Robot path planning algorithm based on particle swarm optimization algorithm and dynamic window method

Abstract

The invention proposes a robot path planning algorithm based on a particle swarm optimization algorithm and a dynamic window method, and relates to the field of control theories and electronic information, and the method comprises the steps: introducing an inertia weight updating strategy based on a state factor, setting adaptive parameters and crossover and mutation operators to improve the global search capability, increase the population diversity, and improve the robot path planning precision. On-line self-adaptive updating of inertia weight and learning factors is realized on line in combination with Q-learning, gene combination modes are enriched through crossover operators, convergence and exploratory performance of the algorithm are improved, an obstacle avoidance strategy of a traditional DWA algorithm is improved, weight parameters of a dynamic window evaluation function are dynamically adjusted according to real-time information of a target and an obstacle, and an obstacle avoidance algorithm is established. According to the method, the global planning is adopted, the path points generated through global planning are adopted as temporary targets, fusion of MOQLCOPSO and the improved DWA algorithm is achieved, local optimum is effectively avoided, the planning efficiency and path safety are improved, and the method is suitable for mobile robot navigation under the complex three-dimensional terrain.

Description

Technical Field

[0001] This invention relates to the field of control theory and control engineering, specifically a robot path planning algorithm based on particle swarm optimization and dynamic window method. Background Technology

[0002] The development of mobile robots is an organic integration of advanced knowledge and skills from multiple disciplines and fields, involving automatic control, environmental perception, computer science, and other disciplines, while also incorporating cutting-edge technologies such as path planning and dynamic decision-making. As a crystallization of human wisdom, the research on mobile robots is not only of profound significance but also shows broad application prospects in many fields. With the continuous development of the economy, society, and science and technology, navigation technology and path planning for mobile robots have become the core focus of their research. Path planning is about finding the optimal, unobstructed path between two points in an environment with obstacles. An excellent path planning algorithm can effectively improve the performance of mobile robots, making them more efficient and flexible. Autonomous navigation capability is a hallmark of mobile robot intelligence, and path planning is one of the core technologies of autonomous navigation.

[0003] With the continuous development and advancement of robotics technology, robots are becoming increasingly specialized in their roles across various fields of production and daily life, and the environments in which they perform tasks are becoming increasingly complex and varied. As the scale of tasks expands, the workplaces of robots are no longer limited to structured environments such as offices, laboratories, and factory workshops, but are gradually extending to unstructured locations such as the wilderness, mountains, harsh battlefields, and disaster sites. This change requires robots not only to adapt to diverse environmental conditions but also to possess more flexible and diverse skills and functions.

[0004] However, most existing path planning techniques rely on a comprehensive understanding of the environment and precise location data, often assuming flat terrain, to calculate a path that satisfies movement requirements while being as optimized as possible. Furthermore, in actual task execution, the environment faced by robots is often complex, unknown, and constantly changing. Especially in environments with undulating terrain, the applicability and effectiveness of path planning methods are greatly limited. Undulating terrain not only increases the complexity of mobile robot path planning but also places higher demands on the robot's stability, obstacle avoidance capabilities, and task execution efficiency.

[0005] Path planning algorithms are mainly divided into two categories: global path planning algorithms and local path planning algorithms. The former constructs a topological model based on complete prior environmental knowledge, generating initial path schemes that meet optimality criteria. However, in unstructured terrain facing sudden dynamic obstacles, its environmental adaptability is significantly lacking, making real-time obstacle avoidance decision-making difficult. The latter relies on multi-source sensor data fusion technology and implements a rapid response mechanism through a dynamic environment perception module. However, its planning results may get stuck in local optima and the path may be overly convoluted. Furthermore, in large-scale complex environments, without intermediate point guidance, local path planning algorithms may fail to plan the optimal path, potentially preventing the robot from reaching its destination. Therefore, a case-by-case analysis should be conducted based on the type and attributes of the path planning algorithm, and appropriate control mechanisms should be set to allow the robot to switch between local and global path planning algorithms under dynamic paths. Summary of the Invention

[0006] To address the problems of existing technologies, this invention provides a robot path planning algorithm based on particle swarm optimization and dynamic windowing. By incorporating state factors, crossover and mutation operators, and combining multiple algorithms, it improves the robot's path planning performance in dynamic environments, better adapts to complex and dynamically changing environments, meets the needs of real-time applications, and avoids the problem of the robot getting stuck in local optima and failing to plan the optimal path.

[0007] This invention provides a robot path planning algorithm based on particle swarm optimization and dynamic window method, comprising the following steps:

[0008] S1. Introduce an inertial weight update strategy based on state factors, and set adaptive parameters and crossover mutation operators in the multi-objective particle swarm optimization algorithm to improve global search capability and increase population diversity.

[0009] S2. Combine the Q-learning algorithm to adaptively update the inertia weights and learning factors of MOPSO online, thereby enhancing the convergence ability of the MOPSO algorithm to the Pareto front.

[0010] S3. Introduce new gene combination methods using crossover operators to increase the explorability and diversity of the population during the iteration process;

[0011] S4. Improve the obstacle avoidance strategy of the traditional DWA algorithm by dynamically adjusting the weight parameters of the dynamic window evaluation function based on the real-time information of the target and obstacles.

[0012] S5. Based on the global static path MOQLCOPSO, the planned path points are used as temporary target points for the improved DWA algorithm in step S4, thus achieving the fusion of MOQLCOPSO and the improved DWA algorithm on the basis of global optimization.

[0013] As a further improvement, step S1 includes the following steps:

[0014] S1.1. The concept of state factor is proposed and defined as:

[0015] (1)

[0016] in, Calculated by the following formula:

[0017] (2)

[0018] Calculated by the following formula:

[0019] (3)

[0020] In the formula, For population size, and For path The objective function, and Let these represent the weights of path length and path undulation, respectively, and satisfy the following conditions: , and The two objective functions are path length and path undulation, respectively, at the th... The optimal value at the next iteration and The first The average path length and path variability at the next iteration are calculated using the following formula:

[0021] (4)

[0022] S1.2 Update the velocity and position of the i-th particle in the particle swarm in the (k+1)-th generation according to the equation shown below:

[0023] (5)

[0024] In the formula, pbest i (k) represents the local optimal position found by the i-th particle, gbest(k) is called the global optimal position, c1 and c2 are learning factors, and rand1 and rand2 are independent random numbers uniformly distributed in [0,1]. ω is the inertia weight, updated by the following formula:

[0025] (6)

[0026] in, , Let be the squared value of the state factor of the i-th particle in the k-th iteration;

[0027] S1.3 Calculate the mutation probability of the k-th generation particles according to the following formula:

[0028] P m (k)=0.1× (7)

[0029] S1.4 For particle i, randomly generate a real number rand i ∈[0,1], if rand i <P m (k), proceed to step S1.5; otherwise, exit the mutation section.

[0030] S1.5 Execute the mutation operation, randomly select a path point m, where m = rand([1, n-1]), and randomly select a value y. im ´ is the new value for path m, where y im = a×rand([1, n-1]).

[0031] In a further improvement, the path length of particle i in step S1 is expressed as:

[0032] (8)

[0033] The path undulation of particle i is expressed by the following formula:

[0034] (9)

[0035] As a further improvement, step S2 includes the following steps:

[0036] S2.1 The parameters inertia weight ω, learning factors c1 and c2 describe different states of the particle, and four behaviors are set to match its search actions. A larger ω value makes the particle more effectively maintain its original trajectory, enhancing global search capability; a smaller ω value strengthens local search capability. c1 reflects the particle's memory of its historical state: a higher c1 value prompts the particle to move towards its historical optimal position, improving global search performance. c2 represents the interaction between particles, driving the particle to converge towards the global optimal solution. GE is global search, LE is local search, CS is slow convergence, and CF is fast convergence.

[0037] S2.2 Obtain the normalized state of the i-th particle. (k), (k) In the state set S={L, , Values ​​are taken from G, where (k) can be obtained from the following two equations:

[0038] (10)

[0039] (11)

[0040] Assign values ​​s1=0.75, s2=0.5, and s3=0.25. (k) represents the normalized state of the particle in the kth generation;

[0041] S2.3. Search the Q-table for the Q-values ​​corresponding to the four operations GE, LD, CS, and CF, and select the operation with the largest Q-value among the four operations, i.e.:

[0042] a k =arg (12)

[0043] Among them, a k Let a be the state and action of the kth generation. k ∈A={GE,LE,CS,CF};

[0044] S2.4. Based on the action selected in S2.3, update parameters ω, c1, and c2;

[0045] S2.5. Update the state of particle i according to formula (5) and the parameters obtained in step S2.4 to obtain ν. i (k+1) and path i (k+1)

[0046] S2.6. Use formulas (10) and (11) to obtain the path corresponding to particle i. i Normalized state of (k+1) (k+1), (k+1) in the state set S={L, , Values ​​are taken from G.

[0047] S2.7 Calculate the updated objective function value Obj of the particle according to formulas (8) and (9). L (path i (k+1)) and Obj R (path i (k+1)), then the reward value r is obtained through the following formula. i (k,k+1):

[0048] (13)

[0049] in, For the first The reward value obtained after each particle update For the first The particle in the first The position of the era, , , , All are normalized objective function values;

[0050] S2.8 Update the Q-table according to the following formula:

[0051] (14)

[0052] Among them, s k It is the state of generation k, and s k ∈S={L, , , G}, α is the learning rate, γ is the discount factor, Q(s) k ,a k ) represents state s k Take action a k The Q value.

[0053] As a further improvement, step S3 includes the following steps:

[0054] S3.1, Set the maximum number of iterations k max The population size N of the MOPSO algorithm s The parameters in step S2.1 are ω, c1 and c2, learning rate α, discount factor γ, and the maximum fluctuation threshold that the robot can tolerate. max Maximum number of adjustments T max The number of path points n in each path, and the side length l of each grid cell;

[0055] S3.2 Initialize the particle swarm, setting the initial position of each particle to pbest. i (k), for population size N s For any particle i within the range, generate its velocity ν i (k) and its location path i (k), and calculate the objective function value by using the path length and path undulation of particle i;

[0056] S3.3 Perform collision detection and collision avoidance operations as described in S1.1 and S1.2 on particle i, filter out non-dominated particles according to the Pareto dominance criterion, and store the positions of these particles in memory;

[0057] S3.4 Within the maximum number of iterations, perform QL operation on particle i according to step S2, and perform crossover operation on particle i according to step S1.

[0058] S3.5. Perform collision detection and collision avoidance operations again, and calculate the updated objective function value of particle i based on the path length and path undulation of particle i.

[0059] S3.6, If the following conditions are met:

[0060] If satisfied Then The value assigned to ;

[0061] S3.7 Filter out the non-dominated positions and store them in external memory;

[0062] S3.8, Update gbest(k);

[0063] S3.9 Output the non-dominated solution from the external memory and convert it into a path displayed on the environment map to guide the robot to the destination.

[0064] As a further improvement, step S4 includes the following steps:

[0065] S4.1 The trajectory evaluation function in the standard DWA algorithm is defined as follows:

[0066] (15)

[0067] in, Here is the azimuth evaluation function, representing the current velocity combination. The velocity difference between the end of the robot's trajectory and the target point. Let be the distance evaluation function, representing the minimum distance between the robot and the obstacle at the given trajectory velocity. This is a linear velocity evaluation function that evaluates the robot's linear velocity at the current moment. For smoothing functions, , , These are the weight coefficients corresponding to the three functions mentioned above;

[0068] S4.2 Normalize the sub-functions;

[0069] S4.3, The linear velocities of the mobile robot and the obstacle are similar, and the distance between them is dist(ν, ) less than the set threshold dist(ν, ) min At that time, the robot's maximum angular velocity maxSet to 0 to maintain the direction of motion unchanged, while reducing the linear velocity ν value to ensure obstacle avoidance safety;

[0070] S4.4 The robot continues along the current trajectory until the distance to the obstacle is greater than the threshold dist(ν, At this time, the angular velocity It returns to normal value and then moves "tail-to-tail" toward the obstacle to complete obstacle avoidance.

[0071] Further improvements are made, and the dynamic adjustment strategy for weight coefficients used in step S4 is as follows:

[0072] Set variables ObstacleDist and GoalDist, output variables α, μ, and ρ, input set represented as {N, F}, output set represented as {S, B}, define dynamic adjustment rules for weight coefficients and weight coefficient rule table, and adjust the values ​​of output variables according to the values ​​of ObstacleDist and GoalDist in the input set.

[0073] Here, ObstacleDist is the closest distance between the robot and the obstacle, and GoalDist is the distance between the robot and the destination. The weight coefficients are dynamically updated based on the specific values ​​of the two. The input set {N, F} represents the close distance and the far distance, respectively, and the output set {S, B} represents the small and large values, respectively. The output variables α, μ, and ρ are the weight coefficients.

[0074] As a further improvement, step S5 includes the following steps:

[0075] S5.1. Apply the MOQLCOPSO algorithm to determine global path points on a map with known static obstacles;

[0076] MOQLCOPSO is the name of the algorithm after the improvements from S1 to S3;

[0077] S5.2. Use the determined global path points as temporary target points for the local path planning of the mobile robot to guide the robot to move in the direction of the optimal path.

[0078] S5.3, Based on the current linear velocity ν and angular velocity collected by the mobile robot The IDWA algorithm is used to predict the trajectory; the IDWA algorithm used is the algorithm after the obstacle avoidance strategy is improved by S4.

[0079] S5.4 Calculate the evaluation function G(ν, using equation (15) The optimal trajectory is selected and considered as the best choice for the mobile robot in local path planning.

[0080] The beneficial effects of this invention are as follows:

[0081] (1) By proposing a new hybrid path algorithm IMOPSO, we realize the combination of adaptive parameter adjustment, biomimetic genetic operator and dynamic feedback mechanism, achieve excellent global search capability, enhance the diversity of solutions, and show robustness in multi-objective path planning.

[0082] (2) Balancing the contradiction between global exploration and local development, while improving the algorithm's convergence efficiency, the model's adaptability is enhanced, ultimately demonstrating significant performance advantages in complex optimization problems. The homogenization of the particle swarm is reduced through path gene recombination, promoting the transmission of high-quality path features between particles.

[0083] (3) The IDWA algorithm is proposed. Based on the global path planning algorithm MOQLCOPSO, the path points planned by MOQLCOPSO are used as temporary target points of IDWA, and the integration of MOQLCOPSO and IDWA algorithms is achieved on the basis of global optimization. Attached Figure Description

[0084] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0085] Figure 1 This is a flowchart of the dynamic path planning algorithm for mobile robots based on the particle swarm optimization (PSO) algorithm and the dynamic window method (DWA) of this invention;

[0086] Figure 2 This is a flowchart of the MOQLCOPSO-IDWA algorithm of the present invention. Detailed Implementation

[0087] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0088] like Figure 1 and 2 As shown, this invention proposes a dynamic path planning algorithm for mobile robots based on Particle Swarm Optimization (PSO) and Dynamic Window Method (DWA), comprising the following five steps:

[0089] Step 1: Introduce an inertial weight update strategy based on state factors, and set adaptive parameters and crossover mutation operators to improve global search capabilities and increase population diversity;

[0090] Step 2: Combine Q-learning online to achieve online adaptive updates of inertia weights and learning factors;

[0091] Step 3: Enrich gene combination methods through crossover operators to improve algorithm convergence and exploratory capabilities;

[0092] Step 4: Improve the obstacle avoidance strategy of the traditional DWA algorithm by dynamically adjusting the weight parameters of the dynamic window evaluation function based on real-time information of the target and obstacles.

[0093] Step 5: Using the path points generated by global planning as temporary targets, integrate MOQLCOPSO with the improved DWA algorithm.

[0094] Furthermore, step one introduces the concept of a state factor, defined as:

[0095] (1)

[0096] in, It can be calculated using the following formula:

[0097] (2)

[0098] in addition, It can be calculated using the following formula:

[0099] (3)

[0100] In the formula, For population size, and For path The objective function, and Let these represent the weights of path length and path undulation, respectively, and satisfy the following conditions: , and The two objective functions are path length and path undulation, respectively, at the th... The optimal value at the next iteration and The first The average path length and path undulation at the next iteration can be calculated using the following formula:

[0101] (4)

[0102] Update the particle swarm according to the equation shown below. The particle in the first Speed ​​and position during the generation:

[0103] (5)

[0104] In the formula Indicates the first The local optimum position found by each particle. This is called the globally optimal position. and As a learning factor, and and These are independent random numbers, uniformly distributed in Among them, The inertial weights can be updated using the following formula:

[0105] (6)

[0106] in, , For the first The particle in the first The squared value of the state factor in the next iteration.

[0107] The mutation probability of the k-th generation particles is calculated using the following formula:

[0108] (7)

[0109] For particles Randomly generate a real number ,like Perform the mutation operation; otherwise, exit the mutation section.

[0110] Based on the above analysis, a mutation operation is performed, and path points are randomly selected. ,in Randomly select a value As a path The new value of , where .

[0111] Specifically, in step S1, the particles The path length can be expressed as:

[0112] (8)

[0113] particle The path undulation can be expressed by the following formula:

[0114] (9)

[0115] Furthermore, as shown in Table 1, the parameter inertia weight is set in step two. Learning factors and Describe the different states of the particle and set four behaviors to match its search action.

[0116]

[0117] Get the first Normalized state of each particle (k), (k) in the state set Take the value from, where, It can be obtained from the following two equations:

[0118] (10)

[0119] (11)

[0120] Assignment =0.75、 =0.5、 =0.25, For the particle in the first The normalized state of the generation.

[0121] Search the table shown in Table 1 for the Q values ​​corresponding to the four operations GE, LD, CS, and CF, and select the operation with the largest Q value among the four operations, i.e.:

[0122] (12)

[0123] in, For the first The state and actions of the generation, Update parameters based on the selected action. , and .

[0124] Update the particles according to formula (5) and the updated parameters. The state to obtain and .

[0125] Particles are obtained using formulas (10) and (11) Corresponding position normalized state , In the state set Take the value from the middle.

[0126] The updated objective function value of the particle is calculated according to formulas (8) and (9). and Then, the reward value is obtained using the following formula. :

[0127] (13)

[0128] in, For the first The reward value obtained after each particle update For the first The particle in the first The position of the era, , , , All are normalized objective function values.

[0129] Update the Q-table according to the following formula:

[0130] (14)

[0131] in, It is the first The state of the generation, and , For learning rate, As a discount factor, For state Take action The Q value.

[0132] Furthermore, in step three, the maximum number of iterations is first set. Population size of the MOPSO algorithm Parameters in step S2.1 , and Learning rate Discount factor The maximum fluctuation threshold that the robot can withstand Maximum number of adjustments The number of path points in each path The side length of each grid cell And initialize the particle swarm, setting the initial position of each particle to... Regarding population size Any particle within Generate its speed and its location The objective function value is calculated using equations (8) and (9).

[0133] For particles Perform collision detection and collision avoidance operations in S1.1 and S1.2, filter out non-dominated particles according to the Pareto dominance criterion, and store the positions of these particles in memory.

[0134] Within the maximum number of iterations, according to step two, the particles... Perform the QL operation, pairing particles according to the steps. Perform cross operations.

[0135] Collision detection and collision avoidance operations are performed again, and the updated objective function value of the particle is calculated according to equations (8) and (9).

[0136] If satisfied Then The value assigned to .

[0137] Then, non-dominated locations are selected, stored in external memory, and updated. .

[0138] The non-dominated solution is output from external memory and converted into a path displayed on the environment map, thereby guiding the robot to its destination.

[0139] Furthermore, in step four, the trajectory evaluation function in the standard DWA algorithm is defined as follows:

[0140] (15)

[0141] in, Here is the azimuth evaluation function, representing the current velocity combination. The velocity difference between the end of the robot's trajectory and the target point. Let be the distance evaluation function, representing the minimum distance between the robot and the obstacle at the given trajectory velocity. This is a linear velocity evaluation function that evaluates the robot's linear velocity at the current moment. For smoothing functions, , , These are the weight coefficients corresponding to the three functions mentioned above.

[0142] To avoid the evaluation results being dominated by the numerical value of a single sub-function, the weight coefficients are dynamically adjusted, and the sub-functions are normalized.

[0143] If the mobile robot and the obstacle have similar linear velocities and the distance between them is... Less than the set threshold The robot's maximum angular velocity Setting it to 0 maintains the direction of motion while reducing the linear velocity. This value is used to ensure obstacle avoidance safety; if the robot continues along the current trajectory until the distance to the obstacle is greater than the threshold, it will continue until the obstacle is within a certain range. angular velocity It returns to normal value and then moves "tail-to-tail" toward the obstacle to complete obstacle avoidance.

[0144] Furthermore, the dynamic adjustment strategy for weight coefficients used in step four follows these steps:

[0145] Set variables ObstacleDist and GoalDist, and output the variable as follows. , , Set the input set to represent as The output set is represented as A dynamic adjustment rule and a weighting rule table for the weighting coefficients are defined. The values ​​of the output variables are adjusted based on the values ​​of ObstacleDist and GoalDist in the input set. ObstacleDist is the closest distance between the robot and an obstacle, and GoalDist is the distance between the robot and the destination. The weighting coefficients are dynamically updated based on the specific values ​​of these two values. Representing near and far distances respectively, output sets Representing small and large values ​​respectively, output variables , , These are the weighting coefficients.

[0146] Furthermore, step five includes the following steps:

[0147] First, the MOQLCOPSO algorithm is applied to determine global path points on a map with known static obstacles. These global path points are then used as temporary target points for the mobile robot's local path planning, guiding the robot towards the optimal path.

[0148] Based on the current linear velocity collected by the mobile robot and angular velocity The IDWA algorithm is used to predict the trajectory, and the evaluation function is calculated using equation (15). The optimal trajectory is selected and considered as the best choice for the mobile robot in local path planning.

[0149] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. In particular, for the device embodiments, the above descriptions are merely preferred embodiments of the present invention. Since they are fundamentally similar to the method embodiments, the descriptions are relatively simple, and relevant parts can be referred to the descriptions of the method embodiments. The above descriptions are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention, without departing from the principle of the present invention, should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A robot path planning algorithm based on particle swarm optimization and dynamic window method, characterized in that: Includes the following steps: S1. Introduce an inertial weight update strategy based on state factors, and set adaptive parameters and crossover mutation operators in the multi-objective particle swarm optimization algorithm to improve global search capability and increase population diversity. S2. Combine the Q-learning algorithm to adaptively update the inertia weights and learning factors of MOPSO online, thereby enhancing the convergence ability of the MOPSO algorithm to the Pareto front. S3. Introduce new gene combination methods using crossover operators to increase the explorability and diversity of the population during the iteration process; S4. Improve the obstacle avoidance strategy of the traditional DWA algorithm by dynamically adjusting the weight parameters of the dynamic window evaluation function based on the real-time information of the target and obstacles. S5. Based on the global static path MOQLCOPSO, the planned path points are used as temporary target points for the improved DWA algorithm in step S4, thus achieving the fusion of MOQLCOPSO and the improved DWA algorithm on the basis of global optimization.

2. The robot path planning algorithm based on particle swarm optimization and dynamic window method according to claim 1, characterized in that: Step S1 includes the following steps: S1.

1. The concept of state factor is proposed and defined as: （1） in, Calculated by the following formula: （2） Calculated by the following formula: （3） In the formula, For population size, and For path The objective function, and Let these represent the weights of path length and path undulation, respectively, and satisfy the following conditions: , and These are the optimal values ​​of the two objective functions, path length and path undulation, at the k-th iteration. and Let be the average path length and path undulation at the k-th iteration, respectively, calculated by the following formula: （4） S1.2 Update the velocity and position of the i-th particle in the particle swarm in the (k+1)-th generation according to the equation shown below: (5) In the formula, pbest i (k) represents the local optimal position found by the i-th particle, gbest(k) is called the global optimal position, c1 and c2 are learning factors, and rand1 and rand2 are independent random numbers uniformly distributed in [0,1]. ω is the inertia weight, updated by the following formula: （6） in, , Let be the squared value of the state factor of the i-th particle in the k-th iteration; S1.3 Calculate the mutation probability of the k-th generation particles according to the following formula: P m (k)=0.1× (7) S1.4 For particle i, randomly generate a real number rand i ∈[0,1], if rand i <P m (k), proceed to step S1.5; otherwise, exit the mutation section. S1.5 Execute the mutation operation, randomly select a path point m, where m = rand([1, n-1]), and randomly select a value y. im ´ is the new value for path m, where y im = a × rand([1, n-1]).

3. The robot path planning algorithm based on particle swarm optimization and dynamic window method according to claim 2, characterized in that: In step S1, the path length of particle i is expressed as: (8) The path undulation of particle i is expressed by the following formula: (9)。 4. The robot path planning algorithm based on particle swarm optimization and dynamic window method according to claim 2, characterized in that: Step S2 includes the following steps: S2.1 The parameters inertia weight ω, learning factors c1 and c2 describe different states of the particle, and four behaviors are set to match its search actions. A larger ω value makes the particle more effectively maintain its original trajectory, enhancing global search capability; a smaller ω value strengthens local search capability. c1 reflects the particle's memory of its historical state: a higher c1 value prompts the particle to move towards its historical optimal position, improving global search performance. c2 represents the interaction between particles, driving the particle to converge towards the global optimal solution. GE is global search, LE is local search, CS is slow convergence, and CF is fast convergence. S2.2 Obtain the normalized state of the i-th particle. (k), (k) In the state set S={L, , Values ​​are taken from G, where (k) can be obtained from the following two equations: (10) (11) Assign values ​​s1=0.75, s2=0.5, and s3=0.

25. (k) represents the normalized state of the particle in the kth generation; S2.

3. Search the Q-table for the Q-values ​​corresponding to the four operations GE, LD, CS, and CF, and select the operation with the largest Q-value among the four operations, i.e.: a k =arg (12) Among them, a k Let a be the state and action of the kth generation. k ∈A={GE, LE, CS, CF}; S2.

4. Based on the action selected in S2.3, update parameters ω, c1, and c2; S2.

5. Update the state of particle i according to formula (5) and the parameters obtained in step S2.4 to obtain ν. i (k+1) and path i (k+1) S2.

6. Use formulas (10) and (11) to obtain the path corresponding to particle i. i Normalized state of (k+1) (k+1), (k+1) in the state set S={L, , Values ​​are taken from G. S2.7 Calculate the updated objective function value Obj of particle i based on the path length and path undulation of particle i. L (path i (k+1)) and Obj R (path i (k+1)), then the reward value r is obtained through the following formula. i (k,k+1): (13) in, For the first The reward value obtained after each particle update For the first The particle in the first The position of the era, , , , All are normalized objective function values; S2.8 Update the Q-table according to the following formula: (14) Among them, s k It is the state of generation k, and s k ∈S={L, , , G}, α is the learning rate, γ is the discount factor, Q(s) k ,a k ) represents state s k Take action a k The Q value.

5. The robot path planning algorithm based on particle swarm optimization and dynamic window method according to claim 4, characterized in that: Step S3 includes the following steps: S3.1, Set the maximum number of iterations k max The population size N of the MOPSO algorithm s The parameters in step S2.1 are ω, c1 and c2, learning rate α, discount factor γ, and the maximum fluctuation threshold that the robot can tolerate. max Maximum number of adjustments T max The number of path points n in each path, and the side length l of each grid cell; S3.2 Initialize the particle swarm, setting the initial position of each particle to pbest. i (k), for population size N s For any particle i within the range, generate its velocity ν i (k) and its location path i (k), and calculate the objective function value by using the path length and path undulation of particle i; S3.3 Perform collision detection and collision avoidance operations as described in S1.1 and S1.2 on particle i, filter out non-dominated particles according to the Pareto dominance criterion, and store the positions of these particles in memory; S3.4 Within the maximum number of iterations, perform QL operation on particle i according to step S2, and perform crossover operation on particle i according to step S1. S3.

5. Perform collision detection and collision avoidance operations again, and calculate the updated objective function value of particle i based on the path length and path undulation of particle i. S3.6, If the following conditions are met: If satisfied Then The value assigned to ; S3.7 Filter out the non-dominated positions and store them in external memory; S3.8, Update gbest(k); S3.9 Output the non-dominated solution from the external memory and convert it into a path displayed on the environment map to guide the robot to the destination.

6. The robot path planning algorithm based on particle swarm optimization and dynamic window method according to claim 1, characterized in that: Step S4 includes the following steps: S4.1 The trajectory evaluation function in the standard DWA algorithm is defined as follows: (15) in, Here is the azimuth evaluation function, representing the current velocity combination. The velocity difference between the end of the robot's trajectory and the target point. Let be the distance evaluation function, representing the minimum distance between the robot and the obstacle at the given trajectory velocity. This is a linear velocity evaluation function that evaluates the robot's linear velocity at the current moment. For smoothing functions, , , These are the weight coefficients corresponding to the three functions mentioned above; S4.2 Normalize the sub-functions; S4.3, The linear velocities of the mobile robot and the obstacle are similar, and the distance between them is dist(ν, ) less than the set threshold dist(ν, ) min At that time, the robot's maximum angular velocity max Set to 0 to maintain the direction of motion unchanged, while reducing the linear velocity ν value to ensure obstacle avoidance safety; S4.4 The robot continues along the current trajectory until the distance to the obstacle is greater than the threshold dist(ν, At this time, the angular velocity It returns to normal value and then moves "tail-wise" toward the obstacle to complete obstacle avoidance.

7. The robot path planning algorithm based on particle swarm optimization and dynamic window method according to claim 6, characterized in that: The dynamic weight adjustment strategy used in step S4 is as follows: Set variables ObstacleDist and GoalDist, output variables α, μ, and ρ, input set represented as {N, F}, output set represented as {S, B}, define dynamic adjustment rules for weight coefficients and weight coefficient rule table, and adjust the values ​​of output variables according to the values ​​of ObstacleDist and GoalDist in the input set. Here, ObstacleDist is the closest distance between the robot and the obstacle, and GoalDist is the distance between the robot and the destination. The weight coefficients are dynamically updated based on the specific values ​​of the two. The input set {N, F} represents the close distance and the far distance, respectively, and the output set {S, B} represents the small and large values, respectively. The output variables α, μ, and ρ are the weight coefficients.

8. The robot path planning algorithm based on particle swarm optimization and dynamic window method according to claim 6, characterized in that: Step S5 includes the following steps: S5.

1. Apply the MOQLCOPSO algorithm to determine global path points on a map with known static obstacles; MOQLCOPSO is the name of the algorithm after the improvements from S1 to S3; S5.

2. Use the determined global path points as temporary target points for the local path planning of the mobile robot to guide the robot to move in the direction of the optimal path. S5.3, Based on the current linear velocity ν and angular velocity collected by the mobile robot The IDWA algorithm is used to predict trajectories. The IDWA algorithm used is the algorithm after the obstacle avoidance strategy was improved by S4. S5.4 Calculate the evaluation function G(ν, using equation (15) The optimal trajectory is selected and considered as the best choice for the mobile robot in local path planning.

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