A Low-Altitude Path Planning Method and System Based on Hierarchical Optimization of Sub-Blocks After Connectivity Component Filtering
By transforming the flight area into a third-order mesh tensor and dividing it into non-uniform sub-blocks, a global optimization model is constructed, which solves the path planning problem of UAVs in complex three-dimensional environments, realizes efficient and safe path planning and multi-UAV collaborative operation, and improves computational efficiency and path continuity.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SICHUAN UNIV
- Filing Date
- 2026-04-29
- Publication Date
- 2026-07-10
AI Technical Summary
Existing UAV path planning methods struggle to achieve efficient and safe path planning in complex 3D environments, especially in scenarios such as urban logistics and emergency rescue. Traditional methods are unable to meet the needs of obstacle avoidance and path planning in complex environments, and lack effective path coordination and resource allocation strategies when multiple UAVs are working together.
The flight area is transformed into a third-order grid tensor. The set of flyable grid points is extracted by breadth-first search. A shortest route model for UAVs based on a single commodity flow is constructed. The grid point set is divided into non-uniform sub-blocks. An expansion region mechanism is introduced to construct a global optimization model to generate the optimal path.
It significantly reduces computational complexity, improves the efficiency and reliability of path planning, solves the path breakage problem caused by segmentation, enhances the stability and robustness of the model in complex spaces, is applicable to a wider range and more complex task scenarios, and supports collaborative planning by multiple UAVs.
Smart Images
Figure CN122363264A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of unmanned aerial vehicles (UAVs), and in particular to a low-altitude path planning method and system based on hierarchical optimization of sub-blocks after connected component filtering. Background Technology
[0002] In the field of low-altitude intelligent flight, achieving high efficiency and safety in UAV navigation is the core objective, and global route planning technology plays a decisive role in the accessibility, stability, and obstacle avoidance capabilities of flight paths. Currently, UAVs rely less on human intervention when performing missions, and path selection and obstacle avoidance are highly dependent on the performance of route planning algorithms. Especially in typical scenarios such as urban logistics delivery, emergency rescue, and inspection and monitoring, the flight environment is characterized by dense obstacles, complex spatial structures, and non-uniform distribution of flyable areas. Traditional methods based on simple search or two-dimensional modeling are insufficient to meet the requirements and cannot effectively address the challenges of obstacle avoidance and path planning in complex environments.
[0003] Meanwhile, in multi-UAV collaborative operation scenarios, route planning not only needs to ensure the connectivity and safety of individual UAV paths, but also needs to achieve path coordination and resource allocation at a global scale, which places higher demands on planning algorithms. Although some existing methods consider spatial information to a certain extent, they still have shortcomings in characterizing complex 3D spatial reachability relationships, adapting to dynamically changing spatial constraints, and improving the planning efficiency and system coordination capabilities of large-scale scenarios. For example, simple search methods may become inefficient due to excessively large search spaces, while 2D modeling methods cannot accurately reflect the actual situation in 3D space, leading to potential safety hazards or ineffective execution of the planned paths during actual flight.
[0004] Therefore, there is a need to provide a low-altitude path planning method and system based on hierarchical optimization of sub-blocks after connected component filtering, in order to improve the efficiency and reliability of UAV path planning. Summary of the Invention
[0005] This invention provides a low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering. The method includes: converting the flight area into a third-order grid tensor and constructing a third-order grid tensor map; determining the set of flyable grid points using a breadth-first search-based connected flyable region extraction algorithm; constructing a drone shortest route model based on a single commodity flow; dividing the set of flyable grid points into multiple non-uniform sub-blocks; constructing and solving a global optimization model based on the drone shortest route model based on a single commodity flow and the multiple sub-blocks to determine the minimum combination of sub-blocks participating in drone-transported goods; and constructing and solving a path optimization model based on the minimum combination of sub-blocks participating in drone-transported goods, the set of flyable grid points, and the drone shortest route model based on a single commodity flow to generate the optimal path.
[0006] Furthermore, the flight region is transformed into a third-order grid tensor, and a third-order grid tensor map is constructed. A set of wingable grid points is determined by a connected wingable region extraction algorithm based on breadth-first search. This includes: transforming the flight region into a third-order grid tensor, encoding wingable grid points as 1 and non-wingable grid points as 0, and constructing a third-order grid tensor map; using a given starting grid point as the search starting point, performing a breadth-first search on the wingable grid points in the third-order grid tensor map based on the 26 adjacency rule, extracting all wingable grid points connected to the search starting point, and generating a set of wingable grid points.
[0007] Furthermore, a drone shortest route model based on a single commodity flow is constructed, including: determining the adjacent grid points of each flyable grid point and generating a set of edges; constructing a decision function and a flow function, wherein the decision function is used to indicate whether a flyable grid point is selected to form a route from the start point to the end point, and the flow function is used to indicate the connectivity between two flyable grid points; constructing a set of constraints; constructing an objective function based on the optimization objective of minimizing the number of flyable grid points included in the route from the start point to the end point; and constructing a drone shortest route model based on a single commodity flow based on the set of edges, the decision function, the flow function, the set of constraints, and the objective function.
[0008] Furthermore, the set of constraints includes at least the coupling constraints of capacity and flow rate and the commodity flow rate conservation constraints.
[0009] Furthermore, the set of flyable grid points is divided into multiple non-uniform sub-blocks, including: converting the flight area into the original third-order grid map; sequentially generating a row segmentation point sequence, a column segmentation point sequence, and a depth segmentation point sequence to divide the set of flyable grid points into multiple non-uniform sub-blocks; and performing dilation processing on the multiple non-uniform sub-blocks to generate multiple dilated sub-blocks.
[0010] Furthermore, the first line of the h-th sub-block is the original third-order grid tensor map. Line, the last line is the first line of the original third-order grid tensor map. OK, The first row in the row segmentation sequence Each row is a dividing point, among which... It is the h-th row split point in the row split point sequence.
[0011] Furthermore, based on the shortest flight path model for drones based on a single commodity flow and multiple sub-blocks, a global optimization model is constructed, including: generating a set of sub-block connecting edges based on the set of boundary grid point coordinates of each expanded sub-block; constructing a decision function and a flow function, wherein the decision function is used to indicate whether an expanded sub-block is selected to form a route from the starting point to the ending point, and the flow function is used to indicate the connectivity between two expanded sub-blocks; constructing a set of constraints, wherein the set of constraints includes at least the coupling constraints of capacity and flow rate and the commodity flow rate conservation constraints; constructing an objective function based on the optimization objective of minimizing the number of expanded sub-blocks included in the route from the starting point to the ending point; and constructing a global optimization model based on the set of sub-block connecting edges, the decision function, the flow function, the set of constraints, and the objective function.
[0012] Furthermore, based on the minimum combination of sub-blocks involved in drone-transported goods, the set of flyable grid points, and the shortest route model for drones based on a single-goods flow, a path optimization model is constructed, including: determining a reduced set of flyable grid points based on the minimum combination of sub-blocks involved in drone-transported goods and the set of flyable grid points; and constructing a path optimization model based on the reduced set of flyable grid points and the shortest route model for drones based on a single-goods flow.
[0013] Furthermore, the path optimization model is as follows: in, To start from the starting point To the finish line Total cost For a reduced set of flyable grid points, Coordinates are The selection function value of the grid point, when the coordinates are If the grid points are selected to form the route from the starting point to the ending point, then... ,otherwise , The selection function value as the starting point, The selection function value for the endpoint. From coordinates The grid point to the coordinates is The flow of the grid points Coordinates are The selection function value of the grid points, Coordinates are The net flow of the grid points for The set of flyable grid points excluding the start and end points. This is the set of edges corresponding to the reduced set of flyable lattice points.
[0014] This invention provides a low-altitude path planning system based on hierarchical optimization of sub-blocks after connected component filtering, comprising: a grid point determination module, used to convert the flight area into a third-order grid tensor and construct a third-order grid tensor map, and determine the set of wingable grid points through a breadth-first search-based connected wingable region extraction algorithm; a model building module, used to construct a drone shortest route model based on a single commodity flow; a global optimization module, used to divide the set of wingable grid points into multiple non-uniform sub-blocks, construct a global optimization model based on the drone shortest route model based on a single commodity flow and multiple sub-blocks, and solve it to determine the minimum combination of sub-blocks participating in drone transportation of goods; and a path optimization module, used to construct a path optimization model based on the minimum combination of sub-blocks participating in drone transportation of goods, the set of wingable grid points, and the drone shortest route model based on a single commodity flow, and solve it to generate the optimal path.
[0015] Compared with existing technologies, the low-altitude path planning method and system based on hierarchical optimization of sub-blocks after connected component filtering provided by this invention has at least the following beneficial effects: 1. This method transforms the 3D mesh space into a third-order mesh tensor map, determines the set of flyable grid points through connected component filtering, and then divides the space into non-uniform sub-blocks and performs dilation processing. It transforms the global path planning problem into a sub-block-level connectivity problem, changing path search from a global grid-level search to a region-level optimization, significantly reducing computational complexity. Simultaneously, the multi-level optimization framework allows global planning and local refinement to proceed collaboratively, improving computational efficiency while ensuring solution accuracy. The introduction of a dilated region mechanism constructs an overlapping search space at the sub-block boundaries, resolving path breakage and cross-region connection problems caused by block division, enhancing the continuity and reliability of path planning results, and effectively improving the model's stability and robustness in complex spaces.
[0016] 2. An expanded region mechanism is introduced to construct an overlapping search space at the boundaries of sub-blocks, effectively solving the problems of path breakage and difficulty in cross-region connection in the block-based method. In complex 3D airspace environments, block processing may lead to paths not being able to connect smoothly between different sub-blocks. The expanded sub-block design allows path search to have more exploration space at the boundaries of sub-blocks, thereby improving the continuity and reliability of path planning results, ensuring that the UAV can fly stably according to the planned path, and reducing the flight risks caused by path discontinuity.
[0017] 3. The hierarchical and block-based strategy enhances the model's scalability, enabling it to be applied to a wider range of airspace and more complex mission scenarios. As the airspace expands or the mission complexity increases, this method can easily address new challenges by adjusting the sub-block division and hierarchical optimization strategy. Simultaneously, it enables multi-UAV collaborative planning and dynamic path adjustment; different UAVs can perform path planning within their respective sub-blocks and achieve collaborative transportation through a global optimization model, meeting diverse mission requirements. Attached Figure Description
[0018] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein: Figure 1 This is a flowchart illustrating a low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering, as shown in some embodiments of this specification. Figure 2 This is a flowchart illustrating the process of constructing a drone shortest route model based on a single commodity flow, according to some embodiments of this specification. Figure 3 This is a schematic diagram of a low-altitude path planning system that performs hierarchical optimization based on sub-blocks filtered by connected components, according to some embodiments of this specification. Detailed Implementation
[0019] To more clearly illustrate the technical solutions of the embodiments in this specification, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some examples or embodiments of this specification. For those skilled in the art, these drawings can be applied to other similar scenarios without creative effort. Unless obvious from the context or otherwise specified, the same reference numerals in the drawings represent the same structures or operations.
[0020] Figure 1 This is a flowchart illustrating a low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering, as shown in some embodiments of this specification. Figure 1 As shown, the low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering can include the following steps.
[0021] Step 110: Convert the flight area into a third-order grid tensor and construct a third-order grid tensor map. Then, determine the set of wingable grid points by using a breadth-first search-based connected wingable region extraction algorithm.
[0022] Specifically, it includes: The flight area is transformed into a third-order grid tensor, and wingable grid points are encoded as 1 and non-wingable grid points are encoded as 0 to construct a third-order grid tensor map. Using a given starting grid point as the search starting point, and based on the 26 adjacency rule, a breadth-first search is performed on the flyable grid points in the third-order grid tensor map to extract all flyable grid points connected to the search starting point and generate a set of flyable grid points.
[0023] Specifically, the flight area Transform into a third-order mesh tensor: ,in, This represents the minimum coordinate value of the flight area along the X-axis. This represents the maximum coordinate value of the flight area along the X-axis. This represents the minimum coordinate value of the flight area along the Y-axis. This represents the maximum coordinate value of the flight area along the Y-axis. This represents the minimum coordinate value of the flight area along the Z-axis. This represents the maximum coordinate value of the flight area along the Z-axis. Coordinates are Grid points, All are integers, and satisfy the following conditions: , The number of rows in the grid. The number of columns in the grid. The depth of the raster. This represents a rectangular prism-sized region, i.e., a fixed-size latitude and longitude window. The resolution of the region is equivalent to the size of the rectangular prism-sized region, which is determined by the target accuracy or computing resources.
[0024] 0-1 encoding is used in the third-order grid tensor map: for any ,definition The 26-adjacent connection standard is adopted, which means that a grid point that has surface contact, edge contact, or point contact with a certain grid point is connected to that grid point. and Adjacent if and only if in, Coordinates are Grid points.
[0025] Let the third-order grid tensor be... ,in Representing grid points The corresponding spatial unit is the flyable area. This indicates a no-fly zone or the presence of insurmountable obstacles.
[0026] Given the coordinates of the starting grid point: and satisfy .
[0027] Output a new third-order 0-1 grid tensor: in The following steps can be used to perform a breadth-first search on the flyable grid points in the third-order grid tensor map, extracting all flyable grid points connected to the search starting point, and generating a set of flyable grid points: Step 1: Initialization Construct access tensor in This indicates that the grid point has not yet been visited.
[0028] Initialize the first-in-first-out queue Q and execute: in, This indicates that the starting grid point has been visited.
[0029] Step 2: Breadth-first search When queue Q is not empty, repeat the following steps: (1) Take the current grid point from the head of queue Q. ; (2) List all of them that satisfy Neighbor grid ; (3) For each neighboring grid point If the following conditions are met simultaneously: Then execute:
[0030] Repeat the above process until the queue is empty. Indicates coordinates as The grid points have not yet been visited.
[0031] Step 3: Generate connected component tensors Traverse all grid points ,definition: The final output tensor A is obtained.
[0032] Results show that the above algorithm can obtain the set of all flyable grid points reachable from the starting point s under the 26 adjacency rules. : Subsequent route planning models are constructed and solved only within this connected region, thereby effectively reducing the search space and improving computational efficiency.
[0033] Step 120: Construct a drone shortest route model based on a single commodity flow.
[0034] Figure 2 This is a flowchart illustrating the construction of a drone shortest route model based on a single commodity flow, as shown in some embodiments of this specification. Figure 2 As shown, in some embodiments, step 120 specifically includes: Determine the adjacent grid points of each flyable grid point and generate a set of edges; Construct a decision function and a flow function, wherein the decision function is used to indicate whether a flyable grid point is selected to form a route from the starting point to the ending point, and the flow function is used to indicate the connectivity between two flyable grid points; Construct a set of constraints, which includes at least the coupling constraints between capacity and flow rate and the commodity flow rate conservation constraints; Based on the optimization objective of minimizing the number of flyable grid points that constitute the route from the starting point to the ending point, an objective function is constructed. Based on the set of edges, decision function, flow function, set of constraints, and objective function, a shortest flight path model for unmanned aerial vehicles (UAVs) based on a single commodity flow is constructed.
[0035] Specifically, the coordinates of all flyable grid points are extracted to form a coordinate set. , denoted as: and 1 and The boundary values of the first component of the coordinate system are 1 and... The boundary values, 1 and 2, are called the second component of the coordinate system. The boundary value is called the third component of the coordinate system, where, For coordinate set The maximum value of Bank of China For coordinate set The maximum value in the middle column, For coordinate set The maximum value for medium depth.
[0036] A 26-adjacency model is used, meaning that any grid point that has face contact, edge contact, or point contact with a given grid point is considered its adjacent grid point. Therefore, each internal grid point (where none of its coordinate components take boundary values) has a maximum of 26 adjacent grid points; a grid point on the surface of the global region (where only one of its coordinate components takes a boundary value) has a maximum of 17 adjacent grid points; a grid point on the edge of the global region (where only one or two of its coordinate components take boundary values) has a maximum of 11 adjacent grid points; and a grid point on the vertex of the global region (where all of its coordinate components take boundary values) has a maximum of 7 adjacent grid points.
[0037] Therefore, we can define the set of edges. : Mark the starting point coordinates End point coordinates .
[0038] We construct decision functions and flow functions to characterize how to select paths and build connectivity.
[0039] Grid selection function , used to indicate Whether a point is selected to form a grid point for the route from the start point to the end point: Flow function This is used to represent the connectivity between two grid points: The set of constraints includes: 1. The starting point and the ending point must be included in the route. If the coordinates of the starting point are... ,but If the endpoint coordinates are ,but .
[0040] 2. Coupling constraints between capacity and flow rate: Only when the grid point Once selected, goods are allowed to flow in or out of that location. To ensure that goods are only transferred between grid points participating in the route, the following rules apply.
[0041] when Grid Only then can products be output to adjacent grid points; if =0, then the grid point You cannot output items to adjacent grid cells. Similarly, when Grid Only then can it receive products input from adjacent grid points; if , then grid points If a product cannot be received from adjacent grid points, then the coupling constraint between capacity and flow rate is: 3. Constraint on the conservation of commodity flow: To ensure the model forms a connected route from the starting point to the ending point, a commodity flow conservation constraint needs to be introduced: Given the starting and ending points of the commodities, all commodities starting from the starting point must eventually reach the ending point, while the sum of the input and output flows of the intermediate grid points participating in the route is 0. Let the sum of the commodity flows at each grid point be denoted as... Then the grid points can be obtained. The net flow rate during the entire transportation process is: Based on the conservation of commodity flow, the following constraints are obtained: Meeting the starting point To the finish line Assuming connectivity, the goal is to minimize the route. Without considering the distance differences between different types of directions (faces, edges, vertices), this is equivalent to minimizing the number of grid points involved in the route. Therefore, the objective function is: In summary, the drone route optimization model based on a single commodity flow is as follows: Step 130: Divide the set of flyable grid points into multiple non-uniform sub-blocks.
[0042] Specifically, it includes: Transform the flight area into a raw 3D grid map; The row segmentation point sequence, column segmentation point sequence, and depth segmentation point sequence are generated sequentially to divide the set of flyable grid points into multiple non-uniform sub-blocks.
[0043] Specifically, a non-uniform sub-block partitioning method is adopted. Generally, uniformly dividing the map according to a fixed size may not be reasonable and may even cause the solution to fail. Therefore, the starting row, column and depth boundaries of each sub-block can be specified.
[0044] First, segment the original third-order grid tensor map into rows to obtain the row segmentation point sequence: We obtain H sub-blocks, denoted as For any The first line of the h-th sub-block is the original third-order mesh tensor map. Line, the last line is the first line of the original third-order grid tensor map. OK, The first row in the row segmentation sequence Each row is a dividing point, among which... It is the h-th row split point in the row split point sequence.
[0045] For example, Sub-block 1: row index 0≤i<4 (rows 1-4). Sub-block 2: row index 4≤i<7 (rows 5-7). Sub-block 3: row index 7≤i≤10 (rows 8-10).
[0046] Based on the above, the map is further divided into columns to obtain the column splitting point sequence:
[0047] Each Divide into L sub-blocks, denoted as For any , sub-block The first column is the original third-order grid tensor map. The last column is the first column of the original third-order grid tensor map. List.
[0048] Finally, the depth is segmented to obtain the depth segmentation point sequence: Each Divide into S sub-blocks, denoted as For any , sub-block The first depth is the original third-order grid tensor map. Depth, the final depth is the th depth of the original third-order grid tensor map. depth.
[0049] In summary, the third-order tensor representation of the sub-block is as follows: ,in ,and Each of them The subscript satisfies: in, This represents the index range of the sub-block along the row dimension. The index range of the sub-block along the column dimension. This represents the index range of the sub-block in the depth dimension.
[0050] Get the complete set of coordinates for each sub-block : This allows us to calculate sub-blocks. The number of rows is The number of columns is Depth is .
[0051] Step 140: Based on the drone shortest route model based on single commodity flow and multiple sub-blocks, construct a global optimization model and solve it to determine the minimum combination of sub-blocks participating in drone transportation of goods.
[0052] In some embodiments, a global optimization model is constructed based on a single-commodity flow-based drone shortest route model and multiple sub-blocks, including: Based on the set of boundary grid point coordinates of each expanded sub-block, generate a set of sub-block connection edges; Construct a decision function and a flow function, wherein the decision function is used to indicate whether an expanded sub-block is selected to form a route from the starting point to the ending point, and the flow function is used to indicate the connectivity between two expanded sub-blocks; Construct a set of constraints, wherein the set of constraints includes at least the coupling constraints of capacity and flow and the commodity flow conservation constraints; Based on the optimization objective of minimizing the number of expanded sub-blocks that make up the route from the starting point to the ending point, an objective function is constructed. A global optimization model is constructed based on the set of sub-block connecting edges, decision function, flow function, constraint set, and objective function.
[0053] Specifically, we first treat the sub-blocks as grid points in a mixed-integer linear programming model and solve for the shortest path, which is the minimum number of sub-block connections from the starting point to the ending point.
[0054] At the global level, only index metrics between sub-blocks are considered: Coordinates of the starting sub-block: ; Coordinates of the endpoint sub-block: .
[0055] sub-block The set of boundary grid point coordinates: The set of connecting edges of the sub-block:
[0056] That is, if a certain grid point Line i is the start or end line of the original sub-block. or If a grid point, or a grid point with similar column and depth conditions, satisfies the original boundary conditions, then that grid point belongs to the boundary of the sub-block.
[0057] Let the starting point in the original problem be... The destination is ; like ,but ; like ,but ; decision function of sub-block , used to indicate Whether a point is selected to form a grid point for the route from the start point to the end point: Flow function This is used to represent the connectivity between two expanded sub-blocks: The set of constraints may include: 1. The starting and ending sub-blocks must participate in the route, therefore: 2. Coupling of capacity and flow rate: Only when the sub-block Once selected, goods are allowed to flow in or out of that location. To ensure that goods are only transferred between sub-blocks participating in the route, the following rules apply.
[0058] when sub-block Only then can products be output to adjacent child blocks; if Then the sub-block You cannot output items to adjacent child blocks. When sub-block Only then can it receive products input from adjacent child blocks; if the child block Then the sub-block Items cannot be received from adjacent sub-blocks. Therefore, the following constraints are derived: 3. Constraint on the conservation of commodity flow: Let the function for summing the product flow of a sub-block be: Then, from the flow function (20), we can obtain the sub-block. The total volume of goods transported during the entire transportation process is as follows: Based on the conservation of commodity flow, the following constraints are obtained: in, It is the set excluding the sub-blocks containing the starting point and the ending point.
[0059] To ensure connectivity from the starting sub-block s to the ending sub-block e, the number of sub-blocks participating in the route must be minimized. Therefore, the global optimization model is: An exact solution algorithm combining branch and bound with cutting planes can be used to solve the global optimization model. Specifically, by calling an optimization solver (such as Gurobi or CPLEX), linear relaxation and integer search are performed on the global optimization model to obtain the optimal solution under flow conservation and connectivity constraints, thereby obtaining the minimum combination of sub-blocks participating in UAV transportation.
[0060] Step 150: Based on the minimum combination of sub-blocks involved in transporting goods by drone, the set of flyable grid points, and the shortest route model of drones based on single-goods flow, construct a path optimization model, solve it, and generate the optimal path.
[0061] In some embodiments, a path optimization model is constructed based on the minimum combination of sub-blocks involved in drone-transported goods, the set of flyable grid points, and a drone shortest route model based on a single-goods flow, including: Based on the minimum combination of sub-blocks participating in drone delivery of goods and the set of flyable grid points, a reduced set of flyable grid points is determined; A path optimization model is constructed based on a reduced set of flyable grid points and a single-commodity flow-based UAV shortest route model.
[0062] Specifically, the optimization results between the sub-blocks in the minimum combination of sub-blocks involved in drone-transported goods output by the global optimization model need to be effectively integrated, which is achieved by setting up expansion regions. The specific method is as follows: in the original form of each sub-block, extend it outwards in the row, column, and depth directions respectively. The number of grid points and the number of extended grid points can be selected according to needs, with the aim of ensuring that each sub-block can be effectively connected to obtain the expanded sub-block. .Right now, The first line is the original third-order mesh tensor map. Line, the last line is the first line of the original third-order grid tensor map. Row; the first column is the original third-order grid tensor map. The last column is the first column of the original third-order grid tensor map. Column; the first depth is the original third-order grid tensor map. Depth, the final depth is the th depth of the original third-order mesh tensor map. Depth. However, it is also necessary to ensure that the expanded sub-blocks remain within the original third-order mesh tensor map, thus requiring a more precise calculation formula: If Then the rows, columns, and depth of the original third-order grid tensor map it covers are as follows: in, This represents the index range of the expanded sub-blocks along the row dimension. The index range of the expanded sub-blocks along the column dimension. This represents the index range of the expanded sub-blocks in the depth dimension.
[0063] Example: Hypothesis , in ;and .Pick That is to Extend the row outwards by 2 grid points, the column outwards by 3 grid points, and the depth outwards by 2 grid points to obtain... ,in .
[0064] Obtain the complete coordinate set of each dilated sub-block .
[0065] All the lattice points included in the expanded sub-blocks are treated as a reduced set of flyable lattice points.
[0066] In some embodiments, the path optimization model is: in, To start from the starting point To the finish line Total cost The reduced set of flyable grid points, i.e., the set of nodes included in the optimal sub-block combination output by the global optimization model, Coordinates are The selection function value of the grid point, when the coordinates are If the grid points are selected to form the route from the starting point to the ending point, then... ,otherwise , The selection function value as the starting point, The selection function value for the endpoint. From coordinates The grid point to the coordinates is The flow of the grid points Coordinates are The selection function value of the grid points, Coordinates are The net flow of the grid points for The set of flyable grid points excluding the start and end points. For the reduced set of flyable grid points, the set of connecting edges is given. and .
[0067] An exact solution algorithm combining branch and bound with cutting planes can be used to solve the path optimization model. Specifically, by calling an optimization solver (such as Gurobi or CPLEX), linear relaxation and integer search are performed on the path optimization model to obtain the optimal solution under flow conservation and connectivity constraints, thereby obtaining the minimum grid point combination for UAV transportation.
[0068] This method transforms the original high-dimensional grid-level path planning problem into a sub-block-level connectivity optimization problem by non-uniformly partitioning the 3D mesh tensor. Compared to traditional methods that directly search the global mesh, this method can significantly reduce the problem size and the number of decision variables while preserving spatial structure information, thereby effectively alleviating the computational bottleneck in large-scale optimization problems.
[0069] In UAV flight path planning tasks in complex 3D airspace, the core objective of model computation optimization methods is to achieve efficient solution and stable connectivity in large-scale spaces. Block-based and multi-level optimization strategies play a direct and crucial role in controlling computational scale and ensuring path continuity. Based on non-uniform block-based computation optimization, this method transforms the original high-dimensional path planning problem into a sub-block-level connectivity problem by structurally partitioning the 3D grid space. This changes the path search process from "global grid-level search" to "region-level optimization," significantly reducing computational complexity. Simultaneously, an expanded region mechanism is introduced to construct overlapping search spaces at sub-block boundaries, effectively solving the problems of path breakage and cross-regional connectivity difficulties in block-based methods, further improving the continuity and reliability of path planning results.
[0070] In large-scale 3D scenes, this method demonstrates irreplaceable engineering application value. Due to the massive number of nodes after discretizing a 3D mesh, direct global optimization often faces problems of insufficient computational resources and low solution efficiency. However, the multi-level optimization framework based on sub-block partitioning can decompose complex problems into several controllable sub-problems, enabling global path planning and local path refinement to proceed in tandem, thereby significantly improving computational efficiency while maintaining solution accuracy. Furthermore, this method can flexibly adjust the partitioning strategy according to spatial structural characteristics, exhibiting good adaptability in both obstacle-dense and sparse regions, providing stable support for path planning in complex environments.
[0071] Model computation optimization methods also have significant implications for engineering practice. On the one hand, by reducing the problem size and optimizing the computational structure, path planning in large-scale three-dimensional airspace becomes computable, providing a technical foundation for the application of UAVs in urban low-altitude environments. On the other hand, the hierarchical and block-based strategies enhance the scalability of the model, enabling it to be applied to a wider range of airspaces and more complex mission scenarios, thus providing possibilities for multi-UAV collaborative planning and dynamic path adjustment.
[0072] From a methodological development perspective, this method combines the concept of block decomposition with optimization modeling, realizing the transformation of complex path planning problems from "centralized solution" to "decompositional solution." Simultaneously, the introduction of an inflated region mechanism and a multi-level optimization framework improves the model's stability and robustness in complex spaces. At the engineering implementation level, this method effectively reduces solution time and computational resource consumption, meeting the efficiency and reliability requirements of practical applications.
[0073] In summary, the low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering not only significantly improves the solution efficiency and stability of the three-dimensional path planning problem, but also achieves the unity of computational scale control and path continuity assurance in complex airspace environments, providing key technical support for the engineering application of UAV flight path planning.
[0074] The following section, combined with experiments, illustrates the beneficial effects of the low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component screening.
[0075] Typical existing methods were selected for comparison, including: graph search-based methods (A*, Dijkstra), random sampling-based methods (RRT, RRT*), and global optimization modeling-based methods (direct MILP or network flow model). The analysis focused on computational scale, solution efficiency, path quality, and engineering feasibility.
[0076] In a 3D high-resolution mesh, the time complexity of the traditional A* or Dijkstra method is approximately: , where N is the number of grid points. In complex 3D scenes, we typically have: In this method, the problem size is transformed into: (The problem is categorized into several parts, with each part being selected based on its connectivity and sub-blocks.) Where |W| is the number of sub-blocks, and
[0077] Therefore, the computational scale is reduced by approximately one to two orders of magnitude. This achieves at least three technical benefits: significantly reducing the number of search nodes, reducing memory consumption, and avoiding invalid searches caused by disconnected regions.
[0078] The RRT and RRT* methods rely on random sampling, and their main problems include: 1) the path results are random; 2) the convergence speed depends on the sampling density; and 3) it is difficult to directly handle complex discrete constraints.
[0079] This method employs deterministic optimization modeling, mainly reflected in: 1. All constraints are explicitly embedded in the model; 2. Ensure path connectivity through flow conservation constraints; 3. The objective function ensures the optimality of the path.
[0080] Based on the three deterministic foundations mentioned above, this method achieves at least three technical effects: stable and repeatable path results, elimination of uncertainty caused by randomness, and higher reliability in complex constraint scenarios.
[0081] Traditional MILP methods model directly on the global mesh, and the scale of its node variables is: The size of the edge variables is When N is large, the solution complexity increases dramatically.
[0082] This method decomposes the problem using a two-layer structure: 1. Sub-block level optimization: variable size ; 2. Local grid optimization: variable scale ,in ; The overall scale is: ,and .
[0083] Based on this technology, at least three technical effects have been achieved: significantly reducing solution time, reducing memory consumption, and improving engineering feasibility.
[0084] In a typical three-dimensional urban environment (grid size approximately 10) 5 The comparison results are shown in Table 1: Table 1 Comparison Results As shown in Table 1, this method has the following advantages: 1. Calculation time is significantly reduced; 2. Memory consumption has decreased significantly; 3. Maintain stable solution capability in complex obstacle environments.
[0085] Figure 3 This is a schematic diagram of a low-altitude path planning system that performs hierarchical optimization based on sub-blocks filtered by connected components, as shown in some embodiments of this specification. Figure 3 As shown, a low-altitude path planning system that performs hierarchical optimization based on sub-blocks filtered by connected components can include a grid point determination module, a model building module, a global optimization module, and a path optimization module.
[0086] The grid point determination module is used to transform the flight area into a third-order grid tensor and construct a third-order grid tensor map. It determines the set of wingable grid points through a breadth-first search-based connected wingable region extraction algorithm. The model building module is used to build the shortest flight path model for drones based on a single commodity flow. The global optimization module is used to divide the set of flyable grid points into multiple non-uniform sub-blocks. Based on the shortest route model of UAVs based on single commodity flow and multiple sub-blocks, a global optimization model is constructed and solved to determine the minimum combination of sub-blocks for UAVs to transport goods. The path optimization module is used to construct a path optimization model based on the minimum combination of sub-blocks involved in drone transportation of goods, the set of flyable grid points, and the shortest route model of drones based on single-goods flow, and then solve the model to generate the optimal path.
[0087] The low-altitude path planning system based on hierarchical optimization of sub-blocks after connected component filtering can be used to execute the low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering, which will not be elaborated here.
[0088] Finally, it should be understood that the embodiments described in this specification are merely illustrative of the principles of the embodiments described herein. Other variations may also fall within the scope of this specification. Therefore, alternative configurations of the embodiments described herein are intended to be consistent with the teachings of this specification, rather than as examples or limitations. Accordingly, the embodiments described herein are not limited to the implementations explicitly presented and described herein.
Claims
1. A low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering, characterized in that, include: The flight area is transformed into a third-order grid tensor, and a third-order grid tensor map is constructed. The set of wingable grid points is determined by a connected wingable region extraction algorithm based on breadth-first search. Construct a drone shortest route model based on a single commodity flow; Divide the set of flyable grid points into multiple non-uniform sub-blocks; Based on the shortest route model of drones based on a single commodity flow and multiple sub-blocks, a global optimization model is constructed and solved to determine the minimum combination of sub-blocks that participate in the transportation of goods by drones. Based on the minimum combination of sub-blocks involved in drone-transported goods, the set of flyable grid points, and the shortest route model for drones based on single-goods flow, a path optimization model is constructed and solved to generate the optimal path.
2. The low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering according to claim 1, characterized in that, The flight region is transformed into a third-order grid tensor, and a third-order grid tensor map is constructed. A connected wingable region extraction algorithm based on breadth-first search is used to determine the set of wingable grid points, including: The flight area is transformed into a third-order grid tensor, and wingable grid points are encoded as 1 and non-wingable grid points are encoded as 0 to construct a third-order grid tensor map. Starting from a given starting grid point, a breadth-first search is performed on the flyable grid points in the third-order grid tensor map based on the 26 adjacency rule to extract all flyable grid points connected to the starting point and generate a set of flyable grid points.
3. The low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering according to claim 2, characterized in that, Construct a drone shortest route model based on a single commodity flow, including: Determine the adjacent grid points of each flyable grid point and generate a set of edges; Construct a decision function and a flow function, wherein the decision function is used to indicate whether a flyable grid point is selected to form a route from the starting point to the ending point, and the flow function is used to indicate the connectivity between two flyable grid points; Construct a set of constraints; Based on the optimization objective of minimizing the number of flyable grid points that constitute the route from the starting point to the ending point, an objective function is constructed. Based on the set of edges, decision function, flow function, set of constraints, and objective function, a shortest flight path model for unmanned aerial vehicles (UAVs) based on a single commodity flow is constructed.
4. The low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering according to claim 3, characterized in that, The set of constraints includes at least the coupling constraints of capacity and flow rate and the constraint of commodity flow rate conservation.
5. The low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering according to claim 1, characterized in that, The set of flyable grid points is divided into multiple non-uniform sub-blocks, including: Transform the flight area into a raw 3D grid map; The row segmentation point sequence, column segmentation point sequence, and depth segmentation point sequence are generated sequentially to divide the set of flyable grid points into multiple non-uniform sub-blocks.
6. The low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering according to claim 5, characterized in that, The first line of the h-th sub-block is the original third-order mesh tensor map. Line, the last line is the first line of the original third-order grid tensor map. OK, The first row in the row segmentation sequence Each row is a dividing point, among which... It is the h-th row split point in the row split point sequence.
7. The low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering according to claim 1, characterized in that, Based on the drone shortest flight path model based on a single commodity flow and multiple sub-blocks, a global optimization model is constructed, including: Based on the set of boundary grid point coordinates of each expanded sub-block, generate a set of sub-block connection edges; Construct a decision function and a flow function, wherein the decision function is used to indicate whether an expanded sub-block is selected to form a route from the starting point to the ending point, and the flow function is used to indicate the connectivity between two expanded sub-blocks; Construct a set of constraints, wherein the set of constraints includes at least the coupling constraints of capacity and flow and the commodity flow conservation constraints; Based on the optimization objective of minimizing the number of expanded sub-blocks that make up the route from the starting point to the ending point, an objective function is constructed. A global optimization model is constructed based on the set of sub-block connecting edges, decision function, flow function, constraint set, and objective function.
8. The low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering, as described in any one of claims 1-6, is characterized in that... Based on the minimum combination of sub-blocks involved in drone-transported goods, the set of flyable grid points, and the shortest route model for drones based on a single-goods flow, a path optimization model is constructed, including: Based on the minimum combination of sub-blocks participating in drone delivery of goods and the set of flyable grid points, a reduced set of flyable grid points is determined; A path optimization model is constructed based on a reduced set of flyable grid points and a single-commodity flow-based UAV shortest route model.
9. The low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering, as described in any one of claims 1-6, is characterized in that... The path optimization model is as follows: in, To start from the starting point To the finish line Total cost For a reduced set of flyable grid points, Coordinates are The selection function value of the grid point, when the coordinates are If the grid points are selected to form the route from the starting point to the ending point, then... ,otherwise , The selection function value as the starting point, The selection function value for the endpoint. From coordinates The grid point to the coordinates is The flow of the grid points Coordinates are The selection function value of the grid points, Coordinates are The net flow of the grid points for The set of flyable grid points excluding the start and end points. This is the set of edges corresponding to the reduced set of flyable lattice points.
10. A low-altitude path planning system based on hierarchical optimization of sub-blocks after connected component filtering, characterized in that, The low-altitude path planning method based on hierarchical optimization of sub-blocks after connected component filtering, as described in any one of claims 1-9, includes: The grid point determination module is used to transform the flight area into a third-order grid tensor and construct a third-order grid tensor map. It determines the set of wingable grid points through a breadth-first search-based connected wingable region extraction algorithm. The model building module is used to build the shortest flight path model for drones based on a single commodity flow. The global optimization module is used to divide the set of flyable grid points into multiple non-uniform sub-blocks. Based on the shortest route model of UAVs based on single commodity flow and multiple sub-blocks, a global optimization model is constructed and solved to determine the minimum combination of sub-blocks that can participate in UAV transportation of goods. The path optimization module is used to construct a path optimization model based on the minimum combination of sub-blocks involved in drone transportation of goods, the set of flyable grid points, and the shortest route model of drones based on single-goods flow, and then solve the model to generate the optimal path.