Multi-robot formation motion method based on improved artificial potential field method hybrid ant colony algorithm

Abstract

The application provides a kind of multi-robot formation movement method based on improved artificial potential field method hybrid ant colony algorithm, first, the global navigation path under the complex obstacle environment is provided for the leader robot using improved ant colony algorithm, and the heuristic matrix, heuristic function and pheromone update strategy are optimized to solve the problems of slow convergence speed, easy to fall into local optimum and path safety of standard ant colony algorithm;Second, the gravity repulsion coefficient and obstacle avoidance function are optimized, which solves the problems of robot easily falling into local optimum, difficult parameter adjustment and easily disturbed by complex environment under the obstacle avoidance strategy of standard artificial potential field method;Then, the formation is constructed by leader-following method, and the multi-robot is adaptively formed based on artificial potential field method hybrid ant colony algorithm, and the follower is adaptively corrected motion speed according to formation threshold at any time to better maintain the formation formation.

Description

Technical Field

[0001] This invention relates to the field of mobile robot path planning technology, specifically to a multi-robot formation motion method based on an improved artificial potential field method and a hybrid ant colony algorithm. Background Technology

[0002] Multi-robot systems can perform complex tasks faster and better than single robots, and have been applied in various scenarios in recent years. With increasing environmental complexity and the difficulty of robotic tasks, multi-robot collaborative formation technology is attracting increasing attention from researchers. Multi-mobile robot formation collaboration, as an important branch of robotic systems, is a further extension of single-robot path planning. The technical challenge lies in considering certain path metrics of multiple robots, such as path length, planning time, and energy consumption, while also ensuring convergence to a specific formation. This poses a significant challenge to multi-robot navigation and obstacle avoidance, especially in environments with high global obstacle density and unknown dynamic obstacles.

[0003] Ant colony optimization (ACO) is a heuristic optimization algorithm that originated in the early 1990s. Initially widely used for solving path planning problems for single robots, it has gradually been extended to multi-robot problems in recent years. Gu Junhua et al. applied an improved ACO to static path planning for multiple robots (Gu Junhua et al. Research on Multi-Robot Path Planning Based on Improved Ant Colony Algorithm [J]. Journal of Hebei University of Technology, 2016). Yang et al. combined the improved ACO with the leader-following method to propose an efficient multi-robot formation path planning method (Yang L, et al. LF-ACO: An effective information path planning for multi-mobile robot [J]. Math. Biosci. Eng, 2022). Pu et al. planned paths to multiple target points for multiple robots based on an improved ACO algorithm and mitigated potential risks between robots through conflict detection and obstacle avoidance algorithms (Pu X, et al. Improved ant colony algorithm in pathplanning of a single robot and multi-robots with multi-objective [J]. Evolutionary Intelligence, 2023).

[0004] The research conducted by the aforementioned scholars lacks consideration of dynamic environmental factors, while the artificial potential field method is mainly used to solve such problems. Zhao et al. proposed a method for assessing collision risk and a collision avoidance strategy to solve the dynamic real-time collision avoidance problem between robots when multiple robot systems cooperate to complete a given task (Zhao T, et al. Multi-robot pathplanning based on improved artificial potential field and fuzzy inference system[J]. Journal of Intelligent & Fuzzy Systems, 2020). Sang Lei et al. conducted research on multi-robot formation control and obstacle avoidance based on the artificial potential field method (Sang Lei, Lü Qiang. Multi-robot formation and obstacle avoidance based on artificial potential field method[J]. Information Systems Engineering, 2020). Fu Lei et al. proposed an obstacle avoidance method based on improved artificial potential field and formation consistency to solve the obstacle avoidance and collision avoidance problems between members of multi-robot systems during formation (Fu Lei et al. Multi-robot formation obstacle avoidance based on improved artificial potential field method[J]. Control Engineering, 2022). Summary of the Invention

[0005] The purpose of this invention is to solve the problems of global path planning and formation motion of multiple robots in complex obstacle environments, and to provide a multi-robot formation motion method based on an improved artificial potential field method and a hybrid ant colony algorithm. This method extends the leader-follower approach to multiple robots in formation, utilizes an improved ant colony algorithm to provide a navigation path for the leader robot in complex environments, and improves the artificial potential field method to enhance the obstacle avoidance capabilities of the robot swarm in environments with dense obstacles and unknown dynamic obstacles.

[0006] The technical solution provided by this invention is a multi-robot formation motion method based on an improved artificial potential field method and a hybrid ant colony algorithm, comprising the following steps:

[0007] Step 1: Establish a global map environment of size N×N.

[0008] More specifically, the map is represented by a matrix, containing impassable obstacle grids, represented by 1; and passable free grids, represented by 0. The coordinates (x, y) of the center point of all grid cells are converted into grid labels according to the following rules:

[0009] Number = N + (x - 0.5)N - y + 0.5

[0010] Step 2: Initialize the parameters of the multi-robot algorithm, the ant colony algorithm, and the artificial potential field method.

[0011] More specifically, the multi-robot parameters include: the navigator's start and end coordinates and the follower's end coordinates, and the expected distance L between the navigator and the follower. d and expected perspective Motion speed v°, node spacing n ds Navigation point reference distance d, expected distance threshold (0, d], formation distance threshold [L] d -0.05, L d +0.05]. Ant colony algorithm parameters include: number of ants M, maximum number of iterations NC, pheromone weight α, heuristic function weight β, pheromone evaporation coefficient ρ, pheromone intensity Q, heuristic function importance x, pheromone importance y and z, heuristic matrix D, and pheromone initialization matrix Tau. Artificial potential field method parameters include: gravity coefficient k. attr repulsion coefficient k rep The maximum influence distance ρ0 of the obstacle's repulsive potential field, the attenuation factor λ, the adjustment parameters k1, k2, k3, and k4, and the maximum values ​​of the attraction and repulsion coefficients α. max and β max .

[0012] More specifically, the standard heuristic matrix D is:

[0013]

[0014] More specifically, the heuristic matrix D is optimized for safety in the eight-neighbor search direction, according to the following rules:

[0015]

[0016] In the formula, mod() represents the modulo operation, Dir() represents the grid number of the eight-neighbor candidate direction, and i and j represent the current grid number where the ant is located and the eight-neighbor candidate direction, respectively.

[0017] Step 3: Determine if the current number of ants has reached the preset value. If so, perform a global pheromone update and jump to step 6; otherwise, execute step 4.

[0018] Step 4: Select walkable grids based on the heuristic matrix D, select the next grid node for the ant to move to using the roulette wheel principle, update the tabu table, and record the grid number and direction traversed by the ant.

[0019] More specifically, the principles of roulette are:

[0020]

[0021] In the formula, m represents the ant number, t represents the current iteration number, i represents the current grid cell where the ant is located, j represents the candidate grid cells for the ant, allowed represents the set of candidate grid cells, and τ ij(t) represents the pheromone, η ij (t) represents a heuristic function.

[0022] More specifically, the standard heuristic function η ij (t) is as follows:

[0023] η ij (t) = 1 / D(i,j)

[0024] More specifically, the heuristic function η ij (t) is as follows:

[0025]

[0026] In the formula, x represents the importance of the heuristic function, and L ij Let Nc and Nc represent the Euclidean distance from grid i to grid j. max These represent the current iteration number and the maximum iteration number, respectively.

[0027] More specifically, the standard pheromone τ ij (t) is as follows:

[0028]

[0029]

[0030] More specifically, the global pheromone τ ij (t) The update rules are as follows:

[0031]

[0032] In the formula, ρ is the pheromone evaporation factor, Q is the pheromone intensity, L is the path length, T is the number of path turns, and y and z are weighting factors.

[0033] Step 5: Determine if the ant has reached the navigator's target point. If so, record the path length and number of turns and return to step 3; otherwise, return to step 4.

[0034] Step 6: Determine if the current iteration number has reached the maximum iteration number. If so, output the navigator's optimal path; otherwise, go to step 5.

[0035] Step 7: Optimal path planned by the discretized ant colony algorithm.

[0036] More specifically, the standard spacing between adjacent path nodes is 1 or The method uses a given node spacing n ds After discretization, the node spacing is unified to n. ds Thus, a new navigator's navigation path is obtained.

[0037] Step 8: Introduce an unknown dynamic interference environment.

[0038] More specifically, the interference environment includes unknown static obstacles and dynamic obstacles: unknown static obstacles are randomly distributed; the movement paths of dynamic obstacles can be planned by the ant colony algorithm provided by this invention (implementation reference steps 1 to 6), and after obtaining the trajectory, it can be assigned a movement speed parameter v and a volume size parameter size.

[0039] Step 9: Multiple robots perform adaptive formation movement toward the navigation point.

[0040] More specifically, the navigation points of the navigator robot are adaptively obtained from the discretized global path at a fixed reference distance d, according to the following rules:

[0041]

[0042] In the formula, Goal(t) and Goal(t+1) represent the navigator's navigation points at the current and next moments, respectively; j represents the node sequence of the current navigation point in the path. The estimated node spacing value is rounded down; d LG This represents the distance from the navigator to the navigation point at the current moment, when d LG When the distance is less than the expected threshold d, the navigation point for the next moment is obtained in advance to avoid multiple robots lingering between navigation points and accelerating or decelerating.

[0043] More specifically, the navigation points of the follower robots are constructed using formation properties, according to the following rules:

[0044]

[0045]

[0046] In the formula, (x F y F (x) represents the coordinates of the follower's navigation point. G y G ) represents the navigator's waypoint, (x L y L This indicates the navigator's current position. and L d These represent the expected formation angle and expected formation distance of the follower and the navigator, respectively.

[0047] Step 10: Calculate the resultant force and direction of motion of the multiple robots based on the attraction and repulsion formulas of the artificial potential field method.

[0048] More specifically, the formulas for calculating the attractive and repulsive forces using the standard artificial potential field method are as follows:

[0049] Fattr =k attr ρ(X, X) G )

[0050]

[0051] In the formula, kattr and k rep ρ(X, X) represents the gravitational coefficient and the repulsive coefficient, respectively; G () represents the distance from the robot's current position X to the navigation point X. G Let ρ(X, X0) represent the relative distance between the robot and the obstacle, and ρ0 be the maximum influence distance of the obstacle's repulsive potential field. When the distance ρ(X, X0) between the mobile robot and the obstacle is greater than the maximum influence distance ρ0, the repulsive potential field of the obstacle on the mobile robot is zero. At this time, the obstacle can be considered to have no effect on the robot's motion. When the distance ρ(X, X0) between the mobile robot and the obstacle is less than the maximum influence distance ρ0, the repulsive potential field will become larger as the distance between the mobile robot and the obstacle gets closer.

[0052] More specifically, the standard artificial potential field method is prone to causing robots to get stuck in a dead loop or move unstably in environments with high obstacle density. Therefore, this method introduces dynamic weighting factors and nonlinear factors into the attraction and repulsion coefficients, respectively, and constructs an S-function using obstacle density and robot speed to evaluate the robot's environment. Furthermore, it enhances the robot's adaptability to complex environments through nonlinearly improved repulsion and attraction forces. The method is as follows:

[0053] F attr =k attr e -λt ρ(X, X) G ) α

[0054]

[0055] α=α max (1-S density (1-S) speed )

[0056] β=β max S density S speed

[0057]

[0058]

[0059] In the formula, t is time, λ is the decay factor, θ is the angle between the robot's motion direction and the obstacle direction, k1, k2, k3 and k4 are adjustment parameters; α and β are parameters that control the growth rate of the gravity function and the repulsion function, respectively, and determine the nonlinearity of the function; density and speed represent the obstacle density in the environment and the robot's motion speed, respectively.

[0060] More specifically, ααα max and β max This represents the maximum value of the gravitational and repulsive force coefficients under worst-case conditions. When both obstacle density and robot speed are low, S... density and S speed Both are close to 0, meaning α is close to its maximum value and β is close to 0, allowing the robot to move quickly through open areas. As density and speed increase, S... density and S speed As the value gradually approaches 1, α will gradually decrease and β will gradually increase, allowing the robot to avoid collisions with obstacles.

[0061] Step 11: The multiple robots move according to their respective resultant force directions and update their position information.

[0062] More specifically, the robot's position update rule is as follows:

[0063]

[0064] In the formula, the robot's current position is (Current_X, Current_Y), v° is the preset velocity, Δt is the sampling time, and θ is the direction of the resultant force.

[0065] More specifically, the follower will determine the formation distance L from the leader. FL If the threshold is not met, the follower's speed is adjusted according to the following formula:

[0066]

[0067] In the formula, the formation distance threshold interval is [L d -0.05, L d +0.05], L d The desired distance for the formation is denoted by rand, which is a random decimal between 0 and 1.

[0068] Step 12: Determine if the multiple robots have reached the target point. If yes, end the process; otherwise, return to step 9.

[0069] The beneficial effects of this invention are:

[0070] This invention proposes a multi-robot formation motion method based on an improved artificial potential field method and a hybrid ant colony algorithm, which has the following advantages: First, the improved ant colony algorithm provides a global navigation path for the navigator robot in complex obstacle environments, and solves the problems of slow convergence speed, difficulty in guaranteeing global optimum, and path safety of the standard ant colony algorithm; Second, the multi-robots perform adaptive formation motion and obstacle avoidance based on the improved artificial potential field method, wherein the navigator adaptively navigates according to the global path, the followers dynamically track the formation navigation points based on the navigator following method, and the followers adaptively adjust their movement speed according to the formation threshold to maintain the multi-robot formation. Attached Figure Description

[0071] Figure 1 The algorithm flowchart provided for the embodiments of the present invention;

[0072] Figure 2 This is a schematic diagram of grid map symbols provided in an embodiment of the present invention;

[0073] Figure 3 This is a schematic diagram of the eight-neighbor search direction provided in an embodiment of the present invention;

[0074] Figure 4 This is a schematic diagram illustrating the safe optimization of paths using the heuristic matrix D provided in an embodiment of the present invention.

[0075] Figure 5 This diagram illustrates the improved ant colony algorithm path discretization and adaptive navigation point selection by the navigator robot, as provided in this embodiment of the invention. From left to right, it represents the original global path, the global path discretization, and the adaptive navigation path.

[0076] Figure 6 This is a schematic diagram illustrating the construction of follower robot navigation points based on formation characteristics, provided in an embodiment of the present invention.

[0077] Figure 7 This is a comparative diagram of the improved ant colony algorithm path planning provided in the embodiments of the present invention. The paths from left to right and from top to bottom are D4-ACO algorithm path, D8-ACO algorithm path, path of the present method, and path length convergence comparison.

[0078] Figure 8 A comparative schematic diagram of the improved artificial potential field method path planning provided in the embodiments of the present invention;

[0079] Figure 9 A schematic diagram of multi-robot path planning in a simple obstacle environment using the improved artificial potential field method hybrid ant colony algorithm provided in an embodiment of the present invention.

[0080] Figure 10A schematic diagram illustrating the multi-robot formation error in a simple obstacle environment using the improved artificial potential field method hybrid ant colony algorithm provided in this embodiment of the invention.

[0081] Figure 11 A schematic diagram illustrating multi-robot path planning in a complex obstacle environment using the improved artificial potential field method hybrid ant colony algorithm provided in an embodiment of the present invention.

[0082] Figure 12 A schematic diagram illustrating the multi-robot formation error in a complex obstacle environment using the improved artificial potential field hybrid ant colony algorithm provided in this embodiment of the invention. Detailed Implementation

[0083] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0084] This invention provides a multi-robot formation motion method based on an improved artificial potential field method and a hybrid ant colony algorithm, the flowchart of which is shown below. Figure 1 As shown, it includes the following steps:

[0085] Step 1: Establish a global map environment of size N×N.

[0086] More specifically, the map is represented by a matrix, containing impassable obstacle grids, represented by 1; and passable free grids, represented by 0. The coordinates (x, y) of the center point of all grid cells are converted into grid labels according to the following rules:

[0087] Number = N + (x - 0.5)N - y + 0.5

[0088] Step 2: Initialize the parameters of the multi-robot algorithm, the ant colony algorithm, and the artificial potential field method.

[0089] More specifically, the multi-robot parameters include: the navigator's start and end coordinates are (1.5, 1.5) and (19.5, 19.5), the follower 1's start coordinates are (1.5, 0.5), the follower 2's start coordinates are (0.5, 1.5), and the expected distance L between the navigator and followers 1 and 2. d For 1m and desired angle The values ​​are -90° and 180° respectively, the velocity v° is 0.5 m / s, and the node spacing n is... ds The value is 0.1, the navigation point reference distance d is 4m, the expected distance threshold is (0, 4m], and the formation distance threshold is [L]. d -0.05, L d+0.05]. Ant colony algorithm parameters include: number of ants M = 50, maximum number of iterations NC = 50, pheromone weight α = 1, heuristic function weight β = 3, pheromone evaporation coefficient ρ = 0.3, pheromone intensity Q = 100, heuristic function importance x = 10, pheromone importance y and z = 1, heuristic matrix D is initialized by the navigator's start and end points, and pheromone matrix Tau is initialized by a constant. Artificial potential field method parameters include: gravity coefficient k. attr The repulsion coefficient is 10, and the repulsion coefficient k is 10. rep The maximum influence distance ρ0 of the obstacle repulsive potential field is 3, the attenuation factor λ is 0.01, the adjustment parameters k1 is 0.4, k2 is 0.4, k3 is 0.2 and k4 is 0.2, and the maximum value of the gravitational coefficient α is 5. max The value is 4, and the maximum repulsion coefficient γ is 4. max It is 7.5.

[0090] More specifically, the standard heuristic matrix D is:

[0091]

[0092] More specifically, the heuristic matrix D is optimized for safety in the eight-neighbor search direction, according to the following rules:

[0093]

[0094] In the formula, mod() represents the modulo operation, Dir() represents the grid number of the eight-neighbor candidate direction, and i and j represent the current grid number where the ant is located and the eight-neighbor candidate direction, respectively.

[0095] Step 3: Determine if the current number of ants has reached the preset value. If so, perform a global pheromone update and jump to step 6; otherwise, execute step 4.

[0096] Step 4: Select walkable grids based on the heuristic matrix D, select the next grid node for the ant to move to using the roulette wheel principle, update the tabu table, and record the grid number and direction traversed by the ant.

[0097] More specifically, the principles of roulette are:

[0098]

[0099] In the formula, m represents the ant number, t represents the current iteration number, i represents the current grid cell where the ant is located, j represents the candidate grid cells for the ant, allowed represents the set of candidate grid cells, and τ ij (t) represents the pheromone, η ij (t) represents a heuristic function.

[0100] More specifically, the standard heuristic function η ij(t) is as follows:

[0101] η ij (t) = 1 / D(i,j)

[0102] More specifically, the heuristic function η ij (t) is as follows:

[0103]

[0104] In the formula, x represents the importance of the heuristic function, and L ij Let Nc and Nc represent the Euclidean distance from grid i to grid j. max These represent the current iteration number and the maximum iteration number, respectively.

[0105] More specifically, the standard pheromone τ ij (t) is as follows:

[0106]

[0107]

[0108] More specifically, the global pheromone τ ij (t) The update rules are as follows:

[0109]

[0110] In the formula, ρ is the pheromone evaporation factor, Q is the pheromone intensity, L is the path length, T is the number of path turns, and y and z are weighting factors.

[0111] Step 5: Determine if the ant has reached the navigator's target point. If so, record the path length and number of turns and return to step 3; otherwise, return to step 4.

[0112] Step 6: Determine if the current iteration number has reached the maximum iteration number. If so, output the navigator's optimal path; otherwise, go to step 5.

[0113] Step 7: Optimal path planned by the discretized ant colony algorithm.

[0114] More specifically, the standard spacing between adjacent path nodes is 1 or The method uses a given node spacing n ds After discretization, the node spacing is unified to n. ds Thus, a new navigator's navigation path is obtained.

[0115] Step 8: Introduce an unknown dynamic interference environment.

[0116] More specifically, the interference environment includes unknown static obstacles and dynamic obstacles: unknown static obstacles are randomly distributed; the movement paths of dynamic obstacles can be planned by the ant colony algorithm provided by this invention (implementation reference steps 1 to 6), and after obtaining the trajectory, it can be assigned a movement speed parameter v and a volume size parameter size.

[0117] Step 9: Multiple robots perform adaptive formation movement toward the navigation point.

[0118] More specifically, the navigation points of the navigator robot are adaptively obtained from the discretized global path at a fixed reference distance d, according to the following rules:

[0119]

[0120] In the formula, Goal(t) and Goal(t+1) represent the navigator's navigation points at the current and next moments, respectively; j represents the node sequence of the current navigation point in the path. The estimated node spacing value is rounded down; d LG This represents the distance from the navigator to the navigation point at the current moment, when d LG When the distance is less than the expected threshold d, the navigation point for the next moment is obtained in advance to avoid multiple robots lingering between navigation points and accelerating or decelerating.

[0121] More specifically, the navigation points of the follower robots are constructed using formation properties, according to the following rules:

[0122]

[0123]

[0124] In the formula, (x F y F (x) represents the coordinates of the follower's navigation point. G y G ) represents the navigator's waypoint, (x L y L This indicates the navigator's current position. and L d These represent the expected formation angle and expected formation distance of the follower and the navigator, respectively.

[0125] Step 10: Calculate the resultant force and direction of motion of the multiple robots based on the attraction and repulsion formulas of the artificial potential field method.

[0126] More specifically, the formulas for calculating the attractive and repulsive forces using the standard artificial potential field method are as follows:

[0127] F attr =k attr ρ(X, X) G )

[0128]

[0129] In the formula, k attr and k rep ρ(X, X) represents the gravitational coefficient and the repulsive coefficient, respectively; G () represents the distance from the robot's current position X to the navigation point X. G Let ρ(X, X0) represent the relative distance between the robot and the obstacle, and ρ0 be the maximum influence distance of the obstacle's repulsive potential field. When the distance ρ(X, X0) between the mobile robot and the obstacle is greater than the maximum influence distance ρ0, the repulsive potential field of the obstacle on the mobile robot is zero. At this time, the obstacle can be considered to have no effect on the robot's motion. When the distance ρ(X, X0) between the mobile robot and the obstacle is less than the maximum influence distance ρ0, the repulsive potential field will become larger as the distance between the mobile robot and the obstacle gets closer.

[0130] More specifically, the standard artificial potential field method is prone to causing robots to get stuck in a dead loop or move unstably in environments with high obstacle density. Therefore, this method introduces dynamic weighting factors and nonlinear factors into the attraction and repulsion coefficients, respectively, and constructs an S-function using obstacle density and robot speed to evaluate the robot's environment. Furthermore, it enhances the robot's adaptability to complex environments through nonlinearly improved repulsion and attraction forces. The method is as follows:

[0131] F attr =k attr e -λt ρ(X, X) G ) α

[0132]

[0133] α=α max (1-S density (1-S) speed )

[0134] β=β max S density S speed

[0135]

[0136]

[0137] In the formula, t is time, λ is the decay factor, θ is the angle between the robot's motion direction and the obstacle direction, k1, k2, k3 and k4 are adjustment parameters; α and β are parameters that control the growth rate of the gravity function and the repulsion function, respectively, and determine the nonlinearity of the function; density and speed represent the obstacle density in the environment and the robot's motion speed, respectively.

[0138] More specifically, α max and β max This represents the maximum value of the gravitational and repulsive force coefficients under worst-case conditions. When both obstacle density and robot speed are low, S... density and S speed Both are close to 0, meaning α is close to its maximum value and β is close to 0, allowing the robot to move quickly through open areas. As density and speed increase, S... density and S speed As the value gradually approaches 1, α will gradually decrease and β will gradually increase, allowing the robot to avoid collisions with obstacles.

[0139] Step 11: The multiple robots move according to their respective resultant force directions and update their position information.

[0140] More specifically, the robot's position update rule is as follows:

[0141]

[0142] In the formula, the robot's current position is (Current_X, Current_Y), v° is the preset velocity, Δt is the sampling time, and θ is the direction of the resultant force.

[0143] More specifically, the follower will determine the formation distance L from the leader. FL If the threshold is not met, the follower's speed is adjusted according to the following formula:

[0144]

[0145] In the formula, the formation distance threshold interval is [L d -0.05, L d +0.05], L d The desired distance for the formation is denoted by rand, which is a random decimal between 0 and 1.

[0146] Step 12: Determine if the multiple robots have reached the target point. If yes, end the process; otherwise, return to step 9.

[0147] Experimental verification of the present invention 1:

[0148] Reference Figure 7The improved ant colony algorithm provided in this invention was tested using a 20×20 grid map (mainly testing steps 1-6). The standard four-neighbor ant colony algorithm D4-ACO and the standard eight-neighbor ant colony algorithm D8-ACO were selected for comparison. Referring to the experimental results in Table 1, D4-ACO only has path search capabilities in four directions, sacrificing path length and smoothness for algorithm speed and security. See also... Figure 3 As shown in Table 1, D8-AC0 has an eight-neighbor search direction. While its algorithm efficiency and security are lower than D4-ACO, its core path metrics (path length and number of turns) are superior. (See also...) Figure 4 The method provided by this invention optimizes the safety of the heuristic matrix in the eight-neighbor search direction in step two, thus combining the advantages of D8-ACO in terms of path length and D4-ACO in terms of path safety. In step four, the method improves the heuristic function, as shown in Table 1, enhancing the algorithm's search efficiency compared to D8-ACO, which also uses eight-neighbor search. Step four also improves the pheromone update strategy, significantly reducing the core path length and turn count metrics compared to D4-ACO and D8-ACO, thus improving path performance. In summary, the improved ant colony algorithm provided in steps 1-6 of this invention provides a good and comprehensive reference for the motion navigation of the navigator robot in subsequent steps.

[0149] Table 1 Comparison of path planning results between traditional ant colony algorithm and our proposed method

[0150] Path length / m 38.0000 32.1421 29.6000 Number of turns / time 26 21 13 Path collision none have none Number of iterations to stabilize 4 24 22 Algorithm computation time / s 0.5686 1.2306 0.8225

[0151] Experimental verification of the present invention 2:

[0152] Reference Figure 5 The navigation path of the robot using this method is obtained by discretizing the navigation path provided in Experiment 1 in step 8. (Refer to...) Figure 8 The improved artificial potential field method provided in this invention was tested and compared using the obstacle layout environment of Experiment 1 and the standard artificial potential field method (mainly testing the obstacle avoidance performance of the navigator robot in steps 7-12). (Refer to...) Figure 8It is evident that the robot using the standard artificial potential field method for obstacle avoidance suffers from poor obstacle avoidance due to the lack of global path guidance and insufficient obstacle avoidance mechanisms in dense obstacle environments, resulting in a distance of 26.2000m after repeatedly traversing the obstacle area to reach the target point. The method provided by this invention combines the robot with a global path implemented using an improved ant colony algorithm in steps 8 and 9, and in step 10, it provides an artificial potential field method based on environmental factors to optimize the robot's obstacle avoidance and navigation capabilities. Ultimately, the robot using this method safely reaches the target point, with an actual path length of 26.8500m, close to the planned path length of 28.1858m.

[0153] Experimental verification of the present invention 3:

[0154] See Figures 9-12 Verify the overall effectiveness of the proposed method for multi-robot formation motion (test complete steps 1-12), where Figure 11 Environment Figure 9 The environment was further enhanced with unknown dynamic obstacles and randomly distributed unknown static obstacles. The starting and ending coordinates of the dynamic obstacles are (19.5, 19.5) and (1.5, 1.5), respectively, with a speed of 0.1 m / s and a volume radius of 0.3 m. From... Figure 9 and Figure 11 As can be seen from the motion path diagrams, in both types of complex environments, multiple robots exhibited good formation movement and obstacle avoidance performance under the guidance of this method. Figure 10 and Figure 12 The formation error diagram shows that during the movement of multiple robots, the formation correction strategy provided in step 11 of this method maintains the formation formation, and the position errors of the navigator and followers are kept within the expected formation distance L. d (Approximately 1m). As can be seen from Table 2, Figure 11 In this case, the multiple robots generated more obstacle avoidance behaviors, therefore the actual path length was slightly greater than [the required length]. Figure 9 Case study.

[0155] Table 2 Results of Multi-Robot Path Planning

[0156]

[0157] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-robot formation motion method based on an improved artificial potential field method and a hybrid ant colony algorithm, characterized in that, The optimization steps include the following: Step 1: Establish a global map environment of size N×N; Step 2: Initialize multi-robot parameters, ant colony algorithm parameters, and artificial potential field method parameters; wherein, the ant colony algorithm parameters include a heuristic matrix optimized for safety in the eight-neighborhood search direction. The artificial potential field method introduces dynamic weighting factors and nonlinear factors into the attraction and repulsion coefficients, respectively, and constructs an S-function using obstacle density and robot speed to evaluate the robot's environment. Furthermore, it enhances the robot's adaptability to complex environments through nonlinearly improved repulsion and attraction forces. The S-function construction method is as follows: In the formula, t is time, λ is the decay factor, θ is the angle between the robot's motion direction and the obstacle direction, k1, k2, k3 and k4 are adjustment parameters; α and β are parameters that control the growth rate of the gravity function and the repulsion function, respectively, and determine the nonlinearity of the function; density and speed represent the obstacle density in the environment and the robot's motion speed, respectively. Step 3: Determine if the current number of ants has reached the preset value. If so, perform a global pheromone update and jump to step 6; otherwise, execute step 4. Step 4: Based on the heuristic matrix Select walkable grids, choose the next grid node for the ant to move to using the roulette wheel principle, update the tabu table, and record the grid number and direction of the ant's movement; Step 5: Determine if the ant has reached the navigator's target point. If so, record the path length and number of turns and return to step 3; otherwise, return to step 4. Step 6: Determine if the current iteration number has reached the maximum iteration number. If yes, output the navigator's optimal path; otherwise, go to step 5. Step 7: Optimal path planned by the discretized ant colony algorithm; Step 8: Introduce an unknown dynamic interference environment; Step 9: Multiple robots perform adaptive formation movement towards a navigation point; wherein, the navigation point of the leader robot is adaptively obtained from the discretized global path at a fixed reference distance d; the follower robots are based on their expected formation distance with the leader robot. and expected formation angle And the current position and navigation point of the navigator robot, and calculate its own navigation point; Step 10: Calculate the resultant force and direction of motion of the multiple robots based on the attraction and repulsion formulas of the artificial potential field method; Step 11: Multiple robots move according to their respective resultant force directions and update their position information; the follower robot calculates its formation distance from the leader robot in real time. ,like If the speed exceeds the threshold range, speed correction will be performed according to preset rules to maintain formation. Step 12: Determine if the multiple robots have reached the target point. If yes, end the process; otherwise, return to step 9.

2. The multi-robot formation motion method based on the improved artificial potential field method and hybrid ant colony algorithm according to claim 1, characterized in that, The map in step 1 uses a matrix. The grid is represented by 1 for impassable obstacle grids and 0 for passable free grids; the coordinates of the center points of all grids are determined according to the following rules. It was converted into a raster label:

3. The multi-robot formation motion method based on the improved artificial potential field method and hybrid ant colony algorithm according to claim 1, characterized in that, Step 2 includes the following multi-robot parameters: the navigator's start and end coordinates, the follower's end coordinates, and the expected distance between the navigator and the follower. and expectations Speed ​​of movement Node spacing Reference distance to navigation point Expected distance threshold Formation distance threshold [ , Ant colony algorithm parameters also include: number of ants M, maximum number of iterations NC, and pheromone weight. heuristic function weights pheromone volatility coefficient pheromone intensity The importance of heuristic functions The importance of pheromones and pheromone initialization matrix The parameters for the artificial potential field method include: gravitational coefficient. repulsion coefficient The maximum influence distance of the repulsive potential field of the obstacle Attenuation factor Adjust parameters , 2. 3 and 4. Maximum values ​​of attraction and repulsion coefficients and ; The standard heuristic matrix D is: The heuristic matrix The safety optimization rules applied in the eight-neighbor search direction are as follows: In the formula, This indicates the modulo operation. The grid label representing the candidate directions in the eight neighboring regions. and These represent the current grid number where the ant is located and the eight neighboring directions to be selected, respectively.

4. The multi-robot formation motion method based on the improved artificial potential field method and hybrid ant colony algorithm according to claim 1, characterized in that, The roulette wheel betting principle in step 4 is as follows: In the formula, Indicates the ant number. Indicates the current iteration number. This indicates the current cell in which the ant is located. This represents the candidate grid for ants. Represents the set of candidate grid cells. Indicates pheromones, Represents a heuristic function; More specifically, standard heuristic functions as follows: More specifically, the heuristic function as follows: In the formula, Indicates the importance of the heuristic function. Indicates from grid To grid European distance, and These represent the current iteration number and the maximum iteration number, respectively. More specifically, standard pheromones as follows: More specifically, the global pheromone The update rules are as follows: In the formula, For pheromone volatile factors, For pheromone strength, For path length, The number of turns on the path. and This is the weighting factor.

5. The multi-robot formation motion method based on the improved artificial potential field method and hybrid ant colony algorithm according to claim 1, characterized in that, In step 7, the standard spacing between adjacent path nodes is 1 or... The method uses a given node spacing After discretization, the node spacing is unified. Thus, a new navigator's navigation path is obtained.

6. The multi-robot formation motion method based on the improved artificial potential field method and hybrid ant colony algorithm according to claim 1, characterized in that, In step 8, the interfering environment includes unknown static obstacles and dynamic obstacles: the unknown static obstacles are randomly distributed; the movement paths of the dynamic obstacles can be planned using the ant colony algorithm provided by this invention (implementation refers to steps 1-6), and after obtaining the trajectory, movement speed parameters can be assigned to them. and volume parameters .

7. The multi-robot formation motion method based on the improved artificial potential field method and hybrid ant colony algorithm according to claim 1, characterized in that, The navigation point acquisition rules for the navigator robot in step 9 are as follows: In the formula, and Indicates the navigator's navigation points for the current and next moments; This represents the sequence of nodes in the path representing the current navigation point; This involves rounding down the estimated node spacing value. This indicates the distance from the navigator to the navigation point at the current moment. Less than the expected distance threshold The navigation point for the next moment can be obtained in advance to avoid multiple robots lingering between navigation points and accelerating or decelerating. More specifically, the navigation points of the follower robots are constructed using formation properties, according to the following rules: In the formula, Indicates the coordinates of the follower's navigation point. Indicates the navigator's waypoint. This indicates the navigator's current position.

8. The multi-robot formation motion method based on the improved artificial potential field method and hybrid ant colony algorithm according to claim 1, characterized in that, The formulas for calculating the attractive and repulsive forces in the standard artificial potential field method in step 10 are as follows: In the formula, and These represent the gravitational coefficient and the repulsive coefficient, respectively. Indicates the robot's current position To the navigation point distance, Indicates the relative distance between the robot and the obstacle. The maximum influence distance of the repulsive potential field of the obstacle; the distance between the mobile robot and the obstacle. Greater than the maximum influence distance When the obstacle's repulsive potential field on the mobile robot is zero, it can be considered that the obstacle point has no temporary impact on the robot's motion; when the distance between the mobile robot and the obstacle... Less than the maximum influence distance At that time, the repulsive potential field will become larger as the distance between the mobile robot and the obstacle increases; More specifically, in the artificial potential field method and This represents the maximum value of the gravitational and repulsive force coefficients under worst-case conditions; when both obstacle density and robot speed are low, and Both are close to 0, which means Approaching the maximum value and When density and speed approach zero, the robot can move quickly through open areas; as density and speed increase, and Gradually approaching 1, this will lead to Gradually decrease, By increasing its size, the robot will avoid colliding with obstacles.

9. The multi-robot formation motion method based on the improved artificial potential field method and hybrid ant colony algorithm according to claim 1, characterized in that, The rule for updating the robot's position information in step 11 is as follows: In the formula, the robot's current position is , For preset speed, Sampling time, It is the direction of the resultant force; More specifically, the formation distance between followers and navigators. When the speed is outside the threshold range, the following formula is used for speed correction: In the formula, the formation distance threshold interval is [ , ] , For the desired formation distance, It is a random decimal number between 0 and 1.

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