CN113155146A - Robot multi-target path planning based on improved barnacle propagation optimization algorithm - Google Patents

Robot multi-target path planning based on improved barnacle propagation optimization algorithm Download PDF

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CN113155146A
CN113155146A CN202110493562.4A CN202110493562A CN113155146A CN 113155146 A CN113155146 A CN 113155146A CN 202110493562 A CN202110493562 A CN 202110493562A CN 113155146 A CN113155146 A CN 113155146A
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barnacle
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barnacles
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应明峰
莫晓晖
程锦翔
杭阿芳
苗甜银
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Jinling Institute of Technology
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Abstract

The robot multi-target path planning method based on the improved barnacle propagation optimization algorithm comprises the following specific steps: (1) a basic barnacle propagation algorithm; (2) an improved barnacle reproduction optimization algorithm; (3) planning a robot path; the robot multi-target path planning method based on the improved barnacle propagation optimization algorithm is characterized in that the robot multi-target path planning is based on the improved optimization of the existing barnacle propagation algorithm, the variation thought of the genetic algorithm is introduced, and then the optimization is carried out by combining the robot multi-target path planning.

Description

Robot multi-target path planning based on improved barnacle propagation optimization algorithm
Technical Field
The invention relates to the technical field of artificial intelligence, in particular to a robot multi-target path planning method based on an improved barnacle propagation optimization algorithm.
Background
In recent years, a novel optimization algorithm, barnacle reproduction optimization algorithm, is applied, and is proposed by a MohdHerwanSulaian team in Malaysia, and the inspiration of the algorithm is derived from barnacle organisms in the sea. The creature swims at birth, adheres to objects in water after the growth of the creature and grows out of the shell, and in order to cope with tidal changes in the sea and life style which does not move basically, the unique breeding mode is that the barnacle has very long genitals which can reach 7 to 8 times of the length of the barnacle, so that the barnacle can contact all neighbors for mating, therefore, the length change of the genitals plays an important role in mating, and the barnacle breeding optimization algorithm can be used for robot multi-target path planning by improving the algorithm, so that the applicant designs the robot multi-target path planning based on the improved barnacle breeding optimization algorithm.
Disclosure of Invention
In order to solve the existing problems, the robot multi-target path planning based on the improved barnacle propagation optimization algorithm is provided, the existing barnacle propagation algorithm is used for improvement and optimization, the variation thought of the genetic algorithm is introduced, and then the robot multi-target path planning is combined for optimization.
The invention provides a robot multi-target path planning based on an improved barnacle propagation optimization algorithm, which comprises the following specific steps:
(1) basic barnacle breeding algorithm:
1) initializing a population;
firstly, a barnacle group matrix variable X is established, wherein M barnacle individuals are contained, the dimension of a problem to be solved is D, the search space of the problem is constrained, and the upper limit is set to ubn ═ ubn1 ubn2 … ubnD]The lower limit is lbn ═ lbn1 lbn2… lbnD]And finally obtaining a barnacle population matrix as follows:
Figure BDA0003053373100000011
after the initial population X is evaluated, sorting the solutions, and placing the current optimal solution on the top of the X;
2) a population selection process;
the algorithm population selection process simulates the breeding mode of barnacles for selection:
1. setting the genital length of barnacle as gl, and randomly selecting the species in the genital length range;
2. each barnacle can only pair with another barnacle at a time for fertilization, and the fertilization mode can be that sperm is provided for the other party or sperm of the other party is received;
3. triggering the remote fertilization process of the barnacles if the selected gl is greater than the set gl in the specific iteration process;
3) and (3) population breeding process:
population propagation of barnacles is mainly based on fertilization of two cases to produce the next generation:
1. and (3) normal fertilization:
when barnacles needing mating are selected to be within the gl value range, the paired father barnacles and mother barnacles propagate for the next generation, the father barnacle gene frequency is set to be p according to the Hadi-Winberg law, namely representing the percentage of father characteristics in the next generation, meanwhile, the mother barnacle gene frequency is set to be q, representing the percentage of mother characteristics in the next generation, and the relationship between p and q is the formula (2):
q＝(1-p) (2)
p is a random number, consisting of [0,1]]The interval is generated uniformly, and the variables of father barnacle and mother barnacle are set as
Figure BDA0003053373100000021
Its propagation yields new progeny variables:
Figure BDA0003053373100000022
2. remote fertilization:
when the barnacle selection to be mated is outside the gl value range, remote fertilization of barnacles will be triggered, i.e. mother barnacles receive sperm released from other barnacles in the water, and new offspring will be generated only from mother barnacles:
Figure BDA0003053373100000023
in the above formula, rand () takes a random number within [0,1 ];
(2) the improved barnacle breeding optimization algorithm comprises the following steps:
improving and optimizing the population breeding process of the algorithm, namely introducing a variation thought of the genetic algorithm in the normal fertilization process of the father barnacle and the mother barnacle, leading the offspring generated by the mating of the father barnacle and the mother barnacle to have a certain probability of variation, introducing a variation factor tau, wherein the tau is less than or equal to 0.05, and obtaining a variation formula (5):
Figure BDA0003053373100000031
in the above formula
Figure BDA0003053373100000032
The operation represents the generation of a random number for each bit of the newly generated child
Figure BDA0003053373100000033
If r is less than or equal to tau, negating the bit, otherwise, not changing:
(3) planning a robot path;
assuming that the working environment of the robot is a two-dimensional space, a limited number of static obstacles are distributed in the space, and the task of path planning of the robot is to find a shortest and smoother path between a starting point and an ending point and avoid all the obstacles;
1) path coding:
and a connecting line between the starting point B and the end point E is an X ' axis to construct a coordinate system BX ' Y ', and then points in the coordinate system OXY are transformed into BX ' Y ', wherein the transformation formula is as follows:
Figure BDA0003053373100000034
wherein (x)b,yb) Is the coordinate of the starting point B in the coordinate system OXY, (X ', Y') is the corresponding point of the point (X, Y) in the coordinate system BX 'Y', theta is the included angle between the X axis and the straight line BE;
by m parallel tufts l1,l2,…,lmAveraging BE into m +1 segments, setting the distance between every two adjacent ordinary straight lines as delta l | | | BE |/(m +1), and constructing a robot movement through one point randomly generated on each straight lineComplete path of motion B, P1,P2,…,PmE, generating all nodes on the path into a barnacle individual coding sequence, and converting the planning problem of the robot moving path into an optimization problem of variables of an aggregation point through a formula (6);
2) fitness function:
the path planning takes into account 3 indicators of length, safety and smoothness.
(1) Length index:
let coordinates of the start point B and the end point E be B (x)b,yb)、E(xe,ye) With the coordinates of the nodes of the arbitrary path set to Pi(xi,yi) I is [1, m ]]Let the path length be fdistanceNormalized to the formula:
Figure BDA0003053373100000041
(2) the safety degree index is as follows:
in order to avoid collision between the robot and the obstacle and make the path smoother, the adopted criterion is that no collision is caused between the robot and the obstacle at the cubic spline interpolation node, and the coordinates (x) of m path nodes are assumed to be known1,y1)，(x2,y2)，…，(xm,ym) And starting point coordinates (x)b,yb) And endpoint coordinate (x)e,ye) D interpolation points are respectively obtained through cubic spline difference values, and the abscissa of the d interpolation points is (x)1,x2,…,xd) The ordinate is (y)1,y2,…,yd) If d interpolation points are needed to be generated, whether collision occurs or not is determined, d is set to be 100, and the path safety degree index is set to be fsecureIt is represented by the following formula:
Figure BDA0003053373100000042
in the above formula, eta represents a safety factor with a value of 100 and Dj,kRepresenting the distance from the jth interpolation point to the kth obstacle center, R (k) representing the radius of the kth obstacle, and H representing the number of obstacles in the path;
(3) smoothness index:
let path nodes be B, P1,P2,…,PmE, the angle between adjacent road sections is denoted byiThe established path smoothness index is:
Figure BDA0003053373100000043
smaller psi indicates better path smoothness;
and fusing the indexes to obtain a comprehensive index S of the robot path planning:
S＝fdistance+fsecure+fflatness
(10)
3.3 robot multi-target path planning algorithm based on improved barnacle propagation optimization algorithm
An improved barnacle propagation optimization algorithm is adopted to plan the moving path of the robot, and the algorithm comprises the following specific steps:
1) transforming a coordinate system, and transforming coordinates of a starting point, an end point and an obstacle position by using an equation (6);
2) establishing m parallel clusters l1,l2,…,lmAveraging BE into m +1 segments, wherein the distance between every two adjacent ordinary straight lines is set as delta l | | | BE |/(m + 1);
3) initialization parameters include N, G, m, ubn, and lbn;
4) at each parallel line ljRandomly generating a point on m which is more than 0 and less than or equal to j, and forming a point set to obtain the barnacle
Figure BDA0003053373100000051
Initializing N barnacles in total;
5) evaluating barnacles by using a fitness function formula (10), and recording the best individual of the current group as F;
6) updating individuals according to the breeding offspring formulas (3) and (4), wherein the first half of individuals are half of the optimal individuals in the parent barnacle group of the previous generation, and the second half of individuals are half of the optimal individuals in the offspring barnacle group;
7) selecting the optimal and worst individuals for the updated individuals, carrying out variation on the optimal and worst individuals through a formula (5), forming new individuals by using the updated dimensionality and the other dimensionalities, comparing the variation of the individual fitness values before and after variation, and if the variation is good, keeping the variation;
8) finding out an optimal individual fitness value, and updating F;
9) judging whether the iteration number requirement or the precision requirement is met, if so, entering a step 10), and otherwise, returning to the step 5);
10) and outputting the optimal individual fitness value.
As a further improvement of the invention, the improved algorithm in the improvement of the barnacle breeding optimization algorithm in the step (2) comprises the following specific steps:
1) randomly initializing barnacle population Xi；
2) Calculating the fitness value of each individual in the population;
3) sequencing the current population, and placing the optimal solution on the top of the population vector;
4) setting a variable B as the current optimal solution;
5) while, i is less than the maximum iteration number num;
6) setting the length gl of the genital organ of the father barnacle;
7) selecting and generating father barnacles and mother barnacles;
8) if couple barnacle distance disf-m≤gl；
9) for each variable;
10) generating offspring barnacles according to formulas (3) and (5);
11)end for；
12)else if disf-m＞gl；
13) for each variable;
14) generating offspring barnacles according to a formula (4);
15)end for；
16)end if；
17) adjusting the boundary of each variable;
18) calculating the fitness value of each population individual;
19) b, sorting and updating;
20)end while；
21)Return B。
the application provides robot multi-target path planning based on an improved barnacle propagation optimization algorithm, the application improves and optimizes the population propagation process of the algorithm, the existing barnacle propagation algorithm is selected by simulating the propagation mode of barnacles in the ocean from the propagation mode of barnacle organisms, but the algorithm is easy to sink into the defect of local optimization in the population propagation process, namely, the variation idea of a genetic algorithm is introduced in the normal fertilization process of father barnacles and mother barnacles, and then optimization is carried out by combining with the robot multi-target path planning, so that the convergence rate is higher compared with the common robot multi-target path planning.
Drawings
FIG. 1 is a schematic diagram of a barnacle reproduction optimization algorithm mating selection process according to the present invention;
FIG. 2 is a representation of the path of the robot of the present invention in an environment.
Detailed Description
The invention is described in further detail below with reference to the following detailed description and accompanying drawings:
the robot multi-target path planning method based on the improved barnacle propagation optimization algorithm is characterized in that the robot multi-target path planning is based on the improved optimization of the existing barnacle propagation algorithm, the variation thought of the genetic algorithm is introduced, and then the optimization is carried out by combining the robot multi-target path planning.
As a specific embodiment of the present invention;
(1) basic barnacle breeding algorithm:
1) initializing a population;
firstly, a barnacle group matrix variable X is established, wherein M barnacle individuals are contained, the dimension of a problem to be solved is D, the search space of the problem is constrained, and the upper limit is set to ubn ═ ubn1 ubn2 … ubnD]The lower limit is lbn ═ lbn1 lbn2… lbnD]And finallyThe barnacle population matrix is obtained as follows:
Figure BDA0003053373100000071
and sequencing the solutions after the initial population X is evaluated, and placing the current optimal solution on the top of the X.
2) A population selection process;
in the existing algorithm, the genetic algorithm also has a selection process, the process simulates pairwise pairing of natural biological genes for crossing, and the algorithm mainly simulates the breeding mode of barnacles for selection:
1. setting the genital length of barnacle as gl, and randomly selecting the species in the genital length range;
2. each barnacle can only pair with another barnacle at a time for fertilization, and the fertilization mode can be that sperm is provided for the other party or sperm of the other party is received;
3. the selected gl is greater than the set gl during a particular iteration, triggering a remote fertilization process of the barnacles.
Taking 10 barnacle sets, assuming that the genital length gl is 7, the mating selection process shown in fig. 1 can be performed. When the barnacle 1 selects neighbors for matching, according to the set length of the genitals, the barnacle 1 can only be paired with any 1 of the barnacles 2-7 for fertilization to generate a next generation, if the barnacle 1 selects the barnacle 9, the barnacle exceeds the normal mating area, remote fertilization is triggered, and at the moment, the barnacle 9 can only randomly generate the next generation.
3) And (3) population breeding process:
population propagation of barnacles is mainly based on fertilization of two cases to produce the next generation:
1. and (3) normal fertilization:
when barnacles needing mating are selected to be within the gl value range, the paired father barnacles and mother barnacles propagate for the next generation, the father barnacle gene frequency is set to be p according to the Hadi-Winberg law, namely representing the percentage of father characteristics in the next generation, meanwhile, the mother barnacle gene frequency is set to be q, representing the percentage of mother characteristics in the next generation, and the relationship between p and q is the formula (2):
q＝(1-p) (2)
p is a random number, consisting of [0,1]]The intervals are generated uniformly. Set the parent barnacle and the father barnacle of the pair as variables
Figure BDA0003053373100000081
Its propagation yields new progeny variables:
Figure BDA0003053373100000082
2. remote fertilization:
when the barnacle selection to be mated is outside the gl value range, remote fertilization of barnacles will be triggered, i.e. mother barnacles receive sperm released from other barnacles in the water, and new offspring will be generated only from mother barnacles:
Figure BDA0003053373100000083
in the above formula, rand () takes a random number within [0,1 ].
(2) The improved barnacle breeding optimization algorithm comprises the following steps:
aiming at the defect that the algorithm is easy to fall into local optimum in the population breeding process, the population breeding process of the algorithm is improved and optimized, namely, the variation thought of the genetic algorithm is introduced in the normal fertilization process of the father barnacle and the mother barnacle, the filial generation generated by the crossing of the father barnacle and the mother barnacle has a certain probability of variation, a variation factor tau is introduced, and the tau is less than or equal to 0.05.
Obtaining a variation formula (5):
Figure BDA0003053373100000084
in the above formula
Figure BDA0003053373100000085
The operation represents for each bit of the newly generated child,generating a random number
Figure BDA0003053373100000091
If r is less than or equal to tau, negating the bit, otherwise, keeping the bit unchanged.
Therefore, the algorithm firstly adopts a random function to initialize a barnacle population, a father barnacle and a mother barnacle generate son barnacles based on formulas (3), (5) or (4), newly generated barnacle offspring and better individuals in the previous generation barnacles are combined and optimized in each iteration in the breeding process of the algorithm population, inferior solutions are discarded after sequencing, optimized solutions with the same population number are reserved, and the current optimal solution is placed at the top of a population vector X, and the algorithm specifically comprises the following steps:
1) randomly initializing barnacle population Xi；
2) Calculating the fitness value of each individual in the population;
3) sequencing the current population, and placing the optimal solution on the top of the population vector;
4) setting a variable B as the current optimal solution;
5) while (i < maximum number of iterations num);
6) setting the length gl of the genital organ of the father barnacle;
7) selecting and generating father barnacles and mother barnacles;
8) if couple barnacle distance disf-m≤gl；
9) for each variable;
10) generating offspring barnacles according to formulas (3) and (5);
11)end for；
12)else if disf-m＞gl；
13) for each variable;
14) generating offspring barnacles according to a formula (4);
15)end for；
16)end if；
17) adjusting the boundary of each variable;
18) calculating the fitness value of each population individual;
19) b, sorting and updating;
20)end while；
21)Return B；
(3) planning a robot path;
assuming that the working environment of the robot is a two-dimensional space, a limited number of static obstacles (convex polygons) are distributed in the space, and the task of the robot path planning is to find a shortest and smoother path between the starting point and the ending point, which avoids all the obstacles. The design adopts a navigation point model to construct a robot working environment, as shown in FIG. 2;
1) path coding:
the line connecting the starting point B and the end point E forms a coordinate system BX ' Y ' for the axis X ', as shown in FIG. 2. The points in the coordinate system OXY are then transformed into BX 'Y' by the following transformation formula:
Figure BDA0003053373100000101
wherein (x)b,yb) Is the coordinate of the starting point B in the coordinate system OXY, (X ', Y') is the point where the point (X, Y) corresponds in the coordinate system BX 'Y', and θ is the angle between the X-axis and the straight line BE.
As shown in fig. 2, with m parallel clusters l1,l2,…,lmThe BE is averaged into m +1 segments, and the distance between each adjacent two ordinary straight lines is Δ l | | | BE |/(m + 1). By randomly generating a point on each line, a complete path (B, P) of the robot movement can be constructed1,P2,…,PmAnd E), generating all nodes on the path into a coding sequence of the barnacle individual. Thus, the planning problem of the moving path of the robot is converted into the optimization problem of the variable of a gathering point through the formula (6).
2) Fitness function:
the path planning mainly considers 3 indexes of length, safety degree and smoothness.
(1) Length index:
let coordinates of the start point B and the end point E be B (x)b,yb)、E(xe,ye) With the coordinates of the nodes of the arbitrary path set to Pi(xi,yi)，i is [1, m ]]. Let the path length be fdistanceNormalized to the formula:
Figure BDA0003053373100000102
(2) the safety degree index is as follows:
in order to avoid collision between the robot and the obstacle and enable the path to be smoother, the design adopts the criterion that no collision exists between the robot and the obstacle at the cubic spline interpolation node. Let it be assumed that the coordinates (x) of the m path nodes are known1,y1)，(x2,y2)，…，(xm,ym) And starting point coordinates (x)b,yb) And endpoint coordinate (x)e,ye). D interpolation points are respectively obtained through cubic spline difference values, and the abscissa of the d interpolation points is (x)1,x2,…,xd) The ordinate is (y)1,y2,…,yd). Whether d generated interpolation points have collision or not is required, d is set to be 100, and the path safety degree index is set to be fsecureIt is represented by the following formula:
Figure BDA0003053373100000111
in the above formula, eta represents a safety factor with a value of 100 and Dj,kRepresents the distance from the jth interpolation point to the kth obstacle center, R (k) represents the radius of the kth obstacle, and H represents the number of obstacles in the path.
(3) Smoothness index:
let the path node be (B, P)1,P2,…,PmE), the angle between adjacent road sections is denoted byiThe path smoothness index established by the design is as follows:
Figure BDA0003053373100000112
a smaller psi indicates a more optimal path smoothness.
And fusing the indexes to obtain a comprehensive index S of the robot path planning:
S＝fdistance+fsecure+fflatness (10)
3.3 robot multi-target path planning algorithm based on improved barnacle propagation optimization algorithm
An improved barnacle propagation optimization algorithm is adopted to plan the moving path of the robot, and the algorithm comprises the following specific steps:
1) transforming a coordinate system, and transforming coordinates of a starting point, an end point and an obstacle position by using an equation (6);
2) establishing m parallel clusters l1,l2,…,lmAveraging BE into m +1 segments, wherein the distance between every two adjacent ordinary straight lines is set as delta l | | | BE |/(m + 1);
3) initializing parameters N, G, m, ubn, lbn and the like;
4) at each parallel line ljRandomly generating a point on (j is more than 0 and less than or equal to m), and forming a point set to obtain the barnacle
Figure BDA0003053373100000121
Initializing N barnacles in total;
5) evaluating barnacles by using a fitness function formula (10), and recording the best individual of the current group as F;
6) and updating the individuals according to the breeding offspring formulas (3) and (4). The first half of individuals are half of the optimal individuals in the parent barnacle group of the previous generation, and the second half of individuals are half of the optimal individuals in the filial generation barnacle group;
7) selecting the optimal and worst individuals for the updated individuals, carrying out variation on the optimal and worst individuals through a formula (5), forming new individuals by using the updated dimensionality and the other dimensionalities, comparing the variation of the individual fitness values before and after variation, and if the variation is good, keeping the variation;
8) finding out an optimal individual fitness value, and updating F;
9) judging whether the iteration number requirement or the precision requirement is met, if so, entering a step 10), and otherwise, returning to the step 5);
10) and outputting the optimal individual fitness value.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, but any modifications or equivalent variations made according to the technical spirit of the present invention are within the scope of the present invention as claimed.

Claims (2)

1. Robot multi-objective path planning based on improved barnacle reproduction optimization algorithm is characterized in that: the method comprises the following specific steps:
(1) basic barnacle breeding algorithm:
1) initializing a population;
firstly, a barnacle group matrix variable X is established, wherein M barnacle individuals are contained, the dimension of a problem to be solved is D, the search space of the problem is constrained, and the upper limit is set to ubn ═ ubn1 ubn2 … ubnD]The lower limit is lbn ═ lbn1 lbn2 … lbnD]And finally obtaining a barnacle population matrix as follows:
Figure FDA0003053373090000011
after the initial population X is evaluated, sorting the solutions, and placing the current optimal solution on the top of the X;
2) a population selection process;
the algorithm population selection process simulates the breeding mode of barnacles for selection:
1. setting the genital length of barnacle as gl, and randomly selecting the species in the genital length range;
2. each barnacle can only pair with another barnacle at a time for fertilization, and the fertilization mode can be that sperm is provided for the other party or sperm of the other party is received;
3. triggering the remote fertilization process of the barnacles if the selected gl is greater than the set gl in the specific iteration process;
3) and (3) population breeding process:
population propagation of barnacles is mainly based on fertilization of two cases to produce the next generation:
1. and (3) normal fertilization:
when barnacles needing mating are selected to be within the gl value range, the paired father barnacles and mother barnacles propagate for the next generation, the father barnacle gene frequency is set to be p according to the Hadi-Winberg law, namely representing the percentage of father characteristics in the next generation, meanwhile, the mother barnacle gene frequency is set to be q, representing the percentage of mother characteristics in the next generation, and the relationship between p and q is the formula (2):
q＝(1-p) (2)
p is a random number, consisting of [0,1]]The interval is generated uniformly, and the variables of father barnacle and mother barnacle are set as
Figure FDA0003053373090000012
Its propagation yields new progeny variables:
Figure FDA0003053373090000013
2. remote fertilization:
when the barnacle selection to be mated is outside the gl value range, remote fertilization of barnacles will be triggered, i.e. mother barnacles receive sperm released from other barnacles in the water, and new offspring will be generated only from mother barnacles:
Figure FDA0003053373090000014
in the above formula, rand () takes a random number within [0,1 ];
(2) the improved barnacle breeding optimization algorithm comprises the following steps:
improving and optimizing the population breeding process of the algorithm, namely introducing a variation thought of the genetic algorithm in the normal fertilization process of the father barnacle and the mother barnacle, leading the offspring generated by the mating of the father barnacle and the mother barnacle to have a certain probability of variation, introducing a variation factor tau, wherein the tau is less than or equal to 0.05, and obtaining a variation formula (5):
Figure FDA0003053373090000021
in the above formula
Figure FDA0003053373090000022
The operation represents the generation of a random number for each bit of the newly generated child
Figure FDA0003053373090000024
If r is less than or equal to tau, negating the bit, otherwise, not changing:
(3) planning a robot path;
assuming that the working environment of the robot is a two-dimensional space, a limited number of static obstacles are distributed in the space, and the task of path planning of the robot is to find a shortest and smoother path between a starting point and an ending point and avoid all the obstacles;
1) path coding:
and a connecting line between the starting point B and the end point E is an X ' axis to construct a coordinate system BX ' Y ', and then points in the coordinate system OXY are transformed into BX ' Y ', wherein the transformation formula is as follows:
Figure FDA0003053373090000023
wherein (x)b,yb) Is the coordinate of the starting point B in the coordinate system OXY, (X ', Y') is the corresponding point of the point (X, Y) in the coordinate system BX 'Y', theta is the included angle between the X axis and the straight line BE;
by m parallel tufts l1,l2,…,lmAveraging BE into m +1 segments, setting the distance between every two adjacent ordinary straight lines as delta l | | | BE |/(m +1), and constructing a complete path B, P of robot movement through a point randomly generated on each straight line1,P2,…,PmE, generating all nodes on the path into a barnacle individual coding sequence, and converting the planning problem of the robot moving path into an optimization problem of variables of an aggregation point through a formula (6);
2) fitness function:
the path planning takes into account 3 indicators of length, safety and smoothness.
(1) Length index:
let coordinates of the start point B and the end point E be B (x)b,yb)、E(xe,ye) With the coordinates of the nodes of the arbitrary path set to Pi(xi,yi) I is [1, m ]]Let the path length be fdistanceNormalized to the formula:
Figure FDA0003053373090000031
(2) the safety degree index is as follows:
in order to avoid collision between the robot and the obstacle and make the path smoother, the adopted criterion is that no collision is caused between the robot and the obstacle at the cubic spline interpolation node, and the coordinates (x) of m path nodes are assumed to be known1,y1)，(x2,y2)，…，(xm,ym) And starting point coordinates (x)b,yb) And endpoint coordinate (x)e,ye) D interpolation points are respectively obtained through cubic spline difference values, and the abscissa of the d interpolation points is (x)1,x2,…,xd) The ordinate is (y)1,y2,…,yd) If d interpolation points are needed to be generated, whether collision occurs or not is determined, d is set to be 100, and the path safety degree index is set to be fsecureIt is represented by the following formula:
Figure FDA0003053373090000032
in the above formula, eta represents a safety factor with a value of 100 and Dj,kRepresenting the distance from the jth interpolation point to the kth obstacle center, R (k) representing the radius of the kth obstacle, and H representing the number of obstacles in the path;
(3) smoothness index:
let path nodes be B, P1,P2,…,PmE, the angle between adjacent road sections is denoted byiThe established path smoothness index is:
Figure FDA0003053373090000033
ψismaller means more optimal path smoothness;
and fusing the indexes to obtain a comprehensive index S of the robot path planning:
S＝fdistance+fsecure+fflatness (10)
3.3 robot multi-target path planning algorithm based on improved barnacle propagation optimization algorithm
An improved barnacle propagation optimization algorithm is adopted to plan the moving path of the robot, and the algorithm comprises the following specific steps:
1) transforming a coordinate system, and transforming coordinates of a starting point, an end point and an obstacle position by using an equation (6);
2) establishing m parallel clusters l1,l2,…,lmAveraging BE into m +1 segments, wherein the distance between every two adjacent ordinary straight lines is set as delta l | | | BE |/(m + 1);
3) initialization parameters include N, G, m, ubn, and lbn;
4) at each parallel line ljRandomly generating a point on m which is more than 0 and less than or equal to j, and forming a point set to obtain the barnacle
Figure FDA0003053373090000034
I is more than 0 and less than or equal to N, and N barnacles are initialized in total;
5) evaluating barnacles by using a fitness function formula (10), and recording the best individual of the current group as F;
6) updating individuals according to the breeding offspring formulas (3) and (4), wherein the first half of individuals are half of the optimal individuals in the parent barnacle group of the previous generation, and the second half of individuals are half of the optimal individuals in the offspring barnacle group;
7) selecting the optimal and worst individuals for the updated individuals, carrying out variation on the optimal and worst individuals through a formula (5), forming new individuals by using the updated dimensionality and the other dimensionalities, comparing the variation of the individual fitness values before and after variation, and if the variation is good, keeping the variation;
8) finding out an optimal individual fitness value, and updating F;
9) judging whether the iteration number requirement or the precision requirement is met, if so, entering a step 10), and otherwise, returning to the step 5);
10) and outputting the optimal individual fitness value.
2. A robot multi-goal path planning based on an improved barnacle propagation optimization algorithm according to claim 1, characterized in that: the improved algorithm in the improvement of the barnacle reproduction optimization algorithm in the step (2) comprises the following specific steps:
1) randomly initializing barnacle population Xi；
2) Calculating the fitness value of each individual in the population;
3) sequencing the current population, and placing the optimal solution on the top of the population vector;
4) setting a variable B as the current optimal solution;
5) while, i is less than the maximum iteration number num;
6) setting the length gl of the genital organ of the father barnacle;
7) selecting and generating father barnacles and mother barnacles;
8) if couple barnacle distance disf-m≤gl；
9) for each variable;
10) generating offspring barnacles according to formulas (3) and (5);
11)end for；
12)else if disf-m＞gl；
13) for each variable;
14) generating offspring barnacles according to a formula (4);
15)end for；
16)end if；
17) adjusting the boundary of each variable;
18) calculating the fitness value of each population individual;
19) b, sorting and updating;
20)end while；
21)Return B。
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