Mobile robot path planning method based on competitive learning mechanism and improved artificial potential field method

Abstract

A mobile robot path planning method based on a competitive learning mechanism and an improved artificial potential field method belongs to the technical field of mobile robot autonomous navigation, and comprises the following steps: 1) establishing a kinematic model of a mobile robot; 2) setting an obstacle avoidance circle and solving the radius of the obstacle avoidance circle by considering the physical sizes of the mobile robot and the obstacle in order to meet the actual movement obstacle avoidance requirement; 3) constructing an improved artificial potential field model, and setting a gravitational field function and a repulsive field function; 4) designing a trigger type random disturbance mechanism, and when it is detected that the mobile robot falls into a local minimum value, adopting a random position updating strategy to help the mobile robot to get out of trouble; 5) establishing a competitive learning particle swarm optimization framework, implementing a hierarchical competitive learning strategy, and optimizing artificial potential field method parameters; and 6) executing path planning, so that the mobile robot can successfully plan a path with optimal length and smoothness. The method can solve the problems that an artificial potential field method is poor in practicability when facing different obstacle environments, and a feasible path cannot be planned.

Description

Technical Field

[0001] The present invention belongs to the technical field of autonomous navigation of mobile robots, and relates to a path planning method for mobile robots based on a competitive learning mechanism and an improved artificial potential field method, specifically to a path planning method combining a competitive learning particle swarm algorithm and an improved artificial potential field method. Background Art

[0002] The path planning technology of mobile robots is one of the core issues in the field of autonomous navigation of robots, and its goal is to plan an optimal or feasible path from the starting point to the target point for the mobile robot in a complex environment.

[0003] The artificial potential field method was first proposed by Khatib in 1985. Due to its advantages such as high computational efficiency and simple implementation, it has been widely used in the field of real-time path planning of mobile robots. Its basic idea is to simulate the electromagnetic field in physics to set a repulsive potential field around obstacles and a gravitational potential field around the target point, and guide the mobile robot to move forward through the combined action of gravity and repulsion. However, in practical applications, due to the algorithm design mechanism, in some special obstacle distribution environments (such as U-shaped traps, symmetric obstacles, etc.), the gravity and repulsion may reach equilibrium, resulting in the mobile robot falling into a local minimum and being unable to reach the target position. In addition, the performance of the traditional potential field method highly depends on parameter settings, and unreasonable parameter combinations will lead to problems such as path oscillation and obstacle avoidance failure. The paths generated by traditional methods will also show "zigzag" trajectories, which are not conducive to actual control. This is mainly because the repulsive force field changes violently at the edge of the obstacle, resulting in sudden changes in the movement direction of the mobile robot.

[0004] Ji Suning et al. [Ji Suning, Cao Jingsheng, Liu Shijiang, etc. Research on obstacle avoidance path planning based on improved artificial potential field method [J]. Modern Electronics Technique, 2025.] proposed an artificial potential field improved based on the simulated annealing algorithm (SA). By setting random target points near the local minimum value and using the simulated annealing algorithm for optimization, it jumps out of the local minimum value and gradually approaches the global optimal or approximate optimal solution. This method conducts multiple searches near the local minimum value, resulting in path oscillation and being unable to obtain the optimal path. Zhang Jiashang et al. [Zhang Jiashang, Chen Zhihua. Improved artificial potential field algorithm based on pre-added virtual force [J]. Journal of Ordnance Equipment Engineering, 2023.] introduced virtual force to solve the problem of the artificial potential field method falling into local minimum values. By adding virtual forces in 8 directions at the local minimum value point and calculating the resultant force according to the virtual force and the potential field force of the artificial potential field to re-plan the path, calculate the lengths of all feasible paths, and select the optimal path. This method requires multiple trajectory simulations and evaluations, reducing the real-time performance of obstacle avoidance. In addition, setting the same artificial potential field method parameters for different obstacle scenarios will lead to path planning failure.

[0005] Many existing research strategies have made many improvements to the deficiencies of the artificial potential field method. However, for different obstacle environments, while overcoming the defects of the artificial potential field method, how to flexibly set parameters to search for the optimal path remains a research hotspot. Summary of the Invention

[0006] The purpose of the present invention is to design a path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method, so that when the artificial potential field method faces different obstacle environments, it can flexibly adjust parameters, while ensuring the safety of the mobile robot, plan the path with the optimal length and smoothness, and improve the applicability of the artificial potential field method in complex environments.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method. The first step of the mobile robot path planning method is to establish a kinematic model of the mobile robot; the second step is to set an obstacle avoidance circle and solve the radius of the obstacle avoidance circle considering the physical sizes of the mobile robot and the obstacles to meet the actual motion obstacle avoidance requirements; the third step is to construct an improved artificial potential field model and set the gravitational field and repulsive field functions; the fourth step is to design a trigger-type random perturbation mechanism. When it is detected that the mobile robot falls into a local minimum, a random position update strategy is adopted to help the mobile robot get out of trouble; the fifth step is to establish a competitive learning particle swarm optimization framework, implement a hierarchical competitive learning strategy, and optimize the parameters of the artificial potential field method; the sixth step is to use the result output in the fifth step to execute path planning so that the mobile robot can successfully plan the path with the optimal length and smoothness. Specifically, it includes the following steps:

[0009] Step 1: Establish a kinematic model of the mobile robot:

[0010] The mobile robot adopts wheeled motion, and its position variable is represented as X = (x, y) T , which respectively represent the abscissa and ordinate of the mobile robot. Then the kinematic model of the mobile robot can be expressed as:

[0011]

[0012] Among them, F(X t ) is the resultant force received by the mobile robot at time t; l is the motion step length within Δt time; X t represents the position of the mobile robot at time t; X t+1 represents the position of the mobile robot at time t + 1; ||.|| represents the two-norm.

[0013] Step 2: To meet the actual motion obstacle avoidance requirements, consider the physical size of the mobile robot and the obstacle, set the obstacle avoidance circle and solve the radius of the obstacle avoidance circle, as follows:

[0014] Common obstacles in the actual environment include cuboids, cylinders, and triangular prisms. These obstacles are projected two-dimensionally to obtain a projection figure. The collision distance threshold of the obstacle is the radius of the circumscribed circle of the obtained projection figure. Let the radius of the circumscribed circle be R0. Similarly, the mobile robot is projected two-dimensionally to obtain a projection figure. The collision distance threshold of the mobile robot is the radius of the circumscribed circle of the obtained projection figure. Let the radius of the circumscribed circle be R1. The mobile robot is regarded as a particle, and an obstacle avoidance circle is set around the obstacle. The radius R of the obstacle avoidance circle is expressed as:

[0015] R=R0+R1 (2)

[0016] Step 3: Construct an improved artificial potential field model and set the gravitational field and repulsive field functions:

[0017] Step 3.1, the gravitational force on the mobile robot in the environment is expressed as:

[0018] F att (X t )=λ att ·(X g -X t ) (3)

[0019] Among them, F att (X t ) represents the gravitational force on the mobile robot at time t; λ att is the gravitational potential field gain coefficient; X g Indicates the location of the end point.

[0020] Step 3.2, construct a repulsion function based on the bimodal Gaussian function, which is composed of a linear component and a nonlinear component in the force direction. The expression of the repulsion force of a single obstacle on the mobile robot is:

[0021]

[0022] Among them, F rep,i (X t ) indicates that the mobile robot is subject to the repulsive force of the ith obstacle at time t; λ repis the repulsive potential field gain coefficient; α and β respectively represent the weights of two Gaussian functions, affecting their contribution degrees. α controls the contribution degree of the first Gaussian function, and β controls the contribution degree of the second Gaussian function; σ1 and σ2 respectively represent the width control parameters of the two Gaussian functions, affecting the decay rate of the repulsive force. σ1 controls the decay rate of the first Gaussian function, and σ2 controls the decay rate of the second Gaussian function; γ and δ are direction correction coefficients, used to control the linear and nonlinear components in the repulsive force direction. γ controls the weight of the linear component in the repulsive force direction, and δ controls the weight of the nonlinear component in the repulsive force direction, ||ρ(X t ,P o,i )|| represents the distance between the mobile robot and the i-th obstacle at time t.

[0023] The expression for the combined repulsive force on the mobile robot by the obstacles is:

[0024]

[0025] Among them, F rep (X t ) represents the combined repulsive force on the mobile robot by the obstacles at time t; N represents the number of obstacles.

[0026] The expression for the resultant force on the mobile robot is:

[0027] F(X t )=F att (X t )+F rep (X t )(6)

[0028] Step 4: Design a trigger-based random perturbation mechanism. When it is detected that the mobile robot is trapped in a local minimum, a random position update strategy is adopted to help the mobile robot get out of trouble. Specifically:

[0029] According to formula (6), when the resultant force on the mobile robot is 0, it will be trapped in a local minimum and stop; in a highly symmetric obstacle map, there is also a phenomenon that the mobile robot oscillates back and forth between two points. At this time, the mobile robot is also trapped in a local minimum problem. According to the motion situation of the local minimum, the following trigger conditions are set for judgment:

[0030]

[0031] Among them, X t-1 represents the position of the mobile robot at time t - 1.

[0032] The principle of the random perturbation mechanism is to introduce a random number at the current position to change the position of the mobile robot.

[0033] For the case where flag1 = 1, the mobile robot falls into a local minimum. At this time, the random perturbation mechanism is triggered to update the position of the mobile robot, and its expression is:

[0034]

[0035] where ε is the perturbation intensity; rand represents a function that generates a random number between 0 and 1.

[0036] For the case where flag1 = 0, the mobile robot does not fall into a local minimum and moves normally.

[0037] Step Five: Establish a competitive learning particle swarm optimization framework, implement a hierarchical competitive learning strategy, and optimize the artificial potential field parameters:

[0038] Step 5.1, the optimized parameters include the gravitational constant λ att , the repulsive constant λ rep , the weights α and β of the Gaussian function, and the width control parameters σ1 and σ2 of the Gaussian function. For the two direction correction coefficients γ and δ, they are set to constant values, where γ = 1 and δ = 0.1. Therefore, the particle dimension is set to 6D, the parameters of the particle swarm algorithm are initialized, and the position state and velocity state of each particle are randomly initialized.

[0039] Step 5.2, set the particle judgment mechanism for path planning failure. Specifically as follows:

[0040] Perform path planning according to the particle position state. Each particle corresponds to a path planned by the artificial potential field method. If the mobile robot collides with an obstacle or does not reach the end point within the limited planning time, it is regarded as a path planning failure. The condition for judging whether the mobile robot collides with an obstacle is expressed as:

[0041]

[0042] where, ||ρ(X t ,P o )|| represents the shortest distance between the mobile robot and all obstacles at time t.

[0043] The condition for judging whether the mobile robot reaches the end point within the limited planning time is expressed as:

[0044]

[0045] where, ||ρ(X t ,X g )|| represents the distance between the mobile robot and the end point at time t, R reach is the threshold for judging whether the end point is reached, and T path is the maximum planning time set for path planning.

[0046] Particles that satisfy the condition of flag2 = 0 or flag3 = 0 are particles with failed path planning, and the remaining particles are particles with successful path planning.

[0047] Step 5.3: Set the fitness function using the trajectory length and smoothness. Let the initial position of the mobile robot be represented as X0 and the orientation be represented as θ0. Then the path length L corresponding to the i-th particle i The expression is:

[0048]

[0049] where T i represents the path planning duration of the artificial potential field method corresponding to the i-th particle.

[0050] The turning angle Q of the mobile robot corresponding to the path of the i-th particle i The expression is:

[0051]

[0052] where θ t and θ t-1 represent the orientations of the mobile robot at the t-th and (t - 1)-th moments respectively, and the angles are expressed in radians.

[0053] Finally, the fitness function F of the i-th particle i The expression is:

[0054] F i = L i + Q i (13)

[0055] Step 5.4: Set the particle partition search strategy for partition search.

[0056] According to Step 5.2, the particles are divided into particles with successful path planning and particles with failed path planning. Set the fitness value of the particles with failed path planning to a constant value M, and classify these particles with failed path planning as particles in the alienation zone; if there are particles with successful path planning, calculate the fitness values of the particles with successful path planning according to Step 5.3, calculate the average value of the fitness values of these particles with successful path planning, classify the particles with fitness values greater than the average value as particles in the reasonable zone, and classify the particles with fitness values less than the average value as particles in the preferred zone; set the particle with the fitness value closest to the average value as the average particle. If there are no particles with successful path planning, the average particle is set to the first particle.

[0057] After each iteration of each particle, the position state with a smaller fitness value within the particle is set as the individual optimal value of the particle, and the individual optimal value of the particle at the initial moment is the particle itself. The particle with the smallest fitness value among all particles is the population optimal value.

[0058] The velocity state v of the particles in the isolated zone i and position state x i The update strategy is:

[0059]

[0060] in, They represent the velocity state of the ith particle after the jth and j+1th iterations respectively; w is the inertia weight; c1 and c2 are learning factors, c1 controls the weight of the particle learning from the optimal value of the population, and c2 controls the weight of the particle learning from the average particle; gbest j is the optimal value of the population searched up to the jth iteration; m is a small positive constraint factor; is the average particle; They represent the position state of the i-th particle after the j-th and j+1-th iterations respectively.

[0061] The velocity state v of the particles in the preferred zone i and position state x i The update strategy is:

[0062]

[0063] Among them, j is the current iteration number, J is the maximum iteration number of the particle swarm algorithm, and η(j) is the control parameter of the variable step length.

[0064] The particles in the reasonable region need to adaptively balance the local search and global search capabilities, and a competitive switching mechanism is designed for this purpose. i j ≠F i j+1 When the condition is met, it indicates that it has not fallen into the local optimum, and its speed state v i and position state x i The update strategy is:

[0065]

[0066] Among them, c3 is the learning factor, which controls the weight of the particle learning from the individual optimal value; rand1 and rand2 are two functions that generate random numbers between 0 and 1; F i j represents the fitness value of the i-th particle after the j-th iteration, F i j+1 Represents the fitness value of the i-th particle after the j+1th iteration.

[0067] The particle satisfies F i j =F i j+1When the condition is met, it indicates that the particle has fallen into the local optimum, and its velocity state v i and position state x i The update strategy is as follows:

[0068]

[0069] Step 5.5, the particle with the minimum fitness value after iteration is the population optimum value, and record the fitness value of the population optimum value. If the current iteration number j has not reached the maximum iteration number J, jump to Step 5.4 and continue to execute; if the current iteration number j has reached the maximum iteration number J, jump to Step 5.6.

[0070] Step 5.6, the particle swarm optimization algorithm ends, and output the population optimum value and the change of the fitness value of the population optimum value.

[0071] Step Six: Adopt the result output by Step Five to execute path planning so that the mobile robot can successfully plan the path with the optimal length and smoothness.

[0072] The beneficial effects of the present invention are as follows:

[0073] The present invention constructs a repulsive force function of the artificial potential field method based on the bimodal Gaussian function, which is composed of a linear component and a non-linear component in the force direction, enhancing the local turning ability of the mobile robot to avoid obstacles. A trigger-type random perturbation mechanism is designed to solve the problem that the mobile robot falls into the local minimum. Finally, a competitive learning particle swarm optimization framework is established, and a hierarchical competitive learning strategy is implemented to optimize the artificial potential field parameters to obtain the path with the optimal length and smoothness. The present invention enables the mobile robot to meet the path planning requirements under different precisions and different environments through flexible parameter settings, and obtain the path with the optimal length and smoothness. Description of the Drawings

[0074] Figure 1 is the flow chart of optimizing the artificial potential field parameters by using the competitive learning particle swarm algorithm of the present invention;

[0075] Figure 2 is the optimization curve of the competitive learning particle swarm algorithm under the map with completely symmetric obstacles constructed by the present invention;

[0076] Figure 3 is the path planning result with the optimized result as the parameters of the artificial potential field method;

[0077] Figure 4 is the optimization curve of the competitive learning particle swarm algorithm under the map with randomly distributed obstacles constructed by the present invention;

[0078] Figure 5 is the path planning result with the optimized result as the parameters of the artificial potential field method. Specific Embodiments

[0079] To make the method problems solved by the present invention, the adopted method solutions, and the achieved method effects clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the present invention, rather than limiting the present invention. In addition, it should be noted that for the convenience of description, only the parts related to the present invention are shown in the accompanying drawings, rather than all the content.

[0080] A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method includes the following steps:

[0081] Step 1: Establish a kinematic model of the mobile robot:

[0082] The mobile robot adopts wheeled motion, and its position variables are represented as X = (x, y) T , which respectively represent the abscissa and ordinate of the mobile robot. Then, the kinematic model of the mobile robot can be expressed as:

[0083]

[0084] where F(X t ) is the resultant force received by the mobile robot at time t; l is the movement step length within Δt time; X t represents the position of the mobile robot at time t; X t+1 represents the position of the mobile robot at time t + 1; ||.|| represents the two-norm.

[0085] Step 2: To meet the actual motion obstacle avoidance requirements, considering the physical sizes of the mobile robot and the obstacles, set an obstacle avoidance circle and solve the radius of the obstacle avoidance circle, specifically as follows:

[0086] Common obstacles in the actual environment include cuboids, cylinders, and triangular prisms. Project these obstacles onto a two-dimensional plane to obtain a projected figure. Then, the collision distance threshold of the obstacle is the radius of the circumscribed circle of the obtained projected figure. Let the radius of this circumscribed circle be R0. Similarly, project the mobile robot onto a two-dimensional plane to obtain a projected figure. Then, the collision distance threshold of the mobile robot is the radius of the circumscribed circle of the obtained projected figure. Let the radius of this circumscribed circle be R1. Regarding the mobile robot as a particle, set an obstacle avoidance circle around the obstacle. The radius R of this obstacle avoidance circle is expressed as:

[0087] R = R0 + R1 (2)

[0088] Step 3: Construct an improved artificial potential field model and set the gravitational field and repulsive field functions:

[0089] Step 3.1, the gravitational force received by the mobile robot in the environment is expressed as:

[0090] Fatt (X t )=λ att ·(X g -X t ) (3)

[0091] Among them, F att (X t ) represents the gravitational force on the mobile robot at time t; λ att is the gravitational potential field gain coefficient; X g Indicates the location of the end point.

[0092] Step 3.2, construct a repulsion function based on the bimodal Gaussian function, which is composed of a linear component and a nonlinear component in the force direction. The expression of the repulsion force of a single obstacle on the mobile robot is:

[0093]

[0094] Among them, F rep,i (X t ) indicates that the mobile robot is subject to the repulsive force of the ith obstacle at time t; λ rep is the repulsive potential field gain coefficient; α and β represent the weights of the two Gaussian functions, affecting their contribution. α controls the contribution of the first Gaussian function, and β controls the contribution of the second Gaussian function; σ1 and σ2 represent the width control parameters of the two Gaussian functions, affecting the attenuation rate of the repulsive force. σ1 controls the attenuation rate of the first Gaussian function, and σ2 controls the attenuation rate of the second Gaussian function; γ and δ are direction correction coefficients, which are used to control the linear and nonlinear components in the direction of the repulsive force and enhance the nonlinear steering ability of the mobile robot when approaching obstacles. γ controls the weight of the linear component in the direction of the repulsive force, and δ controls the weight of the nonlinear component in the direction of the repulsive force. t ,P o,i )|| represents the distance between the mobile robot and the i-th obstacle at time t.

[0095] The designed repulsion function changes more gently, generating a high-gain, narrow-width near-field repulsion peak at very close distances, forming a steep repulsion barrier to achieve fast response to prevent collisions, and generating a low-gain, wide-width mid-field repulsion peak at medium distances, forming a soft early warning repulsion to guide the mobile robot to plan its path in advance. The improved repulsion function realizes that the repulsion will gradually increase when the mobile robot is close to an obstacle, thereby effectively avoiding collisions, and the repulsion will decay rapidly when the distance to the obstacle is far, which can reduce the impact of long-distance obstacles on the mobile robot, so that it can focus more on moving to the target position.

[0096] Introducing the non - linear part, the mobile robot will start making small adjustments when it is far from the obstacle, rather than making large - scale turns when approaching. This makes the changes in the entire path more coherent and natural, greatly broadening the exploration range in terms of direction, optimizing the turning flexibility, making the change of the repulsive force function at the edge of the obstacle more delicate and flexible, and avoiding the "hard turn" or path discontinuity problems that may be caused by the traditional repulsive force function.

[0097] The expression for the resultant repulsive force of the mobile robot affected by the obstacle is:

[0098]

[0099] Among them, F rep (X t ) represents the resultant repulsive force of the mobile robot affected by the obstacle at time t; N represents the number of obstacles.

[0100] The expression for the resultant force of the mobile robot is:

[0101] F(X t ) = F att (X t ) + F rep (X t )(6)

[0102] Step 4: Design a trigger - type random perturbation mechanism. When it is detected that the mobile robot is trapped in a local minimum, a random position update strategy is adopted to help the mobile robot get out of trouble. Specifically:

[0103] According to formula (6), when the resultant force of the mobile robot is 0, it will fall into a local minimum and stop; in a highly symmetric obstacle map, there is also a phenomenon that the mobile robot oscillates back and forth between two points, and at this time, the mobile robot also falls into the local minimum problem. According to the motion situation of the local minimum, the following trigger conditions are set for judgment:

[0104]

[0105] Among them, X t-1 represents the position of the mobile robot at time t - 1.

[0106] The principle of the random perturbation mechanism is to introduce a random number at the current position to change the position of the mobile robot.

[0107] For the case of flag1 = 1, the mobile robot falls into a local minimum. At this time, the random perturbation mechanism is triggered to update the position of the mobile robot, and its expression is:

[0108]

[0109] Among them, ε is the disturbance intensity, and ε = 0.2 is taken; rand represents a function that generates random numbers between 0 and 1.

[0110] For the case of flag1 = 0, the mobile robot does not fall into the local minimum and moves normally.

[0111] Step Five: Establish a competitive learning particle swarm optimization framework, implement a hierarchical competitive learning strategy, and optimize the artificial potential field parameters, as shown in Figure 1 shown below:

[0112] Step 5.1, the optimized parameters include the gravitational constant λ att , the repulsive constant λ rep , the weights α and β of the Gaussian function, and the width control parameters σ1 and σ2 of the Gaussian function. For the two direction correction coefficients γ and δ, they are set to constant values, where γ = 1 and δ = 0.1. Therefore, the particle dimension is set to 6 dimensions, the parameters of the particle swarm algorithm are initialized, and the position state and velocity state of each particle are randomly initialized.

[0113] The particle swarm algorithm adopts a fixed inertia weight w = 0.85 to balance the global exploration and local exploitation capabilities; the learning factors c1 = 1.3, c2 = 1.7, and c3 = 1.3 are set differently; the population size is set to 50 particles to improve the coverage of the search space; the path form is mainly affected by the ratio of the main gravitational coefficient and the repulsive coefficient. Combinations of coefficients with equal ratios have similar planning effects. Therefore, the search range of the gravitational coefficient λ att and the repulsive coefficient λ rep is set to 1 to 3. The search range of the Gaussian function coefficients α and β is set to 0.2 to 3, and the search range of the Gaussian function width control coefficients σ1 and σ2 is set to 0.1 to 3.

[0114] Step 5.2, set the particle judgment mechanism for path planning failure. Specifically as follows:

[0115] Perform path planning according to the particle position state. Each particle corresponds to a path planned by the artificial potential field method. If the mobile robot collides with an obstacle or does not reach the end point within the limited planning time, it is regarded as a path planning failure. The condition for judging whether the mobile robot collides with an obstacle is expressed as:

[0116]

[0117] Among them, ||ρ(X t ,P o )|| represents the shortest distance between the mobile robot and all obstacles at time t.

[0118] The condition for judging whether the mobile robot reaches the end point within the limited planning time is expressed as:

[0119]

[0120] Among them, ||ρ(X t , X g )|| represents the distance between the mobile robot and the end point at time t, and R reach is the threshold for determining whether the end point has been reached, and T path is the maximum planning duration set for path planning.

[0121] Particles that satisfy the condition flag2 = 0 or flag3 = 0 are path planning failure particles, and the remaining particles are path planning success particles.

[0122] Step 5.3, set the fitness function using the trajectory length and smoothness. Let the initial position of the mobile robot be represented as X0 and the orientation be represented as θ0. Then the path length L i of the i-th particle is expressed as:

[0123]

[0124] Among them, T i represents the path planning duration of the artificial potential field method corresponding to the i-th particle.

[0125] The turning angle Q i of the mobile robot corresponding to the i-th particle is expressed as:

[0126]

[0127] Among them, θ t , θ t-1 represent the orientations of the mobile robot at times t and t - 1 respectively, and the angles are expressed in radians.

[0128] Finally, the fitness function F i of the i-th particle is expressed as:

[0129] F i = L i + Q i (13)

[0130] Step 5.4, set the particle partition search strategy for partition search.

[0131] According to Step 5.2, the particles are divided into particles with successful path planning and particles with failed path planning. Set the fitness value of the particles with failed path planning to a constant value M, and classify these particles with failed path planning as particles in the alienation zone; if there are particles with successful path planning, calculate the fitness value of the particles with successful path planning according to Step 5.3, calculate the average value of the fitness values of these particles with successful path planning, classify the particles with fitness values greater than the average value as particles in the reasonable zone, and classify the particles with fitness values less than the average value as particles in the preferred zone; set the particle with the fitness value closest to the average value as the average particle. If there are no particles with successful path planning, the average particle is set as the first particle.

[0132] Set the position state with a smaller fitness value after each iteration of each particle as the individual optimal value of the particle. The individual optimal value of the particle at the initial moment is the particle itself. The particle with the smallest fitness value among all particles is the population optimal value.

[0133] The update strategy for the velocity state v i and the position state x i of the particles in the alienation zone is as follows:

[0134]

[0135] where respectively represent the velocity states of the i-th particle after the j-th and (j + 1)-th iterations; w is the inertia weight; c1 and c2 are learning factors, c1 controls the weight of the particle learning from the population optimal value, and c2 controls the weight of the particle learning from the average particle; gbest j is the population optimal value searched until the j-th iteration; m is the constraint factor of a relatively small positive number; is the average particle; respectively represent the position states of the i-th particle after the j-th and (j + 1)-th iterations.

[0136] The update strategy for the velocity state v i and the position state x i of the particles in the preferred zone is as follows:

[0137]

[0138] where j is the current iteration number, J is the maximum iteration number of the particle swarm algorithm, and η(j) is the control parameter of the mutation step size.

[0139] The particles in the reasonable zone need to adaptively balance the local search and global search capabilities. For this purpose, a competition switching mechanism is designed. When the particles in the reasonable zone satisfy F i j ≠F i j+1 condition, it indicates that they have not fallen into the local optimum. Their velocity state v i and position state xi The update strategy is as follows:

[0140]

[0141] Among them, c3 is the learning factor, which controls the weight of the particle learning from the individual optimal value; rand1 and rand2 are two functions that generate random numbers between 0 and 1; represents the individual optimal value searched by the i-th particle until the j-th iteration; F i j represents the fitness value of the i-th particle after the j-th iteration, F i j+1 represents the fitness value of the i-th particle after the (j + 1)-th iteration.

[0142] When the particle satisfies F i j = F i j+1 condition, it indicates that the particle has fallen into the local optimum, and its velocity state v i and position state x i The update strategy is as follows:

[0143]

[0144] Step 5.5, the particle with the smallest fitness value after iteration is the population optimal value, and record the fitness value of the population optimal value. If the current iteration number j has not reached the maximum iteration number J, jump to Step 5.4 and continue to execute; if the current iteration number j has reached the maximum iteration number J, jump to Step 5.6.

[0145] Step 5.6, the particle swarm optimization algorithm ends, and output the population optimal value and the change of the fitness value of the population optimal value. Figure 2 and Figure 4 show the optimization process of the designed particle swarm optimization algorithm under different obstacle scenarios.

[0146] Step Six: Adopt the result output by Step Five to perform path planning so that the mobile robot can successfully plan the path with the optimal length and smoothness.

[0147] For example Figure 3 and Figure 5 As shown in the path planning result, the blue asterisk in the map represents the starting point of the mobile robot, the red triangle represents the end point, the black dot represents the obstacle, and the cyan dashed circle represents the obstacle avoidance circle. According to the result output by Step Five, set the parameters of the artificial potential field method to plan the feasible path represented by the green circle. The simulation result shows that the mobile robot does not enter the range of the obstacle avoidance circle during the movement process, will not collide with the obstacle during the movement process, and can successfully plan the path with the optimal length and smoothness from the starting point to the end point.

[0148] Matters not covered by the present invention are well-known technologies.

[0149] The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. It is not intended to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims

1. A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method, characterized in that The mobile robot path planning method includes the following steps: First, establish the kinematic model of the mobile robot; Second, to meet the actual motion obstacle avoidance requirements, considering the physical sizes of the mobile robot and the obstacles, set the obstacle avoidance circle and solve the radius of the obstacle avoidance circle; Third, construct an improved artificial potential field model and set the gravitational field and repulsive field functions; Fourth, design a trigger-type random perturbation mechanism. When it is detected that the mobile robot falls into a local minimum, adopt a random position update strategy to help the mobile robot get out of trouble; Fifth, establish a competitive learning particle swarm optimization framework, implement a hierarchical competitive learning strategy, and optimize the parameters of the artificial potential field method; Sixth, adopt the result output in the fifth step to execute path planning so that the mobile robot can successfully plan the optimal path in terms of length and smoothness.

2. The path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method according to claim 1, characterized in that, The specific content of the first step is as follows: The mobile robot adopts wheeled motion, and its position variables are expressed as X = (x, y) T , representing the abscissa and ordinate of the mobile robot respectively. Then, the kinematic model of the mobile robot is expressed as: Among them, F(X t ) is the resultant force received by the mobile robot at time t; l is the movement step length within Δt time; X t represents the position of the mobile robot at time t; X t+1 represents the position of the mobile robot at time t + 1; ||.|| represents the two-norm.

3. A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method according to claim 1, characterized in that, The specific content of the second step is as follows: Perform a two-dimensional projection on the obstacle to obtain a projection graph. Then, the collision distance threshold of the obstacle is the radius of the circumscribed circle of the obtained projection graph. Let the radius of this circumscribed circle be R0. Similarly, perform a two-dimensional projection on the mobile robot to obtain a projection graph. Then, the collision distance threshold of the mobile robot is the radius of the circumscribed circle of the obtained projection graph. Let the radius of this circumscribed circle be R1. Consider the mobile robot as a particle and set an obstacle avoidance circle around the obstacle. The radius R of this obstacle avoidance circle is expressed as: R = R0 + R1 (2).

4. A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method according to claim 1, characterized in that, The specific content of the third step is as follows: Step 3.1, the gravitational force received by the mobile robot in the environment is expressed as: F att (X t ) = λ att ·(X g - X t ) (3) Among them, F att (X t ) represents the gravitational force received by the mobile robot at time t; λ att is the gravitational potential field gain coefficient; X g represents the position of the end point; Step 3.2, construct a repulsive force function based on the double-peak Gaussian function. The force in the force direction is composed of a linear component and a non-linear component. The expression for the repulsive force of the mobile robot received by a single obstacle is: Among them, F rep,i (X t ) represents the repulsive force of the mobile robot from the i-th obstacle at time t; λ rep is the repulsive force potential field gain coefficient; α and β respectively represent the weights of two Gaussian functions, affecting their contribution degrees. α controls the contribution degree of the first Gaussian function, and β controls the contribution degree of the second Gaussian function; σ1 and σ2 respectively represent the width control parameters of the two Gaussian functions, affecting the decay rate of the repulsive force. σ1 controls the decay rate of the first Gaussian function, and σ2 controls the decay rate of the second Gaussian function; γ and δ are direction correction coefficients, used to control the linear and nonlinear components in the repulsive force direction. γ controls the weight of the linear component in the repulsive force direction, and δ controls the weight of the nonlinear component in the repulsive force direction, ||ρ(X t ,P o,i )|| represents the distance between the mobile robot and the i-th obstacle at time t; The expression for the combined repulsive force of the mobile robot received by the obstacles is: Among them, F rep (X t ) represents the resultant repulsive force of the mobile robot from obstacles at time t; N represents the number of obstacles; The expression for the resultant force received by the mobile robot is: F(X t ) = F att (X t ) + F rep (X t )(6).

5. A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method according to claim 4, characterized in that, The specific content of the fourth step is as follows: According to formula (6), when the resultant force received by the mobile robot is 0, it will fall into a local minimum and stop. According to the motion situation of the local minimum, set the following trigger conditions for judgment: where X t-1 represents the position of the mobile robot at time t-1; For the case of flag1 = 0, the mobile robot has not fallen into a local minimum and moves normally; For the case of flag1 = 1, the mobile robot has fallen into a local minimum. At this time, trigger the random perturbation mechanism to update the position of the mobile robot. The random perturbation mechanism is to introduce a random number at the current position to change the position of the mobile robot.

6. A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method according to claim 5, characterized in that, When flag1 = 1, the following expression is used to update the position of the mobile robot: Among them, ε is the perturbation intensity; rand represents a function that generates a random number between 0 and 1.

7. A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method according to claim 5, characterized in that, The specific content of the fifth step is as follows: Step 5.1, the optimization parameters include the gravitational constant λ att , the repulsive constant λ rep , the Gaussian function weights α and β, the Gaussian function width control parameters σ1 and σ2. For the correction coefficients in the γ and δ directions, they are set to constant values. Then, the particle dimension is set to 6 dimensions, the parameters of the particle swarm algorithm are initialized, and the position state and velocity state of each particle are randomly initialized; Step 5.2, set a path planning failure particle judgment mechanism; Perform path planning according to the particle position state. Each particle corresponds to a path planned by the artificial potential field method. If the mobile robot collides with an obstacle or does not reach the end point within the limited planning time, it is regarded as a path planning failure; Step 5.3, set the fitness function using the trajectory length and smoothness; assume that the initial position of the mobile robot is represented as X0 and the orientation is represented as θ0, then the path length L corresponding to the i-th particle i The expression is: Among them, T i represents the path planning duration of the artificial potential field method corresponding to the i-th particle; The turning angle Q of the mobile robot corresponding to the path of the i-th particle i The expression is as follows: where, θ t and θ t-1 represent the orientations of the mobile robot at the t-th and (t-1)-th moments respectively, and the angles are represented in radians; Finally, the fitness function F of the i-th particle i The expression is as follows: F i = L i + Q i (13) Step 5.4, set a particle partition search strategy for partition search; According to Step 5.2, the particles are divided into particles with successful path planning and particles with failed path planning; the fitness value of the particles with failed path planning is set to a constant value M, and the particles with failed path planning are classified as particles in the alienation area; if there are particles with successful path planning, then according to Step 5.3, calculate the fitness value of the particles with successful path planning, calculate the average value of the fitness values of these particles with successful path planning, classify the particles with fitness values greater than the average value as particles in the reasonable area, and classify the particles with fitness values less than the average value as particles in the preferred area; set the particle with the fitness value closest to the average value as the average particle; if there are no particles with successful path planning, then the average particle is set to the first particle; The position state with a smaller fitness value within each particle after each iteration is set as the individual optimal value of the particle, and the individual optimal value of the particle at the initial moment is the particle itself; the particle with the smallest fitness value among all particles is the population optimal value; Determine the velocity state v of the particles in the alienation zone respectively i and the update strategy of the position state x i , the velocity state v of the particles in the preferred zone i and the update strategy of the position state x i , the velocity state v of the particles in the reasonable zone i and the update strategy of the position state x i ; In Step 5.5, the particle with the smallest fitness value after iteration is the population optimal value, and record the fitness value of the population optimal value; if the current iteration number j has not reached the maximum iteration number J, jump to Step 5.4 and continue to execute; if the current iteration number j reaches the maximum iteration number J, jump to Step 5.6; In Step 5.6, the particle swarm optimization algorithm ends, and output the population optimal value and the change of the fitness value of the population optimal value.

8. A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method according to claim 7, characterized in that, In the said Step 5.1, γ = 1 and δ = 0.

1.

9. A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method according to claim 7, characterized in that In the said Step 5.2: The condition for judging whether the mobile robot collides with an obstacle is expressed as: where ||ρ(X t ,P o )|| represents the shortest distance between the mobile robot and all obstacles at time t; The condition for judging whether the mobile robot reaches the end point within the limited planning duration is expressed as: Among them, ||ρ(X t , X g )|| represents the distance between the mobile robot and the end point at time t, and R reach is the threshold for judging whether the end point has been reached, and T path is the set maximum planning duration for path planning; The particles that satisfy the condition of flag2 = 0 or flag3 = 0 are particles with failed path planning, and the remaining particles are particles with successful path planning.

10. A path planning method for a mobile robot based on a competitive learning mechanism and an improved artificial potential field method according to claim 7, characterized in that, In the said Step 5.4: The velocity state v of the particles in the isolated zone i and position state x i The update strategy is: Among them, respectively represent the velocity states of the $i$-th particle after the $j$-th and $(j + 1)$-th iterations; $w$ is the inertia weight; $c_1$ and $c_2$ are learning factors, where $c_1$ controls the weight of the particle learning from the population optimal value, and $c_2$ controls the weight of the particle learning from the average particle; $gbest$ j is the population optimal value searched until the $j$-th iteration; $m$ is a drag factor for a relatively small positive number; is the average particle; respectively represent the position states of the $i$-th particle after the $j$-th and $(j + 1)$-th iterations; The velocity state v of the particles in the preferred area i and the position state x i are updated according to the following strategy: Among them, j is the current iteration number, J is the maximum iteration number of the particle swarm algorithm, and η(j) is the control parameter of the mutation step size; The velocity state v of the particles in the reasonable region i and the position state x i are updated according to the following strategy: Particles in the reasonable region need to adaptively balance local search and global search capabilities and design a competition switching mechanism; when particles in the reasonable region satisfy F i j ≠F i j+1 condition, it indicates that it has not fallen into the local optimum, and the update strategies for its velocity state v i and position state x i are as follows: Among them, c3 is the learning factor that controls the weight of the particle learning from the individual optimal value; rand1 and rand2 are two functions that generate random numbers between 0 and 1; F i j represents the fitness value of the i-th particle after the j-th iteration, F i j+1 represents the fitness value of the i-th particle after the (j + 1)-th iteration; The particle satisfies F i j = F i j+1 When the condition is met, it indicates that the particle has fallen into a local optimum, and its velocity state v i and position state x i The update strategy is as follows:

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