluid in the two-dimensional space to generate flow lines; the flow lines safely wrap the buildings and obstacles in the grid, and the flow line density and length are defined based on the demand to generate a limited number of air corridors.

[0007] To achieve the above purpose, the technical scheme of the application is:

[0008] A low-altitude airspace path generation method based on a space-time distribution field, comprising the following steps:

[0009] Step 1: Discrete hierarchical airspace based on vertical height

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

[0011] For example, the true heading angle interval of the i-th layer plane is set as:

[0012]

[0013] Step 2: Determine the flight heading initialization velocity field of the airspace at different heights

[0014] Traverse all discrete planes and initialize:

[0015] Grid the k-th layer plane at the current height h k , to generate an N×N grid area; if the obstacle height l in the elevation or point cloud data in the unit cell is greater than h k , it indicates that the unit cell intersects with the obstacle, the unit cell is full, otherwise it indicates that the unit cell is free.

[0016] Initialize the velocity field v=(u, v) to provide an iteration starting point for the Navier-Stokes equation, wherein 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 heading angle of the air corridor at this layer; if the flow direction needs to be rotated horizontally by TH k , it can be realized by the rotation matrix of formula (1-1).

[0017]

[0018] Step three: output velocity field calculation Navier-Stokes equation

[0019] The standard Navier-Stokes equation in the momentum conservation formula of two-dimensional incompressible fluid case as 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 p is the fluid density (set to 1). Here the invention does not consider the external force term f (such as gravity, surface tension, etc. External force) in the Navier-Stokes equation, so the velocity update formula based on the Navier-Stokes equation only contains three parts: convection term Pressure gradient term And the diffusion term Effect.

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

[0023] 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 u and v:

[0024]

[0025] Where n is the time step, i, j represent the cell position in two-dimensional space.

[0026] The pressure gradient term is used to calculate the part of the velocity field that does not meet the continuity equation. The pressure gradient term needs to be solved by iterating the Poisson equation, which 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 of the grid point, △t is the time step, △x and △y are the grid spacing in and direction, respectively, and p is the density of the fluid.

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

[0032]

[0033] where μ is the dynamic viscosity coefficient of the fluid.

[0034] In summary, the discrete Navier-Stokes equation velocity field update formula:

[0035]

[0036] Step four: calculate the pressure field by Poisson equation

[0037] The discrete Navier-Stokes equation velocity field update formula as shown in formula (1-6) and (1-7) is updated by iteration at each time step u, v; while the premise of the present application to simulate streamline is the flow of incompressible ideal fluid in two-dimensional space, therefore the velocity field needs to satisfy the mass conservation (i.e. continuity equation) part, in the case of 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 by the pressure term in the Navier-Stokes equation, so that the mass conservation of the fluid is satisfied. From the Navier-Stokes equation, the pressure equation is obtained by taking the divergence operation:

[0040]

[0041] That is, the pressure field p satisfies the Poisson equation. The right half is the source term b from the nonlinear term of the velocity field and the time-varying term. In order to solve numerically, the Poisson equation is discretized into a difference equation, which is discretized by central difference method on two-dimensional grid:

[0042]

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

[0044] Step five: calculate the source term of Poisson equation

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

[0046]

[0047] Discretization (1-11) can be obtained:

[0048]

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

[0050] Further, in the step two, if the cell intersects with the obstacle when initializing the obstacle map, it means that the cell is full; therefore, the velocity field v in two directions of the obstacle cell is 0, and the streamline generated will not pass through the obstacle and its safety interval region, so as to achieve the purpose of collision avoidance.

[0051] The obstacle and the flight path can also be generated with a certain safety interval, that is, the grids around the obstacle cell are also set as unusable cells.

[0052] Further, in the step three, assuming that N×N cells are generated in a certain region, then Δx and Δy should be 1 / N. At the same time, in the actual generation experiment, when the dynamic viscosity coefficient μ of the fluid tends to 0, the streamline generated is smoother; therefore, the time step Δt should also be correspondingly reduced to ensure the stability of the calculation process.

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

[0054] In summary, the present application plans the route according to the characteristics of low-altitude environment and aircraft, and designs an accurate and feasible air flight corridor in the building-dense area such as city by using the fluid mechanics thought. The fluid simulated by the Navier-Stokes equation can generate a high-density air corridor traffic model in a short time, and maximizes the low-altitude traffic throughput under the condition of ensuring the safety interval. At the same time, the two-dimensional space modularization thought can effectively cope with the current irregular low-altitude airspace distribution state in China, and improves the scalability of future low-altitude path generation and planning.

[0055] Advantages

[0056] This paper focuses on route planning in low-altitude environments and aircraft dynamics, utilizing fluid dynamics principles to design accurate and feasible aerial corridors in densely built-up areas such as cities. Unlike traditional rule-based airspace management, this study dynamically generates corridors using fluid dynamics principles, enabling them to adapt to changes in the urban environment and providing a theoretical basis for real-time allocation of airspace resources. The fluid dynamics simulated by the Navier-Stokes equations can generate high-density aerial corridor traffic models in a short time, maximizing low-altitude traffic throughput while ensuring safe separation. Simultaneously, the modular approach in two-dimensional space effectively addresses the current irregular distribution of low-altitude airspace, improving the scalability of future low-altitude route generation and planning, and the use of readily available elevation data enhances the algorithm's usability. Attached image description:

[0057] Figure 1 This is a schematic diagram of a layered airspace structure based on vertical height and flight direction, according to an embodiment of the present invention.

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

[0059] Figure 3 This is a flowchart of a low-altitude airspace path generation algorithm based on a spatiotemporal distribution field according to the present invention. Detailed implementation method:

[0060] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0061] Urban applications primarily focused on logistics, rescue, surveillance, and passenger transport have driven the global market for low-altitude air traffic systems. While current low-altitude missions are diverse, they all share the skies of the same city and are constrained by aircraft level and management methods, resulting in low airspace resource utilization. This invention generates a highly dense aerial corridor system, effectively organizing low-altitude traffic through the complex urban airspace landscape to minimize or completely eliminate traffic conflicts. This novel spatial organization approach can be combined with existing geofencing, no-fly zones, and low-altitude traffic management schemes to maximize transit traffic flow and support flight missions while ensuring safety.

[0062] like Figure 1 This is a schematic diagram of a layered airspace structure based on vertical height and flight direction, according to an embodiment of the present invention.

[0063] like Figure 2 This is a schematic diagram of the spatial path generated based on the Navier-Stokes equations in an embodiment of the present invention;

[0064] like Figure 3A flow chart of a low-altitude airspace path generation algorithm based on a space-time distribution field.

[0065] (I) Three-dimensional space gridding based on 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 application first divides the three-dimensional urban space into a hierarchical airspace structure based on vertical height and flight direction, as shown in Figure 1 , as a prerequisite for generating airspace flight paths.

[0067] 1. Taking Shanghai as an example, the available flight height of the city is H, and if each layer of airspace is h, then the airspace is discretized into a finite number of M layers of planes, where each level has a constant height h i = H / h (i = 1, 2, …, M). On this basis, a uniform flight heading angle is specified for each layer of airspace. Taking the true heading angle as an example, the heading angle interval corresponding to different flight height layers is The purpose of the uniform heading angle of the hierarchical airspace is to effectively reduce the relative flight speed of the aircraft.

[0068] 2. On the basis of the Shanghai elevation or point cloud data map, gridding is performed into N x N cells, and let the k-th layer plane be gridded, with a height of h k ; if the obstacle height l in the elevation or point cloud data is greater than h k , it indicates that the cell intersects with the obstacle, and the cell is full, otherwise it indicates the free state of the cell; in this way, the obstacle map is represented.

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

[0070] After completing the gridding modeling of the urban space elevation data, it is necessary to iteratively calculate the discrete Navier-Stokes equation and the Poisson equation to solve the fluid velocity field and pressure field, simulating 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 heading angle of the layer, for example, the flight corridor heading from due east to due west corresponds to the x-axis direction matrix u of the velocity field being set to all 1 (the same for due west to due east). If the flight corridor heading is from due north to due south, the y-axis direction matrix v of the velocity field is set to all 1 (the same for due south to due north); for other angles, the velocity field can be 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 flow direction, the fluid density, time step and viscosity coefficient parameters need to be determined to calculate the required flow field model by means of iterative loops. First, the Poisson source term b is calculated according to formula (1-12), the source term is substituted into formula (1-10), and the pressure field p is iteratively calculated again; the pressure field boundary conditions need to be set at each loop to ensure the influence of the boundary conditions on the pressure field.

[0073] 3. Based on the calculation of the above steps, the velocity field v=(u,v) and the pressure field p are substituted into the discrete Navier-Stokes equations of formulas (1-6) and (1-7) to obtain the final velocity field matrix; the obstacle matrix should be substituted at each loop. If the cell is in the occupied state, the corresponding position velocity field (u,v)=0; at the same time, expanding the occupied cell can also set the surrounding position velocity field to 0, indicating that increasing the safety interval between the flight path and the obstacle. The obstacle matrix should be substituted into the Navier-Stokes equation at each iteration to ensure that the fluid does not flow into the obstacle, while ensuring the influence of the obstacle on the flow field.

[0074] (III) Generating Streamlines Based on Fluid Velocity Field

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

[0076]

[0077] Based on the velocity field obtained by iteration, the stream equation is solved using numerical methods. Common numerical methods are based on Euler method or fourth-order Runge-Kutta method to integrate the velocity field from the starting point to obtain the streamlines, so as to draw streamlines in the given area, as shown in Figure 2 The starting point of integration can be automatically selected or specified by the user. 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 smoothness of the dynamics of the streamlines is not as expected, the grid accuracy can be increased, that is, the value of N is increased when gridding to generate denser cells; or without increasing the density of the cells, the velocity field can be interpolated 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 modification or modification made by any person skilled in the art based on the technical content disclosed above shall be regarded as an equivalent effective embodiment, and shall fall within the scope of the technical solution protected by the present application.

Claims

1. A method for generating low-altitude airspace paths based on spatiotemporal distribution fields, characterized in that, Includes the following steps: Step 1: Divide the spatial domain into discrete layers based on vertical height The low-altitude airspace is discretized into a finite number of Layered planes, where each plane has a constant height. and a unified range of flight heading angles; Step 2: Determine the flight heading and initialize the velocity field at different altitudes. Traverse all discrete planes and initialize them: At the current height The Layer planar meshing, generating The grid area; if the elevation in the cell or the height of obstacles in the point cloud data If the cell is full, it means that the cell intersects with an obstacle; otherwise, it means that the cell is free. Initialize the velocity field This provides the starting point for iterations of the Navier-Stokes equations, where yes Velocity in the axial direction, yes Velocity in the axial direction; Initialize to a certain constant value; velocity field The initialization determines the flight heading angle of the airspace corridor at this level; if the flow direction needs to be rotated horizontally... Through formula Rotation matrix implementation: Step 3: Output velocity field and calculate Navier-Stokes equations The momentum conservation formula of the standard Navier-Stokes equations in the case of two-dimensional incompressible fluids is as follows: As shown: in For fluid pressure field, The fluid density is given; external force terms in the Navier-Stokes equations are neglected. The velocity update formula based on the Navier-Stokes equations contains only three parts: the convection term. Pressure gradient term and diffusion terms Its function; The velocity field update formula after discretization of the Navier-Stokes equations: Step 4: Calculate the Poisson equation to obtain the pressure field. For the portion of the velocity field that requires mass conservation, in the case of incompressible fluids, the continuity equation is: That is, the velocity field of the fluid must have zero divergence. If the velocity field does not satisfy this condition, it needs to be corrected using the pressure term in the Navier-Stokes equations to ensure the conservation of fluid mass. From the Navier-Stokes equations, the pressure equation is obtained by taking the divergence. That is, pressure field Satisfies the Poisson equation; the right-hand side is the source term. The nonlinear and time-varying terms originate from the velocity field; for numerical solutions, the Poisson equation is discretized into a difference equation, discretized on a two-dimensional grid using the central difference method: Through an iterative process, the final pressure field is gradually approximated. ; Step 5: Calculate the source terms of the Poisson equation In the formula In solving the pressure field using the Poisson equation, it is necessary to calculate the source term. Ensure that the velocity field satisfies the mass conservation condition for incompressible fluids, as shown in the equation. As shown; therefore, to solve for the source term, we need to take the divergence of the momentum conservation equation of the Navier-Stokes equations to obtain: Discretization We can obtain: Finally, by initializing the obstacle mesh, fluid velocity field, and pressure field, the discrete Navier-Stokes equation and Poisson equation are updated and calculated to solve for the fluid velocity field and pressure field; the above steps are repeated until the set number of iterations is reached, and the airspace corridor, i.e. streamline, is generated based on the obtained velocity field.

2. The low-altitude airspace path generation method based on spatiotemporal distribution field according to claim 1, characterized in that, No. The true heading angle interval for the layer plane is set as follows: 。 3. The low-altitude airspace path generation method based on spatiotemporal distribution field according to claim 1, characterized in that, In step two, if a cell intersects with an obstacle during obstacle map initialization, it indicates that the cell is full; the velocity field in both directions of the obstacle cell... All are The generated streamlines will not pass through obstacles and their safe interval areas, thus achieving the purpose of collision avoidance; Set a certain safety interval for obstacles and flight path generation, that is, set the grid around the obstacle cell to be an unusable cell as well.

4. The low-altitude airspace path generation method based on spatiotemporal distribution field according to claim 1, characterized in that, In step three, the Navier-Stokes equations are discretized as follows: The convection term represents the nonlinear velocity term of the fluid in the plane, reflecting the inherent variation of the velocity field, and involves... and velocity components: in For time steps, Represents the position of a cell in two-dimensional space; The pressure gradient term is used to calculate the portion of the velocity field that does not conform to the continuity equation; The pressure gradient term obtained by iteratively solving the Poisson equation drives the correction of the velocity field; right The speed update is as follows: right The speed update is as follows: in, It is the pressure value of the grid point. It is the time step. and These are the grid spacing in the x and y directions, respectively. It is the density of the fluid; The diffusion term is related to the fluid's viscosity coefficient and describes the diffusion of the velocity field due to viscosity; the velocity update for the diffusion term is: in, is the dynamic viscosity coefficient of the fluid.

5. The low-altitude airspace path generation method based on spatiotemporal distribution field according to claim 4, characterized in that, In step three, it is assumed that a certain area is selected for generation. If there are 10 cells, then , for Meanwhile, in actual generation experiments, the dynamic viscosity coefficient of the fluid... Approaching The smoother the generated streamlines, the better; the longer the time step... The corresponding reduction is made to ensure the stability of the calculation process.

6. The low-altitude airspace path generation method based on spatiotemporal distribution field according to claim 4, characterized in that, The Poisson equation described in step four ensures physical consistency by setting boundary conditions for the pressure field.

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