CN115113628A - Routing method of inspection robot based on improved wolf algorithm - Google Patents

Routing method of inspection robot based on improved wolf algorithm Download PDF

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Publication number
CN115113628A
CN115113628A CN202210956948.9A CN202210956948A CN115113628A CN 115113628 A CN115113628 A CN 115113628A CN 202210956948 A CN202210956948 A CN 202210956948A CN 115113628 A CN115113628 A CN 115113628A
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wolf
function
fitness
path
convergence factor
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张倩
宁旭成
潘雷
赵坚
张志强
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Tianjin Chengjian University
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Tianjin Chengjian University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process

Abstract

The invention belongs to the technical field of routing planning of inspection robots, and particularly relates to a routing planning method of an inspection robot based on an improved wolf algorithm, which comprises the following steps of 1, forming an initialization population by utilizing a cross variation idea and a roulette idea; step 2, adding the turning times and the turning angles as penalty values into an adaptability function, calculating the adaptability of the wolf individual and storing three wolfs with the best adaptability; step 3, updating the position and coefficient vector of the wolf according to a formula
Figure DDA0003791744500000011
Value, using arctan function and logarithm function to convergence factor
Figure DDA0003791744500000012
Is improved to update the convergence factor
Figure DDA0003791744500000013
Step 4, calculating the number of wolfsThe fitness of the body and updating the fitness and the position of the three-head wolfs; and 5, judging whether the maximum iteration times are reached, wherein the output wolf alpha wolf position is the optimal solution after the maximum iteration times are reached. The invention improves the gray wolf algorithm in three aspects of population initialization, a convergence factor function and a fitness function, and can output an optimal routing inspection path.

Description

Routing method of inspection robot based on improved wolf algorithm
Technical Field
The invention belongs to the technical field of routing planning of inspection robots, and particularly relates to a routing planning method of an inspection robot based on an improved wolf algorithm.
Background
The routing planning of the inspection robot is to enable the inspection robot to automatically find a collision-free track from a starting point to a target point according to the surrounding environment information. The routing algorithm of the inspection robot is the core of routing planning of the inspection robot. The routing planning of the inspection robot means that after sensing the surrounding environment, the inspection robot can automatically plan an optimal moving path from a starting point to a terminal point, and the optimal moving path can meet the requirements of shortest moving path, shortest consumed time, minimum energy consumption and the like.
According to the current research results, the gray wolf algorithm is a novel intelligent optimization algorithm for simulating the hunting behavior of the gray wolf, and can be applied to the field of path planning. However, the gray wolf algorithm suffers from the following disadvantages: (1) when the position of the population is determined, the position of the wolf individual is determined randomly, so that the algorithm has certain blindness and randomness. (2) Gray wolf algorithm location update forms a containment circle for hunting based on the first three leading wolfs and the target, using the average of the distance of each leading wolf from the target location for update, but this approach does not necessarily target exactly at the average of its distances. (3) When the wolf algorithm is trapped in the local optimal solution, no measures are provided to help the wolf algorithm jump out of the local optimal solution. Therefore, the grayish wolf algorithm still has the defects of easy falling into local optimization, slow convergence in the later period, poor selection precision, poor stability and the like in the path planning application, and often cannot achieve the ideal path planning effect when the routing inspection robot path planning is carried out.
Disclosure of Invention
The invention mainly aims to solve the problems in the prior art and provides an inspection robot path planning method based on an improved wolf algorithm.
The technical problem solved by the invention is realized by adopting the following technical scheme: a routing planning method of an inspection robot based on an improved wolf algorithm,
step 1, an initialized population N1 of an improved wolf algorithm applied to path planning is path nodes randomly generated in a grid map, each path is connected by the same number of nodes to form a wolf individual, the initialized population N1 is crossed to obtain a population N2, the population N with the best fitness is calculated in the populations N1 and N2 by utilizing a roulette thought as an initialized population N for iterative update, and a convergence factor is set
Figure BDA0003791744480000011
Coefficient vector
Figure BDA0003791744480000012
A value;
step 2, improving a fitness function of a wolf algorithm applied to path planning, namely the sum of distances of all nodes of a path obtained by Euclidean distance calculation, adding turning times and turning angles of the obtained path into the fitness function as penalty values, calculating the fitness of a wolf individual according to a fitness function formula, wherein the better the fitness of the wolf individual is, the stronger the path superiority is, storing three wolfs with the best fitness as alpha wolfs, beta wolfs and delta wolfs, and storing the rest wolf groups as omega wolfs;
step 3, calculating and updating the grey wolf position according to the mathematical model of the grey wolf surrounding prey, and calculating and updating the coefficient vector according to the coefficient vector formula
Figure BDA0003791744480000021
Value, using arctan function and logarithm function to convergence factor
Figure BDA0003791744480000022
Is improved and the size of the ratio of the number of obstacles to the area of the map is applied to the collectionConvergence factor
Figure BDA0003791744480000023
In curve improvement, the convergence factor after improvement
Figure BDA0003791744480000024
The curve forms a convergence factor function model, and the convergence factor is calculated and updated according to the convergence factor function model
Figure BDA0003791744480000025
Step 4, calculating the fitness of the individual wolf of the wolf according to a fitness function formula, updating the fitness of the three wolfs of the wolf, and updating and calculating the positions of the three wolfs of the wolf according to a mathematical model of the wolf attacking prey;
and 5, judging whether the maximum iteration number is reached, outputting the head wolf alpha wolf position calculated according to the updating process formula as an optimal solution after the maximum iteration number is reached, obtaining the optimal routing inspection path of the inspection robot, and returning to the step 3 to continue circular calculation if the optimal routing inspection path is not reached.
Further, the mathematic model of the wolf surrounding the prey is
Figure BDA0003791744480000026
Figure BDA0003791744480000027
Wherein t is the current iteration number,
Figure BDA0003791744480000028
representing the length vector between the gray wolf and the game,
Figure BDA0003791744480000029
a position vector representing the current prey,
Figure BDA00037917444800000210
represents the current grayThe position vector of the wolf is determined,
Figure BDA00037917444800000211
representing the updated position vector of the individual wolf,
Figure BDA00037917444800000212
and
Figure BDA00037917444800000213
is a coefficient vector.
Further, the coefficient vector is formulated as
Figure BDA00037917444800000214
Figure BDA00037917444800000215
Wherein the content of the first and second substances,
Figure BDA00037917444800000216
and
Figure BDA00037917444800000217
is a vector of coefficients that is a function of,
Figure BDA00037917444800000218
and
Figure BDA00037917444800000219
is [0,1 ]]A random number in between, and a random number,
Figure BDA00037917444800000220
is a convergence factor.
Further, the convergence factor function model is
Figure BDA00037917444800000221
Figure BDA00037917444800000222
Wherein k is an adjusting parameter, p is the base number of the logarithmic function, T is the maximum iteration number, and T is the current iteration number.
Further, the fitness function is formulated as
L＝L(i)+fix(M)
Figure BDA00037917444800000223
Figure BDA00037917444800000224
Figure BDA00037917444800000225
θ i ＝|θ 2 -θ 1 |
Where L (i) is the sum of nodes of the path, fix () is a function rounded to the left, and (x, y) is the current node coordinate, (x) in the grid map 1 ,y 1 ) Is the coordinate of the last node, (x) 2 ,y 2 ) Is the next node coordinate, θ 1 、θ 2 The tangent angles, θ, generated for the current node and the previous node, the current node and the next node i Is the angle difference between two tangent angles, namely the angle generated by the current turning.
Further, the turn times and the turn angles are normalized by the arc radius M, the penalty value fix (M) of the turn times and the turn angles can be obtained by calculating the arc radius M, and the normalization processing formula is
Figure BDA0003791744480000031
Figure BDA0003791744480000032
Figure BDA0003791744480000033
Wherein, theta i Theta is the sum of the turning angles, A is the angle determination value, and V is the number of turns.
Further, the mathematic model of the gray wolf attack prey is
Figure BDA0003791744480000034
Wherein the content of the first and second substances,
Figure BDA0003791744480000035
and
Figure BDA0003791744480000036
respectively represent the distance vectors of alpha, beta and delta of the wolf head and omega of the wolf body,
Figure BDA0003791744480000037
and
Figure BDA0003791744480000038
respectively representing the current position vectors of the wolf alpha, beta and delta,
Figure BDA0003791744480000039
and
Figure BDA00037917444800000310
coefficient vectors representing the gray wolf omega and the head wolf alpha, beta and delta, respectively,
Figure BDA00037917444800000311
representing the position vector of the gray wolf omega.
Further, the update process formula
Figure BDA00037917444800000312
Figure BDA00037917444800000313
Wherein the content of the first and second substances,
Figure BDA00037917444800000314
respectively represent updated position vectors between the wolf body omega and the wolf alpha, beta and delta, A 1 、A 2 、A 3 Respectively represent the gray wolf individual omega and the head wolf alpha, beta and delta coefficient vectors,
Figure BDA00037917444800000315
and
Figure BDA00037917444800000316
respectively represent the distance vectors of alpha, beta and delta of the wolf head and omega of the wolf body,
Figure BDA00037917444800000317
and
Figure BDA00037917444800000318
respectively representing the current position vectors of the wolf alpha, beta and delta,
Figure BDA00037917444800000319
to represent
Figure BDA00037917444800000320
Figure BDA00037917444800000321
I.e. the final updated position of the individual grayish wolf omega.
The invention has the beneficial effects that:
the invention improves the number of initialization population by utilizing the concept of cross variation and the concept of roulette of a gray wolf algorithm (GWO), and provides a nonlinear convergence factor function capable of adjusting a turning point, which can not only enlarge the early-stage search range, but also accelerate the later-stage convergence speed, and simultaneously adds the turning times and the turning angles of the calculated path into the fitness function of path planning to improve the path selection precision, and finally applies the improved gray wolf algorithm (TPGWO) to the path planning of the inspection robot, so that the output path of the improved gray wolf algorithm (TPGWO) under different map environments is better, the path planning time is shorter, and the solving precision, the stability and the convergence of the output path are improved.
Drawings
Fig. 1 is a flow chart of a routing method of an inspection robot based on an improved wolf algorithm.
Fig. 2 is a flow chart of an improved process of the improved gray wolf algorithm of the present invention.
Fig. 3 is a schematic diagram of the population initialization improvement of the present invention.
FIG. 4 is a graph illustrating the variation of the convergence factor when the logarithmic function of the present invention is based on 1/2.
FIG. 5 is a graph illustrating the variation of the convergence factor when the logarithmic function of the present invention is based on 1/3.
FIG. 6 is a graph illustrating the variation of the convergence factor when the logarithmic function of the present invention is based on 2/3.
FIG. 7 is a diagram illustrating variation curves of different convergence factor functions according to the present invention.
Fig. 8 is a diagram illustrating the normalization of the turning times and the turning angles according to the present invention.
Fig. 9(a) -9(c) are graphs showing the path planning results of PSO, GWO, and TPGWO of the present invention under a 10 × 10 grid map.
Fig. 10(a) -10(c) are the convergence plots of the path planning for PSO, GWO, TPGWO of the present invention under a 10 x 10 grid map.
Fig. 11(a) -11(c) are graphs showing the path planning results of PSO, GWO, and TPGWO of the present invention under a 15 × 15 grid map.
Fig. 12(a) -12(c) are the convergence plots of the path planning for PSO, GWO, TPGWO of the present invention under a 15 × 15 grid map.
Fig. 13(a) -13(c) are graphs of the path planning results of PSO, GWO, and TPGWO of the present invention under a 20 × 20 grid map.
Fig. 14(a) -14(c) are graphs of the convergence of the PSO, GWO, TPGWO of the present invention for path planning under a 20 × 20 grid map.
FIGS. 15(a) -15(b) are graphs of convergence factors of the present invention
Figure BDA0003791744480000041
And a path planning result diagram under the simple map with fewer obstacles.
FIGS. 16(a) -16(b) are graphs showing convergence factors of the present invention
Figure BDA0003791744480000042
A convergence graph of path planning under a simple map with a small number of obstacles.
FIGS. 17(a) -17(b) are graphs showing convergence factors of the present invention
Figure BDA0003791744480000043
And (4) a path planning result graph under a complex map with a large number of obstacles.
FIGS. 18(a) -18(b) are graphs showing convergence factors of the present invention
Figure BDA0003791744480000044
The convergence curve diagram of the path planning under the map with a large number of obstacles and complexity.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
As shown in fig. 1-8, the invention provides a routing method of an inspection robot based on an improved wolf algorithm,
step 1, an initialized population N1 of an improved wolf algorithm applied to path planning is path nodes randomly generated in a grid map, each path is connected by the same number of nodes to form a wolf individual, the initialized population N1 is crossed to obtain a population N2, the population N with the best fitness is calculated in the populations N1 and N2 by utilizing a roulette thought as an initialized population N for iterative update, and a convergence factor is set
Figure BDA0003791744480000051
Coefficient vector
Figure BDA0003791744480000052
A value;
step 2, improving a grey wolf algorithm, applying the fitness function in path planning to the sum of distances of all nodes of a path obtained by Euclidean distance calculation, adding turning times and turning angles of the obtained path into the fitness function as penalty values, calculating the fitness of a grey wolf individual according to a fitness function formula, wherein the better the fitness of the grey wolf individual is, the stronger the path superiority is, the three wolfs with the best fitness are stored as alpha wolfs, beta wolfs and delta wolfs, and the rest wolf groups are omega wolfs;
step 3, calculating and updating the gray wolf position according to the mathematical model of the gray wolf surrounding prey, and calculating and updating the coefficient vector according to the coefficient vector formula
Figure BDA0003791744480000053
Value, using arctangent and logarithm functions on the convergence factor
Figure BDA0003791744480000054
Is improved and the ratio of the number of obstacles to the map area is applied to the convergence factor
Figure BDA0003791744480000055
In curve improvement, the convergence factor after improvement
Figure BDA0003791744480000056
The curve forms a convergence factor function model, and the convergence factor is calculated and updated according to the convergence factor function model
Figure BDA0003791744480000057
Step 4, calculating the fitness of the individual wolf of the wolf according to a fitness function formula, updating the fitness of the three wolfs of the wolf, and updating and calculating the positions of the three wolfs of the wolf according to a mathematical model of the wolf attacking prey;
and 5, judging whether the maximum iteration number is reached, outputting the head wolf alpha wolf position calculated according to the updating process formula as an optimal solution after the maximum iteration number is reached, obtaining the optimal routing inspection path of the inspection robot, and returning to the step 3 to continue circular calculation if the optimal routing inspection path is not reached.
Further, the mathematical model of the gray wolf surrounding the prey is
Figure BDA0003791744480000061
Figure BDA0003791744480000062
Wherein t is the current iteration number,
Figure BDA0003791744480000063
representing the length vector between the gray wolf and the game,
Figure BDA0003791744480000064
a position vector representing the current prey,
Figure BDA0003791744480000065
a position vector representing the current gray wolf,
Figure BDA0003791744480000066
representing the updated position vector of the individual wolf,
Figure BDA0003791744480000067
and
Figure BDA0003791744480000068
is a coefficient vector.
Further, the coefficient vector is formulated as
Figure BDA0003791744480000069
Figure BDA00037917444800000610
Wherein the content of the first and second substances,
Figure BDA00037917444800000611
and
Figure BDA00037917444800000612
is a vector of coefficients that is a function of,
Figure BDA00037917444800000613
and
Figure BDA00037917444800000614
is [0,1 ]]A random number in between, and a random number,
Figure BDA00037917444800000615
is a convergence factor.
Further, the convergence factor function is modeled as
Figure BDA00037917444800000616
Figure BDA00037917444800000617
Wherein k is an adjusting parameter, p is the base number of the logarithmic function, T is the maximum iteration number, and T is the current iteration number.
Further, the fitness function is formulated as
L＝L(i)+fix(M)
Figure BDA00037917444800000618
Figure BDA00037917444800000619
Figure BDA00037917444800000620
θ i ＝|θ 2 -θ 1 |
Where L (i) is the sum of nodes of the path, fix () is a function rounded to the left, and (x, y) is the current node coordinate, (x) in the grid map 1 ,y 1 ) Is the coordinate of the last node, (x) 2 ,y 2 ) As next node coordinate, θ 1 、θ 2 The tangent angles, θ, generated for the current node and the previous node, the current node and the next node i Is the angle difference between two tangent angles, namely the angle generated by the current turning.
Further, the turn times and the turn angles are normalized by the arc radius M, the penalty value fix (M) of the turn times and the turn angles can be obtained by calculating the arc radius M, and the normalization processing formula is
Figure BDA00037917444800000621
Figure BDA00037917444800000622
Figure BDA0003791744480000071
Wherein, theta i Theta is the sum of the turning angles, A is the angle determination value, and V is the number of turns.
Further, the mathematical model of the gray wolf attack prey is
Figure BDA0003791744480000072
Wherein the content of the first and second substances,
Figure BDA0003791744480000073
and
Figure BDA0003791744480000074
respectively represent the distance vectors of alpha, beta and delta of the wolf head and omega of the wolf body,
Figure BDA0003791744480000075
and
Figure BDA0003791744480000076
respectively representing the current position vectors of the wolf alpha, beta and delta,
Figure BDA0003791744480000077
and
Figure BDA0003791744480000078
coefficient vectors representing the gray wolf omega and the head wolf alpha, beta and delta, respectively,
Figure BDA0003791744480000079
representing the position vector of the gray wolf omega.
Further, the process formula is updated
Figure BDA00037917444800000710
Figure BDA00037917444800000711
Wherein the content of the first and second substances,
Figure BDA00037917444800000712
respectively represent updated position vectors between the wolf body omega and the wolf alpha, beta and delta, A 1 、A 2 、A 3 Respectively represent the gray wolf individual omega and the head wolf alpha, beta and delta coefficient vectors,
Figure BDA00037917444800000713
and
Figure BDA00037917444800000714
respectively represent the distance vectors of alpha, beta and delta of the wolf head and omega of the wolf body,
Figure BDA00037917444800000715
and
Figure BDA00037917444800000716
respectively representing the current position vectors of the wolf alpha, beta and delta,
Figure BDA00037917444800000717
to represent
Figure BDA00037917444800000718
Figure BDA00037917444800000719
I.e. the final updated position of the individual grayish wolf omega.
Examples
As shown in fig. 1-8, the route planning of the inspection robot is taken as a research object, the obtained optimal route is taken as a target function, the environment is taken as a constraint condition, and an improved gray wolf optimization algorithm (TPGWO) is provided aiming at the defects of easy local optimization, slow later convergence, poor selection precision, poor stability and the like of a gray wolf optimization algorithm (GWO) in the application of the route planning, the improvement is carried out from three aspects of population initialization, a convergence factor function and a fitness function, the improved gray wolf algorithm (gwtpo) is applied to the route planning of the inspection robot, and the optimization performance of the gwtpo algorithm is verified through a test function and a simulation experiment. The specific implementation process is as follows.
Step 1, an initialized population N1 of an improved wolf algorithm applied to path planning is path nodes randomly generated in a grid map, each path is connected by the same number of nodes to form a wolf individual, the initialized population N1 is crossed to obtain a population N2, the population N with the best fitness is calculated in the populations N1 and N2 by utilizing a roulette thought as an initialized population N for iterative update, and a convergence factor is set
Figure BDA00037917444800000720
Coefficient vector
Figure BDA00037917444800000721
The value is obtained.
The initialization population of the standard gray wolf algorithm (GWO) is generated randomly, the defects that the population quantity is small and the local optimum is easy to fall are existed, and in order to improve the diversity of the initialization population of the gray wolf algorithm, the population initialization of GWO algorithm is improved by using the population crossing idea and the roulette idea. In the routing planning application of the inspection robot, the initialized population of the improved wolf algorithm (TPGWO) represents each path, and the better the fitness of a wolf individual represents the better the superiority of the path. The initialization population of the gray wolf algorithm in the path planning application is path nodes randomly generated in a grid map, and each path is formed by connecting nodes to form a gray wolf individual, so that the number of the path nodes of each path under the same map is the same. As shown in fig. 3, the TPGWO algorithm crosses the initialized population N1 to obtain a population N2, and then calculates the population N with the best fitness from the populations N1 and N2 as the initialized population updated iteratively, so as to improve the search range of the initialized population and the quality of the initialized population.
And 2, improving the fitness function of the wolf algorithm applied to the path planning, namely the sum of the distances of all nodes of the path obtained by Euclidean distance calculation, adding the turning times and the turning angles of the obtained path into the fitness function as penalty values, calculating the fitness of a wolf individual according to a fitness function formula, wherein the better the fitness of the wolf individual is, the stronger the path superiority is, storing three wolfs with the best fitness as alpha wolfs, beta wolfs and delta wolfs, and storing the rest wolf groups as omega wolfs.
In the application of the improved wolf algorithm (TPGWOO) in path planning, the fitness function is the sum of the distances of all nodes of the path obtained by Euclidean distance calculation, and meanwhile, the turning times and the turning angles of the obtained path are added into the fitness function as penalty values, so that the precision of the selected path is improved. In the built grid map, (x, y) is the current node coordinate, (x) 1 ,y 1 ) Is the last node coordinate, (x) 2 ,y 2 ) And (3) as the next node coordinate, V is the turning times, theta is the turning angle, and r and c are the row number and the column number of the map respectively.
Further, the fitness function is formulated as
L＝L(i)+fix(M)
Figure BDA0003791744480000081
Figure BDA0003791744480000082
Figure BDA0003791744480000083
θ i ＝|θ 2 -θ 1 |
Where L (i) is the sum of nodes of the path, fix () is a function rounded to the left, and (x, y) is the current node coordinate, (x) in the grid map 1 ,y 1 ) Is the coordinate of the last node, (x) 2 ,y 2 ) As next node coordinate, θ 1 、θ 2 The tangent angles, θ, generated for the current node and the previous node, the current node and the next node i Is the angle difference between two tangent angles, namely the angle generated by the current turning. In the path planning, if the angle of the obtained path changes, the angle difference of the tangent angle between the nodes is generated, so in the calculation of the fitness function, when tan theta is calculated 1 ≠tanθ 2 When the path is turned once, V is V + 1. In the path planning, each time a turn occurs, a turning angle is generated, and in order to add the turning times and the turning angle to the fitness function, the turning times and the turning angle are normalized.
As shown in fig. 8, in the figure, V is the number of turns (V is 1,2, …), θ is the sum of the turning angles, the turning angle generated each time is 0 to 360 °, and when the number of turns is 1,
Figure BDA0003791744480000084
is 0 to 4; when the number of turns is 2, the number of turns,
Figure BDA0003791744480000085
is 0 to 8; when the number of turns is 3, the number of turns,
Figure BDA0003791744480000091
0 to 12, and when the number of turns is n,
Figure BDA0003791744480000092
the number of the carbon atoms is 0 to 3 n. The number of turns and the turning angle are normalized by the radius M of the arc, and the meaning of fig. 8 is as follows: when 0 is less than or equal to M<When 1, let f be 0; when 1 is less than or equal to M<When 2, let f be 1; when 2 is less than or equal to M<When 3, let f equal to 2; when M is more than or equal to 3<When 4, let f be 3; … …, respectively; when n-1 is less than or equal to M<And when n is greater than the threshold, f is equal to n-1, wherein M is the radius of the corresponding arc, and f is a left rounding function. The penalty values for the number of turns and the turning angle can be determined by calculating the arc radius M, which can be determined by the abscissa and ordinate in fig. 8.
Further, the turn times and the turn angle are normalized by the arc radius M, the penalty value fix (M) of the turn times and the turn angle can be obtained by calculating the arc radius M, and the normalization processing formula is
Figure BDA0003791744480000093
Figure BDA0003791744480000094
Figure BDA0003791744480000095
Wherein, theta i Theta is the sum of the turning angles, A is the angle determination value, and V is the number of turns. The angle determination value a is the ordinate of fig. 8, the number of turns V is the abscissa of fig. 8, (V, a) is the coordinate value in fig. 8, the size M of the arc radius in the above formula is calculated from the coordinate value, and a penalty value fix (M) can be obtained from the arc radius.
Step 3, calculating and updating the gray wolf position according to the mathematical model of the gray wolf surrounding prey, and calculating and updating the coefficient vector according to the coefficient vector formula
Figure BDA0003791744480000096
Value, using arctan function and logarithm function to convergence factor
Figure BDA0003791744480000097
Is improved and the ratio of the number of obstacles to the map area is applied to the convergence factor
Figure BDA0003791744480000098
In curve improvement, the convergence factor after improvement
Figure BDA0003791744480000099
The curve forms a convergence factor function model, and the convergence factor is calculated and updated according to the convergence factor function model
Figure BDA00037917444800000910
The basic idea of improving the gray wolf algorithm is that after a wolf cluster is initialized, three wolfs with the best fitness are selected as head wolfs and are respectively defined as alpha, beta and delta, the positions of the rest wolf clusters omega are updated under the leading of the head wolfs according to the distances between the head wolfs and a prey so as to trap the prey, and the position of the prey represents the optimal solution. The grayish wolf algorithm builds a mathematical model mainly by searching for prey, surrounding prey, attacking prey.
Further, the mathematical model of the gray wolf surrounding the prey is
Figure BDA00037917444800000911
Figure BDA00037917444800000912
The above two formulas represent the distance between the gray wolf and the prey and the location update of the gray wolf individual. Wherein t is the current iteration number,
Figure BDA00037917444800000913
representing the length vector between the gray wolf and the game,
Figure BDA00037917444800000914
a position vector representing the current prey,
Figure BDA00037917444800000915
a position vector representing the current gray wolf,
Figure BDA00037917444800000916
representing the updated position vector of the individual wolf,
Figure BDA00037917444800000917
and
Figure BDA00037917444800000918
is a coefficient vector.
Further, the coefficient vector is formulated as
Figure BDA0003791744480000101
Figure BDA0003791744480000102
Wherein the content of the first and second substances,
Figure BDA0003791744480000103
and
Figure BDA0003791744480000104
is a vector of coefficients that is a function of,
Figure BDA0003791744480000105
and
Figure BDA0003791744480000106
is [0,1 ]]A random number in between, and a random number,
Figure BDA0003791744480000107
is a convergence factor. With number of iterations
Figure BDA0003791744480000108
The linear decrease is from 2 to 0 and,
Figure BDA0003791744480000109
the range of (A) is also reduced, the range being in the interval [ -a, a [ - ]]Internal change when
Figure BDA00037917444800001010
The next position of the gray wolf can be located anywhere between its current position and the hunting position when the value of (d) is within the interval. When in use
Figure BDA00037917444800001011
When the system is used, a wolf group launches an attack to a hunting object, which represents the development capability of a wolf algorithm but is easy to fall into local optimum; when in use
Figure BDA00037917444800001012
In time, the wolf will not attack the prey and force the wolf to separate from the prey, finding a more suitable prey emphasizes the exploratory power of the wolf algorithm and can search for an optimal solution globally. As can be derived from the coefficient vector formula,
Figure BDA00037917444800001013
is [0,2 ]]A random value of between, and
Figure BDA00037917444800001014
in the different way, the first and the second,
Figure BDA00037917444800001015
is a non-linear variation, represents the random weight of the influence of the position of the wolf on the prey,
Figure BDA00037917444800001016
indicating that the influence weight is large, whereas the influence weight is small.
Figure BDA00037917444800001017
The randomness of GWO helps the algorithm avoid falling into local optima during the optimization process.
Of the standard gray wolf algorithm (GWO)Convergence factor
Figure BDA00037917444800001018
Is a linear decreasing function from 2 to 0, and the updating mechanism is that the convergence factor is [2,1 ]]Search within a range of [1,0 ]]The convergence is performed within the range, and thus, the local optimum is liable to be involved and the convergence speed is slow. Therefore, the convergence factor is obtained by using the arc tangent function and the logarithm function
Figure BDA00037917444800001019
The decreasing curve is improved, so that the early search range of the convergence factor is wider, the later convergence speed is higher, and on the basis, the ratio of the number of the obstacles to the area of the map is applied to the decreasing curve, and the parameter value in the function model can be properly adjusted to change the turning point of the convergence factor so as to achieve the optimal selection. The convergence factor function model of the improved grayish wolf algorithm is as follows.
Further, the convergence factor function is modeled as
Figure BDA00037917444800001020
Figure BDA00037917444800001021
Wherein k is an adjusting parameter, p is the base number of the logarithmic function, T is the maximum iteration number, and T is the current iteration number.
(1) Taking T600 as an example, when the logarithmic function is based on 1/2,
Figure BDA00037917444800001022
Figure BDA00037917444800001023
the above equation is the improved convergence factor function when the logarithmic function is based on 1/2, fig. 4 is the variation curve thereof, and the denominator of the adjustment parameter k in the above equation is 300 when the logarithmic function is based on 1/2.
(2) Taking T600 as an example, when the logarithmic function is based on 1/3,
Figure BDA0003791744480000111
Figure BDA0003791744480000112
the above equation is an improved convergence factor function when the logarithmic function is based on 1/3, and fig. 5 is a variation curve thereof, wherein the denominator of the adjustment parameter k in the above equation is 200 when the logarithmic function is based on 1/3.
(3) Taking T600 as an example, when the logarithmic function is based on 2/3,
Figure BDA0003791744480000113
Figure BDA0003791744480000114
the above equation is an improved convergence factor function when the logarithmic function is based on 2/3, and fig. 6 is a variation curve thereof, wherein the denominator of the adjustment parameter k in the above equation is 400 when the logarithmic function is based on 2/3.
In the path planning research, the optimal path is difficult to find in a complex environment map with a large number of obstacles, and the optimal path is easy to find in a simple environment map with a small number of obstacles. Therefore, in an environment map with more obstacles and complexity, the search range and the search time of the optimization algorithm can be properly increased to find the optimal path; in contrast, in an environment map which is simple and has a small number of obstacles, the search range and the search time of the optimization algorithm can be appropriately reduced to find the optimal path. Therefore, the ratio of the number of the obstacles to the area of the map can be added and applied to the function model through the law, when the number of the obstacles is large and complex, the turning point can be delayed, the iteration frequency of the search time is increased, and the iteration frequency during convergence is reduced; when the number of the obstacles is small and simple, the turning point can be advanced, the iteration frequency during searching is reduced, and the iteration frequency during convergence is increased.
The base p of the logarithmic function is used as a variable value and can only be used as a fine adjustment in the application of the ratio of the number of obstacles to the area of the map. As shown in the following formula, taking the maximum number of iterations 600 as an example, when the number of obstacles is relatively small and small, let p be 280/600, reduce the algorithm search time, and increase the convergence speed; when the number of obstacles is relatively large and complex, let p be 320/600, increase algorithm search time, avoid falling into local optimum, promote the selected path precision.
Figure BDA0003791744480000115
The convergence factor function is the convergence factor function when the base number of the logarithm function is unchanged;
Figure BDA0003791744480000116
a convergence factor function when the base number of the logarithm function is adjusted to be small;
Figure BDA0003791744480000117
a convergence factor function when the base number of the logarithm function is increased;
Figure BDA0003791744480000118
is the convergence factor function of the standard grayish wolf algorithm. FIG. 7 is a convergence factor function
Figure BDA0003791744480000119
And
Figure BDA00037917444800001110
compare the curves.
Figure BDA00037917444800001111
Figure BDA0003791744480000121
Figure BDA0003791744480000122
Figure BDA0003791744480000123
Figure BDA0003791744480000124
Figure BDA0003791744480000125
Figure BDA0003791744480000126
And 4, calculating the fitness of the individual wolf of the wolf according to a fitness function formula, updating the fitness of the three wolfs, and updating and calculating the positions of the three wolfs according to a mathematical model of the wolf attacking prey.
The gray wolf gradually approaches to and surrounds the prey in the predation process, attack is initiated on the prey, all initial solutions are continuously approached to the optimal solution along with continuous iteration, the optimal solution is finally obtained, namely the optimal solution is the head wolf alpha, and the second solution and the third solution are the beta wolf and the delta wolf respectively.
Further, the mathematical model of the gray wolf attack prey is
Figure BDA0003791744480000127
Wherein the content of the first and second substances,
Figure BDA0003791744480000128
and
Figure BDA0003791744480000129
respectively represent the distance vectors of alpha, beta and delta of the wolf head and omega of the wolf body,
Figure BDA00037917444800001210
and
Figure BDA00037917444800001211
respectively representing the current position vectors of the wolf alpha, beta and delta,
Figure BDA00037917444800001212
and
Figure BDA00037917444800001213
coefficient vectors representing the gray wolf omega and the head wolf alpha, beta and delta, respectively,
Figure BDA00037917444800001214
representing the position vector of the gray wolf omega.
And 5, judging whether the maximum iteration times are reached, outputting the head wolf alpha wolf position calculated according to the updating process formula as an optimal solution after the maximum iteration times are reached, obtaining an optimal routing inspection path of the inspection robot, and returning to the step 3 to continue circular calculation if the maximum iteration times are reached.
Further, the process formula is updated
Figure BDA00037917444800001215
Figure BDA00037917444800001216
The above two equations represent the position update of the gray wolf body ω and the final moving position of the gray wolf body ω, respectively. Wherein the content of the first and second substances,
Figure BDA00037917444800001217
Figure BDA00037917444800001218
respectively represent updated position vectors between the wolf body omega and the wolf alpha, beta and delta, A 1 、A 2 、A 3 Respectively represent the gray wolf individual omega and the head wolf alpha, beta and delta coefficient vectors,
Figure BDA0003791744480000131
and
Figure BDA0003791744480000132
respectively represent the distance vectors of alpha, beta and delta of the wolf head and omega of the wolf body,
Figure BDA0003791744480000133
Figure BDA0003791744480000134
and
Figure BDA0003791744480000135
respectively representing the current position vectors of the wolf alpha, beta and delta,
Figure BDA0003791744480000136
to represent
Figure BDA0003791744480000137
I.e. the final updated position of the individual grayish wolf omega.
The optimization process of the TPGWO algorithm starts from random initialization of population, and in the iteration process, the position is updated according to the distances between the three-headed wolfs alpha, beta and delta with the best fitness and the prey. Random variable
Figure BDA0003791744480000138
The range of (a) determines that the wolf is approaching a game,
Figure BDA0003791744480000139
indicating that the gray wolf is forced away from the prey to find a more suitable prey and to find the best prey (optimal solution) in the last iteration.
In order to verify that the TPGWO algorithm is better in path and shorter in path planning time than the PSO algorithm and the GWO algorithm under different map environments. And respectively applying an improved grey wolf algorithm (TPGWOO), a standard grey wolf algorithm (GWO) and a particle swarm algorithm (PSO) to path planning to perform simulation test. Assuming that the initial population number N of the three algorithms is 30, the maximum iteration time t max And (2) according to a fitness function formula in the step 2, the environment map is a 10 × 10, 15 × 15 and 20 × 20 grid map with three established areas, each grid map randomly generates different barrier numbers, and finally the path length and the path planning time obtained by three algorithms under three different maps are analyzed. The simulation test results are shown in fig. 9(a) to 14 (c).
TABLE 1 running results of different algorithms in different map environments
Figure BDA00037917444800001310
Fig. 9(a) to 14(c) are the path diagrams and the convergence curves of the path planning under the grid maps 10 × 10, 15 × 15, and 20 × 20 of the three algorithms, respectively. From the graph, under the condition that the maximum iteration number and the initialized population are the same, the three algorithms can all find an reachable path from the starting point to the target point, wherein the TPGWO algorithm has high convergence accuracy under three grid maps with different areas, the PSO algorithm and the GWO algorithm are easy to fall into local optimum in the convergence process, and the TPGWO algorithm can better jump out of the local optimum, find global optimum and improve accuracy. And as can be seen from the operation results of table 1, the path selected by the TPGWO algorithm is more optimal and the time required for path planning is less. Therefore, under the condition that the maximum iteration number is the same as the initialization population, the TPGWO algorithm can better and faster find an reachable path from the starting point to the target point in routing inspection robot path planning than the PSO algorithm and the GWO algorithm.
In order to verify the convergence factor function in the TPGWO algorithm, the convergence speed and accuracy can be improved by adjusting the parameter value, and simulation is carried out in maps with different obstacles. Taking a 15 x 15 grid map as an example, randomly generating an obstacle comparisonThe method comprises the steps of obtaining a few simple maps and a map with more obstacles and complexity, wherein the initial population N of the algorithm is 30, and the maximum iteration time t is max 600, the convergence factor functions are each
Figure BDA00037917444800001311
The simulation test results are shown in fig. 15(a) to 18 (b).
TABLE 2 running results of different convergence factor functions under different maps with the same area and different obstacles
Figure BDA0003791744480000141
Fig. 15(a) to 18(b) are a path diagram and a convergence curve of the TPGWO algorithm under three convergence factor functions. From the graph analysis, it can be seen that in a simple 15 x 15 grid map with few obstacles, a convergence factor function with a slightly advanced turning point is used
Figure BDA0003791744480000142
Convergence factor function invariant to the use of turning points
Figure BDA0003791744480000143
The same effective path can be obtained, but the convergence speed of the effective path is higher; in a 15 x 15 grid map with more obstacles and complexity, a convergence factor function with a slightly delayed turning point is used
Figure BDA0003791744480000144
Function of specific use
Figure BDA0003791744480000145
The accuracy of the resulting path is higher. As can be seen from the data in Table 2, the convergence factor function
Figure BDA0003791744480000146
The planning time and convergence factor function of the algorithm can be effectively improved
Figure BDA0003791744480000147
The accuracy of the algorithm can be effectively improved. Therefore, under the condition that the map area and the number of the obstacles are fixed, the convergence speed and the convergence accuracy of the TPGWO algorithm in the routing planning application of the inspection robot can be effectively improved by properly adjusting the turning point of the convergence factor curve according to the proportion of the number of the obstacles to the map area.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and these modifications or substitutions do not depart from the spirit of the corresponding technical solutions of the embodiments of the present invention.

Claims (8)

1. A routing planning method of a patrol robot based on an improved wolf algorithm is characterized by comprising the following steps:
step 1, an initialized population N1 of an improved wolf algorithm applied to path planning is path nodes randomly generated in a grid map, each path is connected by the same number of nodes to form a wolf individual, the initialized population N1 is crossed to obtain a population N2, the population N with the best fitness is calculated in the populations N1 and N2 by utilizing a roulette thought as an initialized population N for iterative update, and a convergence factor is set
Figure FDA0003791744470000011
Coefficient vector
Figure FDA0003791744470000012
A value;
step 2, improving a fitness function of a wolf algorithm applied to path planning, namely the sum of distances of all nodes of a path obtained by Euclidean distance calculation, adding turning times and turning angles of the obtained path into the fitness function as penalty values, calculating the fitness of a wolf individual according to a fitness function formula, wherein the better the fitness of the wolf individual is, the stronger the path superiority is, storing three wolfs with the best fitness as alpha wolfs, beta wolfs and delta wolfs, and storing the rest wolf groups as omega wolfs;
step 3, calculating and updating the gray wolf position according to the mathematical model of the gray wolf surrounding prey, and calculating and updating the coefficient vector according to the coefficient vector formula
Figure FDA0003791744470000013
Value, using arctan function and logarithm function to convergence factor
Figure FDA0003791744470000014
Is improved and the ratio of the number of obstacles to the map area is applied to the convergence factor
Figure FDA0003791744470000015
In curve improvement, the convergence factor after improvement
Figure FDA0003791744470000016
The curve forms a convergence factor function model, and the convergence factor is calculated and updated according to the convergence factor function model
Figure FDA0003791744470000017
Step 4, calculating the fitness of the individual wolf of the wolf according to a fitness function formula, updating the fitness of the three wolfs of the wolf, and updating and calculating the positions of the three wolfs of the wolf according to a mathematical model of the wolf attacking prey;
and 5, judging whether the maximum iteration number is reached, outputting the head wolf alpha wolf position calculated according to the updating process formula as an optimal solution after the maximum iteration number is reached, obtaining the optimal routing inspection path of the inspection robot, and returning to the step 3 to continue circular calculation if the optimal routing inspection path is not reached.
2. The inspection robot path planning method based on the improved wolf algorithm according to claim 1, characterized in that: the mathematic model of the wolf surrounding the prey is
Figure FDA0003791744470000018
Figure FDA0003791744470000019
Wherein t is the current iteration number,
Figure FDA00037917444700000110
representing the length vector between the gray wolf and the game,
Figure FDA00037917444700000111
a position vector representing the current prey,
Figure FDA00037917444700000112
a position vector representing the current gray wolf,
Figure FDA00037917444700000113
representing the updated position vector of the individual wolf,
Figure FDA00037917444700000114
and
Figure FDA00037917444700000115
is a coefficient vector.
3. The inspection robot path planning method based on the improved wolf algorithm according to claim 1, characterized in that: the coefficient vector is formulated as
Figure FDA00037917444700000116
Figure FDA0003791744470000021
Wherein the content of the first and second substances,
Figure FDA0003791744470000022
and
Figure FDA0003791744470000023
is a vector of coefficients that is a function of,
Figure FDA0003791744470000024
and
Figure FDA0003791744470000025
is [0,1 ]]A random number in between, and a random number,
Figure FDA0003791744470000026
is a convergence factor.
4. The inspection robot path planning method based on the improved wolf algorithm according to claim 1, characterized in that: the convergence factor function model is
Figure FDA0003791744470000027
Figure FDA0003791744470000028
Wherein k is an adjusting parameter, p is the base number of the logarithmic function, T is the maximum iteration number, and T is the current iteration number.
5. The inspection robot path planning method based on the improved wolf algorithm according to claim 1, characterized in that: the fitness function is formulated as
L＝L(i)+fix(M)
Figure FDA0003791744470000029
Figure FDA00037917444700000210
Figure FDA00037917444700000211
θ i ＝|θ 2 -θ 1 |
Where L (i) is the sum of nodes of the path, fix () is a function rounded to the left, and (x, y) is the current node coordinate, (x) in the grid map 1 ,y 1 ) Is the coordinate of the last node, (x) 2 ,y 2 ) As next node coordinate, θ 1 、θ 2 The tangent angles, θ, generated for the current node and the previous node, the current node and the next node i Is the angle difference between two tangent angles, namely the angle generated by the current turning.
6. The inspection robot path planning method based on the improved wolf algorithm according to claim 5, wherein: the turn times and the turn angles are normalized by the arc radius M, the penalty values fix (M) of the turn times and the turn angles can be obtained by calculating the arc radius M, and the normalization processing formula is
Figure FDA00037917444700000212
Figure FDA00037917444700000213
Figure FDA00037917444700000214
Wherein, theta i Theta is the sum of the turning angles, A is the angle determination value, and V is the number of turns.
7. The inspection robot path planning method based on the improved wolf algorithm according to claim 1, characterized in that: the mathematic model of the gray wolf attack prey is
Figure FDA0003791744470000031
Wherein the content of the first and second substances,
Figure FDA0003791744470000032
and
Figure FDA0003791744470000033
respectively represent the distance vectors of alpha, beta and delta of the wolf head and omega of the wolf body,
Figure FDA0003791744470000034
and
Figure FDA0003791744470000035
respectively representing the current position vectors of the wolf alpha, beta and delta,
Figure FDA0003791744470000036
and
Figure FDA0003791744470000037
coefficient vectors representing the gray wolf omega and the head wolf alpha, beta and delta, respectively,
Figure FDA0003791744470000038
representing the position vector of the gray wolf omega.
8. The inspection robot path planning method based on the improved wolf algorithm according to claim 1, characterized in that: the update process formula
Figure FDA0003791744470000039
Figure FDA00037917444700000310
Wherein the content of the first and second substances,
Figure FDA00037917444700000311
respectively represent updated position vectors between the wolf body omega and the wolf alpha, beta and delta, A 1 、A 2 、A 3 Respectively represent the gray wolf individual omega and the head wolf alpha, beta and delta coefficient vectors,
Figure FDA00037917444700000312
and
Figure FDA00037917444700000313
respectively represent the distance vectors of alpha, beta and delta of the wolf head and omega of the wolf body,
Figure FDA00037917444700000314
and
Figure FDA00037917444700000315
respectively representing the current position vectors of the wolf alpha, beta and delta,
Figure FDA00037917444700000316
to represent
Figure FDA00037917444700000317
I.e. the final updated position of the individual grayish wolf omega.
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