A global path planning method for mobile robots adaptive to different grid map complexities

Abstract

The application discloses a kind of global path planning methods of mobile robot suitable for different grid map complexity, improve the adaptive ant colony optimization algorithm based on grid map complexity, first, a kind of grid map complexity quantification method based on obstacle number and distribution and map information entropy is proposed;Second, an adaptive initial pheromone distribution strategy based on grid map complexity is designed;Third, the state transition probability is optimized;Fourth, a kind of pheromone dynamic updating mechanism based on grid map complexity is proposed.The application shows good adaptive adjustment ability and efficiency in different complexity grid map.

Description

Technical Field

[0001] This invention belongs to the field of mobile robot technology, specifically relating to a global path planning method for mobile robots that adapts to different grid map complexities. Background Technology

[0002] Global path planning, as a core module of mobile robot decision-making and planning systems, plays a crucial role in improving their operational efficiency, practicality, and reliability. The effectiveness of global path planning is influenced by several key factors, primarily environment representation, environment modeling, and path planning algorithms. These factors interact in complex ways, significantly impacting the performance and applicability of global path planning. The choice of environment representation method directly affects modeling accuracy and computational efficiency, while in the field of global path planning, the selection of the algorithm is paramount, directly influencing the mobile robot's autonomous navigation efficiency, path optimization, resource utilization, and adaptability in complex environments. Efficient path planning algorithms enable robots to achieve optimal path planning under multi-objective and multi-constraint conditions, while maintaining good robustness and real-time performance.

[0003] The current technical solution for global path planning of mobile robots using ant colony optimization is suitable for path planning of mobile robots in static environments. It mainly includes: 1. System architecture environment modeling: Acquiring environmental information through sensors to construct a real-time dynamic grid map. Each grid in the map represents a state, with obstacle grids and free grids marked. Ant colony initialization: Initializing the ant colony, each ant randomly selects a starting point, and initializing the pheromone matrix and heuristic information matrix to preset values. 2. Path search process: Path selection: Ants choose their next moving position based on state transition probabilities, determined by the state transition probability formula. Path construction: While selecting a path, ants record the nodes they pass through and calculate the path cost, including path length, energy consumption, and the number of dangerous areas traversed. 3. Pheromone update: After each ant traverses a path, the pheromone is locally updated based on pheromone evaporation and path cost to encourage exploration of new paths. After completing one round of search, the pheromone is updated based on the quality of the best path to enhance the attractiveness of high-quality paths. 4. The algorithm terminates after running for a preset number of iterations or finding a path that meets the performance indicators.

[0004] While ant colony optimization (ACO) offers numerous advantages in path planning, it also suffers from several drawbacks. First, its convergence speed is relatively slow, especially in complex environments, often requiring numerous iterations to find the optimal solution. Second, ACO is prone to getting trapped in local optima, particularly in large path search spaces, where its performance may be unsatisfactory. The algorithm is highly sensitive to parameter settings (such as pheromone importance α and heuristic pheromone importance β); inappropriate parameter selection can lead to low search efficiency or unstable results. Furthermore, excessively rapid pheromone evaporation can cause valuable path information to be quickly forgotten, while excessively slow pheromone evaporation can lead to pheromone concentration, hindering exploration capabilities. In large-scale maps or high-dimensional spaces, the algorithm's computational complexity is high, potentially requiring significant computational resources and impacting real-time performance. Although ACO possesses some dynamic adaptability, the speed and accuracy of path adjustments remain insufficient in frequently changing environments. Additionally, the choice of path evaluation metrics also influences algorithmic decisions; overly simplistic evaluation criteria may fail to comprehensively reflect the quality of a path. Therefore, optimizing and improving these shortcomings is crucial for enhancing the performance of ACO. Summary of the Invention

[0005] Objective: To address the above-mentioned problems, this invention proposes a global path planning method for mobile robots that adapts to different grid map complexities, thereby improving the flexibility and adaptability of mobile robots in path planning within grid maps. The aim is to enhance the autonomous navigation capabilities of mobile robots in complex and dynamic environments by optimizing the global path planning algorithm, thus meeting the growing demands for intelligent applications.

[0006] Technical Solution: To achieve the objectives of this invention, the technical solution adopted is: a global path planning method for mobile robots adaptable to different grid map complexities, comprising the following steps:

[0007] The first step is to acquire environmental information, construct a real-time dynamic grid map, and calculate the map complexity based on the number, distribution, and connectivity of obstacles.

[0008] Step 2, Ant colony algorithm initialization: Initialize the ant colony, each ant randomly selects a starting point, and adopts an adaptive initial pheromone allocation strategy based on grid mapping complexity to initialize the pheromone matrix and heuristic pheromone matrix to preset values.

[0009] Step 3, Path Search Process:

[0010] Path selection: An improved ant colony state transition strategy is adopted, which introduces a predefined threshold that varies with map complexity to provide a balance between deterministic and random selection of search directions. Ants select the next moving node based on the state transition probability.

[0011] Path construction: While choosing a path, ants record the nodes they pass through and calculate the path cost;

[0012] Step 4: Pheromone Update

[0013] Each time an ant traverses a path, the pheromone levels are locally updated based on pheromone evaporation and pheromone increase. The grid map complexity and iteration count are incorporated into the expressions for the pheromone evaporation coefficient and intensity coefficient, respectively, to update the path.

[0014] The algorithm terminates after running for the preset number of iterations or finding a path that meets the performance metrics.

[0015] Furthermore, in the first step, the map complexity calculation process is as follows:

[0016] First, the proportion of obstacle grids is calculated as a basic measure of the degree of environmental obstruction. Second, the distribution of obstacles is used to capture map features. Finally, Shannon entropy theory is applied to evaluate the information complexity of the map.

[0017] The formula for calculating map complexity is as follows:

[0018]

[0019] Where G represents the complexity of the raster map, and its value ranges from 0 to 1. The closer the value is to 0, the lower the complexity; the closer the value is to 1, the higher the complexity. N all N represents the sum of the number of obstacle grids and free grids. os N represents the number of obstacle grid cells. ef Indicates the total number of free grid cells adjacent to the obstacle grid; Item This is the Shannon entropy formula, where n=2 indicates that the raster map contains only two types of rasters, and when i=1, x i Represents an obstacle grid; when i = 2, x i p(x) represents a free grid. i ) represents the probability of the occurrence of obstacle grids and free grids, x i Used to calculate the values ​​of the free grid and the obstacle grid, and then calculate the ratio; θ1, θ2 and θ3 represent the proportion of obstacles, the weight coefficients corresponding to the distribution of obstacles and the degree of distribution disorder, respectively.

[0020] Furthermore, in the second step, the pheromone initialization process is as follows:

[0021] During pheromone initialization, the distribution of pheromones is dynamically adjusted at the start based on the complexity of the raster map and the grid distance from the start and end lines. The expression is as follows:

[0022] τ ij (initial)′=e^G*τ ij(initial)*ln(N all (2),

[0023]

[0024] Where, τ ij (initial)′ represents the improved pheromone value, τ ij (initial) represents the initial pheromone value, i and j represent the current node and the next node, respectively, G is the target node, and N... all This represents the sum of the number of obstacle grid cells and the number of free grid cells; u ij (initial) represents the pheromone distribution value determined based on distance, d is the distance of the current node i from the start and end lines, the coordinates of node i are (x, y), and the coordinates of the start point S are (x, y). S ,y S The target point T has coordinates (x...). T ,y T ).

[0025] Furthermore, in the third step, the path search process includes:

[0026] An improved ant colony state transition strategy is designed, which introduces a predefined threshold q0 that varies with map complexity, providing a balance between deterministic and random selection of search directions, as shown in Equations (5) and (6).

[0027]

[0028] in, This represents the probability that ant m moves from node i to node j in the k-th iteration. The argmax function is used to determine the index of the maximum value in the matrix. τ ij (k) represents the pheromone concentration, η ij (k) is the heuristic function, where α and β are the pheromone concentration and the exponent of the heuristic function, respectively. Let q be the state transition probability, q be a random variable uniformly distributed in the interval [0,2], q0 be a predefined threshold, G be the grid map complexity, k be the current iteration number, and K be the total number of iterations.

[0029] According to formula (5), when q≤q0, the algorithm selects the node that maximizes the product of pheromone concentration and heuristic function; when q>q0, the algorithm switches to random selection mode and adopts the roulette wheel selection method in the traditional ant colony algorithm.

[0030] Furthermore, in the third step, the path search process also includes:

[0031] Based on the complexity of raster maps, the Euclidean distance from the ant colony to the destination, and the turning angle of the ant colony path, an improved heuristic function η′ is designed by quantizing the Euclidean distance of the grid and the path turning angle. ij For example, formulas (7) to (10);

[0032]

[0033] Where, η′ ij The improved heuristic function has λ as the global adjustment coefficient used to control the overall strength of the heuristic function, and w1 and w2 are weight coefficients that satisfy the constraint w1 + w2 = 1; d ij Let d be the distance from the current node i to the next node j. iT This represents the Euclidean distance from the current node i to the target node T, calculated using the following formula: (x i ,y i ) and (x T ,y T Let be the coordinates of node i and the target node T, respectively; a(i) represents the path turning angle, defined as the angle between the current node i, the previous node l, and the next node j. Let be the vector from node l to node i in the ant colony. d is the vector from node i to node j in the ant colony; ST Let S be the Euclidean distance from the starting point S to the target point T, k be the current iteration number, K be the total number of iterations, and G be the adjustment parameter, i.e., the complexity of the raster map.

[0034] Furthermore, in the third step, the path search process also includes:

[0035] Design a dynamic coefficient definition mechanism based on cosine annealing strategy, and adjust the pheromone concentration and the exponents α and β of the heuristic function according to the iteration, as shown in formula (11) and formula (12);

[0036]

[0037]

[0038] Where, α max α min The upper and lower boundaries of α and β are respectively. max and β min Let be the upper and lower boundary values ​​of β, respectively; k is the current iteration number; and K is the total number of iterations.

[0039] α max =ln(N) all ) / e, α min =ln(N) all ) / e 2 ,βmax =lg(N) all )*2e,β min =lg(N) all ), where N all This represents the sum of the number of obstacle grids and free grids, where e is a natural number.

[0040] Furthermore, in the fourth step, the pheromone dynamic update mechanism is as follows:

[0041] The mapping complexity and iteration are introduced into the expressions for the pheromone evaporation coefficient and intensity, respectively. Based on this, the pheromone concentration is kept within a preset range according to the definition of map complexity, as shown in formulas (13) to (16).

[0042]

[0043] Where ρ′ is the evaporation coefficient, ρ is the pheromone evaporation coefficient, G is the grid map complexity, M is the number of ants, k is the current iteration number, K is the total number of iterations; Q′ is the improved pheromone intensity, Q is the pheromone intensity; τ ij (k) represents the pheromone concentration along the path; τ max and τ min They are τ ij The maximum and minimum values ​​of (k), τ ij (initial)′ represents the improved initial pheromone distribution, L min N represents the length of the shortest path found by the ant after the k-th iteration. all This represents the sum of the number of obstacle grids and free grids.

[0044] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0045] The present invention discloses a global path planning method for mobile robots that adapts to different grid map complexities. Based on the quantification of grid map complexity in terms of obstacle quantity, distribution, and connectivity, it designs an adaptive initial pheromone allocation strategy based on grid mapping complexity and optimizes the global path planning search strategy. It comprehensively considers the adaptive heuristic function of target point information, corner constraints, and grid map complexity, and a dynamic pheromone update mechanism based on grid map complexity, thereby improving the path planning capability of mobile robots in different environments.

[0046] The new pheromone initialization definition accelerates pheromone accumulation and improves its spatial distribution on early paths, thus rapidly facilitating pheromone concentration on high-potential paths and optimizing convergence speed. The improved initial pheromone value can be dynamically adjusted based on the complexity and scale of the raster map. By dynamically adjusting the unevenness of the initial pheromone distribution, the algorithm enhances its ability to prioritize high-potential areas, thereby improving efficiency in the early stages of the search. By introducing grid mapping complexity into the ant colony algorithm, its adaptability and efficiency are significantly improved while maintaining its inherent advantages. Attached Figure Description

[0047] Figure 1 This is the overall flowchart of the method of the present invention.

[0048] Figure 2 It is the distribution of the obstacle grid.

[0049] Figure 3 It is the change in the initial value of pheromones.

[0050] Figure 4 This is a schematic diagram illustrating the calculation of distance d.

[0051] Figure 5 It is an adaptive change of q0.

[0052] Figure 6 This is a diagram showing the calculation of the turning angle a(i).

[0053] Figure 7 It represents the changing trend of α.

[0054] Figure 8 This represents the trend of β changes.

[0055] Figure 9 It represents the number of convergence iterations for the five ACO variants.

[0056] Figure 10 It is the optimal path for the five ACO variants.

[0057] Figure 11 This is the optimal path for a 20x20 grid map scale.

[0058] Figure 12 It represents the number of convergence iterations for a 20×20 grid map scale.

[0059] Figure 13 It is a real-world experimental map.

[0060] Figure 14 It is the optimal path among the four algorithms in the raster map. Detailed Implementation

[0061] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0062] This invention discloses a global path planning method for mobile robots that adapts to different grid map complexities. First, a method for quantifying grid map complexity based on the number, distribution, and connectivity of obstacles is proposed. Second, an adaptive initial pheromone allocation strategy based on grid mapping complexity is designed. Third, the search strategy for global path planning is optimized. An adaptive heuristic function that comprehensively considers target point information, corner constraints, and grid map complexity is proposed. Fourth, a dynamic pheromone update mechanism based on grid map complexity is proposed.

[0063] To improve the path planning capabilities of mobile robots in different environments, an adaptive ant colony algorithm based on mesh mapping is proposed. By introducing the complexity of mesh mapping into the ant colony algorithm, its adaptability and efficiency are significantly improved while maintaining its inherent advantages. This invention employs four optimization strategy modules.

[0064] First, the map complexity calculation module: First, it calculates the proportion of obstacle grids to provide a basic measure of the degree of environmental obstruction; second, it uses the distribution of obstacles to accurately capture map features; finally, it applies Shannon entropy theory to evaluate the information complexity of the map, as shown in Formula 1.

[0065]

[0066] Where G represents the complexity of the raster map, and its value ranges from 0 to 1. The closer the value is to 0, the lower the complexity; the closer it is to 1, the higher the complexity. N all N represents the sum of the number of obstacle grids and free grids. os N represents the number of obstacle grid cells. ef This indicates the total number of free grid cells adjacent to an obstacle grid cell. (Item) This is the Shannon entropy formula, where p(x) i The probability of occurrence of obstructed and free grid cells is used to determine the information entropy of the grid map. In a grid map, a grid cell is either an obstructed grid cell or a free grid cell, therefore the value of n is 2, and when i = 1, x... i Represents an obstacle grid; when i = 2, x i This represents a free grid. θ1, θ2, and θ3 represent the weighting coefficients corresponding to the proportion of obstacles, the distribution of obstacles, and the disorder of the distribution, respectively. The complexity of the grid map mainly depends on the number of obstacles, so the value of θ1 is set to 0.6. Considering that the distribution of obstacles is as important as the map information entropy, the values ​​of θ2 and θ3 are both set to 0.2.

[0067] Figure 2This study demonstrates different obstacle distribution patterns in a grid map and their impact on map complexity. Each obstacle grid is defined by four boundaries and surrounded by four adjacent grids. The distribution of obstacle grids directly affects the number of surrounding free grids, thus influencing the overall complexity of the grid map. Analysis shows that an obstacle is surrounded by 4 free grids; two connected obstacles by 6 free grids; two independent obstacles by 8 free grids; four connected obstacles by 8 free grids; four consecutive obstacles by 10 free grids; and four completely independent obstacles by 16 free grids. This analysis reveals a significant pattern: with the same number of obstacles, fewer connections between obstacles result in more surrounding free grids. In other words, a dispersed obstacle distribution provides more potential path choices, thus increasing the complexity of path planning. This multi-dimensional complexity assessment method not only objectively and explicitly quantifies the differences between different grid maps but also provides necessary theoretical support for key operations of the ant colony algorithm, including adaptive optimization of pheromone initialization, node search, and pheromone update mechanisms.

[0068] Second, the improved pheromone initialization module: induces the complexity of the mesh graph and the mesh distance from the start and end lines during pheromone initialization, and dynamically adjusts the distribution of pheromones at the start of optimization, as shown in formulas (2), (3) and (4).

[0069] τ ij (initial)′=e^G*τ ij (initial)*ln(N all (2),

[0070]

[0071]

[0072] Where, τ ij (initial)′ represents the improved pheromone value, τ ij (initial) represents the initial pheromone value, i and j represent the current node and the next node, respectively, G is the target node, and N... all This represents the sum of the number of obstacle grid cells and the number of free grid cells; i ij (initial) represents the pheromone distribution value determined based on distance, d is the distance of the current node i from the start and end lines, the coordinates of node i are (x, y), the start point is S, and its coordinates are (x, y). S ,y S The target point is T, and its coordinates are (x, y). T ,y T ).

[0073] The new pheromone initialization definition accelerates pheromone accumulation and improves its spatial distribution along early paths, thus rapidly facilitating pheromone concentration on high-quality paths and optimizing convergence speed. The improved initial pheromone value can be dynamically adjusted based on the complexity and scale of the raster map.

[0074] Figure 3 The dynamic adjustment curve of the initial pheromone is shown. This adaptive mechanism enhances the algorithm's flexibility, enabling it to adapt to map environments of varying complexity. For example, as the complexity of the raster map increases, appropriately increasing the initial pheromone level can accelerate the algorithm's convergence process while enhancing its adaptive adjustment capability. This phenomenon occurs because ants release pheromones along the way when they find a path and return to the starting point. A higher initial pheromone value accelerates the accumulation of pheromones on early paths. This positive feedback mechanism rapidly strengthens the pheromone concentration on high-quality paths, prompting more ants to choose these paths, thereby accelerating algorithm convergence. As d increases, the distance from point i to the straight line connecting S and T increases, reducing its impact on the optimal path and leading to a decrease in the initial pheromone level. By dynamically adjusting the unevenness of the initial pheromone distribution, the algorithm enhances its priority processing capability for high-potential areas, thereby improving efficiency in the early stages of the search. Figure 4 This is an example of how distance d is calculated.

[0075] Third, the node search efficiency improvement module: For ant colony algorithms, the state transition probability is the most critical factor determining the optimization (node ​​search) efficiency and solution quality. Unlike traditional ant colony algorithms, the method of this invention designs a new ant colony state transition strategy based on the ant colony mapping complexity, the Euclidean distance from the ant colony to the destination, and the ant colony path turning angle. In order to improve convergence efficiency while maintaining population diversity and global search capability, a predefined threshold q0 that varies with map complexity is introduced to provide and balance deterministic and random selection of search direction, as shown in formulas (5) to (6). By quantizing the Euclidean distance of the grid and the path turning angle a(i), an improved heuristic function is derived to improve the global search capability of the ant colony algorithm and ensure the smoothness of the path, as shown in formulas (7) to (10). In addition, a dynamic coefficient definition mechanism based on the cosine annealing strategy is proposed, which iteratively adjusts the pheromone concentration and the exponents α and β of the heuristic function, as shown in formulas (11) to (12).

[0076]

[0077]

[0078] in, The τ represents the probability that the improved ant m moves from node i to node j in the k-th iteration; the argmax function is used to determine the index of the maximum value in the matrix. ij (k) represents the pheromone concentration, η ij (k) is the heuristic function, where α and β are the pheromone concentration and the exponent of the heuristic function, respectively. Let q be the state transition probability, q be a random variable uniformly distributed in the interval [0,2], q0 be a preset threshold used to balance exploration and development, G be the grid map complexity, k be the current iteration number, and K be the total number of iterations. According to formula (5), when q≤q0, the algorithm selects the point that maximizes the product of pheromone concentration and heuristic function. This deterministic selection mechanism helps improve the convergence efficiency and local search capability of the algorithm. Conversely, when q>q0, the algorithm switches to random selection mode, using the roulette wheel selection method in the traditional ant colony algorithm. This randomness helps maintain population diversity and enhances the global search capability of the algorithm, thereby reducing the risk of getting trapped in local optima. Figure 5 The adaptive range of q0 is shown. In the early stages, a larger value of q0 is used to select a high-probability deterministic transition, accelerating the search for local optima. In the middle stage of the algorithm, a smaller value of q0 is used to increase the probability of selecting a random transition, preventing local optima. As the algorithm progresses into the later stages, its evolutionary direction is basically determined, and gradually increasing q0 can accelerate the convergence speed. In addition, q0 is positively correlated with the complexity of the grid map, enhancing the adaptability of the algorithm. In formula (7), λ is the global adjustment coefficient, used to control the overall strength of the heuristic function. w1 and w2 are the weight coefficients that satisfy the constraint w1+w2=1. iT This represents the Euclidean distance from the current point i to the target point T, calculated using the following formula: a(i) represents the path turning angle, defined as the angle between the current node i, the previous node l, and the next node j, as shown in formula (8) and Figure 6 As shown; d ST Let λ be the Euclidean distance from the starting point S to the target point T. As the number of iterations increases, the numerator λ gradually decreases while the denominator increases, thus gradually weakening the influence of heuristic information in subsequent iterations and accelerating the convergence process. Furthermore, by introducing the parameter G, its value can be dynamically adjusted according to the complexity of the raster map, thereby enhancing the algorithm's adaptability to raster maps of varying complexity. α max α min The upper and lower boundaries of α and β are respectively. max and β min These are the upper and lower boundary values ​​of β, respectively. Specifically, α max =ln(N) all ) / e,α min =ln(N) all ) / e 2 ,β max=lg(N) all )*2e,β min =lg(N) all ). Figure 7 and Figure 8 The trends of α and β are shown. In the early stages of the algorithm, α is relatively small, while β is relatively large. This configuration gives the heuristic function a larger weight for state transition probabilities, thereby enhancing the guiding role of the goal point in ant path selection. As the number of iterations k increases, the algorithm gradually finds suitable paths, α gradually increases, and β gradually decreases. This change makes the ant colony more inclined to choose already discovered successful paths, promoting convergence to known high-quality solutions and accelerating the overall search efficiency. This embodiment verifies the convergence iteration count through five ACO variants, such as... Figure 9 As shown.

[0079] Fourth, a new dynamic pheromone update mechanism module: Since the pheromone evaporation coefficient and intensity are static, the traditional ant colony algorithm is prone to getting trapped in local optima. To solve this problem, this invention proposes a new dynamic pheromone update mechanism, which introduces mapping complexity and iteration into the expressions for the pheromone evaporation coefficient and intensity, respectively. Based on this, the region that keeps the pheromone concentration within a reasonable range is defined and calculated according to the map complexity, which can prevent the pheromone value from being too high or too low, and avoid premature convergence, as shown in formulas (13) to (16).

[0080]

[0081] Where ρ′ is the evaporation coefficient, ρ is the pheromone evaporation coefficient, G is the grid map complexity, M is the number of ants, k is the current iteration number, K is the total number of iterations; Q′ is the improved pheromone intensity, Q is the pheromone intensity; τ ij (k) represents the pheromone concentration along the path; τ max and τ min They are τ ij The maximum and minimum values ​​of (k), τ ij (initial)′ represents the improved initial pheromone distribution, L min N represents the length of the shortest path found by the ant after the k-th iteration. all This represents the sum of the number of obstacle grids and free grids.

[0082] In formulas (13) and (14), as the number of iterations increases, the pheromone intensity Q′ gradually decreases, while the evaporation coefficient ρ′ gradually increases. This effectively prevents excessive concentration of pheromones and avoids the algorithm getting trapped in local optima. Furthermore, the impact of grid map complexity on pheromone updates is considered. When the grid map complexity increases, the algorithm needs more time to quickly find the optimal path. Therefore, to improve algorithm efficiency, the evaporation coefficient needs to be dynamically reduced and the pheromone intensity increased. Conversely, when the map is simple and its complexity decreases, the algorithm can easily find the optimal path. In this case, the evaporation coefficient should be dynamically increased and the pheromone intensity decreased to avoid getting trapped in local optima. In formulas (15) and (16), τ ij (k) Pheromone concentration along the path, τ max and τ min τ ij The maximum and minimum values ​​of (k). This invention introduces the complexity of the raster map into τ. max and τ min The calculation is performed, and a new calculation method is proposed, as shown in formula (16), where the variable L is... min This represents the shortest path length found by the ant after the k-th iteration. According to the result of formula (16), in τ... ij Within the finite range of (k), not only does the shortest path length exist, but improved parameters such as evaporation coefficient and pheromone intensity are also considered. This will help to find the optimal solution more easily in subsequent iterations. In addition, the impact of dynamic complexity changes is also considered. By keeping the pheromone within a reasonable range, the algorithm can effectively avoid getting trapped in local optimization too early.

[0083] In mobile robot environment modeling and global path planning, grid-based maps are widely used. However, the complexity of grid maps varies significantly across different engineering applications, requiring path planning algorithms to possess high flexibility, efficiency, and adaptability, making the development of general and robust efficient algorithms a significant challenge. To address this issue, this invention proposes an improved adaptive ant colony optimization algorithm based on grid map complexity (GMCACO). This algorithm effectively overcomes the shortcomings of existing technologies through the following innovations: it proposes a method for quantifying grid map complexity based on the number and distribution of obstacles and map information entropy; it designs an adaptive initial pheromone allocation strategy based on map complexity; it optimizes the state transition probability to improve node search efficiency; and it proposes a dynamic pheromone update mechanism based on complexity, thereby enhancing the algorithm's adaptability and robustness. To verify the performance of GMCACO, extensive simulation and experimental studies were conducted. The simulations verified the effectiveness of the improved GMCACO method and compared it with the latest improved ant colony algorithms; the experiments compared GMCACO with commonly used A* and Dijkstra algorithms. The results show that GMCACO has good adaptability and efficiency improvement on grid maps of different complexities.

[0084] Overall, the adaptive ant colony optimization algorithm shows significant improvement in comprehensive performance on real-world maps. Figure 10 This is the optimal path for the five ACO variants. Figure 11 This is the optimal path for a 20×20 grid map scale, demonstrating the effectiveness of various methods. Figure 12 The convergence iteration count is the number of iterations for a 20×20 grid map scale, demonstrating the comparative effect of the adaptive ant colony optimization algorithm and other different algorithms. Figure 13 It is a real-world experimental map; Figure 14 This paper presents the optimal paths for GMCACO and four commonly used algorithms—ACO, A*, and Dijkstra—in raster maps, showcasing the comparative performance of the Adaptive Ant Colony Optimization (AAC) algorithm in practical experiments. These results not only validate the theoretical advantages of AAC but also demonstrate its potential in real-world applications. AAC exhibits superior performance in both simulated and real-world environments. Specifically, by adjusting the initial pheromone allocation strategy, optimizing state transition probabilities, and improving the heuristic function and its exponent, AAC successfully accelerates the convergence speed while reducing path length, execution time, and the number of path turns. Furthermore, AAC introduces a dynamic pheromone evaporation mechanism, effectively preventing the algorithm from prematurely falling into local optima, thus enabling more reliable generation of globally optimal paths and significantly improving the quality of solutions. These innovative improvements enable AAC to demonstrate strong adaptability and excellent performance in path planning tasks under different environments.

Claims

1. A global path planning method for mobile robots that adapts to different grid map complexities, characterized in that, Includes the following steps: The first step is to acquire environmental information, construct a real-time dynamic grid map, and calculate the map complexity based on the number, distribution, and connectivity of obstacles. Step 2, Ant colony algorithm initialization: Initialize the ant colony, each ant randomly selects a starting point, and adopts an adaptive initial pheromone allocation strategy based on grid mapping complexity to initialize the pheromone matrix and heuristic pheromone matrix to preset values. Step 3, Path Search Process: Path selection: An improved ant colony state transition strategy is adopted, which introduces a predefined threshold that varies with map complexity to provide a balance between deterministic and random selection of search directions. Ants select the next moving node based on the state transition probability. Path construction: While choosing a path, ants record the nodes they pass through and calculate the path cost; Step 4: Pheromone Update Each time an ant traverses a path, the pheromone levels are locally updated based on pheromone evaporation and pheromone increase. The grid map complexity and iteration count are incorporated into the expressions for the pheromone evaporation coefficient and intensity coefficient, respectively, to update the path. The pheromone dynamic update mechanism is as follows: The mapping complexity and iteration are introduced into the expressions for the pheromone evaporation coefficient and intensity, respectively. Based on this, the pheromone concentration is kept within a preset range according to the definition of map complexity, as shown in formulas (13) to (16). (13)， (14)， (15)， (16)， in, The volatility coefficient is... The pheromone evaporation coefficient. For the complexity of raster maps, For the number of ants, This represents the current iteration number. This represents the total number of iterations. To improve pheromone strength, Pheromones intensity; The pheromone concentration along the path; and They are The maximum and minimum values, The improved initial pheromone distribution, Indicates the current ant's position in the [number]th [time]. The shortest path length found after the nth iteration This represents the sum of the number of obstacle grids and free grids; The algorithm terminates after running for the preset number of iterations or finding a path that meets the performance metrics.

2. The global path planning method for mobile robots adapting to different grid map complexities according to claim 1, characterized in that, In the first step, the map complexity calculation process is as follows: First, the proportion of obstacle grids is calculated as a basic measure of the degree of environmental obstruction. Second, the distribution of obstacles is used to capture map features. Finally, Shannon entropy theory is applied to evaluate the information complexity of the map. The formula for calculating map complexity is as follows: (1)， in, This represents the complexity of the raster map, with a value ranging from 0 to 1. The closer the value is to 0, the lower the complexity; the closer the value is to 1, the higher the complexity. This represents the sum of the number of obstacle grid cells and the number of free grid cells. Indicates the number of obstacle grid cells. Indicates the total number of free grid cells adjacent to the obstacle grid; Item Here is the Shannon entropy formula, where This indicates that the raster map contains only two types of rasters. hour Represents an obstacle grid. =2 Indicates a free grid. It represents the probability of the occurrence of obstacle grids and free grids. Used to calculate the values ​​of the free grid and the obstacle grid, and then calculate the ratio; , and These represent the weighting coefficients corresponding to the proportion of obstacles, the distribution of obstacles, and the degree of disorder in the distribution, respectively.

3. The global path planning method for mobile robots adapting to different grid map complexities according to claim 1, characterized in that, In the second step, the pheromone initialization process is as follows: During pheromone initialization, the distribution of pheromones is dynamically adjusted at the start based on the complexity of the raster map and the grid distance from the start and end lines. The expression is as follows: (2)， (3)， (4)， in, For the improved pheromone value, The initial pheromone value, These are the current node and the next node, respectively. For the target node, This represents the sum of the number of obstacle grids and free grids; The pheromone distribution value is determined based on distance. For the current node Distance from the start and finish lines, nodes Coordinates are The coordinates of the starting point S are The coordinates of the target point T are .

4. The global path planning method for mobile robots adapting to different grid map complexities according to claim 1, characterized in that, In the third step, the path search process includes: Design an improved ant colony state transition strategy by introducing a predefined threshold that varies with map complexity. It provides deterministic and random choices for balancing search directions, as shown in Equations (5) and (6); (5)， (6)， in, Indicates improved ants In the In the next iteration, from node Move to node The probability, The function is used to determine the index of the maximum value in a matrix. For pheromone concentration, For heuristic functions, These are the pheromone concentration and the exponent of the heuristic function, respectively. Let be the state transition probability. In the interval A random variable that is uniformly distributed within the range. For a predefined threshold, For the complexity of raster maps, This represents the current iteration number. This represents the total number of iterations. According to formula (5), when When the pheromone concentration is maximized, the algorithm selects the node that maximizes the product of the pheromone concentration and the heuristic function; when... At this point, the algorithm switches to random selection mode, using the roulette wheel selection method from the traditional ant colony algorithm.

5. A global path planning method for mobile robots adapting to different grid map complexities according to claim 4, characterized in that, The third step, the path search process, also includes: Based on the complexity of raster maps, the Euclidean distance from the ant colony to the destination, and the turning angle of the ant colony path, an improved heuristic function is designed by quantizing the Euclidean distance of the grid and the path turning angle. , such as formulas (7) to (10); (7)， (8)， (9)， (10)， in, For the improved heuristic function, This is a global adjustment coefficient used to control the overall strength of the heuristic function. and To satisfy the constraints Weighting coefficients; For the current node To the next node distance, Indicates starting from the current node To the target node The Euclidean distance is calculated using the following formula: , and They are nodes and target node The coordinates; Indicates a path turn, defined as the current node. Previous node and the next node The angle between them For ant colonies from nodes To the node The vector, For ant colonies from nodes To the node ; To start from the beginning To the target point Euclidean distance, This represents the current iteration number. This represents the total number of iterations. To adjust the parameters, namely the complexity of the raster map.

6. The global path planning method for mobile robots adapting to different grid map complexities according to claim 4, characterized in that, The third step, the path search process, also includes: Design a dynamic coefficient definition mechanism based on a cosine annealing strategy, which iteratively adjusts the pheromone concentration and the exponent of the heuristic function. and For example, formulas (11) and (12); (11)， (12)， in, , They are respectively upper and lower boundaries, and They are respectively The upper and lower boundary values, This represents the current iteration number. This represents the total number of iterations. ， ， ， ， in, This represents the sum of the number of obstacle grid cells and the number of free grid cells. It is a natural number.

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