CN109945881B - Mobile robot path planning method based on ant colony algorithm - Google Patents
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Abstract
The invention discloses a mobile robot path planning method for an ant colony algorithm, which comprises the following steps: the method comprises the steps of forming a grid map of the mobile robot according to a grid method, forming initial pheromone distribution according to barrier information of a starting point and an end point, forming an expected heuristic function according to a critical barrier influence factor, updating pheromones according to a pheromone updating formula, dynamically adjusting parameters of the pheromone heuristic factor and the expected heuristic factor according to a fuzzy algorithm, and dynamically adjusting pheromone volatilization coefficients. The technical scheme provided by the invention can obtain a better optimal path solution and has higher convergence rate. In addition, the invention proves that the technical scheme is feasible and effective through true simulation verification.
Description
Technical Field
The invention relates to the technical field of robots, in particular to a mobile robot path planning method based on an ant colony algorithm.
Background
Mobile robots have received much attention due to their great potential and research value in the fields of industrial applications, manufacturing, search and rescue, medical services, intelligent logistics, etc. Navigation is the core of research in the mobile robot-related art because it defines how the mobile robot perceives the environment, how it locates in the environment, and how it plans a path in a known map. Path planning is an important component in the research of navigation technology, and the main purpose of the path planning is to construct a collision-free optimal path from a starting point to a target point for a mobile robot in a known environment.
Path planning problems typically consider both static and dynamic environments: a static environment means that the positions of the starting point and the target point are known and the obstacle is also stationary. However, in a dynamic environment, since the position of the obstacle and the target point may change with time, the mobile robot needs to make a corresponding decision by means of the information of the sensor. According to the different perception of the robot to the environment, path planning can be divided into two categories: in the first type, a robot establishes a map for environmental information, so that a path can be planned off-line according to known map information, and the path planning is called global path planning; in the second category, the robot does not input environmental information in advance, an environmental map needs to be established in real time by using a sensor to avoid obstacles and find a proper path, and the path planning is called as local path planning. The embodiment researches a global path planning problem in a static environment.
In recent years, many scholars have conducted extensive research on path planning and proposed feasible methods such as artificial potential field methods, fuzzy algorithms, DWA algorithms, genetic algorithms, immune algorithms, neural network algorithms, and the like. However, these techniques have some disadvantages, such as poor stability, local optimality, poor adaptability, etc.
Disclosure of Invention
In order to solve the limitations and defects in the prior art, the invention provides a mobile robot path planning method of an ant colony algorithm, which comprises the following steps:
forming a grid map of the mobile robot according to a grid method, wherein a calculation formula of sequence coding of the mobile robot on the environment map is as follows:
wherein the robot has coordinates of (x)g，yg) Num is sequence number, NxFor the number of lines of the grid map, NyThe number of columns of the grid map is obtained;
forming initial pheromone distribution according to the barrier information of the starting point and the end point;
forming an expected heuristic function according to the critical obstacle impact factor, the expected heuristic function being:
wherein d isijIs the distance between two adjacent grids, giIs a critical obstacle impact factor, a constant, at node i;
updating the pheromone according to a pheromone updating formula, wherein the pheromone updating formula is as follows:
wherein Q is the pheromone enhancement coefficient, LkTotal length of path traveled by the kth ant in one iteration, Δ τij(t) pheromones added to the path ij at time t, B is a constant, n is the number of iterations,
average value of feasible path solutions for all ants;
dynamically adjusting the alpha/beta parameter according to a fuzzy algorithm;
wherein, alpha is pheromone elicitor, beta is expectation elicitor;
and outputting the optimal path.
Optionally, the step of dynamically adjusting the α/β parameter according to the fuzzy algorithm includes:
judging whether the ant colony algorithm falls into local optimum or not;
if the ant colony algorithm falls into local optimum, dynamically adjusting the pheromone volatilization coefficient according to an adjustment formula, wherein the adjustment formula is as follows:
ρ'＝Cρ (12)
wherein C is a constant which is more than 0 and less than 1, and rho epsilon (0, 1);
if the ant colony algorithm does not fall into the local optimum, the pheromone volatilization coefficient is kept unchanged.
Optionally, the method further includes: and outputting an iterative convergence curve and the optimal path length.
Optionally, the value range of α is [1,4], and the value range of β is [7,9 ].
The invention has the following beneficial effects:
the invention provides a mobile robot path planning method based on an ant colony algorithm, which comprises the steps of forming a grid map of a mobile robot according to a grid method, forming initial pheromone distribution according to barrier information of a starting point and an end point, forming an expected heuristic function according to a critical barrier influence factor, updating pheromones according to a pheromone updating formula, dynamically adjusting the pheromone heuristic factor and parameters of the expected heuristic factor according to a fuzzy algorithm, and dynamically adjusting pheromone volatilization coefficients. The technical scheme provided by the embodiment can obtain a better optimal path solution, and has a faster convergence rate. In addition, the embodiment proves that the technical scheme is feasible and effective through simulation and reality verification.
Drawings
Fig. 1 is a schematic diagram of a grid map model according to an embodiment of the present invention.
Fig. 2 is a schematic diagram illustrating an influence of different α values on algorithm performance according to an embodiment of the present invention.
Fig. 3 is a schematic diagram illustrating an influence of different β values on algorithm performance according to an embodiment of the present invention.
Fig. 4 is a block diagram of fuzzy inference provided in the first embodiment of the present invention.
Fig. 5 is a table diagram of α fuzzy control rules according to a first embodiment of the present invention.
Fig. 6 is a table diagram of a β fuzzy control rule according to a first embodiment of the present invention.
Fig. 7 is a schematic diagram of a simple grid map according to an embodiment of the present invention.
Fig. 8 is a schematic diagram of a complex grid map according to an embodiment of the present invention.
Fig. 9 is a flowchart of an ant colony algorithm according to an embodiment of the present invention.
Fig. 10a to 10c are diagrams illustrating an optimal path trajectory of a mobile robot according to an embodiment of the present invention.
Fig. 11a to 11c are comparison diagrams of optimal path convergence curves of the basic ant colony algorithm and the improved ant colony algorithm according to an embodiment of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following describes in detail a mobile robot path planning method of an ant colony algorithm provided by the present invention with reference to the accompanying drawings.
Example one
The inspiration of the ant colony algorithm is derived from the foraging behavior of real ants in the nature, and is a heuristic intelligent evolutionary algorithm. The ant colony algorithm is gradually applied to the field of path planning of mobile robots due to the advantages of parallel processing, distributed computing, strong robustness and the like. Although the ant colony algorithm shows a good effect in the field of path planning, the shortcomings of long search time, easiness in stagnation, low convergence speed, local optimization and the like cannot be overcome. To improve the performance of the algorithm, many scientists have made relevant studies. Yen and Cheng propose a fuzzy ant colony algorithm, which minimizes the iterative learning error of the ant colony algorithm under fuzzy control. Imen et al have integrated various advantages of the ant colony algorithm and the genetic algorithm, and propose a new hybrid GA-ACO algorithm. Cheng et al verified the efficiency of the ant colony algorithm under the TSP model. Wu et al improve performance by applying a rollback strategy to traditional ant colony algorithms. Rajput and Kumari combine directional motion and vector motion of a mobile robot in a grid map, and a rapid ant colony algorithm is provided. Li et al propose an improved ant colony algorithm based on dynamic parameters and pheromone update mechanisms. Khaled and Farid propose an ant colony algorithm based on infinite step size. GAN et al propose a method for ant colony-based extended path optimization-based planning. Chen et al propose a fast two-stage ant colony algorithm based on the principle of odor diffusion, overcoming the inherent problems of the traditional ant colony algorithm. The Che et al provides an improved ant colony optimization Algorithm (ACO) aiming at the characteristics of the three-dimensional path problem of the explosion-proof mobile robot and the defects of the traditional ant colony algorithm in path planning.
According to the research, the embodiment provides a global path planning method based on an improved ant colony algorithm, firstly, a robot environment map is established through a grid method, then barrier influence factors are introduced, a new pheromone distribution and updating strategy is provided, key parameters are controlled through a fuzzy algorithm, and volatilization coefficients are dynamically adjusted in a segmented mode. Finally, simulation experiments are carried out in various complex environments, and results show that the algorithm is feasible and effective.
The mobile robot environment modeling method mainly comprises a grid method, a visual graph method and a free space method. The grid method can well describe obstacles in any form, and the generated binary information features are convenient for storage and updating of a computer, so that the grid method has remarkable advantages in environmental modeling.
Fig. 1 is a schematic diagram of a grid map model according to an embodiment of the present invention. As shown in fig. 1, the grid method divides the working space of the mobile robot into grid cells, and in the grid map, the moving direction of the robot is not an arbitrary direction, but 8 traveling directions represented by octree. The grid states of the map are only two, namely occupied or free, in the map, a black grid represents obstacle information, a white grid is a movable area of the robot, a blue grid is a starting point of the robot, and a red grid is a target point of the robot. Let the robot coordinate be (x)g，yg) Then, the robot's in-map sequence code can be calculated as follows:
wherein Num represents a sequence number, NxRepresenting the number of grid map lines, NyRepresenting the number of grid map columns.
The ant colony Algorithm (ACO) simulates the foraging behavior of an ant colony, finds an optimal path in an unknown environment, and is a typical heuristic intelligent search algorithm. The existing research results show that the cooperative communication among ants is carried out on the basis of pheromones, and the concentration of the pheromones is inversely proportional to the path length. During the process of randomly exploring the environment for food, ants tend to move towards paths where the concentration of pheromones is high, because they can perceive the intensity of the pheromones. As the number of times ants travel on the same path increases, the pheromone concentration on the path also increases, so that more ants are attracted by the path, and the behavior represents the principle that ants select the optimal path.
In order to improve the efficiency of path planning, a heuristic function η and a tabu table are introduced into the artificial ant colony modelkThe concept of (1). In the random search algorithm, a heuristic function is adopted to improve the searching efficiency of the algorithm. TabukFor recording nodes that ants walk through to ensure that ants do not return to previous nodes.
At time t, the ant k moves from the current node i to an unvisited node j according to the distance information between the ant k and the target point and the intensity of the pheromone on the path, and if a plurality of unvisited nodes exist, the ant k determines the state transition probability among the nodes according to the following formula
Wherein, U ═ { C-tabu ═ C-tabukα is an pheromone heuristic factor, the higher the value is, the more the ant is influenced by the pheromone concentration between nodes when selecting a path, β is an expected heuristic factor, the higher the value is, the stronger the ant has a preference on the distance between the current node and the next node, tauij(t) denotes the pheromone concentration on the path ij at time t ηij(t) is an expected heuristic function defined as the inverse of the Euclidean distance between node i and node j, i.e.:
wherein d isijIs the distance between two adjacent grids, defined as:
when all ants complete the path search, the pheromone is continuously evaporated along with the time, meanwhile, the pheromones on the paths passed by the ants are increased, the pheromones left on each path are updated, and the updating formula is as follows:
τij(t+1)＝(1-ρ)τij(t)+Δτij(4)
where ρ is the pheromone volatility coefficient to avoid excessive accumulation of pheromones, ρ ∈ (0, 1);. DELTA.tauij(t) indicates pheromones added to the path ij at time t;
pheromones representing the increase of ant k after passing through path ij at time t are defined as:
wherein Q is a pheromone enhancement coefficient and is a constant; l iskThe total length of the path that the kth ant has traveled in one iteration.
According to the requirements of the fuzzy control algorithm, the present embodiment defines the following variables:
defining quality of 1 ant colony derived path solution
Value＝Lbest(n)-min{Lbest(n-1),Lbest(n-2),......,Lbest(1)},Value∈[-6,6](7)
Defining 2 degree of evolution of the Ant colony
Wherein N is the current iteration number, N is the total iteration number, and LbestShortest path in contemporary ant colony.
The fuzzy controller designed in this embodiment is a dual-input dual-output fuzzy controller, in which values of Value and Iter are used as fuzzy inputs, and a Value of α/β is used as a fuzzy output. The alpha/beta parameter is dynamically adjusted through the convergence states of the ant colony in different stages, so that the early stage convergence speed is improved, and the phenomenon that the ant colony falls into the local optimization of the algorithm is avoided.
The whole fuzzy control algorithm is divided into 3 stages. In the initial stage of the algorithm, the accumulation of pheromones on each path is insufficient, the difference is not large, and at the moment, the ant colony selection path is mainly related to the expected heuristic factor beta, so that the beta value is set to be large, and the alpha value is set to be small. With the iteration, the pheromone concentration on the shortest path is gradually higher than that on other paths in the middle stage of the algorithm, and at the moment, the positive feedback effect of the pheromone is increased, namely, the value of alpha is increased, and the value of beta is correspondingly reduced. At the later stage of the algorithm, the pheromone concentration on part of paths is far higher than that on other paths, and the risk of the algorithm falling into local optimum is the greatest, so the proportion of the pheromone concentration in path selection is reduced, and the randomness of the algorithm is increased. So alpha is reduced again and beta should be reduced further. In the process of adjusting alpha/beta, Value reflects the ant colony optimization capability, and combines the shortest path solution calculated each time to more accurately control parameters.
Alpha and beta in the traditional ant colony algorithm are generally taken from [1,9], and through a large number of experiments, the embodiment performs related research on the optimal values of alpha and beta. As can be seen from fig. 2, when α is 1,3, the ant colony algorithm can ensure a certain convergence rate while obtaining a shorter path length, and the effect is better. In order to further enhance the dynamic performance of the algorithm, the present embodiment sets the value range of α as [1,4 ]. The experimental results of fig. 3 show that the ant colony algorithm performance improves significantly as the β value increases. When β is 7,9, the ant colony algorithm can be converged stably finally, and the minimum path length can also be obtained, so the present embodiment selects the value range of β as [7,9 ].
The fuzzy controller provided by the embodiment adopts mamdani inference, and a fuzzy inference flow chart is shown in fig. 4. Establishing an input and output rule according to a fuzzy control algorithm, wherein the membership function adopts the uniform distribution of a symmetrical triangle, and the fuzzy rule adopts the following form:
If Iter is A AND Value is B THENα/βis C
the fuzzy inference rule is shown in table 1, and fig. 5 and 6 are graphical forms of fuzzy control rule tables.
TABLE 1 fuzzy rule table for alpha/beta values
The reasonable distribution of the initial pheromone is beneficial to accelerating the initial search efficiency of the algorithm, and the improvement of the embodiment is that the distribution of the initial pheromone is determined according to the barrier information of the starting point and the end point. In the case where there is no obstacle, the shortest route is the line connecting the starting point and the target point, and in the case where there is an obstacle, the route in this case is also the shortest as long as the vehicle travels in the direction of the line and approaches the obstacle as close as possible while avoiding the obstacle. Therefore, in the initial state, the initial value of pheromone is larger than that of other grids at the position close to the connecting line or the obstacle, so that the searching efficiency in the early stage can be greatly accelerated.
Fig. 7 and 8 illustrate how to distribute the initial pheromone by taking different grid maps as examples, wherein "1" and "2" represent the magnitude of the critical obstacle influence factor, and the larger the value, the more pheromones are allocated in the initial state. The two-point connecting line and the periphery of the obstacle crossed by the connecting line correspondingly generate critical obstacle influence factors, and the grid on the connecting line is more important than the grid on the periphery of the obstacle, so that the grid on the connecting line is larger in value.
The expected heuristic function is the reciprocal of the Euclidean distance between two points, and represents that the probability of ants moving to a grid closer to a target is higher, the improved heuristic function adds a critical obstacle influence factor, so that the ants move to the target grid and also consider the information of the obstacles, and the heuristic function is represented by formula (9):
wherein, giThe critical obstacle impact factor at node i, a is a constant, and can be adjusted as required.
In the conventional ant colony algorithm, when all ants search, pheromones on all paths passed by the ants are updated. However, at the later stage of the algorithm, pheromones on the optimal path are accumulated to a certain extent, and the selection of the shortest path by ants tends to be stable, so that if some unnecessary pheromones on all paths are still updated, the stability of the optimal value is inevitably reduced, and the convergence speed at the later stage of the algorithm is influenced. The embodiment provides a method for updating pheromones in stages, which can effectively solve the problem. For this purpose, a constant B is introduced, when the number of iterations n<B, calculating the average value of feasible path solutions obtained by all ants in the generation
And updating pheromone for the paths passed by the ants smaller than the average value. And when n is larger than or equal to B, only updating pheromone of the optimal path passed by the ant. The above-described improvement mechanism is shown in formula (10) and formula (11), where B is a constant related to the total number of iterations N.
As can be known from the formula (11), the improved updating mechanism only updates pheromones of part of ants with relatively short paths in the early stage of the algorithm, and only allows the ants to pass through the optimal paths in the later stage of the algorithm, so that the improvements can accelerate the convergence speed and the optimization capability of the algorithm, and simultaneously avoid the algorithm from being premature.
Local optimal refers to that when the pheromone concentration on a path is increased along with the increase of the iteration number, if a better path is found by one ant, the ant behind the ant is interfered by the strong pheromone concentration of a suboptimal path, so that the ant cannot walk along the optimal path, the ant is called as a local optimal solution of an algorithm, and if no optimal solution is found for continuous generations, the algorithm is in a stagnation state. The ant colony algorithm is prone to fall into the dilemma of local optimal solution in the later iteration stage, and therefore, in order to solve the problem and enhance the global search capability in the later stage of the algorithm, the embodiment dynamically adjusts the pheromone volatilization coefficient rho.
The pheromone volatilization coefficient rho in the improved ant colony algorithm is no longer constant, and when the algorithm is trapped in local optimum, the rho value is correspondingly reduced, so that the positive feedback effect of pheromone concentration is reduced, and meanwhile, the randomness of the algorithm is increased. As shown in equation (12), where C is a constant greater than 0 and less than 1.
ρ'＝Cρ (12)
Fig. 9 is a flowchart of an ant colony algorithm according to an embodiment of the present invention. As shown in fig. 9, the improved ant colony algorithm process described in this embodiment is as follows:
step 1: initializing parameters of an algorithm, establishing a grid map according to the surrounding environment, wherein the number of ants is m, the total iteration number is N, the current iteration number is N, an pheromone heuristic factor is alpha, an pheromone expectation factor is beta, the initial pheromone distribution is determined according to a method in 4.2, the pheromone volatilization coefficient is rho, the pheromone intensity is Q, and setting a starting point and a target point of the mobile robot.
Step 2: ants are placed at the starting point and the starting point is added to the Tabu list. The transition probabilities between nodes ij are calculated according to equation (1), the next node j is selected using roulette, and the current node is added to the tabu table.
And step 3: and judging whether the ants reach the target point, if so, calculating the length of the ants according to the path nodes recorded in the tabu table, and otherwise, continuously searching the next node until the ants reach the target point. And (4) circulating all ants in the generation until all ants complete traversal, and turning to the step 4.
And 4, step 4: the degree of evolution Iter of the ant colony and the ant colony path solution quality Value are calculated according to the equations (7) and (8), and the values are used as the input of the fuzzy controller to adjust the values of the pheromone heuristic factor alpha and the pheromone expectation factor beta. And judging whether the algorithm falls into local optimum or not, if so, adjusting the rho value according to the formula (12), and otherwise, keeping the rho value unchanged. The pheromones are updated in segments according to the strategy of equation (11).
And 5: and determining whether the iteration times of the algorithm meet N ≧ N. Otherwise, go to step 2 to let ant start iteration from the starting point again. If yes, go to step 6
Step 6: and outputting the optimal path, the iterative convergence curve and the optimal path length, and ending the algorithm.
In order to verify the correctness of the improved algorithm provided by the embodiment, the embodiment builds a 20x20 grid map with 3 different complexities by using MATALB R2014b, and observes whether the mobile robot can find a feasible and optimal path in a static obstacle environment. The results of the calculations of the improved ant colony algorithm (IACO) and the basic ant colony Algorithm (ACO) were compared and the corresponding analysis was given. The main parameters of the algorithm are shown in table 2.
Table 2 algorithm initial parameter set
Simulation experiments are performed on the two algorithms under the same parameters, fig. 10a to 10c are optimal path trajectory graphs of the mobile robot, the left graph is an experimental result of the basic ant colony algorithm, the right graph is an experimental result of the improved ant colony algorithm provided by the embodiment, and fig. 11a to 11c are optimal path convergence curve comparison graphs of the two algorithms. The technical scheme provided by the embodiment can obtain a better optimal path solution, and has a faster convergence rate. In addition, the embodiment proves that the technical scheme is feasible and effective through simulation and reality verification.
In fig. 11a, the iteration times for finding the optimal path by the two algorithms are not very different, but the shortest path found by the improved ant colony algorithm is better than that of the basic ant colony algorithm, and the convergence speed is faster.
In fig. 11b, the improved ant colony algorithm searches for the shortest path earlier than the basic ant colony algorithm, the basic ant colony algorithm falls into the locally optimal solution in the later stage of the algorithm, and the improved ant colony algorithm jumps out the locally optimal trap by a method of dynamically adjusting parameters.
In fig. 11c, the basic ant colony algorithm finds the optimal path and can also be stable, but the improved ant colony algorithm uses a shorter number of iterations, which means we can reduce the number of iterations N and shorten the algorithm running time.
TABLE 3 comparison of the results of the Algorithm experiment
As shown in the experimental data in table 3, the improved ant colony algorithm provided in this embodiment can obtain a better optimal path solution and has a faster convergence rate than the basic ant colony algorithm. The effectiveness of the algorithm provided by the embodiment is verified through simulation experiments, and the performance of the algorithm is superior to that of the basic ant colony algorithm.
The embodiment discloses a mobile robot path planning method for an ant colony algorithm, which comprises the following steps: the method comprises the steps of forming a grid map of the mobile robot according to a grid method, forming initial pheromone distribution according to barrier information of a starting point and an end point, forming an expected heuristic function according to a critical barrier influence factor, updating pheromones according to a pheromone updating formula, dynamically adjusting parameters of the pheromone heuristic factor and the expected heuristic factor according to a fuzzy algorithm, and dynamically adjusting pheromone volatilization coefficients. The technical scheme provided by the embodiment can obtain a better optimal path solution, and has a faster convergence rate. In addition, the embodiment proves that the technical scheme is feasible and effective through simulation and reality verification.
It will be understood that the above embodiments are merely exemplary embodiments taken to illustrate the principles of the present invention, which is not limited thereto. It will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the spirit and substance of the invention, and these modifications and improvements are also considered to be within the scope of the invention.
Claims (4)
1. A mobile robot path planning method of an ant colony algorithm is characterized by comprising the following steps:
forming a grid map of the mobile robot according to a grid method, wherein a calculation formula of sequence coding of the mobile robot on an environment map is as follows:
wherein the robot has coordinates of (x)g，yg) Num is sequence number, NxFor the number of lines of the grid map, NyThe number of columns of the grid map is obtained;
forming initial pheromone distribution according to the barrier information of the starting point and the end point;
forming an expected heuristic function according to the critical obstacle impact factor, the expected heuristic function being:
wherein d isijIs the distance between two adjacent grids, giIs a critical obstacle impact factor, a constant, at node i;
updating the pheromone according to a pheromone updating formula, wherein the pheromone updating formula is as follows:
wherein m is the number of ants, Q is the pheromone enhancement coefficient, LkTotal length of path traveled by the kth ant in one iteration, Δ τij(t) pheromones added to the path ij at time t, B is a constant, n is the number of iterations,
average value of feasible path solutions for all ants; l isbestIs the shortest path in the contemporary ant colony;
dynamically adjusting the alpha/beta parameter according to a fuzzy algorithm;
wherein, alpha is pheromone elicitor, beta is expectation elicitor;
and outputting the optimal path.
2. The ant colony algorithm mobile robot path planning method of claim 1, wherein the step of dynamically adjusting the α/β parameters according to the fuzzy algorithm is followed by:
judging whether the ant colony algorithm falls into local optimum or not;
if the ant colony algorithm falls into local optimum, dynamically adjusting the pheromone volatilization coefficient according to an adjustment formula, wherein the adjustment formula is as follows:
ρ'＝Cρ (12)
wherein C is a constant which is more than 0 and less than 1, and rho epsilon (0, 1);
if the ant colony algorithm does not fall into the local optimum, the pheromone volatilization coefficient is kept unchanged.
3. The ant colony algorithm mobile robot path planning method according to claim 2, further comprising: and outputting an iterative convergence curve and the optimal path length.
4. The method for planning a path of a mobile robot according to the ant colony algorithm of claim 1, wherein a is in a range of [1,4] and β is in a range of [7,9 ].
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