A Robot Movement Path Planning Method Based on Ant Colony Optimization Algorithm

Abstract

This invention discloses a robot movement path planning method based on ant colony optimization algorithm. It includes the following steps: environmental modeling of the robot's movement space using a grid method to obtain a grid map, with grid coordinates representing the robot's starting and ending positions; generating an initial path on the grid map using a jump-point search algorithm, and calculating the non-uniform initial pheromone concentration distribution along the initial path; searching for the optimal path on the grid map using the ant colony optimization algorithm; eliminating redundant nodes on the optimal path and performing smoothing processing to obtain the robot's movement path. This invention improves convergence speed and search efficiency by using a non-uniform distribution of the initial pheromone concentration in the grid map, and shortens the planned path length by eliminating redundant nodes on the optimal path and performing smoothing processing.

Description

Technical Field

[0001] This invention relates to the field of robot path planning technology, and in particular to a robot movement path planning method based on ant colony optimization algorithm. Background Technology

[0002] In the logistics management system, warehouse management occupies a crucial position, and intelligent warehouse robots are one of the core components for realizing smart warehousing. To ensure the safe operation of intelligent warehouse robots in environments with obstacles, it is essential to plan a safe and shortest optimal path from the starting point to the destination under environmental constraints.

[0003] Currently, Ant Colony Optimization (ACO) is commonly used for robot path planning. ACO searches for optimal solutions by simulating ant foraging behavior and offers advantages such as parallel processing, distributed computing, robustness, and positive feedback mechanisms. However, traditional ACO and some of its improvements still suffer from the following drawbacks: slow convergence speed, low search efficiency, redundant nodes in the planned path, and lack of smooth transitions at path corners.

[0004] Chinese Patent Publication No. CN113703450A discloses a mobile robot path planning method based on an improved ant colony algorithm with smoothing factors. This method improves heuristic information, increases search directionality, introduces a new path evaluation function, and performs pheromone differential updates on effective paths. However, this method has the following drawbacks: the initial pheromone concentration in the environmental map is uniformly distributed, resulting in slow convergence and low search efficiency; the planned path contains redundant nodes, and the path corners lack smooth transitions, leading to longer planned paths. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a robot movement path planning method based on ant colony optimization algorithm. The initial pheromone concentration in the grid map is non-uniformly distributed, which improves the convergence speed and search efficiency, eliminates redundant nodes on the optimal path, and performs smoothing processing to shorten the planned path length.

[0006] To solve the above problems, the present invention adopts the following technical solution:

[0007] The present invention provides a robot movement path planning method based on ant colony optimization algorithm, comprising the following steps:

[0008] S1: The robot's movement space is modeled using the grid method to obtain a grid map, and the robot's starting position and ending position are represented by grid coordinates;

[0009] S2: Use the jump point search algorithm to generate an initial path on the grid map, and calculate the non-uniform initial pheromone concentration distribution of the grid map along the initial path;

[0010] S3: Use the ant colony optimization algorithm to search for the optimal path on the grid map;

[0011] S4: Eliminate redundant nodes on the optimal path and perform smoothing to obtain the robot's movement path.

[0012] Preferably, step S2 includes the following steps:

[0013] S21: Use the jump point search algorithm to generate an initial path from the starting point to the ending point on the grid map;

[0014] S22: Define the area covered by the free grid traversed by the initial path as... Layer region;

[0015] S23: Along The layers expand outwards sequentially, resulting in Layer region;

[0016] Layer region is The region covered by the free grid adjacent to the outside of the layer region, 1≤r≤L, where L is a positive integer greater than 1;

[0017] S24: Define the area covered by the remaining free grid cells in the raster map as... For each layer region, calculate the initial pheromone concentration distribution of the free grid cells.

[0018] The free grid adjacent to the outer side of the layer region includes... Free grids adjacent to the outer edge and diagonally adjacent free grids in the layer region.

[0019] As a preferred option, along The layer region expands outward to obtain The layer region method includes the following steps:

[0020] Will All free grid cells within a layer region constitute a grid set. , raster set Each grid cell is expanded to its surrounding adjacent grid cells to obtain a mixed grid set. Remove blended raster sets The middle belongs to the raster set The free grid is used to obtain the grid set. raster set The area covered is Layer region, ;

[0021] along The layer region expands outward to obtain The layer region method includes the following steps, 1≤h≤L-1:

[0022] Will All free grid cells within a layer region constitute a grid set. , raster set Each grid cell is expanded to its surrounding adjacent grid cells to obtain a mixed grid set. Remove blended raster sets The middle belongs to the raster set , The free grid is used to obtain the grid set. raster set The area covered is Layer region, .

[0023] As a preferred option, calculation The method for initial pheromone concentration distribution of free grids in a layer region includes the following steps:

[0024] M1: Calculation The initial pheromone concentration of the path between adjacent free grids in the layer region;

[0025] The free grids traversed by the initial path are numbered sequentially from front to back as 1, 2, ..., m. The initial pheromone concentration of the path between free grid i and its adjacent free grid j is calculated using the following formula: 1 ≤ i ≤ m-1, j = i + 1:

[0026] ,

[0027] in, Let be the initial pheromone concentration for the path from free grid i to free grid j. Let be the initial pheromone concentration for the path from free grid j to free grid i. The Euclidean distance is the distance between the free grid cells at the starting and ending positions of the initial path. Let be the Euclidean distance between the starting free grid and free grid i. Let i be the Euclidean distance between free grid i and free grid j. Let be the Euclidean distance between free grid j and the free grid at the endpoint, where a is a constant;

[0028] M2: Calculation The base value of pheromone concentration corresponding to each free grid cell in the layer region;

[0029] The base value of pheromone concentration corresponding to free grid k in the layer region The calculation formula is as follows:

[0030] ,

[0031] in, The pheromone diffusion coefficient is... ;

[0032] Will Free grid in layer region and adjacent grid located in The initial pheromone concentration of the path between free grids in the layer region is assigned the base value of the pheromone concentration corresponding to that free grid.

[0033] As a preferred option, calculation The method for initial pheromone concentration distribution of free grids in a layer region includes the following steps:

[0034] Calculate The base value of pheromone concentration corresponding to each free grid cell in the layer region;

[0035] The base value of pheromone concentration corresponding to the free grid f in the layer region The calculation formula is as follows:

[0036] ,

[0037] Where 1≤f≤n, n is The number of free grid cells in the layer region, For a free grid f to the p-th neighbor located at The initial pheromone concentration of the path of the free grid in the layer region, 1≤p≤e, where e is the pheromone concentration of the path adjacent to the free grid f. The number of free grid cells in the layer region;

[0038] Will The initial pheromone concentration of the path between adjacent free grids in the layer region is assigned to the maximum value among the base values ​​of the pheromone concentration of the two adjacent free grids;

[0039] Will Free grid in layer region and adjacent grid located in The initial pheromone concentration of the path between free grids in the layer region is assigned the base value of the pheromone concentration corresponding to that free grid.

[0040] As a preferred option, calculation The method for initial pheromone concentration distribution of free grids in a layer region includes the following steps:

[0041] Calculate Base value of pheromone concentration corresponding to the layer region The calculation formula is as follows:

[0042] ,

[0043] in, for The base value of pheromone concentration corresponding to the free grid g in the layer region, 1≤g≤w, where w is... Number of free grid cells in the layer region;

[0044] Will The initial pheromone concentration of the path between adjacent free grid cells in the layer region is assigned the base pheromone concentration value. .

[0045] Preferably, step S4 includes the following steps:

[0046] S41: Find all the corner nodes on the optimal path;

[0047] S42: Analyze each corner node sequentially along the optimal path to determine if it is a redundant node;

[0048] If the corner node being analyzed is a redundant node, then remove the redundant node, connect the two adjacent nodes of the redundant node with a straight line, update the corner node on the optimal path, and jump to step S41.

[0049] If none of the corner nodes are redundant, proceed to step S43;

[0050] S43: Find all straight sub-paths on the optimal path, connect the starting node and the ending node of the straight sub-path with a straight line, and remove other nodes in the straight sub-path except for the starting node and the ending node.

[0051] S44: Smooth the corner positions in the optimal path to obtain the robot's movement path.

[0052] As a preferred method, the method for analyzing whether a corner node is a redundant node includes the following steps:

[0053] N1: Determine the two adjacent nodes of the corner node, and determine the reference line based on the grid coordinates of the free grid corresponding to these two adjacent nodes. The grid coordinates are the coordinates of the center point of the free grid.

[0054] N2: Find the smallest rectangular area formed diagonally by these two adjacent nodes on the grid map. Calculate the perpendicular distance from the center point of each obstacle grid cell within this smallest rectangular area to the baseline line. If all calculated perpendicular distances are greater than the threshold D, the corner node is a redundant node; otherwise, the corner node is not a redundant node. Threshold b is the grid side length.

[0055] Preferably, the smoothing of the corner positions in the optimal path is performed using a second-order Bézier curve algorithm.

[0056] Preferably, the method of using a grid method to model the robot's movement space and obtain a grid map includes the following steps:

[0057] The robot's movement space is projected onto a two-dimensional plane. The obstacle projection is extended outward by a set distance F along the obstacle boundary. The set distance F is greater than the radius of the robot's circumcircle. The two-dimensional plane is discretized into uniform, continuous and non-overlapping square grids. Grids with obstacle projections are marked as obstacle grids, and grids without obstacle projections are marked as free grids, thus obtaining a grid map.

[0058] The beneficial effects of this invention are: (1) It uses the Jump Point Search (JPS) algorithm to quickly generate an initial path and distributes the initial pheromone concentration in a layered manner around the path, so that the initial pheromone concentration in the grid map is non-uniformly distributed, which speeds up the convergence speed and enhances the global search capability. (2) It optimizes the generated optimal path, eliminates redundant nodes, and uses the second-order Bézier curve algorithm to smooth the corner positions, thereby further improving the simplicity and smoothness of the path and improving the operational stability and overall efficiency of the robot navigation process. Attached Figure Description

[0059] Figure 1 This is a flowchart of an embodiment;

[0060] Figure 2 This is a schematic diagram of a two-dimensional environment after obstacles in the mobile space are projected onto a two-dimensional plane in an embodiment.

[0061] Figure 3 yes Figure 2 The corresponding raster map;

[0062] Figure 4 This is a schematic diagram illustrating the calculation of non-uniform initial pheromone concentration in a raster map according to an embodiment;

[0063] Figure 5 This is a schematic diagram illustrating the removal of redundant nodes on the optimal path in an embodiment.

[0064] Figure 6 This is a schematic diagram illustrating the removal of nodes other than the start and end nodes from a straight sub-path according to an embodiment.

[0065] Figure 7 This is a schematic diagram illustrating the smoothing of corner positions in the optimal path in an embodiment.

[0066] Figure 8 This is a comparison chart of the optimal paths of different algorithms in Experiment 1;

[0067] Figure 9 This is a comparison of the convergence curves of different algorithms in Experiment 1;

[0068] Figure 10 This is a comparison chart of the optimal paths of different algorithms in Experiment 2;

[0069] Figure 11 This is a comparison of the convergence curves of different algorithms in Experiment 2. Detailed Implementation

[0070] The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

[0071] Example: This example illustrates a robot movement path planning method based on ant colony optimization algorithm, such as... Figure 1 As shown, it includes the following steps:

[0072] S1: The robot's movement space is modeled using the grid method to obtain a grid map. The starting and ending positions of the robot are represented by grid coordinates.

[0073] The method of using the grid method to model the robot's movement space and obtain a grid map includes the following steps:

[0074] The robot's movement space is projected onto a two-dimensional plane. The obstacle projection is extended outward by a set distance F along the obstacle boundary. The set distance F is greater than the radius of the robot's circumcircle. The two-dimensional plane is discretized into uniform, continuous, and non-overlapping square grids. The grid side length is the maximum value of the robot's length and width. Grids with obstacle projections are marked as obstacle grids, and grids without obstacle projections are marked as free grids, thus obtaining a grid map.

[0075] Compared to open road environments, factory and warehouse environments have denser item layouts and more complex potential risk characteristics. To ensure that the robot can perform its work safely and stably, this embodiment extends the obstacle projection outward a certain distance along the obstacle boundary to construct new obstacle boundary constraints, preventing the robot from colliding with obstacles and improving driving safety.

[0076] In a two-dimensional grid map, free grids are represented by 0, and obstacle grids by 1. This embodiment uses a combination of Cartesian coordinates and a numbering system to define grid positions; each grid has a unique number and a set of (x, y) coordinates. In the Cartesian coordinate system, the grid coordinates of each grid are the coordinates of its center point (x, y); in the numbering system, grids are numbered sequentially from left to right and top to bottom, starting from 1 and incrementing. For example, the robot's movement space projected onto a two-dimensional plane is as follows: Figure 2 As shown, the gray area represents the obstacle projection; by extending the obstacle projection outwards along the obstacle boundary by a certain distance and discretizing the two-dimensional plane into a square grid, we obtain... Figure 3 , Figure 3 The grid positions are defined using a combination of Cartesian coordinates and a numbering method. Figure 3 The medium gray grid represents the grid mapped from the initial obstacle projection, the blue grid represents the grid mapped from the extended portion of the initial obstacle projection, and the white grid represents the free grid.

[0077] S2: Use the jump point search algorithm to generate an initial path on the raster map, and calculate the non-uniform initial pheromone concentration distribution of the raster map along the initial path.

[0078] Jump Point Search (JPS) is an efficient heuristic search algorithm for path planning on grid maps. It quickly locates key nodes, or jump points, in the path by performing jump-like searches from the current node along the horizontal, vertical, and diagonal directions, thus significantly improving search efficiency. This process is continuously iterated until the target node is reached.

[0079] Step S2 includes the following steps:

[0080] S21: Use the jump point search algorithm to generate an initial path from the starting point to the ending point on the grid map;

[0081] S22: Define the area covered by the free grid traversed by the initial path as... Layer region;

[0082] S23: Along The layers expand outwards sequentially, resulting in Layer region;

[0083] Layer region is The region covered by the free grid adjacent to the outside of the layer region, 1≤r≤L, where L is a positive integer greater than 1;

[0084] S24: Define the area covered by the remaining free grid cells in the raster map as... For each layer region, calculate the initial pheromone concentration distribution of the free grid cells.

[0085] The free grid adjacent to the outer side of the layer region includes... Free grids adjacent to the outer edge and diagonally adjacent free grids in the layer region.

[0086] Each free grid can have a maximum of 8 adjacent free grids. A free grid in a layer region whose surrounding free grids do not belong to The free grid of a layer is the free grid adjacent to the outside of that free grid; A free grid in a layer region whose surrounding free grids do not belong to layer, The free grid of a layer is the free grid adjacent to the outside of that free grid.

[0087] along The layer region expands outward to obtain The layer region method includes the following steps:

[0088] Will All free grid cells within a layer region constitute a grid set. , raster set Each grid cell is expanded to its surrounding adjacent grid cells to obtain a mixed grid set. Remove blended raster sets The middle belongs to the raster set The free grid is used to obtain the grid set. raster set The area covered is Layer region, ;

[0089] along The layer region expands outward to obtain The layer region method includes the following steps, 1≤h≤L-1:

[0090] Will All free grid cells within a layer region constitute a grid set. , raster set Each grid cell is expanded to its surrounding adjacent grid cells to obtain a mixed grid set. Remove blended raster sets The middle belongs to the raster set , The free grid is used to obtain the grid set. raster set The area covered is Layer region, .

[0091] calculate The method for initial pheromone concentration distribution of free grids in a layer region includes the following steps:

[0092] M1: Calculation The initial pheromone concentration of the path between adjacent free grids in the layer region;

[0093] The free grids traversed by the initial path are numbered sequentially from front to back as 1, 2, ..., m. The initial pheromone concentration of the path between free grid i and its adjacent free grid j is calculated using the following formula: 1 ≤ i ≤ m-1, j = i + 1:

[0094] ,

[0095] in, Let be the initial pheromone concentration for the path from free grid i to free grid j. Let be the initial pheromone concentration for the path from free grid j to free grid i. The Euclidean distance is the distance between the free grid cells at the starting and ending positions of the initial path. Let be the Euclidean distance between the starting free grid and free grid i. Let i be the Euclidean distance between free grid i and free grid j. Let be the Euclidean distance between free grid j and the free grid at the endpoint, where a is a constant;

[0096] M2: Calculation The base value of pheromone concentration corresponding to each free grid cell in the layer region;

[0097] The base value of pheromone concentration corresponding to free grid k in the layer region The calculation formula is as follows:

[0098] ,

[0099] in, The pheromone diffusion coefficient is... ;

[0100] Will Free grid in layer region and adjacent grid located in The initial pheromone concentration of the path between free grids in the layer region is assigned the base value of the pheromone concentration corresponding to that free grid.

[0101] For example: The base value of the pheromone concentration corresponding to the free grid k in the layer region is A free grid k has 8 adjacent free grids, one of which is located in... The layer area, the other 7 free grids are located in In the layer region, the free grid k and these 7 located in The initial pheromone concentration of the path between adjacent free grids in the layer region is .

[0102] calculate The method for initial pheromone concentration distribution of free grids in a layer region includes the following steps:

[0103] Calculate The base value of pheromone concentration corresponding to each free grid cell in the layer region;

[0104] The base value of pheromone concentration corresponding to the free grid f in the layer region The calculation formula is as follows:

[0105] ,

[0106] Where 1≤f≤n, n is The number of free grid cells in the layer region, For a free grid f to the p-th neighbor located at The initial pheromone concentration of the path of the free grid in the layer region, 1≤p≤e, where e is the pheromone concentration of the path adjacent to the free grid f. The number of free grid cells in the layer region;

[0107] Will The initial pheromone concentration of the path between adjacent free grids in the layer region is assigned to the maximum value among the base values ​​of the pheromone concentration of the two adjacent free grids;

[0108] Will Free grid in layer region and adjacent grid located in The initial pheromone concentration of the path between free grids in the layer region is assigned the base value of the pheromone concentration corresponding to that free grid.

[0109] For example: There are 8 adjacent free grids around free grid f in the layer region, of which 2 free grids are located in Layer area, 5 free grids are located Layer region (one of which is denoted as free grid z), one free grid is located in Layer region, The two free grids in the layer region are numbered 1 and 2 respectively; then the base value of the pheromone concentration corresponding to the free grid f is... , Let f be the initial pheromone concentration for the path from free grid f to free grid number 1. The initial pheromone concentration for the path from free grid f to free grid number 2;

[0110] The initial pheromone concentration of the path between free grid f and free grid z is the maximum value among the base values ​​of the pheromone concentration corresponding to free grid f and free grid z;

[0111] Free grid f and located at The initial pheromone concentration of the path between adjacent free grids in the layer region is .

[0112] calculate The method for initial pheromone concentration distribution of free grids in a layer region includes the following steps:

[0113] Calculate Base value of pheromone concentration corresponding to the layer region The calculation formula is as follows:

[0114] ,

[0115] in, for The base value of pheromone concentration corresponding to the free grid g in the layer region, 1≤g≤w, where w is... The number of free grid cells in the layer region, The free grid cells in the layer region are numbered 1, 2, ..., w respectively;

[0116] Will The initial pheromone concentration of the path between adjacent free grid cells in the layer region is assigned the base pheromone concentration value. .

[0117] For example: Figure 4 The image shows a raster map corresponding to a certain environmental space. Gray graticles represent obstacle graticles, and the remaining graticles are free graticles. The path formed by the five red graticles is the initial path generated by the jump point search algorithm, where L=2. The raster map is layered, with the red graticles forming... Layered area, composed of purple grid Layered areas, composed of dark green grids Layered areas, composed of white grids In the layer region, the dark blue arrows indicate the initial pheromone concentration calculation for paths between adjacent free grid cells on the initial path, and the light blue arrows indicate... Free grid in layer region and adjacent grid located in The initial pheromone concentration is calculated for the paths between free grid cells in the layer region; the green arrows indicate this. The initial pheromone concentration distribution of the free grid in the layer region is calculated, indicated by the brown arrow. The initial pheromone concentration distribution of the free grid in the layer region is calculated, and the pink arrow indicates... Calculation of the initial pheromone concentration distribution of the free grid in the layer region. Assume... Free grid A1 in the layer region and If free grid B1 is adjacent in the layer region, then the path between free grid A1 and free grid B1 includes the path from free grid A1 to free grid B1 and the path from free grid B1 to free grid A1.

[0118] This method first uses a jump point search algorithm to quickly generate an initial path, and then distributes the initial pheromone concentration in a layered manner around the initial path, so that the pheromone in the environment map presents a non-uniform distribution. This effectively guides the ant colony to converge to the optimal solution faster and more accurately, speeds up the convergence speed of the algorithm, and also enhances the global search capability.

[0119] S3: Use the ant colony optimization algorithm to search for the optimal path on the grid map.

[0120] Ant Colony Optimization (ACO) solves optimization problems by simulating the foraging behavior of real ant colonies. In ACO, the heuristic value of each grid cell is calculated by a heuristic function and remains constant throughout the search process. However, to accelerate the convergence speed of the algorithm, it is desirable for the heuristic value to be larger in the early stages of iteration and gradually decrease as the iteration progresses. The heuristic function in this embodiment is:

[0121] ,

[0122] in, For the heuristic information from free grid i to free grid j, Scaling factor The maximum number of iterations, This represents the current iteration number. Let be the Euclidean distance from free grid i to the endpoint free grid.

[0123] After all ants complete one iteration, the pheromones on the original path will evaporate in a certain proportion, while the ants release new pheromones along the paths they have traversed. After multiple iterations, the path with the highest concentration of pheromones gradually forms, resulting in the optimal path. The calculation formula for the pheromone update rule in this embodiment is as follows:

[0124] ,

[0125] ,

[0126] ,

[0127] Where Q is the total pheromone constant, The term "volatile" indicates the decay of the original pheromone. Add a term to the pheromone term, representing the new pheromones released by the ant along its walking path during the current iteration. Indicates a reward or punishment item. This represents the reward or penalty value from grid i to grid j in the current iteration loop. The length of the optimal path in the current iteration. The length of the worst path in the current iteration. For adaptive pheromone evaporation coefficient, The adjustment coefficient ranges from 0 to 1.

[0128] Search efficiency is improved by adding extra pheromones on the optimal path to enhance its guiding effect, or by reducing pheromones on the worst path to weaken its misleading influence on subsequent iterations. In the early stages of the algorithm, due to... Larger The pheromone value is small, the difference in pheromone along each path is not significant, and the ant colony has a strong global search capability; as the iteration continues, Gradually getting smaller, As the value of pheromones gradually increases, the difference in pheromones between different paths gradually widens, thereby guiding more ants to choose the optimal path and enabling the algorithm to achieve a faster convergence speed in the later stages.

[0129] S4: Eliminate redundant nodes on the optimal path and perform smoothing to obtain the robot's movement path.

[0130] Step S4 includes the following steps:

[0131] S41: Find all the corner nodes on the optimal path;

[0132] S42: Analyze each corner node sequentially along the optimal path to determine if it is a redundant node;

[0133] If the corner node being analyzed is a redundant node, then remove the redundant node, connect the two adjacent nodes of the redundant node with a straight line, update the corner node on the optimal path, and jump to step S41.

[0134] If none of the corner nodes are redundant, proceed to step S43;

[0135] S43: Find all straight sub-paths on the optimal path, connect the starting node and the ending node of the straight sub-path with a straight line, and remove other nodes in the straight sub-path except for the starting node and the ending node.

[0136] S44: Smooth the corner positions in the optimal path to obtain the robot's movement path.

[0137] The method for analyzing whether a corner node is a redundant node includes the following steps:

[0138] N1: Determine the two adjacent nodes of the corner node, and determine the reference line based on the grid coordinates of the free grid corresponding to these two adjacent nodes. The grid coordinates are the coordinates of the center point of the free grid.

[0139] N2: Find the smallest rectangular area formed diagonally by these two adjacent nodes on the grid map. Calculate the perpendicular distance from the center point of each obstacle grid cell within the smallest rectangular area to the reference line. If all calculated perpendicular distances are greater than the threshold D, then the corner node is a redundant node. b is the grid side length; otherwise, the corner node is not a redundant node.

[0140] For example: Figure 5 As shown, Figure 5 In the grid map of (a), S-1-2-3-E represents the optimal path searched on the grid map using the ant colony optimization algorithm. S represents the starting point of the optimal path, E represents the ending point of the optimal path, and 1, 2, and 3 represent intermediate nodes of the optimal path. Gray grids are obstacle grids, and white grids are free grids. Node 2 is a corner node, and nodes 1 and 3 are adjacent nodes of node 2. The equation of the baseline line is determined based on the grid coordinates of the free grids corresponding to these two adjacent nodes. A, B, and C are parameters, and the smallest rectangular area on the raster map containing these two adjacent nodes is... rectangular area Given a grid containing only one obstacle, calculate the perpendicular distance from the center point of that obstacle grid to the reference line. ,because Therefore, node 2 is a redundant node. Remove node 2 and connect nodes 1 and 3 with a straight line to obtain... Figure 5 The path S-1-3-E is shown in (b). At this point, node 1 becomes a corner node, and nodes S and 3 are adjacent nodes of node 1. Repeating the above steps, we find that node 1 is a redundant node. Therefore, we remove node 1 and connect nodes S and 3 with a straight line to obtain... Figure 5 In the path S-3-E shown in (c), only node 3 is a corner node. Repeating the above steps, we can see that node 3 is not a redundant node.

[0141] For example: Figure 6 As shown, Figure 6In the raster map of (a), S-1-2-3-4-5-6-7-8-E is the optimal path after removing redundant nodes. The straight sub-paths include S-1-2-3, 3-4-5-6, and 6-7-8-E. Connecting the start and end nodes of each straight sub-path with a straight line and removing all nodes except the start and end nodes yields... Figure 6 The path S-3-6-E is shown in (b).

[0142] While path optimization can be achieved to some extent by handling redundant nodes, the optimized path often fails to meet the robot's kinematic characteristics, resulting in discontinuous trajectories that affect ride smoothness. Therefore, it is necessary to perform smoothing optimization on the optimal path to obtain the robot's movement path. A second-order Bézier curve algorithm is used to smooth the corner positions in the optimal path.

[0143] For example: Figure 7 As shown, Figure 7 In the raster map of (a), S-1-2-E is the optimal path, where nodes 1 and 2 are corner nodes. A second-order Bézier curve algorithm is used to smooth the path, and node 1 is regarded as an intermediate control point. Starting points were selected near both sides of node 1. and the end point Constructing Bézier curves Node 2 is considered as an intermediate control point. Starting points were selected near both sides of node 2. and the end point Constructing Bézier curves Thus generating Figure 7 The smooth path curve shown in (b) is shown in the middle.

[0144] This invention optimizes the generated optimal path, eliminates redundant nodes, and uses a second-order Bézier curve algorithm to smooth the corner positions, thereby further improving the simplicity and smoothness of the path and enhancing the operational stability and overall efficiency of the robot navigation process.

[0145] Verification Experiment 1:

[0146] To verify the effectiveness of the method of this invention, the method of this embodiment (JPS-EACO) was simulated in a 20×20 grid environment model, and compared with existing ant colony optimization algorithms (ACO), jump point search algorithms (JPS), improved ant colony optimization algorithms (IACO), and improved ant colony optimization algorithms based on directional information heuristics (MAACO). The initialization parameters used in the simulation experiment are as follows: the number of ants M is 50, and the maximum number of iterations is... The total pheromone constant Q is 100, and the pheromone factor is 100. The heuristic factor is 1.1. The adaptive pheromone evaporation coefficient is 7. The pheromone diffusion coefficient is 0.3. The scaling factor is 0.5. The adjustment factor is 80. The value is 0.6. The robot's starting point is located at the top left corner of the grid map, and the ending point is located at the bottom right corner of the grid map.

[0147] The robot movement paths generated by the methods (JPS-EACO), ACO algorithm, JPS algorithm, IACO algorithm, and MAACO algorithm in this embodiment are as follows: Figure 8 As shown; the convergence curves of the method (JPS-EACO), ACO algorithm, IACO algorithm, and MAACO algorithm in this embodiment are as follows: Figure 9 As shown in Table 1, the relevant statistical results of the five algorithms are as follows:

[0148] Table 1

[0149]

[0150] from Figure 8 It can be seen that all algorithms can find the optimal path from the starting point to the ending point. Among them, only the method in this embodiment (JPS-EACO) generates a path that performs Bézier curve smoothing on the corners after removing redundant nodes, while the paths of other algorithms are polygonal corners. Figure 9 As can be seen, the method in this embodiment (JPS-EACO) has the fastest convergence speed, finding the optimal path in the second iteration, and the path length is also significantly shorter than other algorithms. Table 1 shows that the optimal path length obtained by the method in this embodiment (JPS-EACO) is 29.35596, which is 5.21% shorter than the optimal path length generated by other algorithms (30.97056). The method in this embodiment (JPS-EACO) has the fewest average iterations among all algorithms, at only 1.9, with a standard deviation of 0.538516, indicating that the method in this embodiment not only has a fast convergence speed but also high stability.

[0151] Verification Experiment 2:

[0152] To verify the effectiveness of the method of this invention, the method of this embodiment (JPS-EACO) was simulated in a 30×30 grid environment model, and compared with existing ant colony optimization algorithms (ACO), jump point search algorithms (JPS), improved ant colony optimization algorithms (IACO), and improved ant colony optimization algorithms based on direction information heuristics (MAACO). The initialization parameters used in the simulation experiment were the same as those in verification experiment 1. The robot's starting point was located at the lower left corner of the grid map, and the ending point was located at the upper right corner of the grid map.

[0153] The robot movement paths generated by the methods (JPS-EACO), ACO algorithm, JPS algorithm, IACO algorithm, and MAACO algorithm in this embodiment are as follows: Figure 10 As shown; the convergence curves of the method (JPS-EACO), ACO algorithm, IACO algorithm, and MAACO algorithm in this embodiment are as follows: Figure 11 As shown in Table 2, the relevant statistical results of the five algorithms are as follows:

[0154] Table 2

[0155]

[0156] from Figure 10 It can be seen that the ACO algorithm is prone to getting trapped in local optima, thus making it difficult to find the globally optimal path. In contrast, the JPS, IACO, and CMEACO algorithms can still find the globally optimal path relatively well. Furthermore, the method in this embodiment (JPS-EACO) not only finds the globally optimal path but also effectively removes redundant nodes and smooths corners. Figure 11 As shown in Table 2, the method in this embodiment (JPS-EACO) has the fastest convergence speed, with an average of only 8.2 iterations and a standard deviation of 1.54095. It not only converges quickly but also has good stability. The optimal path length of the ACO algorithm is 45.36, while the optimal path lengths of the JPS, IACO, and CMEACO algorithms are all 44.53. However, the optimal path length of the method in this embodiment (JPS-EACO) is 42.91, which is 3.64% shorter than the latter three. This indicates that its redundant node removal and corner smoothing strategies can effectively optimize the path length.

[0157] The comparison results of verification experiments 1 and 2 show that, compared with other existing methods, the method of the present invention not only has a faster convergence speed, but also can effectively shorten the optimal path length and improve the smoothness of the path.

Claims

1. A robot movement path planning method based on ant colony optimization algorithm, characterized in that, Includes the following steps: S1: The robot's movement space is modeled using the grid method to obtain a grid map, and the robot's starting position and ending position are represented by grid coordinates; S2: Use the jump point search algorithm to generate an initial path on the grid map, and calculate the non-uniform initial pheromone concentration distribution of the grid map along the initial path; S3: Use the ant colony optimization algorithm to search for the optimal path on the grid map; S4: Eliminate redundant nodes on the optimal path and perform smoothing to obtain the robot's movement path; Step S2 includes the following steps: S21: Use the jump point search algorithm to generate an initial path from the starting point to the ending point on the grid map; S22: Define the area covered by the free grid traversed by the initial path as... Layer region; S23: Along The layers expand outwards sequentially, resulting in Layer region; Layer region is The region covered by the free grid adjacent to the outside of the layer region, 1≤r≤L, where L is a positive integer greater than 1; S24: Define the area covered by the remaining free grid cells in the raster map as... For each layer region, calculate the initial pheromone concentration distribution of the free grid cells. along The layer region expands outward to obtain The layer region method includes the following steps: Will All free grid cells within a layer region constitute a grid set. raster set Each grid cell is expanded to its surrounding adjacent grid cells to obtain a mixed grid set. Remove blended raster sets The middle belongs to the raster set The free grid is used to obtain the grid set. raster set The area covered is Layer region, ; along The layer region expands outward to obtain The layer region method includes the following steps, 1≤h≤L-1: Will All free grid cells within a layer region constitute a grid set. raster set Each grid cell is expanded to its surrounding adjacent grid cells to obtain a mixed grid set. Remove blended raster sets The middle belongs to the raster set , The free grid is used to obtain the grid set. raster set The area covered is Layer region, .

2. The robot movement path planning method based on ant colony optimization algorithm according to claim 1, characterized in that, calculate The method for initial pheromone concentration distribution of free grids in a layer region includes the following steps: M1: Calculation The initial pheromone concentration of the path between adjacent free grids in the layer region; The free grids traversed by the initial path are numbered sequentially from front to back as 1, 2, ..., m. The initial pheromone concentration of the path between free grid i and its adjacent free grid j is calculated using the following formula: 1 ≤ i ≤ m-1, j = i + 1: ， in, Let be the initial pheromone concentration for the path from free grid i to free grid j. Let be the initial pheromone concentration for the path from free grid j to free grid i. The Euclidean distance is the distance between the free grid cells at the starting and ending positions of the initial path. Let be the Euclidean distance between the starting free grid and free grid i. Let i be the Euclidean distance between free grid i and free grid j. Let be the Euclidean distance between free grid j and the free grid at the endpoint, where a is a constant; M2: Calculation The base value of pheromone concentration corresponding to each free grid cell in the layer region; The base value of pheromone concentration corresponding to free grid k in the layer region The calculation formula is as follows: ， in, The pheromone diffusion coefficient is... ; Will Free grid in layer region and adjacent grid located in The initial pheromone concentration of the path between free grids in the layer region is assigned the base value of the pheromone concentration corresponding to that free grid.

3. The robot movement path planning method based on ant colony optimization algorithm according to claim 2, characterized in that, calculate The method for initial pheromone concentration distribution of free grids in a layer region includes the following steps: Calculate The base value of pheromone concentration corresponding to each free grid cell in the layer region; The base value of pheromone concentration corresponding to the free grid f in the layer region The calculation formula is as follows: ， Where 1≤f≤n, and n is The number of free grid cells in the layer region, For a free grid f to the p-th neighbor located at The initial pheromone concentration of the path of the free grid in the layer region, 1≤p≤e, where e is the pheromone concentration of the path adjacent to the free grid f. The number of free grid cells in the layer region; Will The initial pheromone concentration of the path between adjacent free grids in the layer region is assigned to the maximum value among the base values ​​of the pheromone concentration of the two adjacent free grids; Will Free grid in layer region and adjacent grid located in The initial pheromone concentration of the path between free grids in the layer region is assigned the base value of the pheromone concentration corresponding to that free grid.

4. The robot movement path planning method based on ant colony optimization algorithm according to claim 3, characterized in that, calculate The method for initial pheromone concentration distribution of free grids in a layer region includes the following steps: Calculate Base value of pheromone concentration corresponding to the layer region The calculation formula is as follows: ， in, for The base value of pheromone concentration corresponding to the free grid g in the layer region, 1≤g≤w, where w is... Number of free grid cells in the layer region; Will The initial pheromone concentration of the path between adjacent free grid cells in the layer region is assigned the base pheromone concentration value. .

5. The robot movement path planning method based on ant colony optimization algorithm according to claim 1, characterized in that, Step S4 includes the following steps: S41: Find all the corner nodes on the optimal path; S42: Analyze each corner node sequentially along the optimal path to determine if it is a redundant node; If the corner node being analyzed is a redundant node, then remove the redundant node, connect the two adjacent nodes of the redundant node with a straight line, update the corner node on the optimal path, and jump to step S41. If none of the corner nodes are redundant, proceed to step S43; S43: Find all straight sub-paths on the optimal path, connect the starting node and the ending node of the straight sub-path with a straight line, and remove other nodes in the straight sub-path except for the starting node and the ending node. S44: Smooth the corner positions in the optimal path to obtain the robot's movement path.

6. The robot movement path planning method based on ant colony optimization algorithm according to claim 5, characterized in that, The method for analyzing whether a corner node is a redundant node includes the following steps: N1: Determine the two adjacent nodes of the corner node, and determine the reference line based on the grid coordinates of the free grid corresponding to these two adjacent nodes. The grid coordinates are the coordinates of the center point of the free grid. N2: Find the smallest rectangular area formed by the two adjacent nodes as diagonals on the grid map. Calculate the vertical distance from the center point of each obstacle grid in the smallest rectangular area to the reference line. If all the calculated vertical distances are greater than the threshold D, the corner node is a redundant node; otherwise, the corner node is not a redundant node.

7. The robot movement path planning method based on ant colony optimization algorithm according to claim 5, characterized in that, The smoothing of the corner positions in the optimal path is performed using a second-order Bézier curve algorithm.

8. The robot movement path planning method based on ant colony optimization algorithm according to claim 1, characterized in that, The method of using the grid method to model the robot's movement space and obtain a grid map includes the following steps: The robot's movement space is projected onto a two-dimensional plane. The obstacle projection is extended outward by a set distance F along the obstacle boundary. The set distance F is greater than the radius of the robot's circumcircle. The two-dimensional plane is discretized into uniform, continuous and non-overlapping square grids. Grids with obstacle projections are marked as obstacle grids, and grids without obstacle projections are marked as free grids, thus obtaining a grid map.

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