CN110347151B - Robot path planning method fused with Bezier optimization genetic algorithm - Google Patents

Abstract

The invention relates to a robot path planning method fusing Bezier optimization genetic algorithm, which belongs to the field of artificial intelligence, and firstly adopts a Bezier curve to optimize paths generated in the initial solution, crossing and mutation processes of the genetic algorithm so as to eliminate peak inflection points and reduce redundant nodes, thereby improving the path smoothness; and then, dynamically adjusting the path obtained by the genetic algorithm by adopting a fitness function with the added safety distance and the self-adaptive penalty factor so as to improve the quality of the planned path. The method can search a path with shorter distance and smoother, so that the robot reduces energy loss caused by frequent switching of the running state due to rapid turning of the path, and further ensures the moving safety of the robot.

Description

Robot path planning method fused with Bezier optimization genetic algorithm

Technical Field

The invention belongs to the field of artificial intelligence, and particularly relates to a robot path planning method fused with a Bezier optimization genetic algorithm.

Background

Path planning is an important research direction in the field of mobile robots and is one of the research difficulties. The path planning problem can be described as: according to a certain evaluation index, a collision-free path from a starting point to a target point is searched in an environment with an obstacle. Path planning has been widely applied in the fields of logistics distribution, intelligent transportation, weapon navigation, etc. Therefore, the research on the rapid and effective path planning method becomes a focus of attention, and the method has higher theoretical significance and practical value.

The genetic algorithm is a bionic optimization algorithm, natural selection and genetic inheritance and variation in Darwin biological evolution theory are taken as theoretical models, and the optimal solution is searched by simulating natural evolution. Although the genetic algorithm can plan a better path under different performance indexes, many problems are generated in the practical process, such as: a plurality of peaks exist in the solved path, so that the robot cannot walk according to the planned path in the moving process; there are a large number of points of inflection in the path, causing excessive energy loss and the like to the robot.

As an artificial intelligent path planning method, the genetic algorithm carries out global search by simulating the biological evolution of the nature, thereby avoiding the problems of prematurity, local optimization and the like. The algorithm generates new filial generations by utilizing operations such as crossing, mutation and the like, and selects an optimal path through a fitness function in the path planning process. The process of the path planning method based on the genetic algorithm is shown in fig. 16.

In fig. 16, the genetic algorithm first generates initial paths and calculates fitness function values for each path; secondly, performing genetic operations such as selection, crossing, mutation and the like on each path according to the fitness value to generate a better offspring path; and finally, judging whether the algorithm termination condition is met, if so, outputting the path with the optimal fitness as the optimal solution, otherwise, continuing the operation until the termination condition is met.

Disclosure of Invention

In order to solve the defects in the prior art, the invention aims to provide a robot path planning method fused with Bezier optimization genetic algorithm, which can optimize paths generated in the crossing and mutation processes of the genetic algorithm, eliminate peak inflection points and reduce redundant nodes, thereby improving the path smoothness; and further, the safety of the robot in the moving process is guaranteed through the safety distance and the self-adaptive penalty factor.

In order to achieve the purpose, the invention adopts the following technical scheme:

a robot path planning method fusing a Bezier optimization genetic algorithm comprises the steps of firstly adopting a traditional genetic algorithm to generate an initial path, and optimizing the generated initial path and paths generated in the crossing and mutation processes by utilizing a Bezier curve, so that a peak inflection point is eliminated, redundant nodes are reduced, and the smoothness of the path is improved; and dynamically adjusting the path obtained by the genetic algorithm by adopting a fitness function with the added safety distance and the self-adaptive penalty factor so as to obtain a high-quality planning path.

As a further optimization of the above scheme, the robot path planning method fusing the Bezier optimized genetic algorithm specifically includes the following steps:

step one, determining population quantity Q, initial population quantity gn, maximum optimization algebra N and maximum population scale Q of genetic algorithm_maxCross probability Re, mutation probability Mu, initial position S and target position T;

generating gn initial paths between the starting position S and the target position T by using a genetic algorithm;

step three, optimizing an initial path generated by the genetic algorithm by adopting a Bezier optimization operator;

adding the safety distance and the self-adaptive penalty factor into the fitness function, and calculating the fitness function value of each path by adopting the fitness function added with the safety distance and the self-adaptive penalty factor;

step five, performing selection, crossing and mutation operations to generate new offspring paths;

step six, judging whether the current optimal value reaches the maximum optimization algebra, if so, stopping the algorithm and turning to step seven, otherwise, updating the path and turning to step three;

and seventhly, outputting the optimal path and the corresponding fitness function value.

As a further optimization of the above scheme, in step one, the population quantity Q, the initial population quantity gn, the maximum optimization algebra N, and the maximum population size Q of the genetic algorithm are determined_maxThe cross probability Re, the mutation probability Mu, the starting position S and the target position T comprise the following steps:

(1) initializing a map boundary;

(2) the position of the obstacle is determined according to the map boundary.

As a further optimization of the above scheme, in step three, the optimizing the initial path generated by the genetic algorithm by using the Bezier optimization operator specifically includes:

introducing a Bezier curve into GA as an optimization operator; by taking each inflection point in the genetic algorithm initialization path as a control point P₀,P₁,P₂,…,P_mObtaining a Bezier curve containing m control points:

where t is a normalized time variable, P_i＝(x_i,y_i)^TCoordinate vector, x, representing the ith control point_iAnd y_iCorresponding to the components of the X and Y coordinates respectively,

is a Bernstein polynomial which is the basis function of a Bezier curve expression, expanded as follows:

as a further optimization of the above scheme, the process of adding the safety distance and the adaptive penalty factor to the fitness function in step four is as follows:

by increasing the safety distance and the self-adaptive penalty factor, a fitness function fit based on safety guarantee is provided_newThe expression is as follows:

therein, fit₁Optimizing path length L for joining Bezier curves_Pt；fit₂For fit with adaptive penalty factor_safe；

fit₁＝L_Pt

fit₂＝fit_safe

Wherein fit_safeA penalty term is a safe distance from the barrier; when the path is at a minimum distance L from the obstacle_minPunishment is carried out when the distance is less than the set safety distance; penalty intensity and L_min(ii) related; the penalty intensity is higher as the distance between the path and the obstacle is closer.

As a further optimization of the above solution, the selection, intersection and mutation operations are performed in step five to generate new paths of children, the process is as follows:

the genetic algorithm generates n paths in the path planning process, wherein the path a_jHas a length of L_jFitness is f (a)_j) (ii) a The selection operator selects the path by adopting a roulette method according to the individual fitness value, wherein the probability that the path is selected is as follows:

the genetic algorithm enables the performance of the obtained new filial path to be superior to that of the parent path before the cross operation by cross operation and cross combination of the better parts of different paths;

the mutation operation is to perform mutation operation on any node except the starting point and the end point in the path, so that the nodes of the partial path are changed, and premature convergence caused by local optimization of the genetic algorithm in the process of searching the path is avoided.

After the scheme is adopted, the robot path planning method fused with the Bezier optimization genetic algorithm is utilized. The method comprises the steps of firstly, optimizing paths generated in the initial solution, crossing and mutation processes of a genetic algorithm by adopting a Bezier curve so as to eliminate peak inflection points and reduce redundant nodes, thereby improving path smoothness; and then, dynamically adjusting the path obtained by the genetic algorithm by adopting a fitness function with the added safety distance and the self-adaptive penalty factor so as to improve the quality of the planned path. The method of the invention is used for planning the path of the robot, the obtained path distance is shorter and smoother, and the robot reduces the energy loss caused by frequent switching of the running state due to sharp turning of the path, and further ensures the moving safety of the robot.

Compared with the prior art, the invention has the following beneficial effects:

(1) by utilizing the smoothness of the Bezier curve and removing redundant nodes in the path, the path is smoother and more coherent, and the energy loss in the movement of the robot is reduced;

(2) by adding a safe distance and a punishment factor into the fitness function, the fitness function is dynamically adjusted according to the distance between the path and the barrier, and the robot is guaranteed to move safely and efficiently;

(3) the algorithm provided by the invention can be used for effectively planning an optimal path;

(4) has excellent searching performance.

Drawings

FIG. 1 is a flow chart of a method of robot path planning incorporating Bezier optimized genetic algorithms;

FIG. 2 is a schematic diagram illustrating a single point crossover process; wherein, the left graph is a single-point crossing front path; the right graph is a path after single-point crossing;

FIG. 3 is a GA path diagram of a conventional genetic algorithm;

FIG. 4 is a path diagram after optimization by the Bezier optimizer;

FIG. 5 is a comparison of paths before and after the introduction of the Bezier optimization operator;

fig. 6 is a schematic view of a robot operating environment 1;

fig. 7 is a schematic view of the robot operating environment 2;

FIG. 8 is a comparison of path planning statistics for different algorithms in Environment 1;

FIG. 9 is a comparison graph of simulation results of path planning of different algorithms under the environment 1;

FIG. 10 is a comparison of path planning statistics for different algorithms in Environment 2;

FIG. 11 is a comparison graph of simulation results of path planning of different algorithms under the environment 2;

FIG. 12 is a schematic illustration of the effect of population size on path length in Environment 1;

FIG. 13 is a graphical illustration of the effect of population size on path length in Environment 2;

fig. 14 is a graph of the shortest path length as a function of the number of iterations N in environment 1;

fig. 15 is a graph of the shortest path length as a function of iteration number N in environment 2;

fig. 16 is a flowchart of a path planning method based on a genetic algorithm.

Detailed Description

The invention aims to provide a robot path planning method fused with Bezier optimization genetic algorithm, which can optimize paths generated in the crossing and mutation processes of the genetic algorithm, eliminate peak inflection points and reduce redundant nodes, thereby improving the path smoothness; and further, the safety of the robot in the moving process is guaranteed through the safety distance and the self-adaptive penalty factor.

The technical solution of the present invention is further described in detail below with reference to the accompanying drawings.

Fig. 1 is a flowchart of a robot path planning method fused with a Bezier optimized genetic algorithm, as shown in the figure, including the following steps:

step one, determining population quantity Q, initial population quantity gn, maximum optimization algebra N and maximum population scale Q of a genetic algorithm_maxCross probability Re, mutation probability Mu, starting position S and target position T; as shown in fig. 6 and 7, the map boundaries are initialized first, and the obstacle positions are determined based on the map boundaries second.

Generating gn initial paths between the starting position S and the target position T by using a genetic algorithm;

step three, optimizing an initial path generated by the genetic algorithm by adopting a Bezier optimization operator;

in order to solve the problem of redundant nodes in path planning, a Bezier curve is used as an optimization operator and introduced into GA, so that the corrected path is smoother, and the robot moves more stably. By taking each inflection point in the genetic algorithm initialization path as a control point P₀,P₁,P₂,…,P_mObtaining a Bezier curve containing m control points:

where t is a normalized time variable, P_i＝(x_i,y_i)^TCoordinate vector, x, representing the ith control point_iAnd y_iCorresponding to the components of the X and Y coordinates respectively,

is a Bernstein polynomial which is the basis function of a Bezier curve expression, expanded as follows:

schematic diagrams of the Bezier curve optimization path are shown in fig. 3-5. When the traditional genetic algorithm is used for path planning, the problems of sharp inflection points and redundant nodes are easily generated, as shown in fig. 3; with the start point S, end point T and inflection point P shown in FIG. 3₁,P₂,P₃,P₄,P₅Introducing a Bezier optimization operator to optimize the genetic algorithm generated path for the control point, so as to obtain a smooth path, as shown in FIG. 4; comparing the before and after effects introduced by the Bezier optimization operator, as shown in fig. 5, it can be known that: the Bezier optimization operator not only simplifies the path redundant nodes, but also smoothes sharp inflection points. Therefore, the Bezier optimization operator is introduced into the genetic algorithm path planning method, path redundant nodes can be simplified, sharp inflection points can be smoothed, and the path is shorter and smoother.

Calculating a fitness function value of each path by adopting a fitness function added with a safety distance and a self-adaptive penalty factor;

fitness function of traditional genetic algorithm

Only the path length is taken as the main criterion for path selection, which can ensure the shortest path, but the path may have a problem of collision due to too small distance between the robot and the obstacle. Therefore, by increasing the safety distance and the adaptive penalty factor, a fitness function fit based on safety guarantee is provided_newThe expression is as follows:

therein, fit₁Optimizing path length L for joining Bezier curves_Pt；fit₂For fit with adaptive penalty factor_safe. Wherein w₁、w₂The value of (2) determines the degree of approximation between the current path selected currently and the obstacle, and the safety of the robot when passing through the path is guaranteed.

fit₁＝L_Pt

fit₂＝fit_safe

Wherein fit_safeAs a penalty term, a safety distance from the obstacle, a minimum distance L between the path and the obstacle_minAnd punishing when the distance is less than the set safety distance. Penalty intensity and L_minIt is related. The penalty intensity is higher as the distance between the path and the obstacle is closer. Therefore, the dynamic adjustment of the fitness function can be realized, and the quality of the planned path is improved.

Step five, performing selection, crossing and mutation operations to generate new offspring paths;

the genetic algorithm generates n paths in the path planning process, wherein the path a_jHas a length of L_jFitness is f (a)_j). The selection operator selects the path by adopting a roulette method according to the individual fitness value, and the probability that the path is selected is as follows:

as shown in fig. 2, the genetic algorithm performs intersection operation by combining the better parts of different paths (such as the single-point intersection process shown in fig. 2, where (7, 8) is the intersection point), so that the performance of the obtained new child path is better than that of the parent path before the intersection operation.

Mutation operations are to increase the diversity of genetic algorithm solutions. The method changes the nodes of the partial path by carrying out mutation operation on any node except the starting point and the end point in the path, and avoids premature convergence caused by local optimum of a genetic algorithm in the process of searching the path.

Step six, judging whether the current optimal value reaches the maximum optimization algebra, if so, stopping the algorithm and turning to step seven, otherwise, updating the path and turning to step three;

and step seven, outputting the optimal path and the corresponding fitness function value.

Example 1

To show the feasibility and effectiveness of the algorithm, environment 1: 20 × 20 and environment 2: the robot path planning problem in the 10 × 10 grid map environment is verified, as shown in fig. 6, in environment 1, the coordinates of the starting point of the robot are (0.5 ), the coordinates of the end point are (19.5 ), and the parameters are set as follows: q is 30, gn is 50, N is 30, Q_max＝30,Re＝0.8,Mu＝0.01,w₁＝0.9,w₂0.1, 1. As shown in fig. 7, in the environment 2, the coordinates of the start point of the robot are (0.5 ), the coordinates of the end point are (9.5 ), and the parameters are set as: q is 30, gn is 50, N is 30, Q_max＝30,Re＝0.7,Mu＝0.01,w₁＝0.9,w₂＝0.1,C＝1。。

To investigate the feasibility of the algorithm herein, experiments were performed in environment 1 using the traditional Ant Colony Algorithm (ACA), the traditional Genetic Algorithm (GA), the modified ant colony algorithm with fused genetic operators (GA-ACO), the genetic algorithm with fused Bezier optimization operators (GA-B) and the genetic algorithm with fused Bezier optimization operators and safe distances (GA-B-Q), respectively. Fig. 9 shows the path planning results of different algorithms. In order to eliminate the influence of various accidental factors such as randomness on the algorithm. The above algorithms were independently run for 30 times, and the statistical results are recorded in the table of fig. 8, where "-" indicates that no statistical results were obtained.

To verify the performance of the genetic algorithm with Bezier optimization under complex environment, a complex environment of 10 × 10 is set up. And respectively adopting a traditional Ant Colony Algorithm (ACA), a modified ant colony algorithm (GA-ACO) of a fusion genetic algorithm, an artificial fish colony genetic algorithm (ASFA-GA) and a design algorithm in the text to carry out comparison experiments. The path planning results of the algorithms are shown in fig. 11. In order to eliminate the influence of various accidental factors such as randomness on the algorithm. The above algorithms were independently run for 30 times, and the statistical results are recorded in the table of fig. 10, where "-" indicates that no statistical results were obtained.

The foregoing is only a partial embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and embellishments can be made without departing from the principle of the present invention, and these should also be construed as the scope of the present invention.

Claims (1)

1. A robot path planning method fused with Bezier optimization genetic algorithm is characterized in that: firstly, generating an initial path by adopting a traditional genetic algorithm, and optimizing the generated initial path and paths generated in the crossing and mutation processes by utilizing a Bezier curve, so that a peak inflection point is eliminated, redundant nodes are reduced, and the smoothness of the path is improved; then, dynamically adjusting the path obtained by the genetic algorithm by adopting a fitness function with the safety distance and the self-adaptive penalty factor added so as to obtain a high-quality planning path;

the robot path planning method fused with the Bezier optimization genetic algorithm specifically comprises the following steps:

step one, determining population quantity Q, initial population quantity gn, maximum optimization algebra N and maximum population scale Q of genetic algorithm_maxCross probability Re, mutation probability Mu, initial position S and target position T;

generating gn initial paths between the starting position S and the target position T by using a genetic algorithm;

step three, optimizing an initial path generated by the genetic algorithm by adopting a Bezier optimization operator;

adding the safety distance and the self-adaptive penalty factor into the fitness function, and calculating the fitness function value of each path by adopting the fitness function added with the safety distance and the self-adaptive penalty factor;

step five, performing selection, crossing and mutation operations to generate new offspring paths;

step six, judging whether the current optimal value reaches the maximum optimization algebra, if so, stopping the algorithm and turning to step seven, otherwise, updating the path and turning to step three;

step seven, outputting the optimal path and the corresponding fitness function value;

in step one, the determination of inheritancePopulation quantity Q, initial population quantity gn, maximum optimization algebra N and maximum population scale Q of algorithm_maxThe cross probability Re, the mutation probability Mu, the starting position S and the target position T comprise the following steps:

(1) initializing a map boundary;

(2) determining the position of an obstacle according to the map boundary;

in the third step, the optimizing the initial path generated by the genetic algorithm by using the Bezier optimization operator specifically includes:

introducing a Bezier curve into GA as an optimization operator; by taking each inflection point in the genetic algorithm initialization path as a control point P₀,P₁,P₂,…,P_mObtaining a Bezier curve containing m control points:

where t is a normalized time variable, P_i＝(x_i,y_i)^TCoordinate vector, x, representing the ith control point_iAnd y_iCorresponding to the components of the X and Y coordinates respectively,

is a Bernstein polynomial which is the basis function of a Bezier curve expression, expanded as follows:

in the fourth step, the process of adding the safety distance and the self-adaptive penalty factor into the fitness function is as follows:

by increasing the safety distance and the self-adaptive penalty factor, a fitness function fit based on safety guarantee is provided_newThe expression is as follows:

therein, fit₁Optimizing path length for joining Bezier curves

fit₂For fit with adaptive penalty factor_safe；

fit₂＝fit_safe

Wherein fit_safeA penalty term is a safe distance from the barrier; when the path is at a minimum distance L from the obstacle_minPunishment is carried out when the distance is less than the set safety distance; penalty intensity and L_min(ii) related; the penalty intensity is higher when the distance between the path and the obstacle is closer;

and step five, executing selection, crossing and mutation operations to generate a new offspring path, wherein the process is as follows:

the genetic algorithm generates n paths in the path planning process, wherein the path a_jHas a length of L_jFitness is f (a)_j) (ii) a The selection operator selects the path by adopting a roulette method according to the individual fitness value, wherein the probability that the path is selected is as follows:

the genetic algorithm makes the performance of the obtained new filial path superior to the parent path before the cross operation by cross operation and cross combination of the superior parts of different paths;

the mutation operation is to perform mutation operation on any node except the starting point and the end point in the path, so that the nodes of the partial path are changed, and premature convergence caused by local optimization of the genetic algorithm in the process of searching the path is avoided.

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