CN114756027A - Mobile robot path planning method based on improved ant colony algorithm and Bezier curve - Google Patents
Mobile robot path planning method based on improved ant colony algorithm and Bezier curve Download PDFInfo
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Abstract
The invention belongs to the field of path planning of mobile robots, and particularly relates to a path planning method of a mobile robot based on an improved ant colony algorithm and a Bezier curve, which comprises the steps of performing primary path planning by adopting the improved ant colony algorithm to obtain all paths successfully reaching a target node; performing secondary path planning on all paths successfully reaching the target node to obtain an optimal path; adopting a Bezier curve to carry out smoothing treatment on the turning point in the optimal path to obtain a smooth optimal path; the path obtained by the invention has higher safety and is smoother, so that the robot can more flexibly run in a working environment, and the working efficiency of the robot is improved.
Description
Technical Field
The invention belongs to the field of mobile robot path planning, and particularly relates to a mobile robot path planning method based on an improved ant colony algorithm and a Bezier curve.
Background
With the continuous progress of science and technology and the continuous promotion of industrial intelligence upgrading, the application of the mobile robot is concerned widely. The path planning of the mobile robot is a research hotspot, and aims to search out an optimal or near-optimal safe collision-free path from a starting position to a target position according to a specified optimization rule in an unknown or known environment. At present, a great deal of research is carried out on the path planning algorithm of the mobile robot at home and abroad, and the research method can be roughly divided into two categories of the traditional path planning algorithm and the intelligent bionic path planning algorithm. The traditional path planning algorithm comprises an artificial potential field method, a Dijkstra algorithm, an A-star algorithm and the like, and the intelligent bionic algorithm comprises an ant colony algorithm, a particle swarm algorithm, a genetic algorithm, a wolf colony algorithm and the like. The problems that the optimal path is easy to fall into local optimization, the convergence speed is low, turning points are multiple and the like exist when the basic ant colony algorithm is adopted to search the optimal path in the two-dimensional static environment. On the basis, Zhang Heng et al provides an improved double-layer ant colony algorithm, the ant colony is divided into a guide layer ant colony and a common layer ant colony, heuristic functions of the two ant colony are respectively improved, a free path-pruning strategy for dealing with the deadlock problem is designed for the guide layer ant colony, pheromone updating is carried out only on a path with a short length, and suppression processing is carried out on pheromone concentration on a suboptimal path. However, the complexity of the improved algorithm is higher, the number of parameters of the algorithm is more, the sensitivity of the algorithm parameters is increased, the planned path is not smooth enough, the number of turning points is more, and the operation of a real robot is not facilitated. Chinese patent (CN111982125A) discloses a path planning method based on an improved ant colony algorithm, which combines an improved Artificial Potential Field (APF) algorithm with an ant colony algorithm, firstly performs initial map planning by using the improved APF algorithm, secondly improves a heuristic function by using an evaluation function of the a-algorithm and a path turning angle, introduces a heuristic information increasing function, and finally improves a state transition rule and adaptively adjusts a threshold of a state transition function. The improvement measure can effectively improve the initial release of the pheromone, but needs to consume certain preprocessing time to plan the initial path, is not suitable for real-time application occasions, has more turning points of the planned path, and is not beneficial to the operation of a real robot.
Disclosure of Invention
In order to solve the above problems, the present invention provides a mobile robot path planning method based on an improved ant colony algorithm and a bezier curve, comprising:
s1, establishing an environment map by a grid method, and initializing parameters;
s2, performing primary path planning by adopting an improved ant colony algorithm to obtain all paths successfully reaching a target node;
s3, performing secondary path planning on all paths successfully reaching the target node to obtain an optimal path;
and S4, smoothing the turning point in the optimal path by adopting a Bezier curve to obtain a smooth optimal path.
Further, the process of primary path planning includes:
s11, setting the maximum iteration times to be 1;
s12, placing ants at an initial node S of the environment map, and initializing a taboo table;
s13, any ant searches for a next node at the current node according to the path searching rule, and the next node is added into a taboo table and the path length is updated;
s14, judging whether the ant completes one iteration, if so, executing the step S15, otherwise, returning to the step S13;
s15, judging whether the ant reaches the target node or not, if not, discarding the ant, otherwise, leaving the ant, and calculating the length of the path of the ant to the target node;
S16, after all ants complete path search, the average value of all path lengths is calculated, and pheromone updating is carried out on all paths which successfully reach a target node according to a reward punishment mechanism;
s17, judging whether the iteration times reach the maximum iteration times, if so, outputting all paths successfully reaching the target node; otherwise, emptying the tabu table, and returning to the step S12 after adding 1 to the iteration number.
Further, the path finding rule is expressed as:
where j denotes the next node sought,. tau.ijThe concentration of pheromones on the path < i, j >,
is the inverse of the Euclidean distance, q, from the next node j to the target node GoIs a dynamic selection factor, etaijIndicating heuristic information from the current node i to the next node j, alpha indicating a pheromone heuristic factor, beta indicating an expected heuristic factor, chi indicating a target point heuristic factor,
represents the state transition probability of the kth ant from the current node i to the next node j, allowedkRepresenting the set of next nodes j that the kth ant can select at the current node i.
Further, the calculation formula of the dynamic selection factor is as follows:
where n represents the current number of iterations.
Further, calculating the lengths of all paths successfully reaching the target node, and based on the maximum and minimum ant model and the elite ant model, providing a reward punishment mechanism to update the pheromone, wherein the reward punishment mechanism comprises:
If the current path is the optimal path, the pheromone update is represented as:
τij(t)＝(1-ρ)×τij(t-1)+λ1×ρ×Δτij(t)；
if the current path length is greater than the optimal path length and is less than the average path length, the pheromone update is expressed as:
τij(t)＝(1-ρ)×τij(t-1)+λ2×ρ×Δτij(t)；
if the current path length is greater than the average path, the pheromone update is represented as:
τij(t)＝(1-ρ)×τij(t-1)-λ3×ρ×Δτij(t)；
wherein λ is1、λ2、λ3The scale factor is increased or decreased for the pheromone, taking the value as a positive number, tauij(t-1) denotes the pheromone concentration, τ, over the path < i, j > after t-1 iterationsij(t) denotes the pheromone concentration over a path < i, j > after t iterations, ρ denotes the pheromone concentration volatility coefficient, where Δ τij(t) represents the pheromone increment, which is calculated by the formula:
Lk(t) represents the path length that the kth ant seeks in the t iteration, and Q represents pheromone strength.
Further, the secondary path planning includes:
s21, setting the maximum iteration times of quadratic programming to be 1;
s22, obtaining path nodes passed by ants which successfully reach the target nodes in the primary path planning, and initializing a tabu table;
s23, any ant searches for a next node b at the current node a according to a quadratic programming rule, and the next node is added into a taboo table and the path length is updated until the ant reaches a target node or a deadlock state occurs;
S24, judging whether all ants finish one iteration, if so, executing the step S25, otherwise, returning to the step S23;
s25, obtaining a path of the ant to the target node, and updating pheromones of the path according to a secondary pheromone updating rule;
and S26, judging whether the iteration number of the quadratic programming reaches the maximum iteration number of the quadratic programming, if so, outputting an optimal path, otherwise, emptying a tabu table, and adding 1 to the iteration number of the quadratic programming and then returning to the step S22.
Further, the quadratic programming rule is expressed as:
wherein,
representing the state transition probability of the kth ant from the node a to the node b, alpha 1 representing a pheromone heuristic factor of quadratic programming, beta 1 representing an expected heuristic factor of quadratic programming, chi 1 representing a target point heuristic factor of quadratic programming, and tauab(t) indicates the pheromone concentration, η, over the path < a, b > in t iterationsab(t) represents a node NaAnd node NbThe euclidean distance between them,
representing a node NbThe inverse of the euclidean distance to the target node G.
Further, the secondary pheromone update rule is expressed as:
τab(t)＝(1-ρ1)×τab(t-1)+ρ1×Δτab(t)；
wherein, tauab(t) denotes the pheromone concentration on the path < a, b > after the t-th iteration, rho 1 denotes the pheromone concentration volatility coefficient during quadratic programming, Delta tau ab(t) represents the pheromone increment, which is calculated by the formula:
wherein n isk(t) the number of turning points of the path planned by the kth ant in the t generation, Lk(t) represents the optimal path length, sm, planned by the kth ant in the t generationk(t) represents the smoothness of the path planned by the kth ant in the t generation.
The invention has the beneficial effects that:
the invention provides a mobile robot path planning method based on an improved ant colony algorithm and a Bezier curve, which comprises the steps of carrying out primary path planning through the improved ant colony algorithm, searching all paths which successfully reach a target point, firstly adopting a pseudorandom state transition rule to carry out next path node selection in the primary path planning, defining a dynamic selection factor to adaptively update a selection proportion, introducing the distance from a next node to the target node into a transition probability, improving the searching efficiency of the algorithm and avoiding the algorithm from falling into local optimization; meanwhile, a reward punishment mechanism is provided to update pheromone increment, so that the guidance of high-quality ants to offspring is enhanced, the misleading of inferior ants to offspring is avoided, and the convergence speed of the algorithm can be improved; when the secondary path planning is carried out, abandoning unnecessary turning points, and evaluating a path by comprehensively considering factors such as optimal path length, the number of the turning points of the path, path smoothness and the like; and finally, smoothing the paths around the residual turning points by adopting a Bezier curve to finally obtain a smooth path. The path obtained by the method is higher in safety and smoother, so that the robot can be more flexibly used in a working environment, and the working efficiency of the robot is improved.
Drawings
Fig. 1 is a flowchart of a mobile robot path planning method based on an improved ant colony algorithm and a bezier curve according to the present invention;
FIG. 2 is a routing diagram of one embodiment of the present invention;
FIG. 3 is a flow chart of the primary path planning of the present invention;
fig. 4 is a flowchart of the quadratic path planning of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a mobile robot path planning method based on an improved ant colony algorithm and a Bezier curve, as shown in figure 1, comprising the following steps:
s1, establishing an environment map by a grid method, and initializing parameters;
s2, performing primary path planning by adopting an improved ant colony algorithm to obtain all paths successfully reaching a target node;
s3, performing secondary path planning on all paths successfully reaching the target node to obtain an optimal path;
And S4, smoothing the turning point in the optimal path by adopting a Bezier curve to obtain a smooth optimal path.
In one embodiment, as shown in fig. 2, a random map is obtained by modeling a robot working environment by a grid method, wherein a white grid is a free grid, i.e., a feasible area of a robot, a black grid is an obstacle grid, i.e., an area where the robot cannot pass, a unit grid is equal to the size of the robot, and grids in the model are encoded from top to bottom from left to right, and one grid represents a position node.
Firstly, an improved ant colony algorithm is adopted to carry out primary path planning, namely, a robot path planning experiment is carried out under a two-dimensional static grid map, a path which ants successfully reach a target node pass is found, and relevant parameters involved in the primary path planning comprise an initial position S, a target position G and the maximum iteration number N of the algorithmmaxThe ant number M, the information heuristic factor α, the expectation heuristic factor β, the target point heuristic factor χ, the pheromone concentration volatility coefficient ρ, the pheromone intensity Q, and the like, all the parameters are initialized, and a specific process of primary path planning is shown in fig. 3, and includes:
S11, setting the maximum iteration times to be 1;
s12, ants are placed on an initial node S of the environment map, and a taboo table is initialized;
the taboo table stores path nodes and barrier nodes which are already walked by ants, and the nodes in the taboo table cannot be selected in subsequent path planning.
S13, searching a next node j by any ant at the current node i according to a path searching rule (a pseudo-random state transition rule), adding the next node j into a taboo table and updating the path length;
specifically, the path finding rule is expressed as:
in the pseudo-random state transition rule, the reciprocal of the distance from the next node to the target node is added into the state transition probability function, so that the searching efficiency and the globality of the algorithm are improved; where j denotes the next node sought,. tau.ijThe concentration of pheromones on the path < i, j >,
is the reciprocal of the Euclidean distance from the next node j to the target node G, alpha represents an information heuristic factor, beta represents an expected heuristic factor, chi represents a target point heuristic factor,
represents the state transition probability of the kth ant from the current node i to the next node j, allowedkRepresents the set of next nodes j, q, of the kth ant selectable at the current node i oIs a dynamic selection factor used for self-adaptively updating the selection proportion and the early stage q of the algorithmoThe method is large, the searching efficiency of the early stage of the algorithm can be improved, and the q of the middle and later stages of the algorithmoThe value is large, the global searching capability of the algorithm can be ensured, and qoThe expression of (c) is:
wherein n represents the current iteration number; etaijThe heuristic information from the current node i to the next node j is represented by the following calculation formula:
(xi,yi) Representing the position coordinates of the current node i, dijRepresenting the euclidean distance of the current node i from the next node j.
S14, judging whether the ant completes one iteration, namely searching a next node all the time, judging whether the ant reaches a target node or is in a deadlock state, if so, executing the step S15, otherwise, returning to the step S13;
s15, judging whether the ant reaches the target node or not, if not, discarding the ant, otherwise, leaving the ant, and calculating the length of the corresponding path which successfully reaches the target node;
s16, after all ants complete path search once, the average value of all path lengths is calculated, and pheromone updating is carried out on all paths which successfully reach a target node according to a reward punishment mechanism;
specifically, based on the maximum and minimum ant model and the elite ant model, a reward punishment mechanism is proposed to update pheromone, which comprises the following steps: calculating the lengths of all paths successfully reaching the target node to obtain an optimal path and performing pheromone updating on the optimal path, wherein the length is expressed as:
τij(t)＝(1-ρ)×τij(t-1)+λ1×ρ×Δτij(t)；
For the optimal path, the highest pheromone concentration reward is given, the guiding effect of the optimal path on the offspring ants is enhanced, and in the rest paths, if the path length experienced by the ants is greater than the optimal path length and is lower than the average path length, the pheromone update is expressed as:
τij(t)＝(1-ρ)×τij(t-1)+λ2×ρ×Δτij(t)；
if the path length experienced by an ant is greater than the average path, and the penalty for a poor path is increased to reduce the misleading effect of the ant on offspring ants, the pheromone update is expressed as:
τij(t)＝(1-ρ)×τij(t-1)-λ3×ρ×Δτij(t)；
wherein λ is1、λ2、λ3The pheromone scaling factor is a pheromone scaling factor with the value range of {0.1,1,5,10,15 and 20}, and an optimal set of pheromone scaling factors tau is obtained through simulation experiment resultsij(t-1) denotes the pheromone concentration, τ, over the path < i, j > after t-1 iterationsij(t) denotes the pheromone concentration over a path < i, j > after t iterations, and ρ denotes the pheromone concentration volatility coefficient, where Δ τij(t) represents the pheromone increment, which is calculated by the formula:
Lk(t) represents the path length that the kth ant seeks in the tth iteration, and Q represents pheromone strength.
S17, judging whether the iteration number reaches the maximum iteration number NmaxIf yes, outputting all paths successfully reaching the target node; otherwise, the tabu table is cleared, and the iteration number is added to 1, and the step S12 is returned.
At present, a path planning experiment of a mobile robot is mainly performed under a two-dimensional grid map, the quality of a path can be influenced by setting a map model, the length of the path is only considered when the optimal path is searched, the actual operation wear condition, the obstacle avoidance condition and the smoothness of the path of the mobile robot are not considered, and the path planning experiment of the mobile robot is not facilitated to be directly applied to a real environment by an algorithm. The invention provides a secondary path planning strategy of the mobile robot, when the primary path planning is finished by using an improved ant colony algorithm, ants which do not reach a target node are abandoned, grid nodes through which all ants which successfully reach the target node pass are recorded, and optimization is carried out based on a planned path.
In an embodiment, after performing the initial path planning by using the improved ant colony algorithm, all paths that successfully reach the target node are saved, where all raster nodes that a path that successfully reaches the target node passes through may be represented as N ═ S, N1,N2,......,Nn-1,NnG, when performing secondary path planning, the direction selected by the next node of the ant is towards the target node, so that the direction selected by the next node is unidirectional when performing secondary path planning. If the existence of barriers between nodes is not considered, when ants are positioned at N i-1And when the next node is selected, the nodes which can be selected by the ants are as follows:
Ni＝{Ni+1,Ni+2,Ni+3,......,Nn-1,Nn,G}；
wherein N isi+1,Ni+2,Ni+3,......,Nn-1,NnG is NiThe subsequent nodes are the N nodes in the raster nodes which are passed by the subsequent nodes in the path which is stored and successfully reaches the target node after the initial path planningiThe subsequent node of (2). Generally, the types and the number of the grid map obstacles are large, and therefore, it is necessary to determine whether an obstacle exists between two nodes. Suppose now that there are two nodes Na、NbIf N isa、NbThere is a barrier between, ants cannot be from NaDirect to NbOtherwise, the specific judgment formula can be as follows:
when the ant is at Ni-1And when the next node is selected, considering the situation of the barrier between the two nodes, the node which can be selected by the ant is represented as:
and when the selection condition of the next node can be accurately judged, performing secondary path planning on the mobile robot after primary path planning.
Preferably, the quadratic path planning strategy comprises a maximum iteration number N of quadratic planningmax1The number M1 of ants that successfully reach the target node, the heuristic pheromone factor α 1 of the quadratic programming, the expected heuristic factor β 1 of the quadratic programming, the heuristic factor χ 1 of the target point of the quadratic programming, the volatility coefficient ρ 1 of the concentration of the pheromone of the quadratic programming, the intensity Q of the pheromone, and other parameters are initialized, and the quadratic path programming specifically includes, as shown in fig. 4:
S21, setting the maximum iteration number of the quadratic programming, and enabling the iteration number of the quadratic programming to be 1;
s22, acquiring the grid nodes passed by the ants which successfully reach the target node in the primary path planning, initializing a tabu table and placing M1 ants at the initial node;
s23, any ant searches for a next node b at the current node a according to a quadratic programming rule (roulette method), adds the next node into a taboo table and updates the path length until the ant reaches a target node or a deadlock state occurs;
specifically, the quadratic programming rule is expressed as:
wherein, χ 1 belongs to {0.5,1,1.5,2,2.5,3}, obtaining the optimal target point heuristic factor of quadratic programming through the simulation experiment result,
represents the state transition probability of the kth ant from the node a to the node b, tauab(t) indicates the pheromone concentration, η, over the path < a, b > in t iterationsab(t) represents a node NaAnd node NbThe euclidean distance between them,
representing a node NbThe reciprocal of the Euclidean distance between the target node G and the target node G is related to the calculation formula as follows:
s24, judging whether all ants finish one iteration, namely all ants finish one search, if so, executing the step S25, otherwise, returning to the step S23;
s25, obtaining a path taken by an ant successfully reaching the target node, and updating pheromones of the path according to a secondary pheromone updating rule;
Specifically, in the secondary path planning, in order to obtain a path more suitable for the mobile robot to run, in the pheromone updating process, factors such as the optimal path length, the number of path turning points, the path smoothness and the like are comprehensively considered to evaluate one path, so that the secondary pheromone updating rule is expressed as:
τab(t)＝(1-ρ1)×τab(t-1)+ρ1×Δτab(t)；
wherein, tauab(t) denotes the pheromone concentration on the path < a, b > after the t-th iteration, rho 1 denotes the pheromone concentration volatility coefficient during quadratic programming, Delta tauab(t) represents the pheromone increment, which is calculated by the formula:
wherein n isk(t) represents the turning point number of the path planned by the kth ant in the t generation, Lk(t) represents the optimal path length, sm, planned by the kth ant in the t generationk(t) represents the smoothness of the path planned by the kth ant in the t generation; the calculation formula of the related parameters is as follows:
wherein, thetai+1Represents the angle between the (i + 2) th node and the (i + 1) th node.
And S26, judging whether the iteration number of the quadratic programming reaches the maximum iteration number of the quadratic programming, if so, outputting an optimal path, otherwise, emptying a tabu table, and adding 1 to the iteration number of the quadratic programming and then returning to the step S22.
After the secondary path planning, turning points of the path can be effectively reduced, broken lines in the path are also obviously reduced, as shown in fig. 2, a very-tortuous curve is the path obtained through the primary planning, a slightly-gentle curve is the path obtained through the secondary planning, the turning points are obviously fewer, the path is smoother, but the path is also a place with turning, in order to ensure that the efficiency is higher when the mobile robot actually operates, and the walking path is smoother, a bezier curve is used for smoothing the path, the bezier curve is a smooth and conductive spline curve, and the n-th-order bezier curve can be expressed as:
piCoordinates representing the ith control point, Bi,n(t) is Bernstein quadratic polynomial, where t has a value in the range of [0, 1%]，
Representing the coefficients of the quadratic term.
The invention adopts a secondary Bezier curve which is commonly used, and the expression of the secondary Bezier curve is as follows:
p(t)＝(1-t)2p0+2t(1-t)p1+t2p2 t∈[0,1]；
wherein p is1、p2、p3Is the control point of the curve. And the optimal path obtained after the quadratic programming is subjected to quadratic Bezier curve smoothing processing, and a smooth curve is finally obtained and is more suitable for the operation of the robot.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (8)
1. A mobile robot path planning method based on an improved ant colony algorithm and a Bezier curve is characterized by comprising the following steps:
s1, establishing an environment map by a grid method, and initializing parameters;
s2, performing primary path planning by adopting an improved ant colony algorithm to obtain all paths successfully reaching a target node;
s3, performing secondary path planning on all paths successfully reaching the target node to obtain an optimal path;
And S4, smoothing the turning point in the optimal path by adopting a Bezier curve to obtain a smooth optimal path.
2. The method for planning the path of the mobile robot based on the improved ant colony algorithm and the bezier curve according to claim 1, wherein the process of the primary path planning comprises:
s11, setting the maximum iteration times to be 1;
s12, ants are placed on an initial node of the environment map, and a taboo table is initialized;
s13, any ant searches for a next node at the current node according to the path searching rule, and the next node is added into a taboo table and the path length is updated;
s14, judging whether the ants finish one iteration, if not, returning to the step S13, otherwise, executing the step S15;
s15, judging whether the ant reaches the target node or not, if not, discarding the ant, otherwise, leaving the ant, and calculating the length of the path of the ant to the target node;
s16, after all ants complete path search, the average value of all path lengths is calculated, and pheromone updating is carried out on all paths which successfully reach a target node according to a reward punishment mechanism;
s17, judging whether the iteration times reach the maximum iteration times or not, and if so, outputting all paths successfully reaching the target node; otherwise, the tabu table is cleared, and the iteration number is added to 1, and the step S12 is returned.
3. The method for planning the path of the mobile robot based on the improved ant colony algorithm and the bezier curve as claimed in claim 2, wherein the path finding rule is expressed as:
where j denotes the next node sought,. tau.ijThe concentration of pheromones on the path < i, j >,
is the reciprocal of the Euclidean distance, q, from the next node j to the target node GoIs a dynamic selection factor, ηijIndicating heuristic information from the current node i to the next node j, alpha indicating a pheromone heuristic factor, beta indicating an expected heuristic factor, chi indicating a target point heuristic factor,
represents the state transition probability of the kth ant from the current node i to the next node j, allowedkRepresenting the set of next nodes j that the kth ant can select at the current node i.
4. The method for planning the path of the mobile robot based on the improved ant colony algorithm and the bezier curve as claimed in claim 3, wherein the calculation formula of the dynamic selection factor is as follows:
where n represents the current number of iterations.
5. The method as claimed in claim 2, wherein the method for planning the path of the mobile robot based on the improved ant colony algorithm and the bezier curve calculates all the paths successfully reaching the target node, and proposes a reward penalty mechanism to update the pheromone based on the maximum and minimum ant models and the elite ant model, including:
If the current path is the optimal path, the pheromone update is represented as:
τij(t)＝(1-ρ)×τij(t-1)+λ1×ρ×Δτij(t)；
if the current path length is greater than the optimal path length and is less than the average path length, the pheromone update is expressed as:
τij(t)＝(1-ρ)×τij(t-1)+λ2×ρ×Δτij(t)；
if the current path length is greater than the average path, the pheromone update is represented as:
τij(t)＝(1-ρ)×τij(t-1)-λ3×ρ×Δτij(t)；
wherein λ is1、λ2、λ3Scaling factor is increased or decreased for pheromone, taking positive value, tauij(t) denotes the pheromone concentration, τ, on the path < i, j > after t iterationsij(t-1) denotes the pheromone concentration on the path < i, j > after t-1 iterations, ρ denotes the pheromone concentration volatility factor, where Δ τij(t) represents the pheromone increment, which is calculated by the formula:
Lk(t) represents the path length that the kth ant seeks in the t iteration, and Q represents pheromone strength.
6. The method for planning the path of the mobile robot based on the improved ant colony algorithm and the bezier curve as claimed in claim 1, wherein the quadratic path planning comprises:
s21, setting the maximum iteration times of quadratic programming to be 1;
s22, obtaining path nodes passed by ants which successfully reach the target nodes in the primary path planning, and initializing a tabu table;
s23, any ant searches for a next node b at the current node a according to a quadratic programming rule, and the next node is added into a taboo table and the path length is updated until the ant reaches a target node or a deadlock state occurs;
S24, judging whether all ants finish one iteration, if so, executing the step S25, otherwise, returning to the step S23;
s25, acquiring a path of the ants to the target node, and updating pheromones of the path according to a secondary pheromone updating rule;
and S26, judging whether the iteration number of the quadratic programming reaches the maximum iteration number of the quadratic programming, if so, outputting an optimal path, otherwise, emptying a tabu table, and adding 1 to the iteration number of the quadratic programming and then returning to the step S22.
7. The method for planning the path of the mobile robot based on the improved ant colony algorithm and the Bezier curve as claimed in claim 6, wherein the quadratic programming rule is expressed as:
wherein,
representing the state transition probability of the kth ant from the node a to the node b, alpha 1 representing a pheromone heuristic factor of quadratic programming, beta 1 representing an expected heuristic factor of quadratic programming, chi 1 representing a target point heuristic factor of quadratic programming, and tauab(t) denotes the pheromone concentration, η, over the path < a, b > in t iterationsab(t) represents a node NaAnd node NbThe euclidean distance between them,
representing a node NbThe inverse of the euclidean distance to the target node G.
8. The method for planning the path of the mobile robot based on the improved ant colony algorithm and the Bezier curve as claimed in claim 6, wherein the quadratic pheromone updating rule is expressed as:
τab(t)＝(1-ρ1)×τab(t-1)+ρ1×Δτab(t)；
Wherein, tauab(t) represents pheromone concentration on a path < a, b > after the t-th iteration, rho 1 represents pheromone concentration volatilization coefficient during quadratic programming, and delta tauab(t) represents the pheromone increment, which is calculated by the formula:
wherein n isk(t) represents the turning point number of the path planned by the kth ant in the t generation, Lk(t) represents the optimal path length, sm, planned by the kth ant in the t generationk(t) represents the smoothness of the path planned by the kth ant in the t generation.
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| CN115560774A (en) * | 2022-10-24 | 2023-01-03 | 重庆邮电大学 | Mobile robot path planning method oriented to dynamic environment |
| CN116222579A (en) * | 2023-05-05 | 2023-06-06 | 西安麦莎科技有限公司 | Unmanned aerial vehicle inspection method and system based on building construction |
| CN116558527A (en) * | 2023-07-10 | 2023-08-08 | 无锡军工智能电气股份有限公司 | Route planning method for underground substation inspection cleaning robot |
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| CN115560774A (en) * | 2022-10-24 | 2023-01-03 | 重庆邮电大学 | Mobile robot path planning method oriented to dynamic environment |
| CN115560774B (en) * | 2022-10-24 | 2023-11-17 | 重庆邮电大学 | Dynamic environment-oriented mobile robot path planning method |
| CN116222579A (en) * | 2023-05-05 | 2023-06-06 | 西安麦莎科技有限公司 | Unmanned aerial vehicle inspection method and system based on building construction |
| CN116558527A (en) * | 2023-07-10 | 2023-08-08 | 无锡军工智能电气股份有限公司 | Route planning method for underground substation inspection cleaning robot |
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