Mobile robot motion planning method for unknown target collection

Abstract

The invention provides an unknown target collection-oriented mobile robot motion planning method. The method comprises the following steps of S1, synchronously constructing a grid map in a moving process of a mobile robot; s2, extracting a boundary region and a passable region; s3, the mobile robot continuously explores the environment; s4, the exploration degree of the local environment is judged according to the balance function; s5, if the exploration of the local environment is completed, the mobile robot collects targets in the task area; s6, the mobile robot completes ascertainment of the sub-regions and region coverage collection; step S7, when all unknown environments are detected and all task area targets are collected, the unknown target collection task is completed; the unknown target collection motion planning method of the mobile robot is good in performance, the mobile robot can rapidly complete exploration of an unknown environment and collection of targets in a task area, and task requirements can be effectively met.

Description

Technical Field

[0001] The invention relates to the technical field of mobile robot motion planning, in particular to a mobile robot motion planning method for unknown target collection. Background Art

[0002] Collection of targets in unknown environments is an important research direction in the field of robotics and is widely used in areas such as stain cleaning and search and rescue. Since stains and search and rescue targets are usually concentrated in different sub-areas in the workspace and the robot does not have prior information about the environment, the robot needs to use onboard sensors to explore the unknown areas in the workspace, identify the locations of all specific task areas, and traverse and collect all targets in the area.

[0003] The unknown environment target collection task relies on robot autonomous exploration and full coverage path planning technology. The boundary-based method and the viewpoint sampling-based method are the main methods to solve the problem of robot autonomous exploration. Yamauch defines the boundary between the known area and the unknown area as the boundary, and the robot moves continuously to the boundary to explore the environment. Although this strategy can fully explore the unknown environment, it is easy to fall into the dilemma of local optimality. Wan et al. regard the boundary area as the candidate exploration target point area, and design the utility function to select the boundary point with the largest function value in the candidate area as the exploration target point. Umari et al. combine the information gain contained in the node and use two global and local RRT trees to explore the environment. Lu et al. proposed a sampling-based boundary block detection method (Sample-based Frontier-Block Detection, SFBD), which reduces useless sampling operations. After all unknown areas are explored, the offline coverage algorithm is called to cover and collect all targets in the specific task area. However, the coverage order of each scattered task area is a traveling salesman problem (TSP). When the number of task areas to be covered increases, the complexity of the problem increases exponentially. Therefore, this problem is NP-hard. In addition, separating environmental detection and task area coverage will cause the robot to increase repeated exploration actions, spending extra time and energy.

[0004] The online full coverage path planning method is another method to solve the unknown environment target collection task. It does not rely on the prior information of the environment and can complete the full coverage of the task area while exploring the unknown area.

[0005] The template-based method predefines the motion pattern mapped by the environment, and uses the stored motion template to complete the coverage task when facing specific environmental features. * Based on the ox-plowing method, a coverage path is generated using A *The search algorithm plans an escape path out of the dead point state and fully covers the new uncovered free area. Spiral-STC constructs a main line that runs through the map and moves along one side of the main line to form a fully covered spiral path.

[0006] ∈ * The algorithm recursively decomposes and constructs a hierarchical potential field map to guide the robot to generate a back-and-forth coverage path. PPCPP is inspired by predators and prey in nature, simulating the prey's predation behavior to guide the robot to plan a full coverage path.

[0007] Although the above online full coverage planning algorithm can complete the target collection task in a completely unknown or partially unknown environment, its path will cover the entire free area instead of being limited to the task area, resulting in a large number of invalid redundant paths.

[0008] Faced with scenarios where the environment and mission target information are unknown, how to effectively design a planning scheme that enables mobile robots to quickly explore the environment and completely collect targets in multiple areas has become an important issue that needs to be explored and solved in this field. Summary of the invention

[0009] In view of this, the purpose of the present invention is to provide a mobile robot motion planning method for unknown target collection, in which the mobile robot can quickly complete the exploration of the unknown environment and collect targets in the task area, and can effectively meet the task requirements.

[0010] To achieve the above object, the present invention adopts the following technical solution: a mobile robot motion planning method for unknown target collection, comprising the following steps:

[0011] Step S1: The mobile robot constructs a grid map using data obtained by the sensors it carries. The grid has three states: a traversable free grid, an obstacle grid, and an unexplored grid.

[0012] Step S2: The mobile robot extracts the boundary area and the passable area according to the constructed grid map;

[0013] Step S3: The mobile robot continuously explores the environment using a boundary-guided planning method;

[0014] Step S4: The mobile robot uses a balance framework to determine the degree of exploration of the local environment according to the balance function;

[0015] Step S5: If the local environment is explored, the mobile robot uses a planning method guided by a coverage point reward function to perform a target collection task in the task area. If the local environment is not explored, return to step 2.

[0016] Step S6: After the mobile robot completes the exploration of the sub-area and the area coverage collection, if there is an unexplored area or the target has not been collected, return to step 2 to continue;

[0017] Step S7: When all unknown environments have been explored and all mission area targets have been collected, the unknown target collection task is completed.

[0018] In a preferred embodiment: the specific method for extracting the boundary area in step S2 is: the mobile robot traverses the free and traversable grids in the grid map, and the free grids with at least one adjacent unexplored grid are marked as boundary points, and are added to the boundary set.

[0019] In a preferred embodiment: the boundary-guided planning method of step S3 specifically includes the following steps:

[0020] Step S31: adding the exploration points of the observation environment generated by sampling at a spacing of δ in the boundary set to the candidate exploration point set;

[0021] Step S32: Calculate the function value of each candidate point according to the information gain function and select the point with the maximum function value as the next exploration target point. The information gain function G(v i )The formula is:

[0022]

[0023] Among them, S(W obs (v i )) and S(W unexp (v i )) is v i The number of obstacle boundary grids and unexplored grids within a certain radius r, ω o represents the weight of the number of obstacle boundary units, K(v 0 ,v i ) is the current position v of the robot 0 To the candidate viewpoint v i Manhattan distance, S(M tar (v i )) is v i The number of task area grids within a certain radius;

[0024] Step S33: The mobile robot passes A * The algorithm plans a path from the robot's current unknown point to the next exploration target point;

[0025] Step S34: The robot receives the exploration path planned by the algorithm, and converts the path in the exploration path solution into the required linear velocity and angular velocity, and controls the robot to move to the target position.

[0026] In a preferred embodiment, the specific method of constructing the balance framework in step S4 is: the mobile robot calculates the rate of change of the number of boundary points and free grids in the map before and after an exploration, and constructs an environmental exploration quantization function. If the function value is less than 0, it means that the local area has been completely explored. If the function value is greater than 0, it means that the local area has not been completely explored. The function calculation formula is:

[0027]

[0028] Among them, △(S F ) and △(S M ) is the difference between the number of boundary points and the number of free area grids before and after an exploration, L(σ e ) is the length of the exploration path, represented by the number of exploration path grids, ω k is the balance frame weight factor, when ω k When it is equal to 0, the algorithm degenerates into covering the task area after fully exploring the map.

[0029] In a preferred embodiment, the planning method based on the coverage point reward function guidance in step S5 specifically comprises the following steps:

[0030] Step S51: The mobile robot removes the exploration path grids located in the task area and adjacent to obstacles, and the remaining task area free grids are used as the current set of areas to be covered.

[0031] Step S52: Use function SetConductor(·) to select The grid with the closest Manhattan distance to the robot position in the middle distance is used as the starting point P of the coverage path s , the next exploration target point is used as the coverage guide point P g ;

[0032] Step S53: Use the function Near(·) to check o k lie in If the grid does not belong to the covered grid set, or obstacle set, then add it to the adjacent grid set N(o k );

[0033] Step S54: If N(o k ) is not empty, traverse the adjacent grid set N(o k ), use the reward function Reward(·) to calculate the reward function value of each grid, and convert o k Add to covered raster collection o k Gather in the current area to be covered Remove from the list and update k The grid with the largest reward function value is used as the next coverage point. If N(o k ) is empty, the mobile robot uses function A * Plan from the robot's current position to The nearest grid point in mid-Manhattan;

[0034] Step S55: If the current set of areas to be covered is If it is empty, the planning ends; otherwise, return to step S52 to continue.

[0035] In a preferred embodiment: the reward function Reward(·) in step S54 is designed to be a function of the distance evaluation value R g (o j ), direction evaluation value R s (o j ), boundary evaluation value R b (o j ), the distance evaluation value is the set of adjacent grids to be covered N(o k ) in the evaluation point o j To cover the guide point P g The distance is:

[0036]

[0037] Among them, D(o j ) is o j With P g The Euclidean distance, D min (o k ) is o k All adjacent grids o j With P g Minimum distance, D max (o k ) is o k All adjacent grids o j With P g The maximum value of the distance;

[0038] The direction evaluation value is the evaluation value of the change in the coverage direction of the mobile robot's current position, and the formula is:

[0039]

[0040] Among them, ∠(o k-1 o k o j ) is the previous covering point o k-1 , the current coverage point o k and j The radian value of the angle between them;

[0041] The boundary evaluation value is the number of closed grids adjacent to the point to be covered, and the formula is:

[0042]

[0043] in, For all o j The maximum number of adjacent closed grids in , is the current evaluation point o j The number of adjacent closed grids;

[0044] The reward function formula is:

[0045] R(o j )=R g (o j )+ω s (R s (o j ))+ω b (R b (o j )) (6)

[0046] Among them, ω s is the smoothness weight factor, ω b is the boundary weight factor.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] (1) The present invention proposes a balancing framework for switching between environmental exploration and target coverage collection actions, designs a balancing function based on the change in the number of feature points in the environment, and combines the target coverage collection task in the local environment exploration process to improve the overall task completion efficiency.

[0049] (2) The present invention proposes a path planning method for autonomous exploration of the environment, which integrates corner obstacle information to design an information gain function, selects the boundary point with the maximum function value as the exploration target point, optimizes the exploration path selection, and guides the mobile robot to prioritize exploring the local environment and reduce repeated exploration.

[0050] (3) The present invention proposes a method for planning a path for full regional coverage, which integrates the exploration trajectory to construct a coverage point reward value model, and gradually selects the grids with the maximum reward value to form a coverage path, thereby ensuring the robot's full coverage of the task area and reducing the repeated coverage rate of the path. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Attached Figure 1 It is a schematic diagram of the process of the present invention;

[0052] Attached Figure 2 is a schematic diagram of a mobile robot of the present invention performing an unknown target collection task;

[0053] Attached Figure 3 is a schematic diagram of the mobile robot of the present invention acquiring an area to be covered;

[0054] Attached Figure 4 is a schematic diagram of a task area covered by a mobile robot of the present invention;

[0055] Attached Figure 5 It is a schematic diagram of a simulation result of a static scene of the present invention;

[0056] Attached Figure 6 It is a schematic diagram of the simulation result of the static scene 2 of the present invention;

[0057] Attached Figure 7 It is a schematic diagram of the simulation results of the static scene three of the present invention;

[0058] Attached Figure 8 It is a static real experiment schematic diagram of the present invention. DETAILED DESCRIPTION

[0059] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0060] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0061] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0062] like Figure 1-8 As shown, a mobile robot motion planning method for unknown target collection includes the following steps:

[0063] Step S1, the mobile robot constructs a grid map using data obtained by the sensors it carries;

[0064] Step S2: The mobile robot extracts the boundary area and the passable area according to the constructed grid map;

[0065] Step S3: The mobile robot uses a boundary-guided planning method to continuously explore the environment, such as Figure 2 (a)

[0066] Step S4: The mobile robot uses a balance framework to determine the degree of exploration of the local environment according to the balance function;

[0067] Step S5: If the local environment is explored, the mobile robot uses a planning method guided by a coverage point reward function to perform a target collection task in the task area, as shown in 2(c). If the local environment is not explored, return to step 2.

[0068] Step S6: After the mobile robot completes the exploration of the sub-area and the area coverage collection, if there is an unexplored area or the target has not been collected, return to step 2 to continue;

[0069] Step S7: When all unknown environments have been explored and all mission area targets have been collected, the unknown target collection task is completed;

[0070] The specific method for extracting the boundary area in step S2 is: the mobile robot traverses the free and traversable grids in the grid map, and the free grids with at least one adjacent unexplored grid are marked as boundary points, and are added to the boundary set.

[0071] The boundary-guided planning method of step S3 specifically includes the following steps:

[0072] Step S31: adding the exploration points of the observation environment generated by sampling at a spacing of δ in the boundary set to the candidate exploration point set;

[0073] Step S32: Calculate the function value of each candidate point according to the information gain function and select the point with the maximum function value as the next exploration target point. The formula of the information gain function is:

[0074]

[0075] Among them, S(W obs (v i )) and S(W unexp (v i )) is v i The number of obstacle boundary grids and unexplored grids within a certain radius r, ω o represents the weight of the number of obstacle boundary units, L(v 0 ,v i ) is the current position v of the robot 0 To the candidate viewpoint v i Manhattan distance, S(M tar (v i )) is v i The number of mission area grids within a certain radius.

[0076] Step S33: The mobile robot passes A *The algorithm plans a path from the robot's current unknown point to the next exploration target point, such as Figure 2 (b)

[0077] Step S34: The robot receives the exploration path planned by the algorithm, and converts the path in the exploration path solution into the required linear velocity and angular velocity, and controls the robot to move to the target position.

[0078] The specific method of constructing the balance framework in step S4 is:

[0079] The mobile robot calculates the rate of change of the number of boundary points and free grids in the map before and after an exploration, and constructs an environmental exploration quantification function. If the function value is less than 0, it means that the local area has been fully explored. If the function value is greater than 0, it means that the local area has not been fully explored. The function calculation formula is:

[0080]

[0081] Among them, △(S F ) and △(S M ) is the difference between the number of boundary points and the number of free area grids before and after an exploration, L(σ e ) is the length of the exploration path, represented by the number of exploration path grids, ω k is the balance frame weight factor, when ω k When it is equal to 0, the algorithm degenerates into covering the task area after fully exploring the map.

[0082] The planning method based on the coverage point reward function guidance of step S5 specifically comprises the following steps:

[0083] Step S51: The mobile robot removes the exploration path grids located in the task area and adjacent to obstacles, and the remaining task area free grids are used as the current set of areas to be covered. like Figure 3 As shown;

[0084] Step S52: Use function SetConductor(·) to select The grid with the closest Manhattan distance to the robot position in the middle distance is used as the starting point P of the coverage path s , the next exploration target point is used as the coverage guide point P g ;

[0085] Step S53: Use the function Near(·) to check o k lie in If the grid does not belong to the covered grid set, or obstacle set, then add it to the adjacent grid set N(o k );

[0086] Step S54: If N(o k ) is not empty, traverse the adjacent grid set N(o k ), use the reward function Reward(·) to calculate the reward function value of each grid, and convert o k Add to the covered grid collection, k Gather in the current area to be covered Remove from the list and update k The grid with the largest reward function value is used as the next coverage point, such as Figure 4 As shown, if N(o k ) is empty, the mobile robot uses function A * Plan from the robot's current position to The nearest grid point in mid-Manhattan;

[0087] Step S55: If the current set of areas to be covered is If it is empty, the planning ends, otherwise, return to step S52 to continue;

[0088] The reward function Reward(·) in step S54 is designed, and the reward function is determined by the distance evaluation value R g (o j ), direction evaluation value R s (o j ), boundary evaluation value R b (o j ), the distance evaluation value is the set of adjacent grids to be covered N(o k ) in the evaluation point o j To cover the guide point P g The distance is:

[0089]

[0090] Among them, D(o j ) is o j With P g The Euclidean distance, D min (o k ) is o k All adjacent grids o j With P g Minimum distance, D max (o k ) is o k All adjacent grids o j With P g The maximum value of the distance;

[0091] The direction evaluation value is the evaluation value of the change in the coverage direction of the mobile robot's current position, and the formula is:

[0092]

[0093] Among them, ∠(o k-1 o k o j ) is the previous covering point o k-1 , the current coverage point o k and j The radian value of the angle between them;

[0094] The boundary evaluation value is the number of closed grids adjacent to the point to be covered, and the formula is:

[0095]

[0096] in, For all o j The maximum number of adjacent closed grids in , is the current evaluation point o j The number of adjacent closed grids;

[0097] The reward function formula is:

[0098] R(o j )=R g (o j )+ω s (R s (o j ))+ω b (R b (o j )) (6)

[0099] Among them, ω s is the smoothness weight factor, ω b is the boundary weight factor.

[0100] Example:

[0101] In this embodiment, the complete pseudo code of the algorithm is as follows:

[0102]

[0103]

[0104]

[0105] Among them, Algorithm 1 is the main part of the algorithm, Algorithm 2 is the exploration path planning part, and Algorithm 3 is the coverage path planning part.

[0106] The following is a detailed description of the implementation of the present invention using specific experiments. The present invention proposes a mobile robot motion planning algorithm for unknown target collection tasks. The effectiveness of the mobile robot in performing target collection tasks in an unknown environment is verified mainly through simulation experiments. The specific experimental settings are as follows:

[0107] Simulation experiment:

[0108] The simulation experiments were carried out in MATLAB R2018b software.

[0109] (1) Land Figure 1

[0110] The size of the simulation map is X=50m, Y=50m, all obstacles are static obstacles, and the detection range of the mobile robot is 4m×4m. The coordinates of the starting point are (4, 4). Figure 5 As shown, Figure 1 The white area in the map is the passable area for the mobile robot, the black area is the impassable area for the mobile robot, the cross represents the target to be collected, and the black solid line is the trajectory of the mobile robot.

[0111] (2) Land Figure 2

[0112] The size of the simulation map is X=50m, Y=50m, all obstacles are static obstacles, and the detection range of the mobile robot is 4m×4m. The coordinates of the starting point are (4, 4). Figure 6 As shown, Figure 2 The white area in the map is the passable area for the mobile robot, the black area is the impassable area for the mobile robot, the cross represents the target to be collected, and the black solid line is the trajectory of the mobile robot.

[0113] (3) Land Figure 3

[0114] The size of the simulation map is X=50m, Y=50m, all obstacles are static obstacles, and the detection range of the mobile robot is 4m×4m. The coordinates of the starting point are (4, 4). Figure 7 As shown, Figure 3 The white area in the map is the passable area for the mobile robot, the black area is the impassable area for the mobile robot, the cross represents the target to be collected, and the black solid line is the trajectory of the mobile robot.

[0115] Real experiment:

[0116] The static real experimental environment is Ubuntu16.04, ROS Kinetic, a Bingda mobile robot using a depth camera and a lidar, a radar detection range of 0.6m×0.6m, and an Intel Core i7-6700HQ, Lenovo laptop with 16GB memory. The scene map size is X=Y=2.4m, all obstacles are known static obstacles, the black and white grid area is the task area, and the positioning is assisted by the lidar and the tag. Figure 8 As shown, it is a static real experimental process. The upper picture is a real shot of the experimental process, and the lower picture is the Rviz visualization interface when the algorithm proposed in the present invention plans the path during the experiment. The white solid line represents the trajectory of the mobile robot.

[0117] The above description is only a preferred embodiment of the present invention. For ordinary technicians in this field, according to the teachings of the present invention, designing different forms of motion planning algorithms does not require creative labor. Without departing from the principles and spirit of the present invention, all equal changes, modifications, substitutions and variations made within the scope of the patent application of the present invention should fall within the scope of the present invention.

Claims

1. A mobile robot motion planning method for unknown target collection, characterized by: The steps include: Step S1: The mobile robot constructs a grid map using data obtained by the sensors it carries. The grid has three states: a traversable free grid, an obstacle grid, and an unexplored grid. Step S2: The mobile robot extracts the boundary area and the passable area according to the constructed grid map; Step S3: The mobile robot continuously explores the environment using a boundary-guided planning method; Step S4: The mobile robot uses a balance framework to determine the degree of exploration of the local environment according to the balance function; Step S5: If the local environment is explored, the mobile robot uses a planning method guided by a coverage point reward function to perform a target collection task in the task area. If the local environment is not explored, return to step 2. Step S6: After the mobile robot completes the exploration of the sub-area and the area coverage collection, if there is an unexplored area or the target has not been collected, return to step 2 to continue; Step S7: When all unknown environments have been explored and all mission area targets have been collected, the unknown target collection task is completed.

2. A mobile robot motion planning method for unknown target collection according to claim 1, characterized in that: The specific method for extracting the boundary area in step S2 is: the mobile robot traverses the free and traversable grids in the grid map, and the free grids with at least one adjacent unexplored grid are marked as boundary points, and are added to the boundary set.

3. The method for mobile robot motion planning for unknown target collection according to claim 1, characterized in that: The boundary-guided planning method of step S3 specifically includes the following steps: Step S31: adding the exploration points of the observation environment generated by sampling at a spacing of δ in the boundary set to the candidate exploration point set; Step S32: Calculate the function value of each candidate point according to the information gain function and select the point with the maximum function value as the next exploration target point. The information gain function G(v i )The formula is: Among them, S(W obs (v i )) and S(W unexp (v i )) is v i The number of obstacle boundary grids and unexplored grids within a certain radius r, ω o represents the weight of the number of obstacle boundary units, L(v0,v i ) is the robot's current position v0 to the candidate viewpoint v i Manhattan distance, S(M tar (v i )) is v i The number of task area grids within a certain radius; Step S33: The mobile robot plans a path from the robot's current unknown point to the next exploration target point through the A* algorithm; Step S34: The robot receives the exploration path planned by the algorithm, and converts the path in the exploration path solution into the required linear velocity and angular velocity, and controls the robot to move to the target position.

4. The method for mobile robot motion planning for unknown target collection according to claim 1, characterized in that: The specific method of constructing the balance framework in step S4 is: the mobile robot calculates the rate of change of the number of boundary points and free grids in the map before and after an exploration, and constructs an environmental exploration quantization function. If the function value is less than 0, it means that the local area has been completely explored. If the function value is greater than 0, it means that the local area has not been completely explored. The function calculation formula is: Among them, Δ(S F ) and Δ(S M ) is the difference between the number of boundary points and the number of free area grids before and after an exploration, L(σ e ) is the length of the exploration path, represented by the number of exploration path grids, ω k is the balance frame weight factor, when ω k When it is equal to 0, the algorithm degenerates into covering the task area after fully exploring the map.

5. The method for mobile robot motion planning for unknown target collection according to claim 1, characterized in that: The planning method based on the coverage point reward function guidance of step S5 specifically comprises the following steps: Step S51: The mobile robot removes the exploration path grids located in the task area and adjacent to obstacles, and the remaining task area free grids are used as the current set of areas to be covered. Step S52: Use function SetConductor(·) to select The grid with the closest Manhattan distance to the robot position in the middle distance is used as the starting point P of the coverage path s , the next exploration target point is used as the coverage guide point P g ; Step S53: Use the function Near(·) to check o k lie in If the grid does not belong to the covered grid set, or obstacle set, then add it to the adjacent grid set N(o k ); Step S54: If N(o k ) is not empty, traverse the adjacent grid set N(o k ), use the reward function Reward(·) to calculate the reward function value of each grid, and convert o k Add to covered raster collection o k Gather in the current area to be covered Remove from the list and update k The grid with the largest reward function value is used as the next coverage point. If N(o k ) is empty, the mobile robot uses the function A* to plan from the robot's current position to The nearest grid point in mid-Manhattan; Step S55: If the current set of areas to be covered is If it is empty, the planning ends; otherwise, return to step S52 to continue.

6. The method for mobile robot motion planning for unknown target collection according to claim 5, characterized in that: The reward function Reward(·) in step S54 is designed, and the reward function is determined by the distance evaluation value R g (o j ), direction evaluation value R s (o j ), boundary evaluation value R b (o j ), the distance evaluation value is the set of adjacent grids to be covered N(o k ) in the evaluation point o j To cover the guide point P g The distance is: Among them, D(o j ) is o j With P g The Euclidean distance, D min (o k ) is o k All adjacent grids o j With P g Minimum distance, D max (o k ) is o k All adjacent grids o j With P g The maximum value of the distance; The direction evaluation value is the evaluation value of the change in the coverage direction of the mobile robot's current position, and the formula is: Among them, ∠(o k-1 o k o j ) is the previous covering point o k-1 , the current coverage point o k and j The radian value of the angle between them; The boundary evaluation value is the number of closed grids adjacent to the point to be covered, and the formula is: in, For all o j The maximum number of adjacent closed grids in , is the current evaluation point o j The number of adjacent closed grids; The reward function formula is: R(o j )=R g (o j )+ω s (R s (o j ))+ω b (R b (o j )) (6) Among them, ω s is the smoothness weight factor, ω b is the boundary weight factor.

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