Mobile robot path planning method based on improved pelican optimization algorithm

Abstract

The invention belongs to the technical field of mobile robot path planning, and particularly relates to a mobile robot path planning method based on an improved pelican optimization algorithm, and the improved pelican optimization algorithm path planning in the method comprises the following steps: constructing a grid map to simulate a robot working environment, initializing a pelican population by adopting Logistic chaotic mapping in an initialization stage, and carrying out Pelican optimization; the diversity and distribution uniformity of the population are enhanced, so that the global search capability of the algorithm is improved; in the exploration stage, a sine and cosine optimization algorithm and a nonlinear inertia weight coefficient are combined to improve the diversity and convergence speed of algorithm search; a level flight strategy is introduced in a development stage to further improve the ability of the algorithm to jump out of a local optimal solution and maintain enough global search ability in the later stage of the algorithm. Simulation results show that the improved algorithm can quickly find an optimal path.

Description

Technical Field

[0001] The present invention belongs to the technical field of mobile robot path planning, and particularly relates to a mobile robot path planning method based on an improved pelican optimization algorithm. Background Art

[0002] Swarm intelligence optimization algorithms originate from the behaviors of organisms in nature such as predation, fighting, and mating. Affected by different constraints such as population size, initial position, food quantity, and environment, the position is updated to search for the optimal position and obtain the best fitness value. During the iterative search process, it usually goes through two stages: global exploration and local exploitation. These two stages are sequential rather than synchronous processes, which may lead to the dilemma of being easily trapped in local optimal solutions. To enhance the global search ability and accelerate the convergence speed, researchers have proposed different thinking strategies for improving the algorithms, aiming to enhance the local search ability while accelerating the convergence speed to obtain the global optimal solution. Among them, the hybrid strategy has the most prominent improvement effect and can achieve higher accuracy in practical engineering applications.

[0003] As a heuristic intelligent optimization algorithm, the pelican optimization algorithm can achieve a faster optimization speed while maintaining good convergence accuracy. It has the characteristics of few parameters and simple operations, and has been widely studied by scholars at home and abroad. The algorithm has shown excellent optimization performance in benchmark test functions and has been successfully applied in fields such as network attack detection models, image problems, and asynchronous motor fault diagnosis. However, in complex engineering problems, such as the field of mobile robot path planning, the algorithm faces parameter sensitivity and is prone to falling into local optima, and needs to be adjusted and improved according to specific applications.

[0004] In view of this, how to design a robot path planning method based on an improved pelican optimization algorithm to improve the speed and accuracy of robot path planning is an urgent problem for those skilled in the art. Summary of the Invention

[0005] The purpose of the present invention is to overcome the above problems existing in the traditional technology, and provide a mobile robot path planning method based on an improved pelican optimization algorithm, which solves the problem of local optimality that occurs during the global optimization of the existing pelican optimization algorithm in the entire iterative process, resulting in weak global search ability and slow convergence speed of the algorithm.

[0006] To achieve the above technical purpose and achieve the above technical effect, the present invention is realized through the following technical solutions:

[0007] The present invention provides a mobile robot path planning method based on an improved pelican optimization algorithm, including the following steps:

[0008] S1. Determine the positions of the starting point, target point, and obstacles, and construct a grid map to simulate the working environment of the robot;

[0009] S2. Initialize the parameters of the improved pelican optimization algorithm path planning method;

[0010] S3. Use the introduced Logistic chaotic map to initialize the population;

[0011] S4. In the exploration stage, use the introduced non - linear inertia adjustment factor θ and sine - cosine optimization algorithm to update the positions of pelican individuals, and detect whether it is a valid update;

[0012] S5. In the exploitation stage, use the introduced Levy flight strategy to update the positions of pelican individuals, and detect whether it is a valid update;

[0013] S6. After reaching the maximum number of iterations, stop the iteration and obtain the optimal path of the mobile robot.

[0014] Further, the implementation process of step S1 is as follows:

[0015] To accurately describe the environment where the mobile robot is located, record the coordinates and environmental information of the mobile robot in units of grids;

[0016] In the grid map, use the number "1" to represent the black grid, which is an obstacle, and use the number "0" to represent the white grid, which is passable. The robot takes the lower - left node as the starting point and the upper - right node as the target point.

[0017] Further, the grid size is mainly determined by the experimental environment, and the grid length formula is:

[0018]

[0019] In the formula, R is the radius of the robot, r is the radius of the obstacle, is the set safety distance.

[0020] Further, in step S2, the corresponding parameters include the population size N, the maximum number of algorithm iterations T, the Logistic chaotic map parameter α, and the Levy flight strategy parameter β.

[0021] Further, in step S3, use the Logistic chaotic map formula to initialize the positions of pelican population individuals; the Logistic chaotic map formula is as follows:

[0022] x k+1 =αx k (1 - x k ), α ∈ (3.57, 4] (2)

[0023] In the formula, xk Indicates the position of an individual in the population.

[0024] Furthermore, in step S4, by introducing a non-linear inertia adjustment factor θ and a sine-cosine optimization algorithm, the position of the pelican individual is updated; where

[0025] Non-linear inertia adjustment factor formula:

[0026]

[0027] In the formula, T is the maximum number of iterations, and t is the current number of iterations;

[0028] Sine-cosine optimization algorithm:

[0029]

[0030] In the formula, Indicates the position component of individual i in dimension j at the t-th iteration; r1, r4 are random numbers in [0, 1]; r2 is a random number in [0, 2π]; r3 ∈ (0, +∞); P best (t) is the optimal solution position at the t-th iteration.

[0031] Furthermore, by fusing formula (3) and formula (4) and introducing them into the pelican position update formula, a new position update formula is obtained:

[0032]

[0033] In the formula, Is the position of the i-th pelican in the j-th dimension in the current stage, x i,j Is the position of the i-th pelican in the j-th dimension, p j Is the position of the prey in the j-th dimension, F P Is the fitness value of the position where the prey is located;

[0034] The effective update formula for the exploration stage is:

[0035]

[0036] In the formula, Is the new position of the i-th pelican in the first stage, F i Is the fitness value of the i-th pelican; Is the fitness value of the i-th pelican after the update in the first stage.

[0037] Furthermore, in step S5, the pelican position update formula for the Levy flight strategy is:

[0038]

[0039] In the formula, β = 1.5;

[0040] The pelican position update formula incorporating the Levy flight strategy is as follows:

[0041]

[0042] In the formula, is the position of the i-th pelican in the j-th dimension after the second-stage update, and x i,j is the position of the i-th pelican in the j-th dimension; rand is a random number within the range of [0, 1], R is a random integer of 0 or 2, t is the current iteration number, and T is the maximum iteration number;

[0043] The effective update formula in the exploration stage is as follows:

[0044]

[0045] The beneficial effects of the present invention are:

[0046] Compared with the POA algorithm, in the initialization stage, the improved algorithm in the present invention incorporates the Logistic chaotic mapping to make the population initialization more random and ergodic; in the exploration stage, the integration of the non-linear inertia factor and the sine-cosine optimization algorithm improves the global search ability of the algorithm and the ability to jump out of the local optimal solution and speeds up the convergence rate of the algorithm; in the exploitation stage, the addition of the Levy flight strategy further increases the ability to jump out of the local optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0048] Figure 1 is the flowchart of the mobile robot path planning method of the present invention;

[0049] Figure 2 is the schematic diagram of the grid map provided by the present invention;

[0050] Figure 3 is the schematic diagram of the Logistic mapping sequence value distribution provided by the present invention;

[0051] Figure 4 is the curve graph of the change of the inertia weight factor provided by the present invention;

[0052] Figure 5 is the schematic diagram of the sine-cosine optimization process provided by the present invention;

[0053] Figure 6Schematic diagram of path convergence curves based on GWO, SSA, POA, and IPOA in the simple grid map provided by the present invention;

[0054] Figure 7 Robot path planning map based on GWO, SSA, POA, and IPOA in the simple grid map provided by the present invention;

[0055] Figure 8 Schematic diagram of path convergence curves based on GWO, SSA, POA, and MPOA in the complex grid map provided by the present invention;

[0056] Figure 9 Robot path planning map based on GWO, SSA, POA, and IPOA in the complex grid map provided by the present invention. Detailed implementation manners

[0057] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0058] As Figure 1 shown, this embodiment provides a mobile robot path planning method based on an improved pelican optimization algorithm, including the following steps:

[0059] Step S1: Determine the positions of the starting point, target point, and obstacles, and construct a grid map to simulate the working environment of the robot;

[0060] To accurately describe the environment where the mobile robot is located, the coordinates and environmental information of the mobile robot are recorded in units of grids.

[0061] In the grid map, as Figure 2 shown, the black grid is represented by the number "1" as an obstacle, and the white grid is represented by the number "0" as passable. The robot takes the lower left node as the starting point and the upper right node as the target point.

[0062] The grid size is mainly determined by the experimental environment, and the grid length formula is

[0063]

[0064] In the formula, R is the radius of the robot, r is the radius of the obstacle, is the set safety distance.

[0065] Step S2: Initialize and set the parameters of the improved pelican optimization algorithm path planning method;

[0066] In the process of initializing the parameters of the improved pelican path planning method, the corresponding parameters include the population size N, the maximum number of algorithm iterations T, the Logistic chaotic mapping parameter α, and the Levy flight strategy parameter β.

[0067] Step S3: Initialize the population using the introduced Logistic chaotic mapping;

[0068] Initialize the individual positions of the pelican population using the Logistic chaotic mapping formula; the Logistic chaotic mapping formula is as follows:

[0069] x k+1 = αx k (1 - x k ), α ∈ (3.57, 4] (2)

[0070] In the formula, x k represents the position of the individual in the population.

[0071] The addition of the Logistic chaotic mapping can effectively increase the diversity of the population, making the individuals more evenly distributed in the entire search space. As Figure 3 shown, it avoids their concentration in certain areas, thus significantly enhancing the global search ability of the algorithm.

[0072] Step S4: In the exploration stage, use the introduced non - linear inertia adjustment factor θ and the sine - cosine optimization algorithm to update the positions of the pelican individuals and detect whether the update is valid;

[0073] To balance the capabilities of global search and local development, the non - linear inertia weight factor θ can be introduced to control the correlation between the update of the pelican individual position and its current state. This method can achieve coordination between global exploration and local optimization, thereby improving the efficiency and accuracy of the optimization process.

[0074] Non - linear inertia adjustment factor formula:

[0075]

[0076] In the formula, T is the maximum number of iterations, and t is the current number of iterations.

[0077] As Figure 4As shown, with the continuous iteration of the algorithm, the change of θ presents a specific pattern. In the initial stage of iteration, θ is small. At this time, the update of the individual position is less affected by the current state, which is conducive to expanding the search space and thus improving the global search performance. As the iteration progresses, θ gradually increases, and the dependence of the individual position update on the current state is enhanced, thereby narrowing the search range and improving the local development ability and convergence speed. By dynamically adjusting the weight, the balance between global search and local optimization can be achieved. In the early stage, the search is broadened to find the optimal solution, and in the later stage, the convergence efficiency and accuracy are concentratedly improved, thus enhancing the overall performance of the algorithm.

[0078] The sine-cosine optimization algorithm constructs an iterative formula by utilizing the periodic fluctuation characteristics of the sine and cosine functions, thereby realizing the two core processes of global exploration and local optimization. The algorithm updates the solution set by applying perturbations and using a simple update iteration equation to improve the search efficiency of the algorithm.

[0079] Sine-cosine optimization algorithm:

[0080]

[0081] In the formula, represents the position component of individual i in dimension j at the t-th iteration; r1, r4 are random numbers in [0, 1]; r2 is a random number in [0, 2π]; r3 ∈ (0, +∞); P best (t) is the position of the optimal solution at the t-th iteration.

[0082] The periodic characteristics of the sine function and the cosine function enable the solution to be flexibly redistributed in adjacent regions, thereby realizing the efficient search for the solution. This mechanism can accelerate the convergence speed and help the algorithm locate the global optimal solution more quickly.

[0083] Such as Figure 5 As shown, the sine and cosine functions play an important role in optimization. When the function value is between -1 and 1, the candidate solution performs local search; when it exceeds this range, global search is executed. By continuously adjusting the position around the current optimal solution, the algorithm combines global exploration and local development, effectively improving the optimization efficiency and performance.

[0084] Fusing the two and introducing them into the pelican position update formula, the new position update formula is obtained:

[0085]

[0086] In the formula, is the position of the i-th pelican in the j-th dimension in the current stage, x i,j is the position of the i-th pelican in the j-th dimension, p j is the position of the prey in the j-th dimension, F P is the fitness value of the position where the prey is located.

[0087] When the pelican population approaches the prey, if the fitness value of the new position is better than that of the original position, it indicates that the movement is successful, and this process is called effective update. In this case, the pelican population will use the new position as its current position. On the contrary, if the fitness value of the position after movement is poor, the pelican population will stay in place unchanged. This effective update process can be described by the following formula:

[0088]

[0089] In the formula, is the new position of the i-th pelican in the first stage, and F i is the fitness value of the i-th pelican; is the fitness value of the i-th pelican after the update in the first stage.

[0090] Step S5. In the exploitation stage, use the introduced Levy flight strategy to update the positions of pelican individuals and detect whether it is an effective update;

[0091] The Levy flight strategy is a very effective mathematical method that provides a random factor. To enhance the ability of the pelican optimization algorithm to jump out of the local optimal solution

[0092] The formula for updating the position of a pelican with the Levy flight strategy is:

[0093]

[0094] In the formula, β = 1.5;

[0095] The formula for updating the position of a pelican incorporating the Levy flight strategy is:

[0096]

[0097] In the formula, is the position of the i-th pelican in the j-th dimension after the update in the second stage, and x i,j is the position of the i-th pelican in the j-th dimension; rand is a random number in the range of [0, 1], R is a random integer of 0 or 2, t is the current iteration number, and T is the maximum iteration number;

[0098] The formula for effective update in the exploitation stage is:

[0099]

[0100] Step six. Reach the maximum iteration number, stop the iteration, and obtain the optimal path of the mobile robot.

[0101] In this embodiment, in order to verify the effectiveness of IPOA in the path planning of mobile robots, MATLAB is used to simulate the path planning of mobile robots in two environments, simple and complex. Simulations are carried out in two grid map environments, simple and complex, respectively, and compared with the traditional P0A algorithm, the Sparrow Search Algorithm (SSA), and the traditional Grey Wolf Optimization Algorithm (GWO).

[0102] The simple grid environment is a 20×20 environment model, and the complex grid environment is a 40×40 environment model. Both start from the bottom-left node and end at the top-right node. The population size is set to 30, and the maximum number of iterations is 100.

[0103] In the simple environment, the obtained path convergence curve graph and the route simulation planning results are as shown in Figure 6 and Figure 7 which shows that this algorithm can achieve global convergence quickly and has a shorter path in a simple map environment;

[0104] In the complex environment, the obtained path convergence curve graph and the route simulation planning results are as shown in Figure 8 and Figure 9 which shows that this algorithm can also achieve global convergence quickly and has a shorter path in a complex map environment.

[0105] The experimental results show that the proposed improved algorithm is feasible in the application of robot path planning in both simple and complex map environments, and has the advantages of fast global convergence and the shortest path.

[0106] The path planning of the improved pelican optimization algorithm in this embodiment includes: constructing a grid map to simulate the working environment of the robot. In the initialization stage, the Logistic chaotic mapping is used to initialize the pelican population, enhancing the diversity and uniform distribution of the population so as to improve the global search ability of the algorithm; in the exploration stage, the sine-cosine optimization algorithm and the non-linear inertia weight coefficient are combined to improve the diversity and convergence speed of the algorithm search; finally, in the exploitation stage, the levy flight strategy is introduced to further improve the ability of the algorithm to jump out of the local optimal solution and maintain sufficient global search ability in the later stage of the algorithm. Finally, through simulation experiments, it shows that the improved pelican optimization algorithm can find a safe and feasible path and has a relatively stable optimization ability.

[0107] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor limit the invention to only the specific embodiments. Obviously, many modifications and changes can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principle and practical application of the present invention, so that those skilled in the relevant technical field can understand and utilize the present invention well. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A path planning method for a mobile robot based on an improved pelican optimization algorithm, characterized in that It includes the following steps: S1. Determine the positions of the starting point, target point and obstacles, and construct a grid map to simulate the working environment of the robot; S2. Initialize and set the parameters of the improved pelican optimization algorithm path planning method; S3. Use the introduced Logistic chaotic mapping to initialize the population; S4. In the exploration stage, use the introduced non-linear inertia adjustment factor θ and sine-cosine optimization algorithm to update the positions of the pelican individuals, and detect whether the update is valid; S5. In the exploitation stage, use the introduced Levy flight strategy to update the positions of the pelican individuals, and detect whether the update is valid; S6. After reaching the maximum number of iterations, stop the iteration to obtain the optimal path of the mobile robot.

2. The path planning method for a mobile robot based on an improved pelican optimization algorithm according to claim 1, wherein The implementation process of step S1 is as follows: To accurately describe the environment where the mobile robot is located, record the coordinates and environmental information of the mobile robot in units of grids; In the grid map, the black grid is represented by the number "1" as an obstacle, and the white grid is represented by the number "0" as passable. The robot takes the lower left node as the starting point and the upper right node as the target point.

3. The path planning method for a mobile robot based on an improved pelican optimization algorithm according to claim 2, wherein The grid size is mainly determined by the experimental environment, and the grid length formula is: where R is the radius of the robot, r is the radius of the obstacle, is the set safety distance.

4. The path planning method for a mobile robot based on an improved pelican optimization algorithm according to claim 1, characterized in that In step S2, the corresponding parameters include the population size N, the maximum number of algorithm iterations T, the Logistic chaotic mapping parameter α, and the Levy flight strategy parameter β.

5. The path planning method for a mobile robot based on an improved pelican optimization algorithm according to claim 1, characterized in that, In step S3, use the Logistic chaotic mapping formula to initialize the positions of the pelican population individuals; the Logistic chaotic mapping formula is as follows: x k+1 = αx k (1 - x k ), α ∈ (3.57, 4] (2) where x k represents the position of an individual in the population.

6. The path planning method for a mobile robot based on an improved pelican optimization algorithm according to claim 1, wherein In step S4, by introducing the non-linear inertia adjustment factor θ and the sine-cosine optimization algorithm, update the positions of the pelican individuals; among them, The non-linear inertia adjustment factor formula: In the formula, T is the maximum number of iterations, and t is the current number of iterations; The sine-cosine optimization algorithm: In the formula, represents the position component of individual i in dimension j at the t-th iteration; r1 and r4 are random numbers in [0, 1]; r2 is a random number in [0, 2π]; r3 ∈ (0, +∞); P best (t) is the optimal solution position at the t-th iteration.

7. The mobile robot path planning method based on the improved pelican optimization algorithm according to claim 6, wherein Fuse formula (3) and formula (4) and introduce them into the pelican position update formula to obtain a new position update formula: In the formula, is the position of the i-th pelican in the j-th dimension in the current stage, and x i,j is the position of the i-th pelican in the j-th dimension, p j is the position of the prey in the j-th dimension, and F P is the fitness value of the position where the prey is located; The effective update formula in the exploration stage is: In the formula, is the new position of the i-th pelican in the first stage, and F i is the fitness value of the i-th pelican; is the fitness value of the i-th pelican after the update in the first stage.

8. The mobile robot path planning method based on the improved pelican optimization algorithm according to claim 1, characterized in that In step S5, the pelican position update formula of the Levy flight strategy is: In the formula, β = 1.5; The pelican position update formula incorporating the Levy flight strategy is: In the formula, is the position of the j-th dimension of the i-th pelican after the second-stage update, and x i,j is the position of the j-th dimension of the i-th pelican; rand is a random number in the range of [0, 1], R is a random integer of 0 or 2, t is the current iteration number, and T is the maximum iteration number; The effective update formula in the exploitation stage is:

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