CN113219986A - Robot global path planning method based on genetic algorithm and cubic spline interpolation - Google Patents
Robot global path planning method based on genetic algorithm and cubic spline interpolation Download PDFInfo
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Abstract
The robot global path planning method based on the genetic algorithm and the cubic spline interpolation adopts a multi-face model representation method to represent the environment space of the robot; representing a path traveled by the robot using the two-dimensional coordinates; an initial path set is generated by adopting two search strategies of random and directional, so that the diversity of the initialized population is ensured; according to the prior knowledge of the environment map information, the characteristics of the barrier and the like, a proper collision detection method is adopted; a fitness function with punishment is used; adopting a roulette selection method, single-point crossing, random variation and other modes to carry out genetic operation on the initialized population; simulation experiments show that the method has better feasibility and effectiveness for solving the global path planning problem of the robot. The invention provides a new idea for solving the problem of global path planning of the mobile robot.
Description
Technical Field
The invention belongs to the field of robots, and relates to a robot global path planning method based on a genetic algorithm and cubic spline interpolation.
Background
The robot technology is the comprehensive and crossed result of modern scientific theory and practice. In the end of the 20 th century and the 60 s, the Stanford research institute developed an autonomous mobile robot, and a path planning method was the key core technology of the autonomous mobile robot. The mobile robot path planning technology is that on the premise that a robot follows some optimization indexes (such as shortest time, optimal path, lowest energy consumption and the like), an optimal path without collision from a starting point to a target point is planned in an operating environment.
The mobile robot path planning is an optimization problem which substantially meets a certain constraint condition, and the algorithm design process has the characteristics of complexity, randomness, multi-objective property, multi-constraint property and the like. Path planning can be divided into two categories, according to the knowledge of the robot about the environment: robots of the first type have a priori knowledge of the environment modeled as a map, and can therefore plan paths based on the available map, such paths being referred to as global path plans, which belong to static plans; the second type of path planning assumes that the robot has no prior information of the environment, so it must sense the obstacle position and construct an estimated environmental map in real time during the search process to avoid the obstacle and obtain a suitable path toward the target position. Such paths are called local path plans, which belong to dynamic planning. According to the information characteristics of the research environment, path planning can be further divided into path planning in a discrete domain range and path planning in a continuous domain range, the path planning in the discrete domain range belongs to a one-dimensional static optimization problem, namely a route optimization problem after the environmental information is simplified, and the path planning problem in the continuous range is a problem in a continuous multi-dimensional dynamic environment.
Genetic Algorithm (GA) is a computational model of the biological evolution process that simulates the natural selection and Genetic mechanism of darwinian biological evolution theory, and is a method for searching for an optimal solution by simulating the natural evolution process. The method is mainly characterized in that the method directly operates the structural object without the limitation of derivation and function continuity; the method has the advantages of inherent hidden parallelism and better global optimization capability; by adopting a probabilistic optimization method, the optimized search space can be automatically acquired and guided without a determined rule, and the search direction can be adaptively adjusted. Genetic algorithms target all individuals in a population and use randomization techniques to guide an efficient search of an encoded parameter space. Wherein the selection, crossover and mutation constitute genetic operations of the genetic algorithm; the core content of the genetic algorithm is composed of five elements of parameter coding, initial population setting, fitness function design, genetic operation design and control parameter setting. The genetic algorithm has strong global optimization capability and adaptability, and is widely applied to the path planning problem or used for improving the original path planning method.
Disclosure of Invention
A robot global path planning method based on a genetic algorithm and cubic spline interpolation comprises the steps of representing an environment space where a robot is located by adopting a multi-face model representation method; representing a path traveled by the robot using the two-dimensional coordinates; an initial path set is generated by adopting two search strategies of random and directional, so that the diversity of the initialized population is ensured; according to the prior knowledge of the environment map information, the characteristics of the barrier and the like, a proper collision detection method is adopted; a fitness function with punishment is used; adopting a roulette selection method, single-point crossing, random variation and other modes to carry out genetic operation on the initialized population; simulation experiments show that the method has better feasibility and effectiveness for solving the global path planning problem of the robot. The invention provides a new idea for solving the problem of global path planning of the mobile robot.
The technical scheme adopted by the invention is as follows: a mobile robot path planning method based on an improved genetic algorithm is characterized by comprising the following steps:
s1: modeling the working environment of the mobile robot by using a multi-face model representation method;
s2: coding;
setting initialization parameters including a path starting point, a path terminal point, a population number, iteration times, a crossing rate and a variation rate;
s4: generating an initialization population;
s5: inserting nodes among the nodes by utilizing a cubic spline interpolation method;
s6: judging whether each path node in the path collides with the obstacle, and adding punishment into the fitness function if the path node collides with the obstacle;
s7: calculating the fitness value of each individual in the initialized population according to the fitness function;
s8: executing selection operation, and updating the path generated by the initialized population;
s9: executing cross operation, and updating the path generated by the selection operation;
s10: performing mutation operation, and updating the path generated by the cross operation;
and judging whether the maximum iteration times is reached, if so, stopping searching and outputting the optimal path, otherwise, jumping to S5 to perform next iteration optimization.
The global robot path planning method based on genetic algorithm and cubic spline interpolation of claim 1, wherein the grid method modeling of step S1 is specifically:
the working environment of the mobile robot is modeled using a multi-faceted model representation. The motion space of the mobile robot is represented by a two-dimensional planar graph, and the vertices of the obstacle are recorded by (x, y). The obstacles are arranged as static, random, known arbitrary irregular polygons.
The global robot path planning method based on genetic algorithm and cubic spline interpolation of claim 1, wherein the encoding operation in step S2 is specifically:
the path traveled by the robot is represented using two-dimensional coordinates.
The global robot path planning method based on the genetic algorithm and the cubic spline interpolation as claimed in claim 1, wherein the initializing population in step S4 specifically comprises:
two search strategies of random and directional are adopted to generate the initialization seed cluster of the genetic algorithm, so that the diversity of the initialization seed cluster is ensured.
The global robot path planning method based on genetic algorithm and cubic spline interpolation of claim 1, wherein the method for inserting nodes in step S5 specifically comprises:
the invention utilizes a cubic spline interpolation method to insert cubic spline insertion points among a path starting point, three intermediate nodes and a path terminal point.
The global robot path planning method based on genetic algorithm and cubic spline interpolation of claim 1, wherein the collision detection method in step S6 is specifically:
the collision detection related to the invention only needs to judge whether the point is positioned in the circular barrier, in other words, whether the distance from the point to the center of the circle is smaller than the radius of the circle.
The global robot path planning method based on the genetic algorithm and the cubic spline interpolation as claimed in claim 1, wherein the fitness function in step S7 is specifically:
wherein, P represents a punishment coefficient and is used for eliminating the generated poor path; c represents the number of collisions between the generated path and the obstacle, and L represents the path length of the robot, and can be calculated according to equation (4).
Wherein (x)i,yi) And (x)i+1,yi+1) The coordinates of the ith and i +1 th points in the path, respectively.
The global robot path planning method based on genetic algorithm and cubic spline interpolation of claim 1, wherein the selecting operation in step S8 is specifically:
a roulette selection method is adopted as the selection operation.
The global robot path planning method based on genetic algorithm and cubic spline interpolation as claimed in claim 1, wherein the crossing operation in step S9 specifically is:
the invention adopts single-point crossing as the crossing operation. When the crossing condition is satisfied, one position of the two individuals except the starting point and the end point is randomly selected as a crossing point, and then the two individuals perform a crossing operation at the crossing point. For example, assume that two individuals participating in the crossover operation are p ═ { s, p, respectively1,…,pi,…,pnumE and q ═ s, q1,…,qi,…,qnum,e}，piAnd q isiIs the cross point, at piAnd q isiPerforming crossover operation at the crossover point, the two new individuals are pnew＝{s,p1,…,qi,…,qnumE } and qnew＝{s,q1,…,pi,…,pnum,e}。
The global robot path planning method based on genetic algorithm and cubic spline interpolation as claimed in claim 1, wherein the variation operation in step S10 is specifically:
the present invention uses random crossover as a mutation operation. And when the variation condition is met, randomly selecting two nodes except the path starting point and the path end point as variation points, and regenerating a new individual at the variation points according to a random search strategy in the initialized population so as to finish the variation operation. For example, let t be { s, t ═ for the individual participating in the mutation operation1,…,ti,…,tnum,e}， tiIs a variation point, and the new individual generated by the random search strategy is u ═ s, u1,…,ui,…,unumE, the new subject uiIs involved in mutation of t in individuals tiThereby generating a new individual tnew＝{s,t1,…,ui,…,tnum,e}。
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FIG. 1 is a general flow chart of the path planning of a mobile robot based on an improved genetic algorithm according to the present invention;
FIG. 2 is a schematic diagram of path planning in a given environment according to an embodiment of the present invention;
FIG. 3 is a graph of an average fitness function under a given environment in an embodiment of the present invention;
Detailed Description
For the convenience of understanding, the technical solutions in the embodiments of the present invention will be described in detail in the following with reference to the accompanying drawings in the embodiments of the present invention. The described embodiments are only some of the embodiments of the present invention.
As shown in fig. 1, a mobile robot path planning method based on an improved genetic algorithm mainly includes the following steps:
s1: modeling the working environment of the mobile robot by using a multi-face model representation method;
the working environment of the mobile robot is modeled using a multi-faceted model representation. The motion space of the mobile robot is represented by a two-dimensional planar graph, and the vertices of the obstacle are recorded by (x, y). The obstacles are arranged as static, random, known arbitrary irregular polygons.
S2: coding;
the path traveled by the robot is represented using two-dimensional coordinates.
S4: generating an initialization population;
two search strategies of random and directional are adopted to generate the initialization seed cluster of the genetic algorithm, so that the diversity of the initialization seed cluster is ensured.
S5: inserting nodes among the nodes by utilizing a cubic spline interpolation method;
and inserting cubic spline insertion points among the path starting point, the three intermediate nodes and the path terminal point by using a cubic spline interpolation method.
S6: judging whether each path node in the path collides with the obstacle, and adding punishment into the fitness function if the path node collides with the obstacle;
the collision detection related to the invention only needs to judge whether the point is positioned in the circular barrier, in other words, whether the distance from the point to the center of the circle is smaller than the radius of the circle.
S7: calculating the fitness value of each individual in the initialized population according to the fitness function;
wherein, P represents a punishment coefficient and is used for eliminating the generated poor path; c represents the number of collisions between the generated path and the obstacle, and L represents the path length of the robot, and can be calculated according to equation (6).
Wherein (x)i,yi) And (x)i+1,yi+1) Respectively the coordinates of the first and the point in the path.
S8: executing selection operation, and updating the path generated by the initialized population;
a roulette selection method is adopted as the selection operation.
S9: executing cross operation, and updating the path generated by the selection operation;
the invention adopts single-point crossing as the crossing operation. When the crossing condition is satisfied, one position of the two individuals except the starting point and the end point is randomly selected as a crossing point, and then the two individuals perform a crossing operation at the crossing point. For example, assume that two individuals participating in the crossover operation are p ═ { s, p, respectively1,…,pi,…,pnumE and q ═ s, q1,…,qi,…,qnum,e}，piAnd q isiIs the cross point, at piAnd q isiPerforming crossover operation at the crossover point, the two new individuals are pnew＝{s,p1,…,qi,…,qnumE } and qnew＝{s,q1,…,pi,…,pnum,e}。
S10: performing mutation operation, and updating the path generated by the cross operation;
the present invention uses random crossover as a mutation operation. When the variation condition is met, two nodes except the path starting point and the path end point are randomly selected as variation points, and the variation points are repeated according to a random search strategy in the initialized populationAnd newly generating a new individual, thereby completing the mutation operation. For example, let t be { s, t ═ for the individual participating in the mutation operation1,…,ti,…,tnum,e}， tiIs a variation point, and the new individual generated by the random search strategy is u ═ s, u1,…,ui,…,unumE, the new individual uiReplacement of t in individuals t involved in mutation operationsiThereby generating a new individual tnew＝{s,t1,…,ui,…,tnum,e}。
Fig. 2 shows the path planning of the result of one experiment in a given environment. Wherein the quadrangle represents the starting point and the pentagram represents the ending point. Fig. 3 shows an iteration curve of the invention in a given environment. Wherein the abscissa represents the number of iterations and the ordinate represents the fitness value. As can be seen from fig. 2 and fig. 3, the local optimum can be skipped in about 125 generations to achieve a global optimum solution, so that a safe collision-free optimum path from the starting point to the end point of the robot can be found. Simulation experiments show that the method has better feasibility and effectiveness for solving the global path planning problem of the robot.
Claims (9)
1. The robot global path planning method based on the genetic algorithm and the cubic spline interpolation is characterized by comprising the following steps of:
s1: modeling the working environment of the mobile robot by using a multi-face model representation method;
s2: coding;
s3: setting initialization parameters including a path starting point, a path terminal point, a population number, iteration times, a crossing rate and a variation rate;
s4: generating an initialization population;
s5: inserting nodes among the nodes by utilizing a cubic spline interpolation method;
s6: judging whether each path node in the path collides with the obstacle, and adding punishment into the fitness function if the path node collides with the obstacle;
s7: calculating the fitness value of each individual in the initialized population according to the fitness function;
s8: executing selection operation, and updating the path generated by the initialized population;
s9: executing cross operation, and updating the path generated by the selection operation;
s10: performing mutation operation, and updating the path generated by the cross operation;
s11: and judging whether the maximum iteration times is reached, if so, stopping searching and outputting the optimal path, otherwise, jumping to S5 to perform next iteration optimization.
2. The method according to claim 1, wherein the grid method modeling of step S1 is specifically:
modeling the working environment of the mobile robot by using a multi-face model representation method; the motion space of the mobile robot is represented by a two-dimensional plane graph, and the vertex of the obstacle is recorded by (x, y); the obstacles are arranged as static, random, known arbitrary irregular polygons.
3. The global robot path planning method based on genetic algorithm and cubic spline interpolation of claim 1, wherein the encoding operation in step S2 is specifically:
the path traveled by the robot is represented using two-dimensional coordinates.
4. The method according to claim 1, wherein the initializing population in step S4 specifically includes:
two search strategies, random and directed, are employed to generate an initialization seed cluster for genetic algorithms to ensure diversity of the initialization population.
5. The method according to claim 1, wherein the method for inserting the node in step S5 specifically is:
and inserting cubic spline insertion points among the path starting point, the three intermediate nodes and the path terminal point by using a cubic spline interpolation method.
6. The method according to claim 1, wherein the fitness function in step S7 is specifically:
wherein, P represents a punishment coefficient and is used for eliminating the generated poor path; c represents the number of times of collision between the generated path and the obstacle, L represents the path length of the robot, and the calculation can be carried out according to the formula (2);
wherein (x)i,yi) And (x)i+1,yi+1) The coordinates of the ith and i +1 th points in the path, respectively.
7. The method according to claim 1, wherein the selecting operation in step S8 is specifically:
a roulette selection method is adopted as the selection operation.
8. The method according to claim 1, wherein the interleaving operation in step S9 specifically includes:
and adopting single-point crossing as a crossing operation:
when the crossing condition is satisfied, one position of the two individuals except the starting point and the end point is randomly selected as a crossing point, and then the two individuals perform a crossing operation at the crossing point.
9. The global robot path planning method based on genetic algorithm and cubic spline interpolation as claimed in claim 1, wherein the variation operation in step S10 is specifically:
random crossover was used as a mutation operation:
and when the variation condition is met, randomly selecting two nodes except the path starting point and the path end point as variation points, and regenerating a new individual at the variation points according to a random search strategy in the initialized population so as to finish the variation operation.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105988468A (en) * | 2015-01-28 | 2016-10-05 | 中国人民公安大学 | Improved genetic algorithm-based mobile robot path planning method |
| CN112686429A (en) * | 2020-12-16 | 2021-04-20 | 天津城建大学 | Mobile robot and path planning method thereof based on adaptive genetic algorithm |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105988468A (en) * | 2015-01-28 | 2016-10-05 | 中国人民公安大学 | Improved genetic algorithm-based mobile robot path planning method |
| CN112686429A (en) * | 2020-12-16 | 2021-04-20 | 天津城建大学 | Mobile robot and path planning method thereof based on adaptive genetic algorithm |
Non-Patent Citations (3)
| Title |
|---|
| 刘志海等: "基于遗传算法的机器人路径规划的种群初始化改进", 《机床与液压》 * |
| 宋宇等: "基于改进遗传算法的移动机器人路径规划", 《现代电子技术》 * |
| 魏彤等: "基于改进遗传算法的移动机器人路径规划", 《北京航空航天大学学报》 * |
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Application publication date: 20210806 |