Path planning method based on quadratic unconstrained binary optimization model

Abstract

The invention discloses a path planning method based on a quadratic unconstrained binary optimization model, which belongs to the technical field of path planning, is used for unmanned system navigation, and comprises the following steps: rasterizing an environment area, determining a starting point, an ending point and the positions of barrier grids, determining a set of the grids where barriers are located, and defining grid binary variables; defining a target function, and establishing an optimization problem of the target function under the conditions of adjacent grid constraints, in-out constraints, obstacle avoidance constraints and starting point and terminal point position constraints; converting the constrained optimization problem into a quadratic unconstrained binary optimization model, solving the quadratic unconstrained binary optimization model, determining the value of each grid variable according to the value of the independent variable when the target function takes the minimum value, and finally obtaining a planned path. According to the method, multiple complex constraint conditions are directly embedded into the target function through the penalty term, the complex constraint conditions do not need to be independently processed, and the logic of the solving process is simplified.

Description

Technical Field

[0001] This invention discloses a path planning method based on a quadratic unconstrained binary optimization model, belonging to the field of path planning technology. Background Technology

[0002] Path planning is a key technology for intelligent devices such as drones, unmanned ships, mobile robots, and autonomous vehicles to achieve safe obstacle avoidance and autonomous navigation. Its core task is to ensure the safety and efficiency of the driving process by generating optimal motion trajectories that meet multiple constraints. With the rapid development of intelligent manufacturing and smart city construction, path planning technology, as a core support for intelligent systems, is becoming increasingly important in engineering applications.

[0003] Quantum computing, as an emerging computing paradigm, can solve some of the challenges in traditional path optimization by virtue of its parallel computing advantages in combinatorial optimization problems. Traditional path planning algorithms, such as Dijkstra's algorithm and A* algorithm, mainly rely on classical computing architectures and cannot be directly applied to quantum computing devices. Quadratic unconstrained binary optimization models, due to their natural compatibility with quantum computing, have become an important bridge connecting path planning and quantum optimization, providing a highly promising research direction for the future development of path planning technology.

[0004] Traditional path planning algorithms currently rely primarily on serial CPU computation, which differs architecturally from the parallelism of quantum computing. Furthermore, adding constraints leads to an exponential increase in computational cost, and the lack of a unified optimization framework for satisfying constraints of different dimensions means that the results may not be optimal. Summary of the Invention

[0005] The purpose of this invention is to provide a path planning method based on a quadratic unconstrained binary optimization model, in order to solve the problems in the prior art, which rely on traditional CPU serial computing, which has architectural differences from the parallelism of quantum computing, where adding constraints leads to an exponential increase in computational load, and where there is a lack of a unified optimization framework for satisfying constraints of different dimensions, resulting in the result not being the optimal solution.

[0006] A path planning method based on a quadratic unconstrained binary optimization model includes: S1. Rasterize the environment area, determine the start point, end point, and the location of obstacle grids, determine the set of grids containing obstacles, and define grid binary variables; S2. Define the objective function and establish the optimization problem of the objective function under the constraints of adjacent grids, entry and exit constraints, obstacle avoidance constraints, and start and end position constraints. S3. Transform the constrained optimization problem into a quadratic unconstrained binary optimization model. This includes defining new variables, adding penalty terms to the objective function based on the new variables, adding penalty terms to the objective function based on adjacent grid constraints, adding penalty terms to the objective function based on entry / exit constraints, adding penalty terms to the objective function based on obstacle avoidance constraints, and adding penalty terms to the objective function based on start and end point position constraints. Transform the objective function with added penalty terms into a quadratic unconstrained binary optimization model. Solve the quadratic unconstrained binary optimization model, determine the values ​​of each grid variable based on the values ​​of the independent variables when the objective function reaches its minimum, and obtain the final planned path.

[0007] S1 includes rasterizing the environmental area into raster map, For row index, , For column indexes, The grid starts with the bottom left grid. Let the starting grid be the grid cell; assume the path originates at grid cell 1. The endpoint is located in the grid. The set of grid cells containing obstacles is , Indexing obstacles This represents the total number of obstacles.

[0008] S2 includes, S2.1, setting a grid. The variable is , 0 indicates that the grid cell does not belong to the planned path, and 1 indicates that the grid cell belongs to the planned path. For the raster map Square array Satisfy the first Line 1 Column elements are : ; Define the objective function : ; Establish An optimization problem under the constraints of adjacent grid cells, grid entry and exit constraints, obstacle avoidance constraints, and path start and end point positions; S2 includes S2.2, establishing adjacent grid constraint conditions: the product of the corresponding variables of any three adjacent grids is always equal to 0, and adjacent grids are grids with a common vertex; S2 includes S2.3, establishing grid entry and exit constraints: There must be exactly one grid adjacent to the starting or ending grid that belongs to the planned path; Except for the starting and ending grids, if the grids... It belongs to the planned path, grid There are exactly two adjacent grid cells that belong to the planned path.

[0009] S2 includes S2.4, establishing obstacle avoidance constraints: ; S2 includes S2.5, establishing constraints on the starting and ending points of the path: ; .

[0010] S3 includes, S3.1, defining new variables: ; In the formula, The total number of variables is There are [number] variables, including direct variables and product variables; the direct variables are [number]. One, corresponding to the original variable The product variable is One, including The set of products of horizontally adjacent elements in the nth row : ; corresponding The variable is indivual; The set of products of the vertically adjacent elements below and the lower right adjacent elements in the first column. : ; corresponding The variable is indivual; The set of products of the left horizontal adjacent elements, the left lower adjacent elements, the bottom vertical adjacent elements, and the right lower adjacent elements of an internal element. : ; corresponding The variable is indivual; The set of products of the left horizontal adjacent elements, the bottom left adjacent elements, and the bottom vertical adjacent elements in the last column. : ; corresponding The variable is indivual.

[0011] S3 includes, S3.2, the penalty term generated by adding a new variable to the objective function, denoted as... To define the penalty coefficient for the new variable, To define a penalty function for the new variable, the penalty term is: .

[0012] S3 includes S3.3, the penalty term generated by adding adjacent grid constraints to the objective function, denoted as... This is the penalty coefficient for the constraint condition between adjacent grid cells. The penalty function for adjacent grid constraints is: .

[0013] S3 includes S3.4, and the penalty term generated by adding entry and exit constraints to the objective function, denoted as... This is the penalty coefficient for grid entry and exit constraints. The penalty function for grid entry and exit constraints is as follows: .

[0014] S3 includes S3.5, and the penalty term generated by adding obstacle avoidance constraints to the objective function, denoted as... The penalty coefficient for obstacle avoidance constraints. The penalty function for the obstacle avoidance constraint is as follows: ; S3 includes S3.6, a penalty term generated by adding start and end grid position constraints to the objective function, denoted as... The penalty coefficient for the start and end grid position constraints. The penalty function is the constraint on the start and end grid positions, and the penalty term is... .

[0015] S3 includes S3.7, which transforms the objective function with added penalty terms into a quadratic unconstrained binary optimization model: ; In the formula, It is the transpose symbol. This refers to the quadratic real symmetric matrix generated when transforming the objective function into a quadratic unconstrained binary optimization model; S3 includes S3.8, solving the quadratic unconstrained binary optimization model, determining the values ​​of each grid variable based on the values ​​of the independent variables when the objective function reaches its minimum value, and obtaining the final planned path.

[0016] Compared with existing technologies, the present invention has the following advantages: The present invention directly embeds multiple complex constraints into the objective function through a penalty term, eliminating the need to handle complex constraints separately and simplifying the logic of the solution process; the quadratic unconstrained binary optimization model can be directly adapted to quantum computing hardware and has good compatibility with traditional optimization algorithms. With the development of quantum computing, the method of the present invention will become more efficient. Attached Figure Description

[0017] Figure 1 This is a flowchart of the invention; Figure 2 This is a schematic diagram of a raster map; Figure 3 It is a graph showing the relationship between grid position and grid variables; Figure 4 This is a schematic diagram illustrating errors in the grid adjacency constraint feature. Figure 5 This is a schematic diagram illustrating the correct state of the grid adjacency constraint feature; Figure 6 This is a diagram illustrating the starting grid entry and exit constraints. Figure 1 ; Figure 7 This is a diagram illustrating the starting grid entry and exit constraints. Figure 2 ; Figure 8 This is a diagram illustrating the starting grid entry and exit constraints. Figure 3 ; Figure 9 This is a diagram illustrating the path grid entry and exit constraints, excluding the start and end grid cells. Figure 1 ; Figure 10 This is a diagram illustrating the path grid entry and exit constraints, excluding the start and end grid cells. Figure 2 ; Figure 11 This is a diagram illustrating the path grid entry and exit constraints, excluding the start and end grid cells. Figure 3 ; Figure 12 This is a schematic diagram of the path planning in a quadratic unconstrained binary optimization model. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0019] A path planning method based on a quadratic unconstrained binary optimization model includes: S1. Rasterize the environment area, determine the start point, end point, and the location of obstacle grids, determine the set of grids containing obstacles, and define grid binary variables; S2. Define the objective function and establish the optimization problem of the objective function under the constraints of adjacent grids, entry and exit constraints, obstacle avoidance constraints, and start and end position constraints. S3. Transform the constrained optimization problem into a quadratic unconstrained binary optimization model. This includes defining new variables, adding penalty terms to the objective function based on the new variables, adding penalty terms to the objective function based on adjacent grid constraints, adding penalty terms to the objective function based on entry / exit constraints, adding penalty terms to the objective function based on obstacle avoidance constraints, and adding penalty terms to the objective function based on start and end point position constraints. Transform the objective function with added penalty terms into a quadratic unconstrained binary optimization model. Solve the quadratic unconstrained binary optimization model, determine the values ​​of each grid variable based on the values ​​of the independent variables when the objective function reaches its minimum, and obtain the final planned path.

[0020] S1 includes rasterizing the environmental area into raster map, For row index, , For column indexes, The grid starts with the bottom left grid. Let the starting grid be the grid cell; assume the path originates at grid cell 1. The endpoint is located in the grid. The set of grid cells containing obstacles is , Indexing obstacles This represents the total number of obstacles.

[0021] S2 includes, S2.1, setting a grid. The variable is , 0 indicates that the grid cell does not belong to the planned path, and 1 indicates that the grid cell belongs to the planned path. For the raster map Square array Satisfy the first Line 1 Column elements are : ; Define the objective function : ; Establish An optimization problem under the constraints of adjacent grids, grid entry and exit, obstacle avoidance, and path start and end point positions; S2 includes S2.2, establishing adjacent grid constraint conditions: the product of the corresponding variables of any three adjacent grids is always equal to 0, and adjacent grids are grids with a common vertex; S2 includes S2.3, establishing grid entry and exit constraints: There must be exactly one grid adjacent to the starting or ending grid that belongs to the planned path; Except for the starting and ending grids, if the grids... It belongs to the planned path, grid There are exactly two adjacent grid cells that belong to the planned path.

[0022] S2 includes S2.4, establishing obstacle avoidance constraints: ; S2 includes S2.5, establishing constraints on the starting and ending points of the path: ; .

[0023] S3 includes, S3.1, defining new variables: ; In the formula, The total number of variables is There are [number] variables, including direct variables and product variables; the direct variables are [number]. One, corresponding to the original variable The product variable is One, including The set of products of horizontally adjacent elements in the nth row : ; corresponding The variable is indivual; The set of products of the vertically adjacent elements below and the lower right adjacent elements in the first column. : ; corresponding The variable is indivual; The set of products of the left horizontal adjacent elements, the left lower adjacent elements, the bottom vertical adjacent elements, and the right lower adjacent elements of an internal element. : ; corresponding The variable is indivual; The set of products of the left horizontal adjacent elements, the bottom left adjacent elements, and the bottom vertical adjacent elements in the last column. : ; corresponding The variable is indivual.

[0024] S3 includes, S3.2, the penalty term generated by adding a new variable to the objective function, denoted as... To define the penalty coefficient for the new variable, To define a penalty function for the new variable, the penalty term is: .

[0025] S3 includes S3.3, the penalty term generated by adding adjacent grid constraints to the objective function, denoted as... This is the penalty coefficient for the constraint condition between adjacent grid cells. The penalty function for adjacent grid constraints is: .

[0026] S3 includes S3.4, and the penalty term generated by adding entry and exit constraints to the objective function, denoted as... This is the penalty coefficient for grid entry and exit constraints. The penalty function for grid entry and exit constraints is as follows: .

[0027] S3 includes S3.5, and the penalty term generated by adding obstacle avoidance constraints to the objective function, denoted as... The penalty coefficient for obstacle avoidance constraints. The penalty function for the obstacle avoidance constraint is as follows: ; S3 includes S3.6, a penalty term generated by adding start and end grid position constraints to the objective function, denoted as... The penalty coefficient for the start and end grid position constraints. The penalty function is the constraint on the start and end grid positions, and the penalty term is... .

[0028] S3 includes S3.7, which transforms the objective function with added penalty terms into a quadratic unconstrained binary optimization model: ; In the formula, It is the transpose symbol. This refers to the quadratic real symmetric matrix generated when transforming the objective function into a quadratic unconstrained binary optimization model; S3 includes S3.8, solving the quadratic unconstrained binary optimization model, determining the values ​​of each grid variable based on the values ​​of the independent variables when the objective function reaches its minimum value, and obtaining the final planned path.

[0029] The following explanation, in conjunction with the accompanying drawings, further clarifies the matter. Figure 1 As shown, the environment area is first rasterized into... raster maps, such as Figure 2 As shown in the diagram, the green grid represents obstacles, and the black grid represents the start and end points; Figure 3 As shown, after defining the raster binary variable, the raster... The corresponding variable is denoted as .

[0030] Define the objective function and establish an optimization problem for the objective function under the constraints of adjacent grids, entry and exit constraints, obstacle avoidance constraints, and start and end point position constraints. For example... Figure 4 , Figure 5 As shown, the adjacent grid constraint condition aims to minimize the number of grids in the planned path. For any pair of three adjacent grids, at most two grids can belong to the planned path simultaneously. That is, the product of the variables corresponding to any three adjacent grids is always equal to 0. The specific constraint conditions are as follows: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; .

[0031] The grid entry and exit constraints must ensure that the planned path connects the start and end grids, contains the fewest possible grids, and that exactly one of the grids adjacent to either the start or end grid belongs to the planned path. In other words, the sum of the variables of all grids adjacent to either the start or end grid must be 1. Figure 6 , Figure 7 , Figure 8 Examples of three starting grid directions are shown in the figure; the arrows in the figure indicate the planned path direction. Figure 9 , Figure 10 and Figure 11 As shown, for all rasters except the starting or target raster, if the current raster (the raster with the red star in the diagram) belongs to the planned path, then there are exactly two rasteres adjacent to it that also belong to the planned path. That is, the sum of the variables of all rasteres adjacent to the current raster can only be 2. Assuming... For undetermined constants, determine... Does it belong to a set? If it belongs to, then ,otherwise Specific constraints include the bottom left grid. The corresponding constraints are: ; bottom right corner grid The corresponding constraints are: ; Top left grid The corresponding constraints are: ; Top right corner grid The corresponding constraints are: ; Lower boundary grid The corresponding constraints are: ; Upper boundary grid The corresponding constraints are: ; Left boundary grid The corresponding constraints are: ; Right boundary grid The corresponding constraints are: ; Internal grid The corresponding constraints are: .

[0032] To establish obstacle avoidance constraints, the planned path must avoid obstacles, meaning the path grid must never pass through an obstacle grid. The constraints are as follows: ; Establish location constraints for the start and end points of the path, ensuring that the planned path passes through both the start and end grid cells. The constraints are as follows: ; .

[0033] The constrained optimization problem is transformed into a quadratic unconstrained binary optimization model. The specific process includes defining new variables: ; Including components corresponding to direct variables. : ; Corresponding to The amount : ; Corresponding to The amount : ; ; Corresponding to The amount : ; ; ; ; Corresponding to The amount : ; ; .

[0034] The objective function adds a penalty term for the new variable it defines, let's call it... To define the penalty coefficient for the new variable, the penalty term is: , To define the penalty function for the new variable: ; In the formula, for The middle corresponds to The penalty function for defining the new variable corresponding to the component, For indexing, ; The middle corresponds to The penalty function corresponding to the component : ; ; ; ; ; In the formula, To replace the variable, for The middle corresponds to The penalty function corresponding to a variable in the component; The middle corresponds to The penalty function corresponding to the component : ; The penalty function corresponding to the new variable generated by the product of vertically adjacent elements below. for: ; ; ; ; ; In the formula, The penalty function for one of the new variables generated from the product of the vertically adjacent elements below; The penalty function corresponding to the new variable generated by the product of the lower right adjacent elements for: ; ; ; ; ; In the formula, The penalty function for one of the new variables generated from the product of the elements to the right and next to it; The middle corresponds to The penalty function corresponding to the component : ; The penalty function corresponding to the new variable generated by the product of the left-hand horizontal adjacent elements for: ; ; ; ; ; In the formula, The penalty function is given to one of the new variables generated from the product of the left-hand horizontal adjacent elements. The penalty function corresponding to the new variable generated by the product of the lower left adjacent elements : ; ; ; ; ; In the formula, The penalty function for one of the new variables generated from the product of the left and right adjacent elements; The penalty function corresponding to the new variable generated by the product of vertically adjacent elements below. for: ; ; ; ; ; In the formula, The penalty function for one of the new variables generated by the product of the vertically adjacent elements below; The penalty function corresponding to the new variable generated by the product of the lower right adjacent elements : ; ; ; ; ; In the formula, The penalty function for one of the new variables generated from the product of the elements to the right and next to it; The middle corresponds to The penalty function corresponding to the component : ; The penalty function corresponding to the new variable generated by the product of the left-hand horizontal adjacent elements : ; ; ; ; ; In the formula, The penalty function is given to one of the new variables generated from the product of the left-hand horizontal adjacent elements. The penalty function corresponding to the new variable generated by the product of the lower left adjacent elements for: ; ; ; ; ; In the formula, The penalty function for one of the new variables generated from the product of the left and right adjacent elements; The penalty function corresponding to the new variable generated by the product of vertically adjacent elements below. : ; ; ; ; ; In the formula, This is a penalty function for one of the new variables generated from the product of the vertically adjacent elements below.

[0035] The objective function adds a penalty term generated by the adjacent grid constraint, denoted as... The penalty coefficient for adjacent grid constraints is given by the penalty term. , The penalty function for adjacent grid constraints: ; In the formula, This is a penalty function for the constraints of adjacent grid cells corresponding to grid cells at different locations. The adjacent grid cell constraints include horizontal and vertical adjacency. For indexing, ; The penalty function for the constraint conditions of adjacent grid cells corresponding to the first row of grid cells includes the penalty function for the constraint conditions of adjacent grid cells corresponding to the leftmost grid cell. : ; ; ; Penalty function for the constraint conditions of adjacent grid cells corresponding to the middle grid cell : ; ; ; ; ; In the formula, This is the penalty function for the constraint conditions of adjacent grid cells corresponding to a grid cell in the middle of the first row; Penalty function for the constraint conditions of adjacent grid cells corresponding to the right-hand grid cell : ; ; ; Penalty function for the constraint conditions of adjacent grid cells corresponding to the first column of grid cells : ; ; ; ; ; In the formula, This is the penalty function for the constraint conditions of adjacent grid cells corresponding to a grid cell in the first column of grid cells; Penalty function for the constraint conditions of adjacent grid cells corresponding to internal grid cells : ; ; ; ; ; ; In the formula, To replace the variable, This is the penalty function for the constraint conditions of adjacent graticles corresponding to a graticle in the internal grid. Penalty function for the constraint conditions of adjacent grid cells corresponding to the last grid cell : ; ; ; ; ; In the formula, This is the penalty function for the constraint conditions of adjacent cells corresponding to a cell in the last column of cells; The penalty function for the adjacent constraints of the last row of grid cells includes the penalty function for the adjacent grid constraints of the leftmost grid cell. : ; ; ; Penalty function for the constraint conditions of adjacent grid cells corresponding to the middle grid cell : ; ; ; ; ; In the formula, This is the penalty function for the constraint conditions of adjacent grid cells corresponding to a grid cell in the middle of the last row; Penalty function for the constraint conditions of adjacent grid cells corresponding to the right-hand grid cell : ; ; .

[0036] The objective function adds a penalty term generated by the entry and exit constraints. Let... Let be an undetermined constant, if , ;like , ,remember The penalty coefficient for grid entry and exit constraints is given by the penalty term. , Penalty function for grid entry and exit constraints: ; In the formula, This is the penalty function for the grid entry and exit constraints corresponding to grid cells at different positions. For indexing, ,set up To substitute variables; The penalty function for grid entry and exit constraints corresponding to corner grids includes the penalty function for grid entry and exit constraints corresponding to the bottom left grid. : ; ; ; ; ; ; Penalty function for grid entry and exit constraints corresponding to the bottom right grid : ; ; ; ; ; ; Penalty function for grid entry and exit constraints corresponding to the top left grid : ; ; ; ; ; ; Penalty function for grid entry and exit constraints corresponding to the top right grid : ; ; ; ; ; ; The penalty functions for grid entry and exit constraints corresponding to the boundary grids include the penalty functions for grid entry and exit constraints corresponding to the lower boundary grids. : ; ; ; ; ; ; ; ; ; ; In the formula, To replace the variable, This is the penalty function for the grid entry / exit constraints corresponding to a grid cell in the lower boundary grid. Penalty function for grid entry and exit constraints corresponding to the upper boundary grid : ; ; ; ; ; ; ; ; ; ; ; ; In the formula, To replace the variable, This is the penalty function for the grid entry and exit constraints corresponding to a grid cell in the upper boundary grid; Penalty function for grid entry and exit constraints corresponding to the left boundary grid : ; ; ; ; ; ; ; ; ; ; ; ; In the formula, This is the penalty function for the grid entry / exit constraints corresponding to a grid cell in the left boundary grid; Penalty function for grid entry and exit constraints corresponding to the right boundary grid : ; ; ; ; ; ; ; ; ; ; In the formula, This is the penalty function for the grid entry and exit constraints corresponding to a grid cell in the right boundary grid; Penalty function for grid entry and exit constraints corresponding to internal grids : ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; In the formula, To replace the variable, This is the penalty function for the grid entry and exit constraints corresponding to a grid cell within the internal grid.

[0037] The objective function adds a penalty term resulting from obstacle avoidance constraints, denoted as... The penalty coefficient for obstacle avoidance constraints. The penalty function for obstacle avoidance constraints: ; Penalty items for: .

[0038] The objective function adds a penalty term generated by the start and end grid position constraints, denoted as... The penalty coefficient for the start and end grid position constraints. Penalty function for start and end grid position constraints: ; Penalty items for: ; .

[0039] like Figure 12 As shown, after transforming the constrained optimization problem into a quadratic unconstrained binary optimization model, the planned path is obtained after solving it. The planned path avoids obstacles and is the shortest grid path, thus realizing global path planning. In the figure, the green grid represents obstacles and the black grid represents the planned path.

[0040] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A path planning method based on a quadratic unconstrained binary optimization model, characterized in that, include: S1. Rasterize the environment area, determine the start point, end point, and the location of obstacle grids, determine the set of grids containing obstacles, and define grid binary variables; S2. Define the objective function and establish the optimization problem of the objective function under the constraints of adjacent grids, entry and exit constraints, obstacle avoidance constraints, and start and end position constraints. S3. Transform the constrained optimization problem into a quadratic unconstrained binary optimization model. This includes defining new variables, adding penalty terms to the objective function based on the new variables, adding penalty terms to the objective function based on adjacent grid constraints, adding penalty terms to the objective function based on entry / exit constraints, adding penalty terms to the objective function based on obstacle avoidance constraints, and adding penalty terms to the objective function based on start and end point position constraints. Transform the objective function with added penalty terms into a quadratic unconstrained binary optimization model. Solve the quadratic unconstrained binary optimization model, determine the values ​​of each grid variable based on the values ​​of the independent variables when the objective function reaches its minimum, and obtain the final planned path.

2. The path planning method based on a quadratic unconstrained binary optimization model according to claim 1, characterized in that, S1 includes rasterizing the environmental area into raster map, For row index, , For column indexes, The grid starts with the bottom left grid. Let the starting grid be the grid cell; assume the path originates at grid cell 1. The endpoint is located in the grid. The set of grid cells containing obstacles is , Indexing obstacles This represents the total number of obstacles.

3. The path planning method based on a quadratic unconstrained binary optimization model according to claim 2, characterized in that, S2 includes, S2.1, setting a grid. The variable is , 0 indicates that the grid cell does not belong to the planned path, and 1 indicates that the grid cell belongs to the planned path. For the raster map Square array Satisfy the first Line number Column elements are : ； Define the objective function : ； Establish An optimization problem under the constraints of adjacent grids, grid entry and exit, obstacle avoidance, and path start and end point positions; S2 includes S2.2, establishing adjacent grid constraint conditions: the product of the corresponding variables of any three adjacent grids is always equal to 0, and adjacent grids are grids with a common vertex; S2 includes S2.3, establishing grid entry and exit constraints: There must be exactly one grid adjacent to the starting or ending grid that belongs to the planned path; Except for the starting and ending grids, if the grids... It belongs to the planned path, grid There are exactly two adjacent grid cells that belong to the planned path.

4. The path planning method based on a quadratic unconstrained binary optimization model according to claim 3, characterized in that, S2 includes S2.4, establishing obstacle avoidance constraints: ； S2 includes S2.5, establishing constraints on the starting and ending points of the path: ； 。 5. The path planning method based on a quadratic unconstrained binary optimization model according to claim 4, characterized in that, S3 includes, S3.1, defining new variables: ； In the formula, The total number of variables is There are [number] variables, including direct variables and product variables; the direct variables are [number]. One, corresponding to the original variable The product variable is One, including The set of products of horizontally adjacent elements in the nth row : ； corresponding The variable is indivual; The set of products of the vertically adjacent elements below and the lower right adjacent elements in the first column. : ； corresponding The variable is indivual; The set of products of the left horizontal adjacent elements, the left lower adjacent elements, the bottom vertical adjacent elements, and the right lower adjacent elements of an internal element. : ； corresponding The variable is indivual; The set of products of the left horizontal adjacent elements, the bottom left adjacent elements, and the bottom vertical adjacent elements in the last column. : ； corresponding The variable is indivual.

6. The path planning method based on a quadratic unconstrained binary optimization model according to claim 5, characterized in that, S3 includes, S3.2, the penalty term generated by adding a new variable to the objective function, denoted as... To define the penalty coefficient for the new variable, To define a penalty function for the new variable, the penalty term is: .

7. The path planning method based on a quadratic unconstrained binary optimization model according to claim 6, characterized in that, S3 includes S3.3, the penalty term generated by adding adjacent grid constraints to the objective function, denoted as... This is the penalty coefficient for the constraint condition between adjacent grid cells. The penalty function for adjacent grid constraints is: .

8. The path planning method based on a quadratic unconstrained binary optimization model according to claim 7, characterized in that, S3 includes S3.4, and the penalty term generated by adding entry and exit constraints to the objective function, denoted as... This is the penalty coefficient for grid entry and exit constraints. The penalty function for grid entry and exit constraints is as follows: .

9. The path planning method based on a quadratic unconstrained binary optimization model according to claim 8, characterized in that, S3 includes S3.5, and the penalty term generated by adding obstacle avoidance constraints to the objective function, denoted as... The penalty coefficient for obstacle avoidance constraints. The penalty function for the obstacle avoidance constraint is as follows: ; S3 includes S3.6, a penalty term generated by adding start and end grid position constraints to the objective function, denoted as... The penalty coefficient for the start and end grid position constraints. The penalty function is the constraint on the start and end grid positions, and the penalty term is... .

10. The path planning method based on a quadratic unconstrained binary optimization model according to claim 9, characterized in that, S3 includes S3.7, which transforms the objective function with added penalty terms into a quadratic unconstrained binary optimization model: ； In the formula, It is the transpose symbol. This refers to the quadratic real symmetric matrix generated when transforming the objective function into a quadratic unconstrained binary optimization model; S3 includes S3.8, solving the quadratic unconstrained binary optimization model, determining the values ​​of each grid variable based on the values ​​of the independent variables when the objective function reaches its minimum value, and obtaining the final planned path.

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