CN115933693A - Robot path planning method based on adaptive chaotic particle swarm algorithm - Google Patents

Robot path planning method based on adaptive chaotic particle swarm algorithm Download PDF

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CN115933693A
CN115933693A CN202211719251.6A CN202211719251A CN115933693A CN 115933693 A CN115933693 A CN 115933693A CN 202211719251 A CN202211719251 A CN 202211719251A CN 115933693 A CN115933693 A CN 115933693A
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刘朋
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Liuzhou Vocational and Technical College
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Abstract

The invention belongs to the field of robot path planning, and discloses a robot path planning method based on a self-adaptive chaotic particle swarm algorithm, which comprises the steps of firstly carrying out environment modeling, and formulating a fitness function by using three control parameters of path length, obstacle risk degree and path smoothness so as to meet the requirement of robot path planning in a complex environment; then, in the iterative process, a new self-adaptive updating strategy is adopted for three control parameters in the algorithm, so that the global exploration and local development capability of the algorithm is dynamically adjusted; and finally, when the population is trapped in a local extreme value, guiding the population to jump out of the local extreme value point by utilizing the proposed self-adaptive Logistic chaotic mapping, and recovering the optimization searching capability of the algorithm, thereby obtaining a better path from the initial position to the target position.

Description

Robot path planning method based on adaptive chaotic particle swarm algorithm
Technical Field
The invention belongs to the field of robot path planning, and particularly relates to a robot path planning method based on an adaptive chaotic particle swarm algorithm.
Background
The mobile robot path planning technology is one of core contents in the robot research field, and finding a collision-free and feasible better path is the final target for path planning of the mobile robot. In recent years, with continuous optimization based on a population search strategy and the proposition of different kinds of objective function models, theoretical research on path planning of mobile robots has gradually changed from a traditional algorithm (such as an artificial potential field method, a grid method, an a-star algorithm and the like) to a population intelligent optimization algorithm, and various bionic algorithms such as a particle swarm algorithm (PSO), an ant colony algorithm, a firefly algorithm, an artificial bee colony algorithm, a bat algorithm and the like are proposed in the field of path planning, wherein the PSO algorithm has the advantages of simplicity in operation, few control parameters and the like compared with other population intelligent optimization algorithms, and can provide similar or even better optimization results in most cases. However, the standard PSO algorithm has the problems of too high dependency of search performance on parameters and low convergence rate, and the calculation efficiency and reliability of path planning are seriously affected. In order to solve the above problems, the PSO algorithms in the prior art with different modified versions generate feasible paths for mobile robots, for example, a binary particle swarm algorithm with dual-structure particle encoding and mutation operators is introduced into an environment with obstacles to accelerate the convergence speed of a particle swarm; when the algorithm is trapped in local optimum in the process of searching an optimum solution, a particle correction method is adopted to generate new particles to replace original particles so as to guide the algorithm to get rid of a local optimum value and search a feasible path; and a convergence guarantee adaptive particle swarm optimization (RDSAPSO) algorithm is adopted, and the inertia weight is adaptively updated according to the individual extreme value of the particle and the global extreme value of the particle in the iterative process, so that the exploration capacity of the global optimal particle is enhanced. However, although the existing particle swarm algorithm has better convergence and less parameters needing to be adjusted, the existing particle swarm algorithm has the problems of weaker global exploration and local development capability and easy falling into local extreme values, a robot path planning of an improved particle swarm algorithm introducing a jump-out mechanism and traction operation is also provided in the prior art document, the diversity of the population and the global search capability are maintained through the jump-out mechanism, and the convergence speed of the algorithm is accelerated through the traction operation.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a robot path planning method based on a self-adaptive chaotic particle swarm algorithm, which is used for path planning of a mobile robot, can further improve the quality and efficiency of generating a path solution in the path planning process of the traditional particle swarm algorithm, and solves the problems of long operation time, high energy consumption, poor safety and the like of the mobile robot in the path planning process.
In order to achieve the purpose, the invention adopts the following technical scheme:
a robot path planning method based on a self-adaptive chaotic particle swarm algorithm comprises the following steps:
step 1: establishing a robot moving environment map, and determining an initial position S and a target position G of the robot;
and 2, step: obtaining a group of mutually parallel linear clusters (L) according to coordinate transformation in a robot moving environment map 1 ,L 2 ,L 3 ,···L d Solving from the intersection of the linear cluster and the map
Figure BDA0004028191690000021
And &>
Figure BDA0004028191690000022
According to>
Figure BDA0004028191690000023
And &>
Figure BDA0004028191690000024
Determining the maximum speed at which a particle flies in each dimension>
Figure BDA0004028191690000025
Wherein it is present>
Figure BDA0004028191690000026
And 3, step 3: setting the number n of particle populations, the maximum iteration number itermax, the radius r of the circular robot, the maximum chaos optimization number Chaosmax of self-adaptive Logistic mapping and the maximum acting distance l of harmful influence of the obstacle max Minimum working distance l min And a path pairSearch range l of peripheral obstacle o Initializing parameters in a group particle algorithm, including path length, obstacle risk degree and path smoothness; initializing the initial speed and the initial position of each particle under a coordinate system S-X 'Y' by the following formula;
Figure BDA0004028191690000027
wherein r is a random number on (0, 1), i =1,2 ·, n is the number of population particles, j =1,2 ·, d is the dimension of the particles;
and 4, step 4: calculating an initial fitness function value f of each particle by a fitness function f of the path planning of the mobile robot i 0 According to f i 0 Value update of
Figure BDA0004028191690000028
And &>
Figure BDA0004028191690000029
And evaluating an initial inertial weight for each particle>
Figure BDA00040281916900000210
Then based on>
Figure BDA00040281916900000211
Calculating an initial acceleration coefficient of each particle;
and 5: updating the speed and position of each particle, and calculating according to the maximum value if the speed and position of the particle exceed the maximum value and the boundary value;
step 6: calculating the fitness function value f of each particle under the current iteration number i t According to f i t First, the inertial weight for the next iteration is determined
Figure BDA00040281916900000212
And is selected by>
Figure BDA00040281916900000213
Finding the acceleration factor at the next iteration, then using f i t Update the individual optimum position of the particle>
Figure BDA00040281916900000214
And particle global optimum position>
Figure BDA00040281916900000215
And 7: calculating the size beta of the particle population density at the current iteration moment t Will beta t Comparing with a preset threshold value if beta t If the particle size is smaller than the preset threshold value, the particle is trapped in a local extreme value, and step 8 is executed, otherwise step 9 is executed; the size beta of the population density of the particles t As shown in the following formula:
Figure BDA0004028191690000031
wherein x i,j The current ith particle is at the j-dimension coordinate value, x g,j The j-dimension coordinate value of the global optimum particle is obtained;
and step 8: performing chaotic optimization on globally optimal particles by adopting an improved self-adaptive search strategy and utilizing self-adaptive Logistic chaotic mapping to guide the population to jump out of a local extreme point;
and step 9: and judging whether the maximum iteration number itermax is reached, and if not, returning to the step 5.
As a further improvement of the present invention, in step 4, a fitness function f for path planning of the mobile robot is defined as a weighted combination of path length, risk degree of the obstacle, and smoothness of the path, and the smaller the value of the fitness function f is, the higher the quality of the path solution is.
As a further improvement of the present invention, in step 5, the method for updating the speed and the position of each particle is as follows: assuming that n particles exist in the d-dimensional search space, the position and flight speed of the ith particle at the t-th iteration are respectively expressed as vectors
Figure BDA0004028191690000032
And vector->
Figure BDA0004028191690000033
The speed and position updating method of the ith particle in the t +1 iteration is expressed by the following formula:
Figure BDA0004028191690000034
Figure BDA0004028191690000035
/>
where ω is the inertial weight factor, r 1 And r 2 To obey random variables of uniformly distributed U (0, 1), c 1 And c 2 Is the acceleration factor.
As a further improvement of the present invention, in the step 8, the improved adaptive search strategy is: before chaotic optimization, firstly, arranging fitness function values of all particles in the current iteration number from large to small; then, taking the first 80% of the particles, and obtaining the minimum value a (j, t) and the maximum value b (j, t) of each particle in the j dimension; and finally, taking the minimum value and the maximum value on each dimension as the search range of the particles when the inverse mapping is carried out on the original solution space.
Compared with the prior art, the invention has the following beneficial effects:
1. the robot path planning method based on the adaptive chaotic particle swarm algorithm is used for path planning of a mobile robot, and can further improve the quality and efficiency of generating a path solution in the path planning process of the traditional particle swarm algorithm. Before iteration is started, environment modeling is firstly carried out on the algorithm, an actual scene is compressed into a two-dimensional problem, and a fitness function is formulated by using three control parameters of path length, obstacle risk degree and path smoothness, so that the requirement of robot path planning in a complex environment is met; then, in the iterative process, a new self-adaptive updating strategy is adopted for three control parameters in the algorithm, so that the global exploration and local development capability of the algorithm is dynamically adjusted; and finally, when the population is trapped in a local extreme value, guiding the population to jump out of the local extreme value point by using the provided self-adaptive Logistic chaotic mapping, and recovering the optimizing capability of the algorithm, so that a better path from the initial position to the target position is obtained, and a new idea is provided for planning an optimal path of the mobile robot in a complex environment.
2. The invention uses the self-adaptive inertia weight factor omega and the dynamically adjusted acceleration coefficients c1 and c2, can effectively accelerate the convergence of the algorithm, and effectively shortens the planning time, thereby quickly obtaining the optimal path of the mobile robot.
3. According to the invention, a plurality of evaluation functions are converted into the comprehensive fitness function with consistent monotonicity, and factors such as path length, barrier danger degree and path smoothness are comprehensively considered, so that safe and stable navigation of the mobile robot can be realized, and large-angle change of a planned path is avoided.
4. The technical scheme provided by the invention can obtain a better optimal path, has high convergence speed, less corner turning times and smoother path, reduces the energy consumption loss of the mobile robot, and enables the mobile robot to safely and quickly move to a target point. In addition, the feasibility and the effectiveness of the technical scheme are proved through true simulation verification in the embodiment.
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FIG. 1 is a mathematical modeling coordinate of a robot mobile environment of the present invention;
FIG. 2 is a schematic view of the obstacle risk detection of the present invention;
FIG. 3 is a routing diagram of three algorithms in scenario one in the practice of the present invention;
FIG. 4 is a graph of an optimal fitness function for three algorithms in scenario one according to an embodiment of the present invention;
FIG. 5 is a routing diagram for three algorithms in scenario two in the practice of the present invention;
FIG. 6 is a graph of an optimal fitness function of three algorithms in scenario two according to an embodiment of the present invention;
FIG. 7 is a flow chart of a robot path planning method based on an adaptive chaotic particle swarm algorithm according to the present invention;
Detailed Description
The invention is further described with reference to the following figures and examples. It should be noted that the specific embodiments of the present invention are only for clearly describing the technical solutions, and should not be taken as a limitation to the scope of the present invention.
In order to further improve the quality and efficiency of a path solution generated by a Particle Swarm Optimization (PSO) algorithm in a path planning process, the invention provides an improved PSO algorithm, namely a robot path planning method called as a self-adaptive chaotic particle swarm optimization (SACPSO). The general idea is as follows: firstly, environment modeling is carried out, an actual scene is compressed into a two-dimensional problem, and a fitness function is formulated by using three evaluation functions of path length, obstacle danger degree and path smoothness, so that the requirement of robot path planning in a complex environment is met; then, in the iterative process, a new self-adaptive updating strategy is adopted for three control parameters in the algorithm, so that the global exploration and local development capability of the algorithm is dynamically adjusted; and finally, when the population is trapped in a local extreme value, guiding the population to jump out of the local extreme value point by utilizing the proposed self-adaptive Logistic chaotic mapping, and recovering the optimizing capability of the algorithm, thereby obtaining a better path from the initial position to the target position
Referring to fig. 1 to 7, a robot path planning method based on an adaptive chaotic particle swarm algorithm includes the following steps:
step 1: establishing a robot moving environment map, and determining an initial position S and a target position G of the robot;
as shown in fig. 1, in the coordinate system O-XY, the start position and the target position are defined as a point S and a point G, respectively, and black entities of different shapes and sizes are defined as obstacles. Connecting a point S and a point G, equally dividing the line segment SG into d +1 segments, making a perpendicular line at each equally divided point to obtain a group of mutually parallel linear clusters { L } 1 ,L 2 ,···L d The intersection point of the straight line cluster and any one path can correspond to a point sequence (p) 1 ,p 2 ,···p d ). Defining pointsS and G are respectively p 0 And p d+1 Thus, the mobile robot path planning problem can be formulated as finding a set of least costly sequences of points (p) 0 ,p 1 ,p 2 ,···p d+1 ) The point sequence is a non-obstacle point, and no obstacle exists between any adjacent point sequences.
In order to reduce the dimension of decision variables in the coordinate system O-XY, a new local rectangular coordinate system S-X ' Y ' is established by taking the straight line where SG is positioned as an X ' axis, and the corresponding coordinate transformation formula is as follows:
Figure BDA0004028191690000051
wherein theta is the included angle between the X' axis and the X axis (X) s ,y s ) The coordinates of the point S under O-XY, (X, Y) and (X ', Y') are the coordinates of the same point under different coordinate systems O-XY and S-X 'Y', respectively.
The path length L is calculated as:
Figure BDA0004028191690000052
wherein l (p) j ,p j+1 ) The Euclidean distance between adjacent points is represented, and under an S-X 'Y' coordinate system, the above formula is represented as follows:
Figure BDA0004028191690000053
as can be seen from the above formula, the path planning problem is finally converted into solving under the S-X ' Y ' coordinate system, and only corresponding to each dimension in the S-X ' Y
Figure BDA0004028191690000054
Is related to.
Step 2: obtaining a group of mutually parallel linear clusters (L) according to coordinate transformation in a robot moving environment map 1 ,L 2 ,L 3 ,···L d And solving the intersection point of the straight line cluster and the map
Figure BDA0004028191690000055
And &>
Figure BDA0004028191690000056
According to>
Figure BDA0004028191690000057
And &>
Figure BDA0004028191690000058
Determining the maximum speed at which a particle flies in each dimension>
Figure BDA0004028191690000061
Wherein it is present>
Figure BDA0004028191690000062
And 3, step 3: setting the number n of particle populations, the maximum iteration number itermax, the radius r of the circular robot, the maximum chaos optimization number Chaosmax of self-adaptive Logistic mapping and the maximum acting distance l of harmful influence of the obstacle max Minimum working distance l min And search range l of path for peripheral obstacle o Initializing parameters in the group particle algorithm, including path length, obstacle risk degree and path smoothness; initializing the initial speed and the initial position of each particle under a coordinate system S-X 'Y' by the following formula;
Figure BDA0004028191690000063
wherein r is a random number on (0, 1), i =1,2 ·, n is the number of population particles, j =1,2 ·, d is the dimension of the particles;
the goal of path planning is to generate an optimal collision-free path while taking into account some performance criteria. In the present invention, the quality of the generated path is measured by three evaluation functions (path length, obstacle risk level and path smoothness).
For the first oneThe evaluation function, path length L calculation formula, has given a formula to solve for the global path length. For the second evaluation function, the degree of danger caused by the obstacle can be evaluated by calculating the amount of the safety distance reserved between the path and the surrounding obstacle. Because the distribution of the obstacles in the map is complex and the number of the obstacles is large, only the periphery l of the path is selected for simplifying the calculation o The obstacles in the range and the points on the obstacles closest to the path are calculated, and the selected obstacles are numbered as the m (m =1,2,3,) th obstacle. Considering the actual situation of robot motion in real environment, as shown in fig. 2, a circular robot is used for detecting the danger level of an obstacle, and the center of the circle of the robot is O c Radius r, l (OS) m ) As a center of circle O c Shortest distance to an obstacle m in the environment, l m ＝l(OS m ) -r is the shortest distance of the robot from the obstacle.
Definition of l max Maximum distance of action for which the obstacle may have a detrimental effect,/ min The minimum distance of action for which an obstacle may have a detrimental effect. As can be seen from fig. 2, if there is an obstacle m in the environment, the shortest distance l between the robot and the obstacle is m < 0 or an arbitrary path (p) j ,p j+1 ) If the obstacle exists, the robot cannot pass through the path, and the path is a failure path, and the iterative optimization is continued without participating in the judgment of the final path quality. For all l m And the danger degree of the obstacle with the mark number m to the path is calculated by the following formula:
Figure BDA0004028191690000064
in the above formula, when l m ≥l max When the path is absolutely safe, the risk level is 0, when l m ≤l min The path is absolutely critical, with a degree of danger of 1. When l is max ＞l m ＞l min When is driven by m The magnitude of the value determines the degree of risk of the obstacle m to the path. Ring of robotIn the environment, the path periphery l o The sum of the degrees of risk posed by all obstacles within the range is calculated by the following formula.
Figure BDA0004028191690000071
For the third evaluation function, in order to evaluate the smoothness of the path, the criterion of the smoothness of the path can be obtained from the deflection angle α (α ∈ [0, π ]) between two line segments connecting three adjacent nodes, and it can be seen from FIG. 2 that the greater the deflection angle α, the smoother the path. The path smoothness is calculated by using the following formula:
Figure BDA0004028191690000072
and 4, step 4: calculating an initial fitness function value f of each particle by a fitness function f of the path planning of the mobile robot i 0 According to f i 0 Value update of
Figure BDA0004028191690000073
And &>
Figure BDA0004028191690000074
And finds the initial inertial weight ≦ for each particle>
Figure BDA0004028191690000075
Then based on>
Figure BDA0004028191690000076
Calculating an initial acceleration coefficient of each particle; in practical application, the advantages of evaluating the path performance are inconsistent, and in order to balance all the advantages and obtain better overall performance, the invention uses the idea of an additive weighting method to solve the problem, specifically, a fitness function f of the path planning of the mobile robot is defined as a weighted combination of the path length, the risk degree of the obstacle and the path smoothness, and the smaller the value of the fitness function f is, the higher the quality of the path solution is, and the better the overall performance isThe calculation process is shown in the following formula:
Figure BDA0004028191690000077
and 5: updating the speed and position of each particle, and if the speed and position of the particle exceed the maximum value and the boundary value, calculating according to the maximum value; the method for updating the speed and the position of each particle comprises the following steps: assuming that n particles exist in the d-dimensional search space, the position and flight speed of the ith particle at the t-th iteration are respectively expressed as vectors
Figure BDA0004028191690000078
And vector->
Figure BDA0004028191690000079
The speed and position updating method of the ith particle in the t +1 iteration is expressed by the following formula:
Figure BDA00040281916900000710
Figure BDA00040281916900000711
where ω is the inertial weight factor, r 1 And r 2 To obey the random variables of uniformly distributed U (0, 1), c 1 And c 2 Is the acceleration factor.
Step 6: calculating the fitness function value f of each particle under the current iteration number i t According to f i t First, the inertial weight for the next iteration is determined
Figure BDA00040281916900000712
And is selected by>
Figure BDA00040281916900000713
Finding the acceleration factor at the next iteration, then using f i t Update the particle unitOptimum position>
Figure BDA00040281916900000714
And particle global optimum position>
Figure BDA00040281916900000715
And 7: calculating the size beta of the particle population density at the current iteration moment t Will beta t Comparing with a preset threshold value, if beta is larger than the preset threshold value t If the particle size is smaller than the preset threshold value, the particle is trapped in a local extreme value, and step 8 is executed, otherwise step 9 is executed; the size beta of the population density of the particles t As shown in the following formula:
Figure BDA0004028191690000081
wherein x i,j Is the current ith particle at the jth coordinate value, x g,j A j-dimension coordinate value of the global optimal particle;
and 8: carrying out chaotic optimization on global optimal particles by adopting an improved self-adaptive search strategy and utilizing self-adaptive Logistic chaotic mapping to guide the population to jump out of a local extreme point;
the chaotic mapping is a random motion state obtained by a deterministic equation, and the unique traversal characteristic of the chaotic mapping enables chaotic variables to traverse all states in a certain range without repeating according to self rules, so that the chaotic mapping has wide application, such as image data compression, high-speed retrieval, prediction of nonlinear time sequences and the like. According to the invention, the global optimal particles are subjected to chaotic optimization by introducing the self-adaptive Logistic chaotic mapping, so that the population is guided to jump out of a local extreme point and the global optimization capability of the algorithm is recovered. The common chaotic optimization process for globally optimal particles using Logistic mapping is as follows:
(1) When the population is trapped in a local extreme value, firstly, the current global optimal particle X is obtained g ＝(x g,1 ,x g,2 ,···,x g,d ) Is mixing X g Is mapped to Logistic by formula 17In the domain of the equation, a set of solutions { z } is obtained j }(j＝1,2,···d)。
Figure BDA0004028191690000082
Wherein
Figure BDA0004028191690000083
And &>
Figure BDA0004028191690000084
The minimum value and the maximum value in each dimension are respectively, and the values in the path planning process are selected from a group of parallel straight line families { L 1 ,L 2 ,···L d The intersection of the map boundary and the boundary of the map.
(2) Will { z j Substituting the initial solution of the Logistic equation into 16 iteration to generate a chaotic sequence
Figure BDA0004028191690000085
And the resulting chaotic sequence is then inverse mapped->
Figure BDA0004028191690000086
Returning to the original solution space to obtain
Figure BDA0004028191690000087
(3) Calculate and compare
Figure BDA0004028191690000088
The fitness function value of each feasible solution is used for updating X by the obtained optimal solution pbest And X gbest The value of (c).
For the particle swarm algorithm, in the early stage of iteration, when the algorithm falls into a local extreme, a better particle in a global range is required to generate stronger disturbance so as to enhance the global exploration capability of the algorithm, in the later stage of iteration, the particle is already gradually close to a global optimal position, and when the algorithm falls into a local extreme value again, a better particle in a local range is required to generate disturbance so as to improve the local search capability of the algorithm. The basic Logistic chaos optimization is used for directly returning the generated chaos sequence to an original solution space from inverse mapping without considering the searching range of the particles at the moment, so that the adaptive value of unnecessary particles is calculated, and the calculation amount of the algorithm is increased.
In order to avoid the blindness of calculation, a new and improved adaptive search strategy is provided for the search range of the chaotic sequence. Before chaotic optimization, firstly, arranging fitness function values of all particles in the current iteration times (t times) from large to small; then, taking the first 80% of the particles (S particles in total), and obtaining the minimum value a (j, t) and the maximum value b (j, t) of each particle in the jth dimension; and finally, mapping the minimum value and the maximum value on each dimension as the search range of the particles when the inverse is mapped to the original solution space. In the inverse mapping process, if the coordinate value on any dimension exceeds the range, the particle is directly discarded, so that the algorithm can escape from a local extreme point, the calculation amount is reduced, and the chaotic optimization searching efficiency is improved.
And step 9: and judging whether the maximum iteration number itermax is reached or not, and if not, returning to the step 5.
In order to verify the effectiveness of the improved algorithm in solving the path planning problem, a comparison experiment is carried out on the algorithm (SACPSO) provided by the invention, a standard PSO algorithm and a self-adaptive particle swarm algorithm (RDSAPSO) with Gaussian disturbance under the same environment model.
Assuming that the simulation experiment is performed in a two-dimensional space of 100m × 100m, the experimental scene is divided into a scene one and a scene two according to the distribution of the obstacles, the number of particles used in the experiment n =40, the maximum iteration number itermax =80, and the particle dimensions d in the scene one and the scene two are 13 and 17, respectively. Circular robot radius r =1 for testing path quality generation in SACPSO algorithm, and search range l of obstacles around path o =8, maximum (minimum) distance of action for which obstacle has a detrimental effect/ max ＝r＝1(l min = r/2= 0.5), the weighting factor ω of the fitness function f 1 ＝0.6、ω 2 ＝0.3、ω 3 =0.1, the population density threshold is 0.05, and the chaos optimization times Chaosmax =200. Standard PSOInertial weight factor ω =0.5, learning factor c in the algorithm 1 ＝c 2 Control parameter in the algorithm of =2,rdsapso is ω max ＝0.9，ω min ＝0.4，c 1i ＝c 2f ＝2，c 1f ＝c 2i ＝0.5。
The final path searched by the three algorithms is output after 40 particles are iterated for 80 times under two different scenes. The starting position S and the target position G of the robot in the first scene are (0, 0) and (100 ), respectively, and the starting position S and the target position G of the robot in the second scene are (0, 50) and (100, 50), respectively. After the simulation is finished, the planning results of the three algorithms in the first scene and the second scene are respectively given in fig. 3-6, and tables 1 and 2 summarize data generated by the three algorithms after the iteration is finished, wherein the data mainly comprises the total time AllTime/s spent when the iteration is finished, the fitness function value f of the output path, the iteration times Iter when the optimal solution starts to converge and the execution time/s.
Table 1 data generated in scenario one
Figure BDA0004028191690000091
Table 2 data generated in scenario two
Figure BDA0004028191690000092
Analyzing the planning results in fig. 3-6, it can be seen clearly that the standard PSO algorithm is trapped in the local extremum in the iterative process, while the RDSAPSO algorithm and the SACPSO algorithm are not affected by the trapping of the population in the extremum in the iterative process, and both generate a better path after the iteration is finished; then, comparing the paths generated by the RDSAPSO algorithm and the SACPSO algorithm, it can be seen from the figure that part of the paths generated by the RDSAPSO algorithm will be close to the edge of the obstacle, and the SACPSO algorithm always keeps a certain safety distance when approaching the obstacle because the risk of collision with the obstacle is considered, so compared with the prior art, the path generated by the SACPSO algorithm more conforms to the requirement of robot path planning in reality, and the quality of the path solution is higher.
Analyzing the data in table 1 and table 2 shows that the standard PSO algorithm has the highest fitness function value of the output path due to the local extremum; the ACPSO algorithm introduces a parameter self-adaptive updating strategy and chaotic optimization, so that the calculation amount of the algorithm is increased, and the time spent by the algorithm at the end of iteration is longest; the RDSAPSO algorithm and the ACPSO algorithm have similar fitness function values of output paths and belong to a global optimal path, but the iteration times Iter and the execution time used by the RDSAPSO algorithm when the RDSAPSO algorithm starts to converge to a global optimal solution are respectively 14 times and 3.95 seconds more than those of the ACPSO algorithm in a first scene and 13 times and 5.18 seconds more than those of the ACPSO algorithm in a second scene, which shows that although the calculation amount of the ACPSO algorithm is larger than that of the RDSAPSO algorithm, the efficiency of the SACPSO algorithm in generating the global optimal path solution is higher than that of the RDSAPSO algorithm.
Finally, comparing the dimension of the particle in the two scenes with the total time spent when the iteration is finished, it can be easily found that when the dimension of the particle is increased, more time is consumed to calculate the information of the node on the increased dimension, so that the calculation amount of the algorithm is increased, and the calculation time is increased. By adopting the technical scheme provided by the invention, a better optimal path can be obtained, the convergence speed is high, the turn times are less, the path is smoother, and the accuracy is higher.
The above description is intended to describe in detail the preferred embodiments of the present invention, but the embodiments are not intended to limit the scope of the claims of the present invention, and all equivalent changes and modifications made within the technical spirit of the present invention should fall within the scope of the claims of the present invention.

Claims (4)

1. A robot path planning method based on an adaptive chaotic particle swarm algorithm is characterized by comprising the following steps of:
step 1: establishing a robot moving environment map, and determining an initial position S and a target position G of the robot;
step 2: obtaining a group of mutual flatness according to coordinate transformation in a robot moving environment mapLine cluster of rows { L 1 ,L 2 ,L 3 ,···L d Solving from the intersection of the linear cluster and the map
Figure FDA0004028191680000011
And &>
Figure FDA0004028191680000012
According to>
Figure FDA0004028191680000013
And &>
Figure FDA0004028191680000014
Determining the maximum speed at which a particle flies in each dimension>
Figure FDA0004028191680000015
Wherein it is present>
Figure FDA0004028191680000016
And 3, step 3: setting the number n of particle populations, the maximum iteration number itermax, the radius r of the circular robot, the maximum chaos optimization number Chaosmax of self-adaptive Logistic mapping and the maximum acting distance l of harmful influence generated by the obstacle max Minimum working distance l min And the search range l of the path for the peripheral obstacle o Initializing parameters in the group particle algorithm, including path length, obstacle risk degree and path smoothness; initializing the initial speed and the initial position of each particle under a coordinate system S-X 'Y' by the following formula;
Figure FDA0004028191680000017
wherein r is a random number on (0, 1), i =1,2 ·, n is the number of population particles, j =1,2 ·, d is the dimension of the particles;
and 4, step 4: adaptation of path planning by mobile robotsDegree function f calculating initial fitness function value f of each particle i 0 According to f i 0 Value update of
Figure FDA0004028191680000018
And &>
Figure FDA0004028191680000019
And finds the initial inertial weight ≦ for each particle>
Figure FDA00040281916800000110
Then is selected by>
Figure FDA00040281916800000111
Calculating an initial acceleration coefficient of each particle;
and 5: updating the speed and position of each particle, and calculating according to the maximum value if the speed and position of the particle exceed the maximum value and the boundary value;
and 6: calculating the fitness function value f of each particle under the current iteration number i t According to f i t First, the inertial weight for the next iteration is determined
Figure FDA00040281916800000112
And is selected by>
Figure FDA00040281916800000113
Finding the acceleration factor at the next iteration, and using f i t Update the individual optimum position->
Figure FDA00040281916800000114
And particle global optimum position->
Figure FDA00040281916800000115
And 7: calculating the size beta of the particle population density at the current iteration moment t Will beta t Comparing with a preset threshold value if beta t If the particle size is smaller than the preset threshold value, the particle is trapped in a local extreme value, and step 8 is executed, otherwise step 9 is executed; the size beta of the population density of the particles t As shown in the following formula:
Figure FDA00040281916800000116
wherein x i,j The current ith particle is at the j-dimension coordinate value, x g,j The j-dimension coordinate value of the global optimum particle is obtained;
and 8: carrying out chaotic optimization on global optimal particles by adopting an improved self-adaptive search strategy and utilizing self-adaptive Logistic chaotic mapping to guide the population to jump out of a local extreme point;
and step 9: and judging whether the maximum iteration number itermax is reached, and if not, returning to the step 5.
2. The robot path planning method based on the adaptive chaotic particle swarm algorithm according to claim 1, wherein in the step 4, a fitness function f of the mobile robot path planning is defined as a weighted combination of a path length, an obstacle risk degree and a path smoothness, and the smaller the value of the fitness function f is, the higher the quality of a path solution is.
3. The method for robot path planning based on the adaptive chaotic particle swarm algorithm according to claim 1, wherein in the step 5, the method for updating the speed and the position of each particle comprises the following steps: assuming that n particles exist in the d-dimensional search space, the position and flight speed of the ith particle at the t-th iteration are respectively expressed as vectors
Figure FDA0004028191680000021
And vector->
Figure FDA0004028191680000022
The speed and position updating method of the ith particle in the t +1 iteration is expressed by the following formula:
Figure FDA0004028191680000023
Figure FDA0004028191680000024
where ω is the inertial weight factor, r 1 And r 2 To obey the random variables of uniformly distributed U (0, 1), c 1 And c 2 Is the acceleration factor.
4. The method for robot path planning based on the adaptive chaotic particle swarm optimization according to claim 1, wherein in the step 8, the improved adaptive search strategy is: before chaotic optimization, firstly, arranging fitness function values of all particles in the current iteration number from large to small; then, taking the first 80% of the particles, and obtaining the minimum value a (j, t) and the maximum value b (j, t) of each particle in the j dimension; and finally, taking the minimum value and the maximum value on each dimension as the search range of the particles when the inverse mapping is carried out on the original solution space.
CN202211719251.6A 2022-12-30 2022-12-30 Robot path planning method based on adaptive chaotic particle swarm algorithm Pending CN115933693A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116820110A (en) * 2023-08-28 2023-09-29 武汉市自然资源保护利用中心 Ecological environment monitoring task planning method and device based on intelligent optimization algorithm
CN117170413A (en) * 2023-11-03 2023-12-05 北京卓翼智能科技有限公司 Unmanned aerial vehicle path planning method and device based on modified sine and cosine algorithm

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116820110A (en) * 2023-08-28 2023-09-29 武汉市自然资源保护利用中心 Ecological environment monitoring task planning method and device based on intelligent optimization algorithm
CN116820110B (en) * 2023-08-28 2023-11-28 武汉市自然资源保护利用中心 Ecological environment monitoring task planning method and device based on intelligent optimization algorithm
CN117170413A (en) * 2023-11-03 2023-12-05 北京卓翼智能科技有限公司 Unmanned aerial vehicle path planning method and device based on modified sine and cosine algorithm
CN117170413B (en) * 2023-11-03 2024-01-30 北京卓翼智能科技有限公司 Unmanned aerial vehicle path planning method and device based on modified sine and cosine algorithm

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