A mobile robot path planning method based on improved ant colony algorithm and Bezier curve

Abstract

The present invention belongs to the field of mobile robot path planning, and specifically relates to a mobile robot path planning method based on an improved ant colony algorithm and a Bezier curve, comprising: using the improved ant colony algorithm for initial path planning to obtain all paths that successfully reach a target node; performing secondary path planning on all paths that successfully reach the target node to obtain an optimal path; using the Bezier curve to smooth the turning points in the optimal path to obtain a smooth optimal path; the path obtained by the present invention is safer and smoother, so that the robot can be more flexible in the working environment, thereby improving the working efficiency of the robot.

Description

Technical Field

[0001] The present invention belongs to the field of mobile robot path planning, and in particular relates to a mobile robot path planning method based on an improved ant colony algorithm and a Bezier curve. Background Art

[0002] With the continuous advancement of science and technology and the continuous advancement of industrial intelligence upgrades, the application of mobile robots has received widespread attention. Among them, the path planning of mobile robots is a research hotspot. Its purpose is to search for an optimal or near-optimal safe and collision-free path from the starting position to the target position according to the specified optimization rules in an unknown or known environment. At present, a lot of research has been done on the path planning algorithms of mobile robots at home and abroad. The research methods can be roughly divided into two categories: traditional path planning algorithms and intelligent bionic path planning algorithms. Traditional path planning algorithms include artificial potential field method, Dijkstra algorithm, A* algorithm, etc., and intelligent bionic algorithms include ant colony algorithm, particle swarm algorithm, genetic algorithm, wolf pack algorithm, etc. Using the basic ant colony algorithm to find the optimal path in a two-dimensional static environment will easily fall into local optimality, slow convergence speed, and many turning points. On this basis, Zhang Heng et al. proposed an improved double-layer ant colony algorithm, which divides the ant colony into a guiding layer ant colony and a common layer ant colony, and improves the heuristic functions of the two ant colonies respectively, designs a free path-finding-pruning strategy for the guiding layer ant colony to deal with the deadlock problem, only updates pheromones for shorter paths, and suppresses the pheromone concentration on the suboptimal path. The experimental results show that the improved algorithm improves the search efficiency and optimization ability of the ant colony, and the convergence speed is also improved. However, the complexity of the improved algorithm has increased, the algorithm has more parameters, and the sensitivity of the algorithm parameters has increased. The planned path is not smooth enough, and there are more turning points, which is not conducive to the operation of the real robot. Chinese patent (CN111982125A) discloses a path planning method based on an improved ant colony algorithm, which combines an improved artificial potential field (APF) algorithm with an ant colony algorithm. First, the improved APF algorithm is used for initial map planning, and then the evaluation function of the A* algorithm and the path turning angle are used to improve the heuristic function, and the heuristic information increasing function is introduced. Finally, the state transition rule is improved and the threshold of the state transition function is adaptively adjusted. This improvement measure can effectively improve the initial release of pheromones, but it requires a certain amount of preprocessing time for initial path planning and is not suitable for real-time applications. The planned path has many turning points, which is not conducive to the operation of real robots. Summary of the invention

[0003] To solve the above problems, the present invention provides a mobile robot path planning method based on an improved ant colony algorithm and a Bezier curve, comprising:

[0004] S1. Use the grid method to build an environment map and initialize parameters;

[0005] S2. Use the improved ant colony algorithm to perform initial path planning and obtain all paths that successfully reach the target node;

[0006] S3. Perform secondary path planning on all paths that successfully reach the target node to obtain an optimal path;

[0007] S4. Use Bezier curve to smooth the turning points in the optimal path to obtain a smooth optimal path.

[0008] Furthermore, the initial path planning process includes:

[0009] S11. Set the maximum number of iterations to 1;

[0010] S12. Place an ant at the initial node S of the environment map and initialize the taboo table;

[0011] S13. Any ant searches for the next node at the current node according to the path search rule, adds the next node to the taboo table and updates the path length;

[0012] S14. Determine whether the ant has completed one iteration. If so, execute step S15, otherwise return to step S13;

[0013] S15. Determine whether the ant has reached the target node. If not, abandon the ant. Otherwise, keep the ant and calculate the length of the path for the ant to reach the target node.

[0014] S16. After all ants have completed the path search, the average length of all paths is calculated, and the pheromone of all paths that successfully reach the target node is updated according to the reward and penalty mechanism;

[0015] S17. Determine whether the number of iterations reaches the maximum number of iterations. If so, output all paths that successfully reach the target node; otherwise, clear the taboo table, increase the number of iterations by 1, and return to step S12.

[0016] Furthermore, the path finding rule is expressed as:

[0017]

[0018]

[0019] Among them, j represents the next node to be found, τ ij represents the pheromone concentration on the path <i,j>, is the inverse of the Euclidean distance from the next node j to the target node G, q o is the dynamic selection factor, η ijrepresents the heuristic information from the current node i to the next node j, α represents the pheromone heuristic factor, β represents the expected heuristic factor, and χ represents the target point heuristic factor. represents the state transition probability of the kth ant from the current node i to the next node j, allowed k Represents the set of next nodes j that the kth ant can choose at the current node i.

[0020] Furthermore, the calculation formula of the dynamic selection factor is:

[0021]

[0022] Where n represents the current iteration number.

[0023] Furthermore, the length of all paths that successfully reach the target node is calculated, and based on the maximum and minimum ant model and the elite ant model, a reward and penalty mechanism is proposed to update pheromones, including:

[0024] If the current path is the optimal path, the pheromone update is expressed as:

[0025] τ ij (t)=(1-ρ)×τ ij (t-1)+λ1×ρ×Δτ ij (t);

[0026] If the current path length is greater than the optimal path length and lower than the average path length, the pheromone update is expressed as:

[0027] τ ij (t)=(1-ρ)×τ ij (t-1)+λ2×ρ×Δτ ij (t);

[0028] If the current path length is greater than the average path, the pheromone update is expressed as:

[0029] τ ij (t)=(1-ρ)×τ ij (t-1)-λ3×ρ×Δτ ij (t);

[0030] Among them, λ1, λ2, and λ3 are the coefficients of pheromone increase and decrease, which are positive numbers, and τ ij (t-1) represents the pheromone concentration on the path <i,j> after t-1 iterations, τ ij (t) represents the pheromone concentration on the path <i,j> after t iterations, ρ represents the pheromone concentration volatility coefficient, where Δτ ij (t) represents the pheromone increment, and its calculation formula is:

[0031]

[0032] L k (t) represents the length of the path found by the k-th ant in the t-th iteration, and Q represents the pheromone intensity.

[0033] Furthermore, the secondary path planning includes:

[0034] S21. Set the maximum number of iterations of the quadratic programming to 1;

[0035] S22. Obtain the path nodes that the ants that successfully reach the target node pass through in the initial path planning, and initialize the taboo table;

[0036] S23. Any ant searches for the next node b at the current node a according to the quadratic planning rule, adds the next node to the taboo table and updates the path length until the ant reaches the target node or a deadlock occurs;

[0037] S24. Determine whether all ants have completed one iteration. If so, execute step S25, otherwise return to step S23;

[0038] S25. Obtain the path for the ant to reach the target node, and update the pheromone of the path according to the secondary pheromone update rule;

[0039] S26. Determine whether the number of iterations of the quadratic programming reaches the maximum number of iterations of the quadratic programming. If so, output the optimal path. Otherwise, clear the taboo table, add 1 to the number of iterations of the quadratic programming, and return to step S22.

[0040] Furthermore, the quadratic programming rule is expressed as:

[0041]

[0042] in, represents the state transition probability of the kth ant from node a to node b, α1 represents the pheromone heuristic factor of the quadratic programming, β1 represents the expected heuristic factor of the quadratic programming, χ1 represents the target point heuristic factor of the quadratic programming, τ ab (t) represents the pheromone concentration on the path <a,b> in the tth iteration, η ab (t) represents node N a With node N b The Euclidean distance between Represents node N b The inverse of the Euclidean distance to the target node G.

[0043] Furthermore, the secondary pheromone update rule is expressed as:

[0044] τab (t)=(1-ρ1)×τ ab (t-1)+ρ1×Δτ ab (t);

[0045] Among them, τ ab (t) represents the pheromone concentration on the path <a, b> after the tth iteration, ρ1 represents the volatility coefficient of the pheromone concentration during quadratic programming, Δτ ab (t) represents the pheromone increment, and its calculation formula is:

[0046]

[0047] Among them, n k (t) represents the number of turning points in the path planned by the kth ant in the tth generation, L k (t) represents the optimal path length planned by the kth ant in the tth generation, sm k (t) represents the smoothness of the path planned by the kth ant in the tth generation.

[0048] Beneficial effects of the present invention:

[0049] The present invention provides a mobile robot path planning method based on an improved ant colony algorithm and a Bezier curve. The improved ant colony algorithm is used to perform initial path planning to find all paths that successfully reach the target point. In the initial path planning, a pseudo-random state transfer rule is first used to select the next path node, a dynamic selection factor is defined to adaptively update the selection ratio, and the distance from the next node to the target node is introduced into the transfer probability, thereby improving the search efficiency of the algorithm and avoiding the algorithm from falling into a local optimum; at the same time, a reward and penalty mechanism is proposed to update the pheromone increment, strengthen the guidance of high-quality ants to their offspring, avoid the misleading of low-quality ants to their offspring, and improve the convergence speed of the algorithm; when performing secondary path planning, unnecessary turning points are discarded, and a path is evaluated by comprehensively considering factors such as the optimal path length, the number of path turning points, and the path smoothness; finally, the Bezier curve is used to smooth the path around the remaining turning points, and finally a smooth path is obtained. The path obtained by the method is safer and smoother, so that the robot can be more flexible in the working environment and the work efficiency of the robot is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of a mobile robot path planning method based on an improved ant colony algorithm and a Bezier curve of the present invention;

[0051] Figure 2 A path planning diagram according to an embodiment of the present invention;

[0052] Figure 3is a flow chart of the initial path planning of the present invention;

[0053] Figure 4 It is a flow chart of the secondary path planning of the present invention. DETAILED DESCRIPTION

[0054] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] The present invention provides a mobile robot path planning method based on an improved ant colony algorithm and Bezier curves. Figure 1 As shown, including:

[0056] S1. Use the grid method to build an environment map and initialize parameters;

[0057] S2. Use the improved ant colony algorithm to perform initial path planning and obtain all paths that successfully reach the target node;

[0058] S3. Perform secondary path planning on all paths that successfully reach the target node to obtain an optimal path;

[0059] S4. Use Bezier curve to smooth the turning points in the optimal path to obtain a smooth optimal path.

[0060] In one embodiment, if Figure 2 As shown in the figure, the grid method is used to model the robot's working environment to obtain a random map, in which the white grid is a free grid, that is, the feasible area of ​​the robot, and the black grid is an obstacle grid, that is, the area where the robot cannot pass. The unit grid is equivalent to the size of the robot, and the grids in the model are encoded from left to right and from top to bottom, and one grid represents a position node.

[0061] First, the improved ant colony algorithm is used for the initial path planning, that is, the robot path planning experiment is carried out under the two-dimensional static grid map to find the path that the ants have taken to successfully reach the target node. The relevant parameters involved in the initial path planning include the starting position S, the target position G, and the maximum number of iterations of the algorithm N. max , ant number M, information heuristic factor α, expected heuristic factor β, target point heuristic factor χ, pheromone concentration volatility coefficient ρ, pheromone intensity Q, etc., all parameters are initialized, and the specific process of the initial path planning is as follows Figure 3 As shown, including:

[0062] S11. Set the maximum number of iterations to 1;

[0063] S12. Place an ant at the initial node S of the environment map and initialize the taboo table;

[0064] The taboo table stores the path nodes and obstacle nodes that the ants have already walked through. In subsequent path planning, the nodes in the taboo table cannot be selected.

[0065] S13. Any ant searches for the next node j at the current node i according to the path search rule (pseudo-random state transition rule), adds the next node j to the taboo table and updates the path length;

[0066] Specifically, the path finding rule is expressed as:

[0067]

[0068]

[0069] In the pseudo-random state transition rule, the state transition probability function adds the inverse of the distance from the next node to the target node, which improves the search efficiency and globality of the algorithm; where j represents the next node to be found, τ ij represents the pheromone concentration on the path <i,j>, is the inverse of the Euclidean distance from the next node j to the target node G, α represents the information heuristic factor, β represents the expected heuristic factor, and χ represents the target point heuristic factor. represents the state transition probability of the kth ant from the current node i to the next node j, allowed k represents the set of next nodes j that the kth ant can choose at the current node i, q o It is a dynamic selection factor, which is used to adaptively update the selection ratio. o Large, which can improve the search efficiency in the early stage of the algorithm, and in the middle and late stages of the algorithm o A larger value can ensure the global search capability of the algorithm. o The expression is:

[0070]

[0071] Where n represents the current number of iterations; η ij Represents the heuristic information from the current node i to the next node j, and its calculation formula is:

[0072]

[0073] (x i ,y i ) represents the position coordinates of the current node i, d ijRepresents the Euclidean distance between the current node i and the next node j.

[0074] S14. Determine whether the ant has completed one iteration, that is, has been looking for the next node, and whether the ant has reached the target node or a deadlock state has occurred. If so, execute step S15, otherwise return to step S13;

[0075] S15. Determine whether the ant has reached the target node. If not, abandon the ant. Otherwise, keep the ant and calculate the length of the path that successfully reaches the target node.

[0076] S16. After all ants have completed a path search, the average length of all paths is calculated. According to the reward and penalty mechanism, pheromones are updated for all paths that successfully reach the target node.

[0077] Specifically, based on the maximum-minimum ant model and the elite ant model, a reward-penalty mechanism is proposed to update pheromones, including: calculating the length of all paths that successfully reach the target node, obtaining the optimal path and updating its pheromone, which is expressed as:

[0078] τ ij (t)=(1-ρ)×τ ij (t-1)+λ1×ρ×Δτ ij (t);

[0079] For the optimal path, the highest pheromone concentration reward should be given to strengthen the guiding role of the optimal path for future generations of ants. In the remaining paths, if the path length experienced by the ants is greater than the optimal path length and lower than the average path length, the pheromone update is expressed as:

[0080] τ ij (t)=(1-ρ)×τ ij (t-1)+λ2×ρ×Δτ ij (t);

[0081] If the path length experienced by the ants is greater than the average path, the penalty for the poor path should be increased to reduce its misleading effect on the next generation of ants. The pheromone update is expressed as:

[0082] τ ij (t)=(1-ρ)×τ ij (t-1)-λ3×ρ×Δτ ij (t);

[0083] Among them, λ1, λ2, and λ3 are the pheromone increase and decrease coefficients, and their value range is {0.1, 1, 5, 10, 15, 20}. The optimal set of pheromone increase and decrease coefficients τ is obtained through simulation experimental results. ij(t-1) represents the pheromone concentration on the path <i,j> after t-1 iterations, τ ij (t) represents the pheromone concentration on the path <i,j> after t iterations, ρ represents the volatility coefficient of pheromone concentration, where Δτ ij (t) represents the pheromone increment, and its calculation formula is:

[0084]

[0085] L k (t) represents the length of the path found by the k-th ant in the t-th iteration, and Q represents the pheromone intensity.

[0086] S17. Determine whether the number of iterations reaches the maximum number of iterations N max If so, output all paths that successfully reach the target node; otherwise, clear the taboo table, increase the number of iterations by 1, and return to step S12.

[0087] At present, mobile robot path planning experiments are mainly carried out under two-dimensional grid maps. The setting of the map model will affect the quality of the path. In addition, when finding the optimal path, only the length of the path is considered, and the wear and tear of the actual operation of the mobile robot, obstacle avoidance, and the smoothness of the route are not considered. This will not be conducive to the direct application of the algorithm to the mobile robot path planning experiment in the real environment. Therefore, the present invention proposes a secondary path planning strategy for mobile robots. After the initial path planning is completed using the improved ant colony algorithm, the ants that have not reached the target node are abandoned, and the grid nodes passed by all ants that successfully reach the target node are recorded, and optimization is performed based on the planned path.

[0088] In one embodiment, after the initial path planning is performed by the improved ant colony algorithm, all paths that successfully reach the target node are saved, where all grid nodes that a path that successfully reaches the target node passes through can be represented as N = {S, N1, N2, ..., N n-1 ,N n ,G}, when performing secondary path planning, the direction of the next node selected by the ant is towards the target node, so the direction of the next node selected during secondary path planning is unidirectional. If the existence of obstacles between nodes is not considered, when the ant is located at N i-1 When selecting the next node, the nodes that ants can choose are as follows:

[0089] N i = {N i+1 ,N i+2 ,N i+3 ,......,N n-1 ,N n ,G};

[0090] Where Ni+1 ,N i+2 ,N i+3 ,......,N n-1 ,N n ,G is N i The subsequent node is the N grid nodes in the path that successfully reaches the target node after the initial path planning. i The subsequent nodes. Generally speaking, there are many types and quantities of obstacles in the grid map, so it is necessary to determine whether there are obstacles between two nodes. Suppose there are two nodes N a 、N b , if N a 、N b If there is an obstacle between N and a Directly to N b , otherwise it can be passed, the specific judgment formula is as follows:

[0091]

[0092] At this time, when the ant is at N i-1 When selecting the next node, the obstacles between the two nodes are taken into account. The nodes that the ant can choose are expressed as:

[0093]

[0094] When the selection of the next node can be accurately determined, the secondary path planning of the mobile robot is carried out after the initial path planning.

[0095] Preferably, the secondary path planning strategy includes the maximum number of iterations N of the secondary planning. max1 , the number of ants that successfully reach the target node M1, the pheromone heuristic factor α1 of the quadratic planning, the expected heuristic factor β1 of the quadratic planning, the target point heuristic factor χ1 of the quadratic planning, the pheromone concentration volatility coefficient ρ1 of the quadratic planning, the pheromone intensity Q and other parameters. These parameters are initialized, and the secondary path planning is as follows Figure 4 As shown, specifically including:

[0096] S21. Set the maximum number of iterations of the quadratic programming to 1;

[0097] S22. Obtain the grid nodes that the ants that successfully reach the target node in the initial path planning pass through, initialize the taboo table and place M1 ants at the initial node;

[0098] S23. Any ant searches for the next node b at the current node a according to the quadratic programming rule (roulette method), adds the next node to the taboo table and updates the path length until the ant reaches the target node or a deadlock occurs;

[0099] Specifically, the quadratic programming rule is expressed as:

[0100]

[0101] Among them, χ1∈{0.5,1,1.5,2,2.5,3}, the optimal target point heuristic factor of quadratic programming is obtained through simulation experimental results. represents the state transition probability of the kth ant from node a to node b, τ ab (t) represents the pheromone concentration on the path <a,b> in the tth iteration, η ab (t) represents node N a With node N b The Euclidean distance between Represents node N b The reciprocal of the Euclidean distance to the target node G is calculated as follows:

[0102]

[0103]

[0104] S24. Determine whether all ants have completed one iteration, that is, all ants have completed one search. If so, execute step S25, otherwise return to step S23;

[0105] S25. Obtain the path taken by the ants that successfully reach the target node, and update the pheromone of the path according to the secondary pheromone update rule;

[0106] Specifically, in the secondary path planning, in order to obtain a path that is more suitable for the operation of the mobile robot, in the pheromone update process, the optimal path length, the number of path turning points, the path smoothness and other factors are comprehensively considered to evaluate a path, so the secondary pheromone update rule is expressed as:

[0107] τ ab (t)=(1-ρ1)×τ ab (t-1)+ρ1×Δτ ab (t);

[0108] Among them, τ ab (t) represents the pheromone concentration on the path <a, b> after the tth iteration, ρ1 represents the volatility coefficient of the pheromone concentration during quadratic programming, Δτ ab (t) represents the pheromone increment, and its calculation formula is:

[0109]

[0110] Among them, n k(t) represents the number of turning points in the path planned by the kth ant in the tth generation, L k (t) represents the optimal path length planned by the kth ant in the tth generation, sm k (t) represents the smoothness of the path planned by the kth ant in the tth generation; the calculation formula of the relevant parameters is:

[0111]

[0112]

[0113]

[0114] Among them, θ i+1 Represents the angle between the i+2th node and the i+1th node.

[0115] S26. Determine whether the number of iterations of the quadratic programming reaches the maximum number of iterations of the quadratic programming. If so, output the optimal path. Otherwise, clear the taboo table, add 1 to the number of iterations of the quadratic programming, and return to step S22.

[0116] After secondary path planning, the turning points of the path can be effectively reduced, and the broken lines in the path are also significantly reduced, such as Figure 2 As shown in the figure, the very tortuous curve is the path obtained after the initial planning, and the slightly gentle curve is the path obtained after the secondary planning. Obviously, there are fewer turning points and the path is smoother, but the path still has turning points. In order to make the mobile robot more efficient in actual operation and the walking path smoother, the Bezier curve is used to smooth the path. The Bezier curve is a smooth and differentiable spline curve. The n-order Bezier curve can be expressed as:

[0117]

[0118]

[0119] p i represents the coordinates of the ith control point, B i,n (t) is a Bernstein quadratic polynomial, where t ranges from [0,1], represents the coefficient of the quadratic term.

[0120] The present invention adopts a relatively common quadratic Bezier curve, and the expression of the quadratic Bezier curve is as follows:

[0121] p(t)=(1-t) 2 p0+2t(1-t)p1+t 2 p2 t∈[0,1];

[0122] Among them, p1, p2, and p3 are the control points of the curve. The optimal path obtained after quadratic planning is smoothed by a quadratic Bezier curve, and finally a smooth curve is obtained, which is more suitable for robot operation.

[0123] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A mobile robot path planning method based on improved ant colony algorithm and Bezier curve, characterized in that: include: S1. Use the grid method to build an environment map and initialize parameters; S2. Use the improved ant colony algorithm to perform initial path planning and obtain all paths that successfully reach the target node; The initial path planning process includes: S11. Set the maximum number of iterations to 1; S12. Place an ant at the initial node of the environment map and initialize the taboo table; S13. Any ant searches for the next node at the current node according to the path search rule, adds the next node to the taboo table and updates the path length; S14. Determine whether the ant has completed one iteration. If not, return to step S13, otherwise, execute step S15; S15. Determine whether the ant has reached the target node. If not, abandon the ant. Otherwise, keep the ant and calculate the length of the path for the ant to reach the target node. S16. After all ants have completed the path search, the average length of all paths is calculated, and the pheromone of all paths that successfully reach the target node is updated according to the reward and penalty mechanism; S17. Determine whether the number of iterations reaches the maximum number of iterations. If so, output all paths that successfully reach the target node; otherwise, clear the taboo table, increase the number of iterations by 1, and return to step S12; The path finding rule is expressed as: Among them, j represents the next node to be found, τ ij represents the pheromone concentration on the path <i,j>, is the inverse of the Euclidean distance from the next node j to the target node G, q o is the dynamic selection factor, η ij represents the heuristic information from the current node i to the next node j, α represents the pheromone heuristic factor, β represents the expected heuristic factor, and χ represents the target point heuristic factor. represents the state transition probability of the kth ant from the current node i to the next node j, allowed k represents the set of next nodes j that the kth ant can choose at the current node i; The dynamic selection factor is calculated as: Where n represents the current number of iterations; S3. Perform secondary path planning on all paths that successfully reach the target node to obtain an optimal path; S4. Use Bezier curve to smooth the turning points in the optimal path to obtain a smooth optimal path.

2. A mobile robot path planning method based on improved ant colony algorithm and Bezier curve according to claim 1, characterized in that: Calculate all paths that successfully reach the target node, and propose a reward-penalty mechanism to update pheromones based on the maximum-minimum ant model and the elite ant model, including: If the current path is the optimal path, the pheromone update is expressed as: t ij (t)=(1-ρ)×τ ij (t-1)+λ1×ρ×Δτ ij (t); If the current path length is greater than the optimal path length and lower than the average path length, the pheromone update is expressed as: t ij (t)=(1-ρ)×τ ij (t-1)+λ2×ρ×Δτ ij (t); If the current path length is greater than the average path, the pheromone update is expressed as: t ij (t)=(1-ρ)×τ ij (t-1)-λ3×ρ×Δτ ij (t); Among them, λ1, λ2, and λ3 are the coefficients of pheromone increase and decrease, which are positive numbers, and τ ij (t) represents the pheromone concentration on the path <i,j> after t iterations, τ ij (t-1) represents the pheromone concentration on the path <i,j> after t-1 iterations, ρ represents the volatility coefficient of pheromone concentration, where Δτ ij (t) represents the pheromone increment, and its calculation formula is: L k (t) represents the length of the path found by the k-th ant in the t-th iteration, and Q represents the pheromone intensity.

3. The mobile robot path planning method based on improved ant colony algorithm and Bezier curve according to claim 1, characterized in that: Secondary path planning includes: S21. Set the maximum number of iterations of the quadratic programming to 1; S22. Obtain the path nodes that the ants that successfully reach the target node pass through in the initial path planning, and initialize the taboo table; S23. Any ant searches for the next node b at the current node a according to the quadratic planning rule, adds the next node to the taboo table and updates the path length until the ant reaches the target node or a deadlock occurs; S24. Determine whether all ants have completed one iteration. If so, execute step S25, otherwise return to step S23; S25. Obtain the path for the ant to reach the target node, and update the pheromone of the path according to the secondary pheromone update rule; S26. Determine whether the number of iterations of the quadratic programming reaches the maximum number of iterations of the quadratic programming. If so, output the optimal path. Otherwise, clear the taboo table, add 1 to the number of iterations of the quadratic programming, and return to step S22.

4. The mobile robot path planning method based on improved ant colony algorithm and Bezier curve according to claim 3 is characterized in that: The quadratic programming rule is expressed as: in, represents the state transition probability of the kth ant from node a to node b, α1 represents the pheromone heuristic factor of the quadratic programming, β1 represents the expected heuristic factor of the quadratic programming, χ1 represents the target point heuristic factor of the quadratic programming, τ ab (t) represents the pheromone concentration on the path <a,b> in the tth iteration, η ab (t) represents node N a With node N b The Euclidean distance between Represents node N b The inverse of the Euclidean distance to the target node G.

5. The mobile robot path planning method based on improved ant colony algorithm and Bezier curve according to claim 3 is characterized in that: The secondary pheromone update rule is expressed as: t ab (t)=(1-ρ1)×τ ab (t-1)+ρ1×Δτ ab (t); Among them, τ ab (t) represents the pheromone concentration on the path <a, b> after the tth iteration, ρ1 represents the volatility coefficient of the pheromone concentration during quadratic programming, Δτ ab (t) represents the pheromone increment, and its calculation formula is: Among them, n k (t) represents the number of turning points in the path planned by the kth ant in the tth generation, L k (t) represents the optimal path length planned by the kth ant in the tth generation, sm k (t) represents the smoothness of the path planned by the kth ant in the tth generation.

Images