A path planning method based on a quadratic unconstrained binary optimization model

Abstract

The application discloses a path planning method based on a quadratic unconstrained binary optimization model, belongs to the technical field of path planning, and is used for unmanned system navigation, and comprises the following steps: rasterizing an environment region, determining the positions of a starting point, an ending point and obstacle grids, determining a set of grids where the obstacles are located, and defining grid binary variables; a target function is defined, and an optimization problem of the target function under adjacent grid constraints, entry and exit constraints, obstacle avoidance constraints and starting point and ending point position constraint conditions is established; the constraint optimization problem is converted into a quadratic unconstrained binary optimization model, the quadratic unconstrained binary optimization model is solved, the values of the grid variables are determined according to the values of the independent variables when the target function takes a minimum value, and finally a planned path is obtained. The application directly embeds multiple complex constraint conditions into the target function through a penalty term, does not need to separately process the complex constraint conditions, and simplifies the logic of a solving process.

Description

TECHNICAL FIELD

[0001] The application discloses a path planning method based on a quadratic unconstrained binary optimization model and belongs to the technical field of path planning. BACKGROUND

[0002] Path planning is a key technology for intelligent devices such as unmanned aerial vehicles, unmanned ships, mobile robots and autonomous vehicles to realize safe obstacle avoidance and autonomous navigation. Its core task is to generate an optimal motion trajectory that meets multiple constraint conditions to ensure safety and efficiency during travel. With the rapid development of intelligent manufacturing and smart city construction, path planning technology, as the core support of intelligent systems, is becoming increasingly important in engineering applications.

[0003] Quantum computing, as a new computing paradigm, can solve some problems in traditional path optimization due to its parallel computing advantage in combinatorial optimization problems. Traditional path planning algorithms, such as Dijkstra algorithm and A* algorithm, mainly rely on classical computing architecture and cannot be directly applied to quantum computing devices. The quadratic unconstrained binary optimization model, due to its natural adaptability to quantum computing, has become an important bridge connecting path planning and quantum optimization, providing a promising research direction for the development of future path planning technology.

[0004] Traditional path planning algorithms currently mainly rely on traditional CPU serial computing, which has architectural differences with the parallelism of quantum computing. In addition, increasing constraint conditions will cause the computational complexity to grow exponentially, and there is a lack of a unified optimization framework for constraint conditions that need to be met in different dimensions, resulting in the possibility that the result is not the optimal solution. SUMMARY

[0005] The purpose of the present application is to provide a path planning method based on a quadratic unconstrained binary optimization model to solve the problem that the current technology relies on traditional CPU serial computing, which has architectural differences with the parallelism of quantum computing, and increasing constraint conditions will cause the computational complexity to grow exponentially, and there is a lack of a unified optimization framework for constraint conditions that need to be met in different dimensions, resulting in the possibility that the result is not the optimal solution.

[0006] A path planning method based on a quadratic unconstrained binary optimization model, comprising:

[0007] S1, rasterizing an environmental area, determining the positions of a starting point, an ending point and obstacle grids, determining a set of grids where obstacles are located, and defining grid binary variables;

[0008] S2, defining an objective function, and establishing an optimization problem of the objective function under adjacent grid constraint conditions, entry and exit constraint conditions, obstacle avoidance constraint conditions and starting point and ending point position constraint conditions;

[0009] S3, converting the constraint optimization problem into a quadratic unconstrained binary optimization model, including defining new variables, adding a penalty term to the objective function generated by the definition of new variables, adding a penalty term to the objective function generated by the adjacent grid constraint condition, adding a penalty term to the objective function generated by the access constraint condition, adding a penalty term to the objective function generated by the obstacle avoidance constraint condition, and adding a penalty term to the objective function generated by the start point and end point position constraint condition, and converting the objective function with added penalty terms 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 objective function takes the minimum value, and obtaining the final planning path.

[0010] S1 includes, griding the environment area into a grid map, row index, , column index, , the grid takes the lower left grid as the starting grid; set the path start point at grid , the end point at grid , and the set of grids where the obstacles are located as , obstacle index, total number of obstacles.

[0011] S2 includes, S2.1, setting the variable of grid as , 0 indicates that the grid does not belong to the planning path, and 1 indicates that the grid belongs to the planning path, and setting as an order square matrix corresponding to the grid map, satisfying the element in the th row and the th column :

[0012] ;

[0013] defining the objective function :

[0014] ;

[0015] establishing the optimization problem under the adjacent grid constraint condition, the grid access constraint condition, the obstacle avoidance constraint condition, and the path start point and end point position constraint condition;

[0016] S2 includes, S2.2, establishing the adjacent grid constraint condition: the product of the corresponding variables of any three adjacent grids is always equal to 0, and the adjacent grids are grids with common vertices;

[0017] S2 includes S2.3, establishing a grid access constraint condition: there is and only one grid belonging to the planning path in the adjacent grid of the start grid or the end grid; except the start grid and the end grid, if a grid belongs to the planning path, there are and only two grids belonging to the planning path in all the adjacent grids of the grid.

[0018] S2 includes S2.4, establishing an obstacle avoidance constraint condition:

[0019]

[0020] S2 includes S2.5, establishing a path start and end position constraint condition:

[0021]

[0022]

[0023] S3 includes S3.1, defining new variables:

[0024]

[0025] In the formula, the total number of variables is , including direct variables and product variables; the direct variables are , corresponding to the original variables ; the product variables are , including the set of horizontally adjacent element products of the nth row elements of :

[0026]

[0027] The corresponding variable is ; the set of vertically adjacent element products below the first column elements of :

[0028]

[0029]

[0030] The corresponding variable is ; the set of right-down adjacent element products of the first column elements of :

[0031] ​​​​​​​​​​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. :

[0032] ;

[0033] corresponding The variable is indivual;

[0034] 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. :

[0035] ;

[0036] corresponding The variable is indivual.

[0037] 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: .

[0038] 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: .

[0039] 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: .

[0040] 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: ;

[0041] S3 includes S3.6, a penalty term generated by adding start and end grid position constraints to the objective function, denoted as... The penalty coefficients for the start and end grid position constraints. The penalty function of the start point and end point grid position constraint condition is .

[0042] S3 comprises S3.7, converting the target function after adding the penalty term into a quadratic unconstrained binary optimization model:

[0043] ;

[0044] In the formula, is a transpose symbol, is a quadratic form real symmetric matrix generated when the target function is converted into the quadratic unconstrained binary optimization model;

[0045] S3 comprises S3.8, 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 obtaining the final planning path.

[0046] Compared with the prior art, the present application has the following beneficial effects: the present application directly embeds multiple complex constraint conditions into the target function through the penalty term, without the need to separately process complex constraint conditions, thereby simplifying the logic of the solving process; the quadratic unconstrained binary optimization model can be directly adapted to quantum computing hardware, and has good compatibility with traditional optimization algorithms, and with the development of quantum computing, the method of the present application will also be more efficient. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 is a flowchart of the present application;

[0048] Figure 2 is a schematic diagram of a grid map;

[0049] Figure 3 is a grid position and grid variable relationship diagram;

[0050] Figure 4 is a schematic diagram of an error situation of adjacent constraint features of a grid;

[0051] Figure 5 is a schematic diagram of a correct situation of adjacent constraint features of a grid;

[0052] Figure 6 is a schematic diagram of start point grid access constraint Figure 1 ;

[0053] Figure 7 is a schematic diagram of start point grid access constraint Figure 2 ;

[0054] Figure 8 is a schematic diagram of start point grid access constraint Figure 3 ;

[0055] Figure 9is a path grid access constraint diagram except for the start and end grids Figure 1 ;

[0056] Figure 10 is a path grid access constraint diagram except for the start and end grids Figure 2 ;

[0057] Figure 11 is a path grid access constraint diagram except for the start and end grids Figure 3 ;

[0058] Figure 12 is a path planning diagram of a quadratic unconstrained binary optimization model. DETAILED DESCRIPTION

[0059] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0060] A path planning method based on a quadratic unconstrained binary optimization model, comprising:

[0061] S1, rasterizing an environment area, determining the positions of start, end and obstacle grids, determining the set of grids where the obstacles are located, and defining grid binary variables;

[0062] S2, defining an objective function, and establishing an optimization problem of the objective function under the constraints of adjacent grid constraints, access constraints, obstacle avoidance constraints and start and end position constraints;

[0063] S3, converting the constraint optimization problem into a quadratic unconstrained binary optimization model, including defining new variables, adding a penalty term generated by the new variables to the objective function, adding a penalty term generated by the adjacent grid constraints to the objective function, adding a penalty term generated by the access constraints to the objective function, adding a penalty term generated by the obstacle avoidance constraints to the objective function, and adding a penalty term generated by the start and end position constraints to the objective function, and converting the objective function after adding the penalty terms into a quadratic unconstrained binary optimization model; solving the quadratic unconstrained binary optimization model, determining the values of each grid variable according to the values of the independent variables when the objective function takes the minimum value, and obtaining the final planned path.

[0064] S1 includes rasterizing an environment area into a grid map of , is a row index, , is a column index, , the grid at the lower left corner of the grid is the starting grid; the path start point is located at the grid , the end point is located at the grid , the set of grids where the obstacles are located is , is the obstacle index, is the total number of obstacles.

[0065] S2 includes S2.1, setting the grid variable , , 0 indicates that the grid does not belong to the planned path, and 1 indicates that the grid belongs to the planned path, and is a order square matrix corresponding to the grid map, satisfies the row and column element is :

[0066] ;

[0067] Define the objective function :

[0068] ;

[0069] Establish the optimization problem under the constraints of adjacent grids, grid entry and exit constraints, obstacle avoidance constraints, and path start and end point position constraints;

[0070] S2 includes S2.2, establishing adjacent grid constraints: the product of the corresponding variables of any three adjacent grids is always equal to 0, and adjacent grids are grids with common vertices;

[0071] S2 includes S2.3, establishing grid entry and exit constraints: there is only one grid belonging to the planned path among the adjacent grids of the start grid or the end grid; except for the start grid and the end grid, if the grid belongs to the planned path, there are only two grids belonging to the planned path among all the adjacent grids of the grid .

[0072] S2 includes S2.4, establishing obstacle avoidance constraints:

[0073] ;

[0074] S2 includes S2.5, establishing path start and end point position constraints:

[0075] ;

[0076] .

[0077] S3 includes S3.1, defining new variables:

[0078] ;

[0079] wherein, the total number of variables is , including direct variables and product variables; the direct variables are , corresponding to the original variables ; the product variables are , including the set of horizontally adjacent element products of the nth row elements of :

[0080] ;

[0081] the corresponding variables are ;

[0082] the set of vertically adjacent element products below the first column elements of :

[0083] ;

[0084] the corresponding variables are ;

[0085] the set of horizontally adjacent element products to the left of the internal elements, vertically adjacent element products below, and right-down adjacent element products of :

[0086] ;

[0087] the corresponding variables are ;

[0088] the set of horizontally adjacent element products to the left of the last column elements of :

[0089] ;

[0090] the corresponding variables are .​

[0091] S3 includes, S3.2, the objective function increases the penalty term generated by defining new variables, recorded as is the penalty coefficient of defining new variables, is the penalty function of defining new variables, and the penalty term is .

[0092] S3 includes, S3.3, the objective function increases the penalty term generated by adjacent grid constraints, recorded as is the penalty coefficient of adjacent grid constraints, is the penalty function of adjacent grid constraints, and the penalty term is .

[0093] S3 includes, S3.4, the objective function increases the penalty term generated by the in-out constraint, recorded as is the penalty coefficient of grid in-out constraint, is the penalty function of grid in-out constraint, and the penalty term is .

[0094] S3 includes, S3.5, the objective function increases the penalty term generated by the obstacle avoidance constraint, recorded as is the penalty coefficient of obstacle avoidance constraint, is the penalty function of obstacle avoidance constraint, and the penalty term is .

[0095] S3 includes, S3.6, the objective function increases the penalty term generated by the start and end grid position constraint, recorded as is the penalty coefficient of start and end grid position constraint, is the penalty function of start and end grid position constraint, and the penalty term is .

[0096] S3 includes, S3.7, the objective function after increasing the penalty term is converted into a quadratic unconstrained binary optimization model:

[0097] ;

[0098] In the formula, is the transpose symbol, is the quadratic form real symmetric matrix generated when the objective function is converted into a quadratic unconstrained binary optimization model;

[0099] S3 includes, S3.8, solving the quadratic unconstrained binary optimization model, determining the value of each grid variable according to the value of the independent variable when the objective function takes the minimum value, and obtaining the final planning path.

[0100] Further described below in conjunction with the drawings. As shown in the accompanying Figure 1As shown, the environment area is first rasterized into a grid map, as shown in Figure 2 , where green grids are obstacles and black grids are start and end points; as shown in Figure 3 , after defining grid binary variables, the grid corresponding variables are recorded as .

[0101] Define the objective function and establish the optimization problem of the objective function under the constraints of adjacent grid, entry and exit, obstacle avoidance, and start and end point positions. As shown in Figure 4 , Figure 5 , the adjacent grid constraint condition is to make the number of grids contained in the planned path reach the minimum, and at most two grids of the three adjacent grids can belong to the planned path at the same time, that is, the product of the corresponding variables of any three adjacent grids is always equal to 0, and the specific constraint conditions are as follows:

[0102] ;

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] ;

[0109] ;

[0110] ;

[0111] ;

[0112] ;

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] .

[0118] The grid access constraint condition is to make the planning path connect the start grid and the end grid with the least number of grids, and only one grid adjacent to the start grid or the end grid belongs to the planning path, that is, the sum of all grid variables adjacent to the start grid or the end grid can only be 1, Figure 6 、 Figure 7 、 Figure 8 For the example of three start grid forward directions, the arrow in the figure is the planning path forward direction; as shown in Figure 9 、 Figure 10 and Figure 11 , except for the start grid or the target grid, if the current grid (the grid where the red star is in the figure) belongs to the planning path, only 2 grids adjacent to it belong to the planning path, that is, the sum of all grid variables adjacent to the grid can only be 2, assuming is an undetermined constant, judge whether it belongs to the set , if it does, then , otherwise , the specific constraint conditions include the left lower corner grid The corresponding constraint condition is:

[0119] ;

[0120] The right lower corner grid The corresponding constraint condition is:

[0121] ;

[0122] The left upper corner grid The corresponding constraint condition is:

[0123] ;

[0124] The right upper corner grid The corresponding constraint condition is:

[0125] ;

[0126] The lower boundary grid The corresponding constraint condition is:

[0127] ;

[0128] The upper boundary grid The corresponding constraint condition is:

[0129] ;

[0130] The left boundary grid The corresponding constraint condition is:

[0131] ;

[0132] Right boundary grid The corresponding constraint condition is:

[0133] ;

[0134] Internal grid The corresponding constraint condition is:

[0135] .

[0136] The obstacle avoidance constraint condition is established to make the planned path avoid obstacles, that is, the path grid does not pass through the obstacle grid at all, and the constraint condition is:

[0137] ;

[0138] The start and end position constraint condition of the path is established to make the planned path pass through the start grid and the end grid, and the constraint condition is:

[0139] ;

[0140] .

[0141] The constraint optimization problem is converted into a quadratic unconstrained binary optimization model, and the specific process includes defining new variables:

[0142] ;

[0143] including the component corresponding to the direct variable :

[0144] ;

[0145] The component corresponding to :

[0146] ; The component corresponding to

[0147] : ;

[0148] ;

[0149] ;

[0150] The component corresponding to :

[0151] ​​ ;

[0152] ;

[0153] ;

[0154] ;

[0155] corresponding to the component :

[0156] ;

[0157] ;

[0158] .

[0159] The objective function adds a penalty term for the new variables generated, denoted by is the penalty coefficient for the new variables, and the penalty term is , is the penalty function for the new variables:

[0160] ;

[0161] where is the penalty function for the new variables corresponding to the component, is the index, ;

[0162] the penalty function for the new variables corresponding to the component :

[0163] ;

[0164] ;

[0165] ;

[0166] ;

[0167] ;

[0168] where is the substitution variable, is the penalty function for one variable in the component corresponding to ;

[0169] corresponding to the component of :

[0170] ;

[0171]

[0172] ;

[0173] ;

[0174] ;

[0175] ;

[0176] ;

[0177] wherein is the penalty function corresponding to one of the new variables generated by the product of the vertically adjacent elements below;

[0178]

[0179] ;

[0180] ;

[0181] ;

[0182] ;

[0183] ;

[0184] wherein is the penalty function corresponding to one of the new variables generated by the product of the right-down adjacent elements;

[0185] corresponding to the component of :

[0186] ;

[0187]

[0188] ; ​​​​​​​​

[0189] ;

[0190] ;

[0191] ;

[0192] ;

[0193] wherein, is the penalty function corresponding to one variable of the new variable generated by the product of the left side horizontally adjacent elements;

[0194] is the penalty function corresponding to one variable of the new variable generated by the product of the left lower adjacent elements :

[0195] ;

[0196] ;

[0197] ;

[0198] ;

[0199] ;

[0200] wherein, is the penalty function corresponding to one variable of the new variable generated by the product of the left lower adjacent elements;

[0201] is the penalty function corresponding to one variable of the new variable generated by the product of the lower side vertically adjacent elements is:

[0202] ;

[0203] ;

[0204] ;

[0205] ;

[0206] ;

[0207] wherein, is the penalty function corresponding to one variable of the new variable generated by the product of the lower side vertically adjacent elements;

[0208] is the penalty function corresponding to one variable of the new variable generated by the product of the right lower adjacent elements :

[0209] ;

[0210] ;

[0211] ;

[0212] ;

[0213] ;

[0214] wherein, is the penalty function corresponding to one variable of the new variable generated by the right-down adjacent element product;

[0215] corresponds to the component of :

[0216] ;

[0217] the penalty function corresponding to one variable of the new variable generated by the left-side horizontal adjacent element product :

[0218] ;

[0219] ;

[0220] ;

[0221] ;

[0222] ;

[0223] wherein, is the penalty function corresponding to one variable of the new variable generated by the left-side horizontal adjacent element product;

[0224] the penalty function corresponding to one variable of the new variable generated by the left-down adjacent element product is:

[0225] ;

[0226] ;

[0227] ;

[0228] ;

[0229] ;

[0230] wherein, ​a penalty function corresponding to one of the new variables generated by the product of the left lower adjacent elements;

[0231] a penalty function corresponding to one of the new variables generated by the product of the lower vertical adjacent elements :

[0232] ;

[0233] ;

[0234] ;

[0235] ;

[0236] ;

[0237] wherein, a penalty function corresponding to one of the new variables generated by the product of the lower vertical adjacent elements.

[0238] The objective function increases the penalty term generated by the adjacent grid constraint condition, denoted as is the penalty coefficient of the adjacent grid constraint condition, and the penalty term is , is the penalty function of the adjacent grid constraint condition:

[0239] ;

[0240] wherein, is the penalty function of the adjacent grid constraint condition corresponding to the grid at different positions, and the adjacent grid constraint condition includes horizontal adjacent and vertical adjacent, is the index, ;

[0241] The penalty function of the adjacent grid constraint condition corresponding to the first row of grids includes the penalty function of the adjacent grid constraint condition corresponding to the left end grid :

[0242] ;

[0243] ;

[0244] ;

[0245] The penalty function of the adjacent grid constraint condition corresponding to the middle grid :

[0246] ;

[0247] ;

[0248] ;

[0249] ;

[0250] ;

[0251] wherein, is the penalty function of the adjacent grid constraint condition corresponding to one grid in the first row middle grid;

[0252] is the penalty function of the adjacent grid constraint condition corresponding to the right end grid :

[0253] ;

[0254] ;

[0255] ;

[0256] is the penalty function of the adjacent grid constraint condition corresponding to the first column grid :

[0257] ;

[0258] ;

[0259] ;

[0260] ;

[0261] ;

[0262] wherein, is the penalty function of the adjacent grid constraint condition corresponding to one grid in the first column;

[0263] is the penalty function of the adjacent grid constraint condition corresponding to the internal grid :

[0264] ;

[0265] ;

[0266] ;

[0267] ;

[0268] ;

[0269] ;

[0270] wherein, is a substitution variable, is a penalty function of the adjacent grid constraint condition corresponding to one grid in the internal grid;

[0271] is a penalty function of the adjacent grid constraint condition corresponding to one grid in the last column of grids

[0272]

[0273]

[0274]

[0275]

[0276]

[0277] wherein, is a penalty function of the adjacent grid constraint condition corresponding to one grid in the last column of grids;

[0278] is a penalty function of the adjacent constraint condition corresponding to the last row of grids, including a penalty function of the adjacent grid constraint condition corresponding to the left end grid

[0279]

[0280]

[0281]

[0282] is a penalty function of the adjacent grid constraint condition corresponding to one grid in the middle grid of the last row

[0283]

[0284]

[0285]

[0286]

[0287]

[0288] wherein, is a penalty function of the adjacent grid constraint condition corresponding to one grid in the middle grid of the last row;

[0289] is a penalty function of the adjacent grid constraint condition corresponding to the right end grid​​​​​​​​​​​​​​​​ :

[0290] ;

[0291] ;

[0292] .

[0293] The objective function increases the penalty term generated by the in-out constraint condition, set as a to-be-determined constant, if , ; if , , record as the penalty coefficient of the grid in-out constraint condition, and the penalty term is , The penalty function of the grid in-out constraint condition is:

[0294] ;

[0295] In the formula, is the penalty function of the grid in-out constraint condition corresponding to the grid at different positions, is the index, , set as the substitution variable;

[0296] The penalty function of the grid in-out constraint condition corresponding to the corner grid includes the penalty function of the grid in-out constraint condition corresponding to the lower left corner grid :

[0297] ;

[0298] ;

[0299] ;

[0300] ;

[0301] ;

[0302] ;

[0303] The penalty function of the grid in-out constraint condition corresponding to the lower right corner grid :

[0304] ;

[0305] ;

[0306] ;

[0307] ;

[0308] ;

[0309] ;

[0310] penalty function of the grid entry-exit constraint condition corresponding to the upper-left corner grid :

[0311] ;

[0312] ;

[0313] ;

[0314] ;

[0315] ;

[0316] ;

[0317] penalty function of the grid entry-exit constraint condition corresponding to the upper-right corner grid :

[0318] ;

[0319] ;

[0320] ;

[0321] ;

[0322] ;

[0323] ;

[0324] penalty function of the grid entry-exit constraint condition corresponding to the boundary grid, including a penalty function of the grid entry-exit constraint condition corresponding to the lower boundary grid :

[0325] ;

[0326] ;

[0327] ;

[0328] ;

[0329] ;

[0330] ;

[0331] ;

[0332] ;

[0333] ;

[0334] ;

[0335] wherein, is a substitution variable, is a penalty function of a grid in-out constraint condition corresponding to a lower boundary grid;

[0336] a penalty function of a grid in-out constraint condition corresponding to an upper boundary grid :

[0337] ;

[0338] ;

[0339] ;

[0340] ;

[0341] ;

[0342] ;

[0343] ;

[0344] ;

[0345] ;

[0346] ;

[0347] ;

[0348] ;

[0349] wherein, is a substitution variable, is a penalty function of a grid in-out constraint condition corresponding to an upper boundary grid;

[0350] a penalty function of a grid in-out constraint condition corresponding to a left boundary grid :

[0351] ;

[0352] ;

[0353] ;

[0354] ;

[0355] ;

[0356] ;

[0357] ;

[0358] ;

[0359] ;

[0360] ;

[0361] ;

[0362] ;

[0363] wherein, is the penalty function of the grid entry-exit constraint condition corresponding to one grid in the left boundary grid;

[0364] is the penalty function of the grid entry-exit constraint condition corresponding to one grid in the right boundary grid :

[0365] ;

[0366] ;

[0367] ;

[0368] ;

[0369] ;

[0370] ;

[0371] ;

[0372] ;

[0373] ;

[0374] ;

[0375] wherein, is the penalty function of the grid in-out constraint condition corresponding to one grid in the right boundary grid;

[0376] is the penalty function of the grid in-out constraint condition corresponding to the internal grid :

[0377] ;

[0378] ;

[0379] ;

[0380] ;

[0381] ;

[0382] ;

[0383] ;

[0384] ;

[0385] ;

[0386] ;

[0387] ;

[0388] ;

[0389] ;

[0390] ;

[0391] ;

[0392] ;

[0393] ;

[0394] ;

[0395] ;

[0396] ;

[0397] ;

[0398] wherein, is a penalty function of the grid in-out constraint condition corresponding to one grid in the internal grid. The objective function increases a penalty term generated by the obstacle avoidance constraint condition, denoted as

[0399] is a penalty coefficient of the obstacle avoidance constraint condition, is a penalty function of the obstacle avoidance constraint condition:

[0400] ;

[0401] The penalty term is:

[0402] .

[0403] The objective function increases a penalty term generated by the start and end grid position constraint condition, denoted as is a penalty coefficient of the start and end grid position constraint condition, is a penalty function of the start and end grid position constraint condition:

[0404] ;

[0405] The penalty term is:

[0406] ;

[0407] .

[0408] As shown in Figure 12 , after the constraint optimization problem is converted into a quadratic unconstrained binary optimization model, the planning path is obtained by solving, the planning path avoids obstacles while being the shortest grid path, global path planning is achieved, and the green grid in the figure is an obstacle and the black grid is a planning path.

[0409] The above examples are only used to illustrate the technical solutions of the present application, and not to limit it. Although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can still be modified, or some or all of the technical features can be replaced by equivalents, and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.​

Claims

1. A path planning method based on a quadratic unconstrained binary optimization model, characterized in that, The method comprises the following steps: S1, rasterizing an environmental area, determining a start point, an end point and a position of an obstacle grid, determining a set of grids where the obstacle is located, and defining a grid binary variable; S2, defining an objective function, and establishing an optimization problem of the objective function under the constraints of adjacent grids, entry and exit, obstacle avoidance, and the positions of the start point and the end point; S3, converting the constrained optimization problem into a quadratic unconstrained binary optimization model, including defining a new variable, adding a penalty term generated by the new variable to the objective function, adding a penalty term generated by the adjacent grid constraint condition to the objective function, adding a penalty term generated by the entry and exit constraint condition to the objective function, adding a penalty term generated by the obstacle avoidance constraint condition to the objective function, and adding a penalty term generated by the start point and end point position constraint condition to the objective function, and converting the objective function after adding the penalty terms 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 objective function takes the minimum value, and obtaining a final planning path.

2. The path planning method based on a quadratic unconstrained binary optimization model according to claim 1, characterized in that, S1 comprises rasterizing the environment area into a grid map of , , , , , , , , , , .

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 represents that the grid does not belong to the planned path, and 1 represents that the grid belongs to the planned path, wherein is a order square matrix corresponding to the grid map, satisfies the first row and the first column element is : ； Defining an objective function : ； Establish Optimization problems under the constraints of adjacent grid, grid access and exit, obstacle avoidance, and path start and end position S2 includes S2.2, establishing an adjacent grid constraint condition: the product of the variables corresponding to any three adjacent grids is always equal to 0, and the adjacent grids are grids with a common vertex; S2 includes S2.3, establishing a grid access constraint condition: there is and only one grid belonging to the planning path in the adjacent grid of the start grid or the end grid; except the start grid and the end grid, if the grid belongs to the planning path, there are and only two grids belonging to the planning path in all the adjacent grids of the grid .

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 an obstacle avoidance constraint condition: ； S2 includes S2.5, establishing a path start point and end point position constraint condition: ； 。 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 a new variable: ； In the formula, The total number of variables of is , including direct variables and product variables; the direct variables are , corresponding to the original variables ; the product variables are , including a set of horizontally adjacent element products of the nth row elements of : ； corresponding variable for one; a set of vertically adjacent element products below the first column of elements of the matrix : ； corresponding variable for one; a set of products of the left-hand horizontally adjacent element, the lower-left adjacent element, the vertically lower adjacent element, and the lower-right adjacent element of the interior element of : ； corresponding variable for one; a set of left-hand horizontally adjacent element products, left-bottom adjacent element products, and bottom vertically adjacent element products to the left of the last column element of the : ； corresponding variable for one.

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 objective function increases a penalty term for the new variable, denoted as for the penalty coefficient for defining the new variable, for the penalty function for defining 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 objective function adds a penalty term for the adjacent grid constraint condition, denoted as is the penalty coefficient for the adjacent grid constraint condition, is the penalty function for the adjacent grid constraint condition, and the penalty term 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, the objective function increases the penalty term generated by the in-out constraint condition, recorded as The penalty coefficient of the grid in-out constraint is The penalty function of the grid in-out constraint condition, the penalty term is .

9. The path planning method based on a quadratic unconstrained binary optimization model according to claim 8, characterized in that, S3 includes, S3.5, the target function increases the penalty term generated by the obstacle avoidance constraint condition, recorded as The penalty coefficient of the obstacle avoidance constraint condition is The penalty function of the obstacle avoidance constraint condition is ; S3 includes, S3.6, a penalty term generated by the start and end grid position constraint condition of the objective function increase, recorded as the penalty coefficient of the start and end grid position constraint condition, the penalty function of the start and end grid position constraint condition, the penalty term is .

10. The path planning method based on a quadratic unconstrained binary optimization model according to claim 9, wherein, S3 includes S3.7, converting the objective function after adding the penalty terms into a quadratic unconstrained binary optimization model: ； wherein is the transpose symbol, is a quadratic form real symmetric matrix resulting from the conversion of the objective function into a quadratic unconstrained binary optimization model; S3 includes S3.8, solving the quadratic unconstrained binary optimization model, determining the value of each grid variable according to the value of the independent variable when the objective function takes the minimum value, and obtaining a final planning path.

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