CN115016508A - Robot path planning method based on region segmentation multi-target particle swarm optimization algorithm - Google Patents
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Abstract
The invention discloses a robot path planning method based on a region segmentation multi-target particle swarm optimization algorithm. Convergence and diversity archives are employed to balance convergence and diversity of the solution. And the quality of the solution is improved by combining the region segmentation idea and the cross operation in the improved particle swarm optimization. The region division is to divide the search region continuously to achieve the purpose of rapidly reducing the convergence region, and meanwhile, the diversity of the particles is improved by random selection. The crossover operation of the present invention uses crossover operators in a differential evolution algorithm to generate new particles to replace inferior particles. In the multi-target robot path planning, the optimal path searched by the algorithm avoids the problem that the particle swarm algorithm is easy to fall into local optimization in the later evolution stage, improves the convergence speed of the algorithm, and realizes the balance of the known convergence and diversity.
Description
Technical Field
The invention belongs to the field of multi-objective optimization, and particularly relates to a robot path planning method based on a region segmentation multi-objective particle swarm optimization algorithm.
Background
In modern scientific research and social life, there are many targets that are expected to reach optimal value, and there are some conflicts between these targets, and it is not possible to optimize multiple targets simultaneously, i.e. multi-objective optimization problem (MOP). When there are more than 3 targets to optimize, the MOP is called a high-dimensional multi-objective optimization problem (MaOP). Optimization is the process of finding the best combination of variables or parameters that satisfy the constraints to minimize or maximize the objective function. In real life, the optimization problem is ubiquitous, and the method is widely applied to various fields such as economic management, engineering practice, industrial and agricultural production, scientific research, transportation and the like. For the path planning of multi-target performance, many researches have been carried out at home and abroad, and the common performance of the path is as follows: path length, time, energy, safety, and smoothness. There are many algorithms currently used to solve the multi-objective path planning problem, n.setyawan et al uses adaptive gaussian parameter update rules for the inertial weight and the two acceleration parameters to balance the global and local search of the search space, and then calculates the weighted sum functions of the three objectives using an improved particle swarm algorithm to plan a feasible path. In order to search out a plurality of feasible paths, Wang Jiahai et al propose an improved vehicle path planning problem of a multi-objective evolutionary algorithm, balance convergence speed and diversity indexes by adopting a two-stage strategy, and design a mixed domain structure for solving and improving so as to improve path searching efficiency. However, when some complex multi-objective path plans are processed, most of the results obtained by the plans are not good in diversity, and the precision of convergence on the Pareto front edge is not high. Therefore, it is necessary to further improve the algorithm and the model to obtain more solutions with better performance for the actual path planning problem.
The meta-heuristic optimization method derived by enlightening simple concepts in the nature is one of the most popular ways to solve the optimization problem, especially the engineering optimization problem. The group-based algorithm is one of metaheuristic optimization methods, and is generally a method formed by simulating social behaviors of a population. The Particle Swarm Optimization (PSO), proposed in 1995 by Eberhart and Kennedy et al, is a typical Swarm-based intelligent Optimization algorithm. The method has the advantages of simple concept, few parameters and relatively high convergence rate, and is widely applied to the fields of engineering practice, function optimization and the like. But the method has the defects of low convergence speed and easy falling into local optimization at the later stage of evolution to cause precocity, and particularly optimizes complex functions such as high-dimensional multiple peaks and the like. To improve these shortcomings, researchers at home and abroad use different technologies or algorithms to improve the defects. The following two categories can be mainly distinguished:
the first category is an improvement to the algorithm itself. For example, Yuhui Shi and Russell c.eberhart propose to dynamically adjust the inertial weights using a fuzzy system to improve the performance of the particle swarm algorithm. Xianli Deng and Bo Wei et al propose a multi-population-based adaptive migration PSO algorithm, and by fusing two common neighbor topological structures, on the basis of parallel evolution of a plurality of sub-populations, different search characteristics are given to each sub-population by using combinations of different acceleration factors, and further historical performance of the sub-populations is evaluated periodically, so that migration operation of individuals is guided on the basis, reasonable allocation of cooperation and computing resources among the sub-populations is realized, and finally, comprehensive performance of the algorithm is improved.
The second category is the combination with other algorithms. The Haifeng Lin and Chengpei Tang introduce partial operations of the NSGA-II algorithm into the PSO, and provides an improved multi-target self-adaptive particle swarm optimization (MOAPSO) which has the characteristics of high convergence rate, high efficiency, low calculation complexity and the like. Bin, Xin and the like combine the differential evolution algorithm with the PSO, update the probability of selecting the two algorithms, and improve the execution efficiency of the algorithms.
Disclosure of Invention
The invention aims to overcome the defects, provides a robot path planning method based on a region segmentation multi-target particle swarm optimization algorithm, combines the advantages of the region segmentation-based particle swarm optimization algorithm and the advantages of two filing algorithms, and balances the convergence and diversity of solutions by using a convergence filing CA and a diversity filing DA, so that the algorithm is applied to the multi-target path planning problem.
In order to achieve the above object, the present invention comprises the steps of:
s1, modeling a robot working space by adopting a two-dimensional plane space, and presenting the obstacles in an XOY coordinate system in the two-dimensional plane space in the form of entities with different shapes and sizes;
s2, equally dividing the line segment from the starting point S to the target point T into D +1 segments, D being the number of path points needed by the mobile robot path, determining the vertical line from the starting point S to the target point T passing through each path point, and randomly selecting a node P on the vertical line i Connecting the discrete path points, the starting point S and the target point T in sequence to form a complete path;
s3, taking a straight line from the starting point S to the target point T as a horizontal axis, projecting path points in an XOY coordinate system on an X ' SY ' coordinate system, wherein the projection lengths of each path sequence on the X ' axis are the same;
s4, setting N D-dimensional particle individuals in the path population, and taking the D-th dimension of each particle as each dimension of each particle to map corresponding nodes, so that each particle is a candidate path, and the specific method of the multi-target particle swarm optimization algorithm based on region segmentation comprises the following steps:
s41, initializing the population and parameters, and randomly generating a group of initial particle speeds and positions;
s42, judging whether the speed and the position of the initial particle meet the stop standard, if so, outputting the speed and the position of the particle; otherwise, executing S43;
s43, generating a new population PP, and simultaneously executing S44 and S45;
s44, selecting a solution with convergence meeting the requirements from the population PP, and carrying out region segmentation;
performing a crossover operation to replace the inferior particles with the obtained new particles to form a new population P1;
classifying the solutions in the population P1, evaluating the solutions in each class, and reserving the solution with the minimum Chebyshev function value;
determining a converged archive, executing S46;
s45, performing binary crossing on the population PP, and selecting a solution meeting the requirement to form a new population P2;
selecting any solution with a distance greater than the requirement in the population P2 to be put into a diversity archive;
determining diversity archiving, executing S46;
s46, merging the convergence archiving and the diversity archiving to form a population EPOP, and outputting the speed and the position of the particles;
s5, searching the optimal position of each particle in an X 'SY' coordinate system according to the position and the speed of each particle, and calculating the fitness of each particle, so that the path length, the collision risk degree and the path smoothness are reduced;
and S6, establishing a traveling path of the robot according to the path length, the collision risk degree and the path smoothness.
In S3, the path point in the XOY coordinate system is transformed into a point (X ', y') in the X 'SY' coordinate system by the following equation;
wherein alpha is the included angle between the XOY coordinate system and the X 'SY' coordinate system, (X) s ，y s ) Representing the coordinates of the starting point S in XOY.
The specific method for forming a new population P1 in S44 is as follows:
s441, sorting according to Euclidean distances from the particles to the global optimal position, and dividing the particle region into an area inside the boundary and an area outside the boundary by taking the preset Euclidean distances as the boundary, wherein the area inside the boundary is excellent particles, and the area outside the boundary is inferior particles;
s442, selecting two particles from the optimal particles, and performing a crossing operation, namely crossing the speed and the position of the two particles to generate speed and position information of a new particle;
s443, replacing the information of one inferior particle with the information of the new particle;
s444, repeatedly executing S442 and S443 until all inferior particles are replaced, and forming a new population P1.
The specific method for classifying the solutions in the population P1 and evaluating the solutions in each class to retain the solution with the smallest chebyshev function value is as follows:
the method comprises the steps of sorting solutions in a population P1 in a non-dominated mode, determining all non-dominated solutions, evaluating the non-dominated solutions according to a Chebyshev aggregation function, selecting the solution with the minimum Chebyshev function value as one of parents of a cross operation, and randomly selecting the other parent in the non-dominated solution; the chebyshev function is as follows:
wherein λ ═ λ (λ) 1 ，λ 2 ，...，λ m ) Is a set of weight vectors, z ═ z 1 ，z 2 ，...，z m ) Is a reference point, z i ＝min{f i (x)|x∈Ω}。
The method of interleaving is as follows:
generating children using crossover operations in a differential evolution algorithm:
wherein x is i Is a solution in the superior particles,
is a parent solution x r1 A value in the i-th dimension of the decision space, i ═ 1, 2., n; CR is the crossover probability, F is the scaling factor, rand is [0,1 ]]Uniformly distributed random number, x r2 Divide x for random selection r1 And (4) external solution.
The determination method of convergence archiving is as follows:
based on the set of weight vectors generated by the initial population and the convergence profile, the solution sets in the convergence profile are ranked by:
wherein, i is 1,2,3,N，Z＝(z 1 ，z 2 ，...，z m ) Is a set of ideal points, taking the minimum value of each target, Δ (F (x), r i ) Is represented by r i And the cosine of the angle between F (x) -Z;
assessment of CA by Chebyshev function i And (4) selecting the minimum solution of the Chebyshev function to carry out convergence archiving.
The calculation method of any distance in the population P2 is as follows:
d(x)＝min{||F(x)-F(y)|| 2 *||F(x)-F(y)|| ∞ |y∈POP∩y≠x}
wherein | | F (x) -F (y) | messaging 2 And | | F (x) -F (y) | non-combustible phosphor ∞ Representing the distance difference between the two solutions.
The method of calculating the velocity and position of the particle is as follows:
wherein the content of the first and second substances,
is the velocity of the particle i in the d-th dimension in the k-th iteration,
is the current position of particle i in the d-th dimension in the kth iteration;
the position of the d-dimension individual extreme point of the particle i in the k iteration is obtained, namely the optimal solution is obtained by searching the ith particle after the k iteration;
is the position of the global extreme point of the whole population in the d-th dimension in the k-th iteration, i.e. after the k-th iterationOptimal solutions throughout the population of particles; r is 1 And r 2 Are all intervals of [0,1 ]]Random number of inner, c 1 And c 2 Are acceleration coefficients, w is an inertial weight, and as the iteration progresses, the value of w decreases linearly.
The inertial weight w is adjusted as follows:
wherein w max And w min A maximum and a minimum of w, respectively; iter and iter max Respectively the current iteration number and the maximum iteration number.
The path length is calculated as follows:
calculating the distance between two adjacent path nodes, and adding the distances between all two adjacent path nodes to obtain the path length;
the calculation method of the collision risk degree comprises the following steps:
calculating the risk degrees of the path and all the obstacles, and adding all the risk degrees to obtain a collision risk degree;
the path smoothness is calculated as follows:
wherein α i is a deflection angle of the ith path, the deflection angle being composed of any three adjacent path points, (P) i -P i-1 )·(P i+1 -P i ) Is the inner product between two vectors, | P i -P i-1 II and II P i+1 -P i And |' denotes the norm of the vector.
Compared with the prior art, the invention improves the convergence rate by linearly adjusting the inertia weight and utilizing the idea of region segmentation of information intersection. Convergence and diversity archives are employed to balance convergence and diversity of the solution. And the quality of the solution is improved by combining the region segmentation idea and the cross operation in the improved particle swarm optimization. The region division is to divide the search region continuously to achieve the purpose of quickly reducing the convergence region, and meanwhile, the diversity of the particles is improved by random selection. The crossover operation of the present invention uses crossover operators in a differential evolution algorithm to generate new particles to replace inferior particles. In the invention, in the multi-target robot path planning, experiments are carried out in two maps with different complexity, and the optimal path searched by the algorithm is obtained, so that the problem that the particle swarm algorithm is easy to fall into local optimization in the later evolution stage is avoided, the convergence speed of the algorithm is improved, and the balance between the known convergence and diversity is realized.
Drawings
FIG. 1 is a flow chart of a multi-objective particle swarm optimization algorithm based on region segmentation in the invention;
FIG. 2 is an environmental model of robot path planning;
FIG. 3 is a simple environment map;
FIG. 4 is a complex environment map;
FIG. 5 is a diagram of a path planning result for a simple environment;
fig. 6 is a diagram of a path planning result in a complex environment.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
In order to establish the geometric model of the environment space, firstly, several assumptions need to be made: assuming that a motion space is a two-dimensional plane, the mobile robot is considered as a particle regardless of the size and shape of the particle; the robot can move to any direction on the assumption that the motion of the robot is not limited; it is assumed that there are only static obstacles in the environment. The robot working space is modeled by a two-dimensional plane space method, as shown in fig. 2. In this model, a two-dimensional coordinate system XOY is established, the obstacles are represented in the form of entities of different shapes and sizes, denoted O j (j ═ 1, 2.., n), there is a certain degree of risk of collision. The robot bypasses the obstacle to reach the target point from the starting point and searches for a path with optimal performance. Equally dividing a line segment from the starting point S to the target point T into D +1 segments, wherein D represents the number of path points required by the path of the mobile robot; then draw the ST upper meridianThe vertical line through each waypoint, denoted L 1 ，L 2 ，...，L i ，...，L D (ii) a Finally at L i Randomly selecting a node P on a vertical line of (1, 2.. D) i The discrete path points and the start and target points are connected in sequence to form a complete path.
The invention comprises the following steps:
s1, modeling a robot working space by adopting a two-dimensional plane space, and presenting the obstacles in an XOY coordinate system in the two-dimensional plane space in the form of entities with different shapes and sizes;
s2, equally dividing the line segment from the starting point S to the target point T into D +1 segments, D being the number of path points needed by the mobile robot path, determining the vertical line from the starting point S to the target point T passing through each path point, and randomly selecting a node P on the vertical line i Connecting the discrete path points, the starting point S and the target point T in sequence to form a complete path;
s3, taking a straight line from the starting point S to the target point T as a horizontal axis, projecting path points in an XOY coordinate system on an X ' SY ' coordinate system, wherein the projection lengths of each path sequence on the X ' axis are the same; the path point in the XOY coordinate system is transformed into a point (X ', y') in the X 'SY' coordinate system by the following equation;
wherein alpha is the included angle between the XOY coordinate system and the X 'SY' coordinate system, (X) s ，y s ) Representing the coordinates of the starting point S in XOY.
S4, setting N D-dimension particle individuals in the path population, and mapping the D-dimension of each particle as each dimension of each particle to a corresponding node, so that each particle is a candidate path, the speed limit value of the particle is limited by a position limit value, and L in a map i The intersection point with the map boundary is X imin And X imax . The maximum of the velocity is determined by the range of motion of the particle, as followsShown in the figure:
V imax ＝0.1×(X imax -X imin )
since the abscissa of each dimension of each particle is already known in a given local X 'SY' coordinate system, the path planning algorithm only finds the ordinate of each dimension of each particle, i.e. only needs to locate the vertical dashed line L i Find the optimal location at ( i 1, 2.., D). During iteration, the algorithm can evaluate the fitness value of the particles and update the population position to reduce the overall objective function value to the maximum extent. Thus, each particle is constantly refined in path, optimizing the length, collision risk and smoothness in the path, improving the quality of the path.
Referring to fig. 1, a specific method of the multi-objective particle swarm optimization algorithm based on region segmentation is as follows:
s41, initializing the population and parameters, and randomly generating a group of initial particle speeds and positions;
s42, judging whether the speed and the position of the initial particle meet the stop standard, if so, outputting the speed and the position of the particle; otherwise, executing S43;
s43, generating a new population PP, and simultaneously executing S44 and S45;
s44, selecting a solution with convergence meeting the requirements from the population PP, and carrying out region segmentation;
performing a crossover operation to replace the inferior particles with the obtained new particles to form a new population P1;
classifying the solutions in the population P1, evaluating the solutions in each class, and reserving the solution with the minimum Chebyshev function value;
determining a converged archive, executing S46;
s45, performing binary crossing on the population PP, and selecting a solution meeting the requirement to form a new population P2;
selecting any solution with a distance greater than the requirement in the population P2 to be put into a diversity archive;
determining diversity archiving, executing S46;
s46, merging the convergence archiving and the diversity archiving to form a population EPOP, and outputting the speed and the position of the particles;
s5, searching the optimal position of each particle in an X 'SY' coordinate system according to the position and the speed of each particle, and calculating the fitness of each particle, so that the path length, the collision risk degree and the path smoothness are reduced;
and S6, establishing a traveling path of the robot according to the path length, the collision risk degree and the path smoothness.
The area division idea is to achieve the purpose of rapidly reducing the convergence area by continuously dividing the search area, and simultaneously, to improve the diversity of the particles by random selection, and the specific method for forming the new population P1 is as follows:
s441, sorting the particles in the whole search interval according to Euclidean distances from the particles to the global optimal position, and dividing the particle area into an area in the boundary and an area outside the boundary by taking the preset Euclidean distances as the boundary, wherein the area in the boundary is excellent particles, and the area outside the boundary is inferior particles;
s442, selecting two particles from the optimal particles, and performing a crossing operation, namely crossing the speed and the position of the two particles to generate speed and position information of a new particle;
s443, replacing the information of one inferior particle with the information of the new particle;
s444, repeatedly executing S442 and S443 until all inferior particles are replaced, and forming a new population P1;
s445, S441 to S444 are repeatedly executed, and the search area is divided a plurality of times by continuing the intersection.
The specific method of classifying the solutions in the population P1, evaluating the solutions in each class, and retaining the solution with the smallest chebyshev function value is as follows:
sorting the solutions in the population P1 in a non-dominated mode, determining all non-dominated solutions, evaluating the non-dominated solutions according to a Chebyshev aggregation function, selecting the solution with the minimum Chebyshev function value as one of parents of the cross operation, and randomly selecting the other parent from the non-dominated solutions; the chebyshev function is as follows:
wherein λ ═ λ (λ) 1 ，λ 2 ，...，λ m ) Is a set of weight vectors, z ═ z 1 ，z 2 ，...，z m ) Is a reference point, z i ＝min{f i (x)|x∈Ω}。
The method of interleaving is as follows:
generating children using crossover operations in a differential evolution algorithm:
wherein x is i Is a solution in the superior particles,
is a parent solution x r1 The value in the ith dimension of the decision space, i ═ 1,2, …, n; CR is the crossover probability, taken to be 0.5, F is the scaling factor, taken to be 0.5, and rand is [0,1 ]]Uniformly distributed random number, x r1 Determined from a selection operator in the inertial weight w, x r2 Divide x for random selection r1 And (4) external solution.
The mathematical description of a certain weight ratio is as follows:
wherein v is j And v k For randomly selected velocities, v, of two preferred particles j and k i Is the velocity of the new particle i, a is constant at [0,1 ]]In the meantime. x is the number of j And x k For randomly selected positions of two preferred particles j and k, x i Is the position of the new particle i.
The determination method of convergence archiving is as follows:
a set of weight vectors (r) generated based on the initial population 1 ,r 2 ,…,r m ) And a convergence file, wherein the solution sets in the convergence file are graded according to the following formula, so that more and more uniformly distributed and well converged solution sets are obtained in an iteration process:
wherein i is 1,2,3, N, Z is (Z) 1 ，z 2 ，...，z m ) Is a set of ideal points, taking the minimum value of each target, Δ (F (x), r i ) Represents t i And the cosine of the angle between F (x) -Z; CA i There may be 0 solutions or multiple solutions. Assessment of CA by Chebyshev function i The minimum solution of the Chebyshev function is selected, so that some better solutions are reserved for convergence archiving.
In order to maintain population diversity, it is desirable to select as different solutions as possible from the others so that a globally optimal solution can be obtained without prematurely falling into a local optimum. Therefore, in the diversity file DA, the solution with a large distance difference is selected preferentially. The calculation method for any distance in the population P2 is as follows:
d(x)＝min{||F(x)-F(y)|| 2 *||F(x)-F(y)|| ∞ |y∈POP∩y≠x}
wherein | | F (x) -F (y) | messaging 2 And | | F (x) -F (y) | non-combustible phosphor ∞ Representing the distance difference between the two solutions.
The basic framework of the multi-target particle swarm optimization algorithm based on region segmentation is as follows:
the method of calculating the velocity and position of the particle is as follows:
wherein the content of the first and second substances,
is the velocity of the particle i in the d-th dimension in the k-th iteration,
is the current position of particle i in the d-th dimension in the k-th iteration;
the position of the d-dimension individual extreme point of the particle i in the k iteration is obtained, namely the optimal solution is obtained by searching the ith particle after the k iteration;
the position of the global extreme point of the whole population in the d dimension in the kth iteration is shown, namely the optimal solution in the whole population of the population is obtained after the kth iteration; r is 1 And r 2 Are all intervals of [0,1 ]]Random number of inner, c 1 And c 2 Are acceleration coefficients, w is an inertial weight, and as the iteration progresses, the value of w decreases linearly.
When considering the practical optimization problem, it is often desirable to first use global search to make the search space converge to a certain region quickly, and then use local fine search to obtain a high-precision solution. Therefore, the larger the weight w is, the stronger the global search capability is, and the smaller w is, the algorithm is prone to local search. Therefore, the inertial weight w is adjusted as follows:
wherein, w max And w min The maximum and minimum values of the weight w, respectively; iter and iter max Respectively the current iteration number and the maximum iteration number. The weight w is initialized to 0.9 (max) and decreases linearly to 0.4 (min) with increasing number of iterations.
The path length is calculated as follows:
calculating the distance L (P) between two adjacent path nodes:
adding the distances L (P) of all two adjacent path nodes to obtain the path length;
the calculation method of the collision risk degree comprises the following steps:
the invention adopts the technical scheme that as long as the obstacle is within the safe distance of the robot, the danger degree exists between the sub-path and the obstacle, and all the danger degrees are added up to be used as the total danger degree:
the collision risk of the robot and the obstacle j is defined as:
wherein R is rob，obsj (X robi ，X obsj ) Representing the collision risk between the robot and the obstacle j, n is the number of obstacles, | X robi -X obs And | is the shortest distance between the position of the robot on the ith path segment and the obstacle j. Robot and obstacleThe collision risk of object j is defined as middle, d f Is the safe distance between the robot and the obstacle, and the maximum influence range of the obstacle j is 3d f . ρ determines the area of influence of the obstacle, while the positive integer c determines the effective range of the obstacle. In general, the values of the parameters ρ and c are set to 3 and 1, respectively.
The path smoothness is calculated as follows:
wherein α i is a deflection angle of the ith path, the deflection angle being composed of any three adjacent path points, (P) i -P i-1 )·(P i+1 -P i ) Is the inner product between two vectors, | | P i -P i-1 I and P i+1 -P i And | | represents the norm of the vector.
In order to better balance the performance among various targets of robot path planning and achieve better overall performance, a weight is added to each performance index, so that a fitness function of a robot path is defined as a weighted combination of the three performance indexes, and a mathematical expression of the fitness function is as follows:
J(P，X rob ，X obs )＝w 1 ×L(P)+w 2 ×R(X rob ，X obs )+w 3 ×S(P)
wherein w 1 ，w 2 ，w 3 Is a weight coefficient between 0 and 1, and the values of the weight coefficient are obtained according to the actual working environment and the actual experience of the mobile robot, and the parameters are respectively taken as follows: w is a 1 ＝0.6，w 2 ＝0.3，w 3 0.1. Thus, the robot path planning can be expressed as an optimization problem with a constrained global fitness function minimization:
where Ω represents an obstacle and a position beyond the boundary. In the experiment, the smaller J, the better the quality of the obtained path.
Simulation experiment and result:
two different robot working environments are provided, the simulated environment being 24 x 24m in size, in which obstacles of different sizes and shapes are generated to represent a complex environment, as shown in fig. 3 and 4. Safety distance d of robot f 1 m. In order to verify the effectiveness of the algorithm, the path planning of a multi-target particle swarm optimization algorithm, a PSO algorithm and a MOAPSO algorithm based on region segmentation is compared in environment maps with different complexities. The parameters of the algorithm are set as follows: the maximum number of iterations K is 150, the population size N is 100, the particle dimension D is 40, c 1 ＝0.5，c 2 ＝2，w＝[0.4，0.9]。
In order to compare the optimization effects of the proposed algorithm and the other two PSO algorithms, simulation experiments were performed in two maps of different complexity. Fig. 3 shows a fully convex obstacle, the environment is simple, and the obstacle arrangement situation of fig. 4 makes it easy for the robot to enter a concave obstacle, and thus to fall into local optima. The starting point coordinates of the robot are (1, 1), and the end point coordinates are (24, 24).
Fig. 5 and 6 show the optimal paths searched by the three algorithms, and the solid line, the dotted line, and the dotted line show the optimal paths searched by the algorithm, the PSO algorithm, and the MOAPSO algorithm, respectively. From the path planning result, each algorithm successfully searches a path avoiding the obstacle and reaches the end point position, but the path obtained by the multi-objective particle swarm optimization algorithm based on region segmentation is smoother and farther away from the obstacle. The path performance searched by the algorithm provided by the invention is superior to that of other algorithms, and a path with better quality can be searched.
The algorithm for selecting comparison in the invention is as follows: in the standard PSO and the aforementioned MOAPSO, the algorithm adopts a uniform parameter setting, and in order to reduce accidental errors, variables such as the population size, the maximum iteration number, the function evaluation number and the like which need to be input in the experiment are the same. Independent parameters of different algorithms are set according to the original literature. Both comparative algorithms use code embedded in the PlatEMO platform on which the experimental procedure will also be tested. The algorithm provided by the invention is implemented in MATLAB _ R2020b by adopting Matlab language, and a Mac operating system M1 chip is used as a hardware condition.
The invention selects DTLZ series test problems, wherein the problems of DTLZ1, DTLZ2, DTLZ3, DTLZ4, DTLZ5, DTLZ6 and DTLZ7 with the target number of 5 are selected, the problems have real pareto sets, each test problem independently and continuously runs for 20 times, and the obtained average value is taken as a final result. The Inverse Generation Distance (IGD) is selected as an index for evaluating the performance of the algorithm. The inverse generation distance represents the distance between the actually obtained solution set to the true solution set. It comprehensively measures the diversity and convergence of the solutions we obtain. The smaller the IGD value, the closer the population is to the Pareto frontier, the better the convergence and diversity of the algorithm, and the IGD is calculated by equation (9). Table 1 below is a comparison of the three algorithms.
Wherein P is a solution set obtained by an algorithm, P * Is a set of uniformly distributed reference points, d (x), sampled from the PF * P) is a reference set P * Midpoint x * Euclidean distances to points P in the solution set P.
TABLE 1 IGD mean and standard deviation calculated from the algorithm, PSO and MOAPSO proposed by the present invention
| The algorithm proposed by the invention | MOAPSO | PSO | |
| DTLZ1 | 5.2694e-2(1.69e-5) | 5.4200e-2(7.49e-4) | 1.1737e-1(7.99e-2) |
| DTLZ2 | 1.6513e-1(3.71e-6) | 1.6760e-1(4.90e-4) | 2.0726e-1(4.74e-3) |
| DTLZ3 | 1.6554e-1(4.77e-4) | 1.6600e-1(4.24e-4) | 3.6243e-1(4.34e-3) |
| DTLZ4 | 1.6730e-1(4.04e-3) | 1.6940e-1(6.94e-4) | 2.1159e-1(1.79e-2) |
| DTLZ5 | 1.1067e-1(9.98e-3) | 2.4800e-2(1.20e-3) | 4.9682e-2(1.52e-2) |
| DTLZ6 | 1.1474e-1(1.41e-2) | 2.4300e-2(7.27e-4) | 1.3171e+0(8.75e-1) |
| DTLZ7 | 3.1365e-1(8.90e-1) | 7.8900e-1(8.15e-2) | 3.6081e-1(8.69e-3) |
As can be seen from table 1, on the 5-dimensional target, IGD metric values obtained by the algorithm provided by the present invention on the 5 problems DTLZ1-DTLZ4 and DTLZ7 are significantly better than those of the other two comparative algorithms, that is, for most of the test problems, the performance of the algorithm provided by the present invention is better than that of the PSO algorithm and the MOAPSO algorithm, which also shows that the algorithm can maintain better diversity and convergence of the solution set, and proves the effectiveness of the multi-target particle swarm optimization algorithm based on region segmentation.
Claims (10)
1. The robot path planning method based on the region segmentation multi-target particle swarm optimization algorithm is characterized by comprising the following steps of:
s1, modeling a robot working space by adopting a two-dimensional plane space, and presenting the obstacles in an XOY coordinate system in the two-dimensional plane space in the form of entities with different shapes and sizes;
s2, equally dividing the line segment from the starting point S to the target point T into D +1 segments, D being the number of path points needed by the mobile robot path, determining the vertical line from the starting point S to the target point T passing through each path point, and randomly selecting a node P on the vertical line i Connecting the discrete path points, the starting point S and the target point T in sequence to form a complete path;
s3, taking a straight line from the starting point S to the target point T as a horizontal axis, projecting path points in an XOY coordinate system on an X ' SY ' coordinate system, wherein the projection lengths of each path sequence on the X ' axis are the same;
s4, setting N D-dimensional particle individuals in the path population, and taking the D-th dimension of each particle as each dimension of each particle to map corresponding nodes, so that each particle is a candidate path, and the specific method of the multi-target particle swarm optimization algorithm based on region segmentation comprises the following steps:
s41, initializing the population and parameters, and randomly generating a group of initial particle speeds and positions;
s42, judging whether the speed and the position of the initial particle meet the stop standard, if so, outputting the speed and the position of the particle; otherwise, executing S43;
s43, generating a new population PP, and simultaneously executing S44 and S45;
s44, selecting a solution with convergence meeting the requirements from the population PP, and carrying out region segmentation;
performing a crossover operation to replace the inferior particles with the obtained new particles to form a new population P1;
classifying the solutions in the population P1, evaluating the solutions in each class, and reserving the solution with the minimum Chebyshev function value;
determining a converged archive, executing S46;
s45, performing binary crossing on the population PP, and selecting a solution meeting the requirement to form a new population P2;
selecting any solution with a distance greater than the requirement in the population P2 to be put into a diversity archive;
determining diversity archive, performing S46;
s46, merging the convergence archiving and the diversity archiving to form a population EPOP, and outputting the speed and the position of the particles;
s5, searching the optimal position of each particle in an X 'SY' coordinate system according to the position and the speed of each particle, and calculating the fitness of each particle, so that the path length, the collision risk degree and the path smoothness are reduced;
and S6, establishing a traveling path of the robot according to the path length, the collision risk degree and the path smoothness.
2. The method for robot path planning based on multi-objective particle swarm optimization algorithm for region segmentation as claimed in claim 1, wherein in S3, the path point in XOY coordinate system is transformed into point (X ', y') in X 'SY' coordinate system by the following formula;
wherein alpha is the included angle between the XOY coordinate system and the X 'SY' coordinate system, (X) s ,y s ) Representing the coordinates of the starting point S in XOY.
3. The robot path planning method based on the region segmentation multi-objective particle swarm optimization algorithm according to claim 1, wherein a specific method for forming a new population P1 in S44 is as follows:
s441, sorting according to Euclidean distances from the particles to the global optimal position, and dividing the particle region into an area inside the boundary and an area outside the boundary by taking the preset Euclidean distances as the boundary, wherein the area inside the boundary is excellent particles, and the area outside the boundary is inferior particles;
s442, selecting two particles from the optimal particles, and performing a crossing operation, namely crossing the speed and the position of the two particles to generate speed and position information of a new particle;
s443, replacing the information of one inferior particle with the information of the new particle;
s444, repeatedly executing S442 and S443 until all inferior particles are replaced, and forming a new population P1.
4. The method for planning the robot path based on the region segmentation multi-objective particle swarm optimization algorithm according to claim 1, wherein the solutions in the population P1 are classified, the solution in each class is evaluated, and the specific method for retaining the solution with the minimum Chebyshev function value is as follows:
the method comprises the steps of sorting solutions in a population P1 in a non-dominated mode, determining all non-dominated solutions, evaluating the non-dominated solutions according to a Chebyshev aggregation function, selecting the solution with the minimum Chebyshev function value as one of parents of a cross operation, and randomly selecting the other parent in the non-dominated solution; the chebyshev function is as follows:
wherein λ ═ λ (λ) 1 ,λ 2 ,…,λ m ) Is a set of weight vectors, z ═ z 1 ,z 2 ,…,z m ) Is a reference point, z i ＝min{f i (x)|x∈Ω}。
5. The robot path planning method based on the region segmentation multi-objective particle swarm optimization algorithm according to claim 1, characterized in that the method of cross operation is as follows:
generating children using crossover operations in a differential evolution algorithm:
wherein x is i Is a solution in the superior particles,
is a parent solution x r1 The value in the ith dimension of the decision space, i ═ 1,2, …, n; CR is the crossover probability, F is the scaling factor, rand is [0,1 ]]Uniformly distributed random number, x r2 Divide x for random selection r1 And (4) external solution.
6. The robot path planning method based on the region segmentation multi-objective particle swarm optimization algorithm according to claim 1, wherein the convergence filing determining method comprises the following steps:
based on the set of weight vectors generated by the initial population and the convergence profile, the solution sets in the convergence profile are ranked by:
wherein i is 1,2,3, N, Z is (Z) 1 ,z 2 ,…,z m ) Is a set of ideal points, taking the minimum value of each target, Δ (F (x), r i ) Is represented by r i And the cosine of the angle between F (x) -Z;
assessment of CA by Chebyshev function i And (4) selecting the minimum solution of the Chebyshev function to carry out convergence filing.
7. The robot path planning method based on the region segmentation multi-objective particle swarm optimization algorithm according to claim 1, wherein the calculation method of any distance in the population P2 is as follows:
d(x)＝min{||F(x)-F(y)|| 2 *||F(x)-F(y)|| ∞ |y∈POP∩y≠x}
wherein | F (x) -F (y) | 2 And | F (x) -F (y) | ∞ Representing the distance difference between the two solutions.
8. The robot path planning method based on the region segmentation multi-objective particle swarm optimization algorithm according to claim 1, wherein the method for calculating the speed and the position of the particles is as follows:
wherein the content of the first and second substances,
is the velocity of the particle i in the d-th dimension in the k-th iteration,
is the current position of particle i in the d-th dimension in the k-th iteration;
the position of the d-dimension individual extreme point of the particle i in the k iteration is obtained, namely the optimal solution is obtained by searching the ith particle after the k iteration;
the position of the global extreme point of the whole population in the d dimension in the kth iteration is shown, namely the optimal solution in the whole population of the population is obtained after the kth iteration; r is 1 And r 2 Are all intervals of [0,1 ]]Random number of inner, c 1 And c 2 Are acceleration coefficients, w is an inertial weight, and as the iteration progresses, the value of w decreases linearly.
9. The robot path planning method based on the region segmentation multi-objective particle swarm optimization algorithm is characterized in that the method for adjusting the inertia weight w is as follows:
wherein, w max And w min A maximum and a minimum of w, respectively; iter and iter max Respectively the current iteration number and the maximum iteration number.
10. The robot path planning method based on the region segmentation multi-objective particle swarm optimization algorithm according to claim 1, wherein the path length is calculated as follows:
calculating the distance between two adjacent path nodes, and adding the distances between all two adjacent path nodes to obtain the path length;
the calculation method of the collision risk degree comprises the following steps:
calculating the risk degrees of the path and all the obstacles, and adding all the risk degrees to obtain a collision risk degree;
the path smoothness is calculated as follows:
wherein α i is a deflection angle of the ith path, the deflection angle being composed of any three adjacent path points, (P) i -P i-1 )·(P i+1 -P i ) Is the inner product between two vectors, | P i -P i-1 II and II P i+1 -P i |' denotes the norm of the vector.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106327502A (en) * | 2016-09-06 | 2017-01-11 | 山东大学 | Multi-scene multi-target recognition and tracking method in security video |
| CN106447022A (en) * | 2016-08-03 | 2017-02-22 | 长沙理工大学 | Multi-objective particle swarm optimization based on globally optimal solution selected according to regions and individual optimal solution selected according to proximity |
| WO2018176596A1 (en) * | 2017-03-31 | 2018-10-04 | 深圳市靖洲科技有限公司 | Unmanned bicycle path planning method based on weight-improved particle swarm optimization algorithm |
| KR20210061268A (en) * | 2019-11-19 | 2021-05-27 | 치루 유니버시티 오브 테크놀로지 | Method and system for planning path of user following robot with restrictions on direction of travel |
-
2022
- 2022-07-29 CN CN202210912285.0A patent/CN115016508A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106447022A (en) * | 2016-08-03 | 2017-02-22 | 长沙理工大学 | Multi-objective particle swarm optimization based on globally optimal solution selected according to regions and individual optimal solution selected according to proximity |
| CN106327502A (en) * | 2016-09-06 | 2017-01-11 | 山东大学 | Multi-scene multi-target recognition and tracking method in security video |
| WO2018176596A1 (en) * | 2017-03-31 | 2018-10-04 | 深圳市靖洲科技有限公司 | Unmanned bicycle path planning method based on weight-improved particle swarm optimization algorithm |
| KR20210061268A (en) * | 2019-11-19 | 2021-05-27 | 치루 유니버시티 오브 테크놀로지 | Method and system for planning path of user following robot with restrictions on direction of travel |
Non-Patent Citations (2)
| Title |
|---|
| 翁理国;纪壮壮;夏旻;王安;: "基于改进多目标粒子群算法的机器人路径规划", 系统仿真学报, no. 12, 8 December 2014 (2014-12-08) * |
| 陈侃松;阮玉龙;戴磊;兰智高;邵建设;: "区域分割的自适应变异粒子群算法", 电子学报, no. 08, 15 August 2017 (2017-08-15) * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115576333A (en) * | 2022-12-08 | 2023-01-06 | 青岛科技大学 | Optimal direction obstacle avoidance strategy |
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