CN111610788B - Hierarchical fuzzy-artificial potential field path planning method - Google Patents
Hierarchical fuzzy-artificial potential field path planning method Download PDFInfo
- Publication number
- CN111610788B CN111610788B CN202010538510.XA CN202010538510A CN111610788B CN 111610788 B CN111610788 B CN 111610788B CN 202010538510 A CN202010538510 A CN 202010538510A CN 111610788 B CN111610788 B CN 111610788B
- Authority
- CN
- China
- Prior art keywords
- unmanned ship
- path
- point
- obstacle
- potential field
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 51
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 63
- 230000035772 mutation Effects 0.000 claims abstract description 23
- 230000002068 genetic effect Effects 0.000 claims abstract description 17
- 238000001514 detection method Methods 0.000 claims description 17
- 230000003044 adaptive effect Effects 0.000 claims description 16
- 230000004888 barrier function Effects 0.000 claims description 11
- 230000014759 maintenance of location Effects 0.000 claims description 10
- 210000000349 chromosome Anatomy 0.000 claims description 9
- 230000033001 locomotion Effects 0.000 claims description 9
- 239000000126 substance Substances 0.000 claims description 8
- 238000012937 correction Methods 0.000 claims description 7
- 230000008569 process Effects 0.000 claims description 7
- 230000009471 action Effects 0.000 claims description 6
- 108090000623 proteins and genes Proteins 0.000 claims description 6
- 230000002829 reductive effect Effects 0.000 claims description 6
- 230000000717 retained effect Effects 0.000 claims description 4
- 230000003247 decreasing effect Effects 0.000 claims description 3
- 238000009795 derivation Methods 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 3
- 239000002994 raw material Substances 0.000 claims description 3
- 230000006798 recombination Effects 0.000 claims description 3
- 238000005215 recombination Methods 0.000 claims description 3
- 108010046685 Rho Factor Proteins 0.000 claims description 2
- 238000004387 environmental modeling Methods 0.000 claims 1
- 230000005484 gravity Effects 0.000 claims 1
- 238000010586 diagram Methods 0.000 description 8
- 238000004088 simulation Methods 0.000 description 5
- 238000011161 development Methods 0.000 description 2
- 229910052731 fluorine Inorganic materials 0.000 description 2
- 125000001153 fluoro group Chemical group F* 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 239000002245 particle Substances 0.000 description 2
- 230000003068 static effect Effects 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 238000005265 energy consumption Methods 0.000 description 1
- 230000000670 limiting effect Effects 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000037361 pathway Effects 0.000 description 1
- 238000007781 pre-processing Methods 0.000 description 1
- 230000002028 premature Effects 0.000 description 1
- 230000001846 repelling effect Effects 0.000 description 1
- 238000010845 search algorithm Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/0206—Control of position or course in two dimensions specially adapted to water vehicles
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/0088—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots characterized by the autonomous decision making process, e.g. artificial intelligence, predefined behaviours
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
- G01C21/203—Specially adapted for sailing ships
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Automation & Control Theory (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Aviation & Aerospace Engineering (AREA)
- Business, Economics & Management (AREA)
- Artificial Intelligence (AREA)
- Evolutionary Computation (AREA)
- Game Theory and Decision Science (AREA)
- Medical Informatics (AREA)
- Health & Medical Sciences (AREA)
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
The invention provides a method for planning a hierarchical fuzzy-artificial potential field path, which comprises the following steps: s1, modeling an environment; s2, executing an improved elite genetic algorithm, and planning a global path of the unmanned ship; s3, executing a fuzzy-artificial potential field algorithm with fuzzy decision, and planning a local path of the unmanned ship; and S4, inserting a virtual return point on the global path of the unmanned ship, and fusing the global path of the unmanned ship and the local path of the unmanned ship. The method combines elite reservation, diversity increment, self-adaptive mutation probability and self-adaptive genetic algorithm to generate the optimal sparse path point and smooth the path. In order to completely adapt to unpredictable environments, a fuzzy-artificial potential field algorithm with fuzzy decision is developed, and an unmanned ship is prevented from being trapped in singular points. And inserting a virtual return point on the global path to enable the global path and the local path to be perfectly fused. The method has higher safety and flexibility, and the unmanned ship can safely and quickly complete the optimal path planning.
Description
Technical Field
The invention relates to the technical field of unmanned ships, in particular to a hierarchical fuzzy-artificial potential field path planning method.
Background
The development of oceans is becoming important today where land resources are becoming scarce. The unmanned surface vehicle is important equipment for performing surface operation and is very important for ocean resource development. Path planning for unmanned ships can be divided into global planning and local planning, wherein algorithms commonly used for global planning include grid map-based algorithms such as a-x algorithm, dijkstra algorithm, etc., but the above algorithms are easy to generate paths which are not practical. Intelligent search algorithms, such as: genetic algorithms, ant colony algorithms, particle swarm algorithms, and the like. And according to the inspiration of the nature, obtaining an unobstructed path through continuous iterative computation. For a complex marine environment, a local planning algorithm is used for dynamic obstacle avoidance and is an extremely important part for path planning, and common local path planning algorithms include an artificial potential field method, a digital-to-analog algorithm, a dynamic window method and the like. The artificial potential field method is a local path planning algorithm widely applied at present due to simple mathematical model and small calculated amount, but the algorithm is easy to enter a local minimum point. The D algorithm is too computationally inefficient and also belongs to a heuristic algorithm, which easily produces paths that are not practically feasible. The curvature of the path generated by the dynamic window method is changed all the time, and the energy consumption of the unmanned ship is increased.
Disclosure of Invention
In accordance with the technical problem set forth above, a method for hierarchical fuzzy-artificial potential field path planning is provided. The technical means adopted by the invention are as follows:
a method of hierarchical fuzzy-artificial potential field path planning, comprising the steps of:
s1, modeling an environment;
s2, executing an improved elite genetic algorithm, and planning a global path of the unmanned ship;
s3, executing a fuzzy-artificial potential field algorithm with fuzzy decision, and planning a local path of the unmanned ship;
and S4, inserting a virtual return point on the global path of the unmanned ship, and fusing the global path of the unmanned ship and the local path of the unmanned ship.
Further, the step S1 of modeling an environment, that is, modeling a detection area of the unmanned ship, and detecting a position of the obstacle by defining the detection area of the unmanned ship, so as to enable a path of the unmanned ship to be far away from the obstacle; specifically, the method comprises the following steps:
s11, defining a detection area of the unmanned ship, and as follows:
wherein d is s Radius of detection, p, for unmanned ships b ＝[x b ,y b ] T Is the position of the unmanned ship, p (t) = [ x, y =] T The position of the monitored point in the environment; x is a radical of a fluorine atom b ,y b Respectively representing the horizontal coordinate and the vertical coordinate of the current unmanned ship, and x and y respectively representing the horizontal coordinate and the vertical coordinate of a detected point;
s12, setting a navigation area:
wherein it is present>
Is a feasible region>
Is an infeasible area; />
Is a detection area of an unmanned ship>
Is a navigation area;
s13, acquiring a starting point p in the set navigation area S ＝[x s ,y s ] T To the end point p E ＝[x E ,y E ] T A collision-free path of (a); x is a radical of a fluorine atom S ,y S Respectively representing the abscissa and ordinate of the origin, x E ,y E Respectively represent the horizontal and vertical coordinates;
s14, distinguishing the no-pass area and the free-run area by using a mode of carrying out grid binarization on the original color map by using a formula h (p) =0.5R (p) +0.5G (p) +0B (p), and obtaining a corresponding binarization map
Wherein R (p), G (p) and B (p) are red, green and blue three-color values corresponding to the p points respectively, H (p) is the average value of the gray values in the surrounding 10 pixels, and G (p) s ) =0 denotes that the area is a feasible area, g (p) s ) =255 represents that the area is an infeasible area; finally obtaining feasible area
And an impracticable area->
Further, an improved artificial potential field algorithm is executed in the step S2, and the method for planning the global path of the unmanned ship includes the following sub-steps:
s21, calculating the self-adaptive degree of the individual;
s22, simplifying the complexity of global path planning through a genetic algorithm by adopting a coding mode of a decimal system;
s23, performing elite reservation operation;
s24, executing diversified incremental operation;
and S25, performing selection, crossing and adaptive mutation operations.
Further, the method for calculating the fitness of the individual in step S21 includes:
adopting a fitness function containing a B spline, wherein the fitness function is designed as follows:
wherein l, Δ are constants and Δ > 0;
is the control point of the basis function in the B-spline, <' > is>
Is the nth waypoint in the ith iteration;
L p is the path length:
l p is the closest distance between a certain path point and the obstacle, l p Expressed by euclidean distance as:
wherein the content of the first and second substances,
is the distance waypoint->
The nearest obstacle position of; />
Respectively showing the abscissa and ordinate of the nth barrier; />
Wherein the content of the first and second substances,
represents a positive integer set, and>
representing the set of path points in the ith iteration, p d,i (u)＝[x(u),y(u)] T ,/>
Represents a set of real numbers, and->
Vector of nodes
Cutting the raw materials into pieces; />
Denotes the Nth w + k +1 nodes, Ω θ Is a non-decreasing node sequence; n is a radical of i,k (u) is a B-spline basis function of order i k defined by the Boor-Cox recursive function, expressed as follows:
wherein the content of the first and second substances,
represents a sequence of nodes that is not decremented and->
Further, the method for performing the elite reservation operation in step S23 includes:
calculating the fitness of all individuals according to a path length formula, wherein the fitness is more than 0 and less than P e :＝n e /N p Elite retention < 1, all subjects were assignedAnd sorting according to fitness and preserving elite. Wherein, P e Represents the elite retention, n e Indicates the number of elite units retained, N p Representing the total number of individuals.
Further, the method for performing diversified increment operations in step S24 includes:
by adopting a formula of 0 < P d :＝n d /N p (ii) a diversified increment ratio from feasible region of < 1 >
In random generation of n d ·N w Orderly combination of candidate waypoints as n d An individual, wherein P d Denotes the diversity increment ratio, n d Indicating an increased number of individuals.
Further, the method for performing selection, crossover, and adaptive mutation operations in step S25 includes:
s251, performing a selection operation, i.e.
Individuals with high fitness values are reserved in a wheel probability selection mode, and the individuals with high fitness values have higher selection probability to enter the next generation, so that the probability that the ith individual in the population is selected is as follows:
wherein, epsilon (p) d,i ) Calculating according to a formula of a fitness function;
s252, performing a crossover operation, i.e.
The process of gene recombination, i.e. generating new chromosome, of chromosome between different individuals is expressed by the following crossover operations:
a qj ＝a qj (1-b)a lj b
a lj ＝a lj (1-b)a kj b
wherein, a qj ,a lj Values representing the jth gene in the qth and the ith chromosome, respectively; b is from [0,1 ∈ [ ]]The random number of (2);
s253, performing adaptive mutation operation, namely
And (3) adopting an adaptive mutation operation to determine the mutation probability of the individual through the adaptive value of the individual:
wherein, P m,max And P m,min Respectively representing the maximum and minimum mutation probabilities of the individuals; epsilon (p) d,max ) And ε (p) d,avg ) The maximum and mean fitness values in the population are indicated separately.
Further, the fuzzy-artificial potential field algorithm with fuzzy decision executed in the step S3 has a function expression as follows:
where ζ is a self-correcting blurring factor, ρ 0 The maximum radius of the acting range of the repulsive force field of the obstacle; wherein, the repulsion force correction coefficient is adopted, the repulsion force of the obstacle to the unmanned ship is gradually reduced along with the action of two components of the repulsion force, the attraction force of the target point to the unmanned ship is gradually increased, and the lambda belongs to (0,1), k r And k a Is the thrust and attraction coefficients, ρ λ (p x ,p E ) The power of λ, ρ (p), representing the distance of the USV to the target point b ,p E )ρ(p b ,p obs ) The distances from the obstacle and the target point to the current position, respectively, are:
ρ(p x ,p * )＝||p x ,p * || 2
in order to ensure that the unmanned ship can safely complete local collision avoidance and quickly return to a preset global course, the following three aspects are analyzed:
1) When the obstacle is not on the global path
When the unmanned ship is in the action range of the repulsive force field of the obstacle, the corrected repulsive force field is respectively opposite to rho (p) x ,p obs ) And ρ λ (p x ,p E ) Derivation to obtain two components of the correction repulsion
And &>
The expression form is as follows:
wherein ρ (p) x ,p obs ) Distance of obstacle to USV, ρ (p) x ,p E ) Is the distance of the target point to the USV, vector component
In a direction in which the obstacle points towards the unmanned ship, with a vector component->
The direction of the unmanned ship is the motion direction of the unmanned ship and the safety area d s The tangential direction of (a);
the gravitational component is the negative gradient of its potential field, expressed as follows:
from this, the resultant force F h Is a repulsive force
And the gravitational force F a The sum of (1):
2) When the obstacle is on the global path
By component of repulsive force
And the repulsive force component->
By changing the resultant force F of the force applied by the potential field h The USV can successfully bypass the barrier to complete local path planning, the distance between the USV and the barrier is gradually reduced at the moment, the self-correcting fuzzy factor zeta is increased, the repulsive force of the barrier is increased, and the navigation safety of the USV is ensured.
3) Fast return to global path after collision avoidance
Safety range d when unmanned ship s When no obstacle is detected in the unmanned ship, the dynamic collision avoidance is proved to be completed, at the moment, the potential field of the obstacle and a target point is closed, a course decision angle gamma is introduced, and the unmanned ship is enabled to quickly return to a preset global path by setting attraction points Q and K, specifically:
making a ray with an included angle gamma from the current position of the unmanned ship to a global path, intersecting the global path at a point Q, taking a point K on the global path at a distance eta in front of the Q, and introducing a gravitational potential field function at the point Q and the point K respectively, wherein the gravitational potential field function is defined as:
in the formula, k a Processing the negative gradient of the gravitational field to obtain gravitational force F for the gravitational potential field gain factor psi ∈ { Q, K }, and obtaining the gravitational force t (Ψ) is:
since the attraction force is proportional to the distance between the USV and the reference point Ψ, it is possible to ensure that the USV can safely and smoothly return to the global path, since the distance between the USV and the point K is always greater than the point Q, and further, the direction of the attraction force is always biased toward the point K and directed toward the global path, so that the USV can pass through a certain point between the point Q and the point K, so that the return angle can be restricted to conform to the motion characteristics of the USV.
Compared with the prior art, the invention has the following advantages:
1. according to the method for planning the hierarchical fuzzy-artificial potential field path, the path length and the safety can be considered in the global path planning.
2. According to the method for planning the hierarchical fuzzy-artificial potential field path, provided by the invention, the fuzzy coefficient is adopted for local planning, the situation that the target cannot be reached is avoided, and the collision avoidance performance is optimized.
3. The method for planning the hierarchical fuzzy-artificial potential field path provided by the invention adopts a smoother path to return to the global path, and avoids generating an overlarge course angle.
4. The method for planning the hierarchical fuzzy-artificial potential field path can better cope with complex and changeable marine environments, and improves the capability of real-time risk avoidance of the unmanned ship.
For the above reasons, the present invention can be widely applied to the field of unmanned ships and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic view of the detection range of the unmanned ship provided by the embodiment of the invention.
Fig. 3 is a schematic diagram of coefficient distribution of basis functions provided in an embodiment of the present invention.
FIG. 4 is a schematic diagram of a genetic algorithm encoding method provided in an embodiment of the present invention.
Fig. 5 is an overall framework of an adaptive genetic algorithm provided in an embodiment of the present invention.
FIG. 6 is a schematic diagram of a chromosome crossing process provided by an embodiment of the present invention.
Fig. 7 is a schematic view of a vector direction of the correction force provided by the embodiment of the invention.
Fig. 8 is a schematic diagram illustrating a repulsive force function introduced into a moving direction of the unmanned ship according to an embodiment of the present invention.
Fig. 9 is a schematic diagram of an obstacle not in a global path according to an embodiment of the present invention.
Fig. 10 is a schematic diagram of a global path of an obstacle according to an embodiment of the present invention.
Fig. 11 is a schematic diagram of a fast return global path of the unmanned ship according to the embodiment of the present invention.
Fig. 12 is a real world chart according to an embodiment of the present invention.
Fig. 13 is a binarized chart according to an embodiment of the present invention.
Fig. 14 is a comparison chart of the AGA and other global path planning algorithms according to the embodiment of the present invention.
Fig. 15 is a fitness curve of AGA in two environments according to an embodiment of the present invention.
Fig. 16 is a schematic diagram illustrating a comparison of mixing paths according to an embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, 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.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in other sequences than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention provides a method for planning a hierarchical fuzzy-artificial potential field path, which comprises the following steps: s1, modeling an environment; s2, executing an improved elite genetic algorithm, and planning a global path of the unmanned ship; s3, executing a fuzzy-artificial potential field algorithm with fuzzy decision, and planning a local path of the unmanned ship; and S4, inserting a virtual return point on the global path of the unmanned ship, and fusing the global path of the unmanned ship and the local path of the unmanned ship. The method combines elite reservation, diversity increment, self-adaptive mutation probability and self-adaptive genetic algorithm to generate the optimal sparse path points and smooth the path. In order to completely adapt to unpredictable environments, an innovative fuzzy-artificial potential field algorithm with fuzzy decision is developed, and the situation that the unmanned ship is trapped in singular points is avoided. And inserting a virtual return point on the global path to enable the global path and the local path to be perfectly fused. The designed path planning method has higher safety and flexibility, so that the unmanned ship can safely and quickly complete the optimal path planning.
The embodiments of the present invention will be described in detail with reference to the accompanying drawings.
A method of hierarchical fuzzy-artificial potential field path planning, as shown in fig. 1, comprising the steps of:
s1, modeling an environment;
s2, executing an improved elite genetic algorithm, and planning a global path of the unmanned ship;
s3, executing a fuzzy-artificial potential field algorithm with fuzzy decision, and planning a local path of the unmanned ship;
and S4, inserting a virtual return point on the global path of the unmanned ship, and fusing the global path of the unmanned ship and the local path of the unmanned ship.
The step S1 of environment modeling, namely modeling a detection area of the unmanned ship, and detecting the position of an obstacle by defining the detection area of the unmanned ship so as to enable the path of the unmanned ship to be far away from the obstacle; specifically, the method comprises the following steps:
s11, as shown in FIG. 2, defining a detection area of the unmanned ship as follows:
wherein, d s Radius of detection, p, for unmanned vessels b ＝[x b ,y b ] T Is the position of the unmanned ship, p (t) = [ x, y =] T The position of the monitored point in the environment; x is the number of b ,y b Respectively representing the horizontal coordinate and the vertical coordinate of the current unmanned ship, and x and y respectively representing the horizontal coordinate and the vertical coordinate of a detected point;
s12, setting a navigation area:
wherein it is present>
Is a feasible region>
Is an infeasible area;/>
is a detection area of an unmanned ship>
Is a navigation area;
s13, acquiring a starting point p in the set navigation area S ＝[x S ,y S ] T To the end point p E ＝[x E ,y E ] T A collision-free path of (a); x is the number of S ,y S Respectively representing the abscissa and ordinate of the origin, x E ,y E Respectively represent the horizontal and vertical coordinates;
s14, distinguishing the no-pass area and the free-run area by using a mode of carrying out grid binarization on the original color map by using a formula h (p) =0.5R (p) +0.5G (p) +0B (p), and obtaining a corresponding binarization map
Wherein, R (p), G (p) and B (p) are the red, green and blue three-color values corresponding to the p points respectively, H (p) is the average value of the gray values in the surrounding 10 pixels, G (p) s ) =0 denotes that the area is a feasible area, g (p) s ) =255 represents that the area is an infeasible area; finally obtaining feasible area
And an impracticable area->
In the step S2, an improved artificial potential field algorithm is executed, and the method for planning the global path of the unmanned ship comprises the following sub-steps:
s21, calculating the self-adaptive degree of the individual;
s22, simplifying the complexity of global path planning through a genetic algorithm by adopting a decimal coding mode; the specific encoding scheme is shown in FIG. 4, where φ * ，*∈{1,2，...，N W The ordinal number is the sequential route point serial number in the navigation area;
s23, performing elite reservation operation;
s24, executing diversified incremental operation;
and S25, performing selection, crossing and adaptive mutation operations.
Specifically, the method for calculating the fitness of the individual in step S21 includes:
and adopting a fitness function containing a B spline to ensure that the final smooth global path is safe. The fitness function is designed as:
wherein l, Δ are constants and Δ > 0;
are the control points of the basis functions in the B-spline,
is the nth waypoint in the ith iteration;
L p is the path length:
l p is the closest distance between a certain waypoint and the obstacle,/ p Expressed by euclidean distance as:
wherein the content of the first and second substances,
is the distance waypoint->
The nearest obstacle position of; />
Respectively representing the abscissa and the ordinate of the nth obstacle;
wherein the content of the first and second substances,
represents a positive integer set, and>
representing the set of path points in the ith iteration, p d,i (u)＝[x(u),y(u)] T ,/>
Represents a set of real numbers, and->
By node vector
Cutting the raw materials into pieces; />
Denotes the Nth w + k +1 nodes, Ω θ Is a non-decreasing node sequence; as shown in FIG. 3, N i,k (u) is a B-spline basis function of order i k defined by the Boor-Cox recursive function, expressed as follows:
wherein, the first and the second end of the pipe are connected with each other,
represents a sequence of nodes that is not decremented and->
Specifically, the method for executing the elite reservation operation in step S23 includes:
the whole genetic algorithm process is shown in FIG. 5, and when the retention operation is performed, fitness calculation is performed on all individuals through a path length formula, and the fitness is calculated according to the condition that 0 is less than P e :＝n e /N p And (3) the elite retention rate is less than 1, and all individuals are sorted according to the fitness and subjected to elite retention. Wherein, P e Represents the elite retention, n e Indicates the number of Elite individuals retained, N p Representing the total number of individuals.
Specifically, the method for performing diversified increment operations in step S24 includes:
in order to avoid the premature genetic algorithm and enable the algorithm to have certain exploration capacity, P is more than 0 d :＝n d /N p (ii) a diversified increment ratio from feasible region of < 1 >
In random generation of n d N w Orderly combination of candidate waypoints as n d And (4) individuals. Wherein, P d Denotes the diversity increment ratio, n d Indicating an increased number of individuals.
Specifically, the method for performing the selecting, crossing and adaptive mutation operations in step S25 includes:
s251, perform selection operation, i.e.
The selection operation is similar to the operation retention operation, individuals with high fitness values are retained in a roulette probability selection mode, and the individuals with high fitness values have higher selection probability to enter the next generation, so that the probability that the ith individual in the population is selected is as follows:
wherein, epsilon (p) d,i ) Calculating according to a formula of a fitness function;
s252, performing a crossover operation, i.e.
As shown in fig. 6, the process of gene recombination, i.e. generating new chromosome, between different individuals is represented by the following crossover operations:
a qj ＝a qj (1-b)a lj b
a lj ＝a lj (1-b)a kj b
wherein, a qj ,a lj Values representing the jth gene in the qth and the ith chromosome, respectively; b is from [0,1 ∈ [ ]]The random number of (2);
s253, performing adaptive mutation operation, namely
In order to further enhance the diversity of the population and to obtain a better pathway in the population, the individual may be subjected to genetic mutation, i.e., mutation manipulation. In addition, in order to ensure that excellent individuals are not destroyed by the operation, an adaptive mutation operation is adopted, and the mutation probability of an individual is determined by an adaptive value of the individual:
wherein, P m,max And P m,min Respectively representing the maximum mutation probability and the minimum mutation probability of the individual; epsilon (p) d,max ) And epsilon (p) d,avg ) The maximum and mean fitness values in the population are indicated separately.
The fuzzy-artificial potential field algorithm with fuzzy decision-making executed in the step S3 comprises a completely new repulsion function, and precise collision avoidance is completed through a fuzzy control algorithm, so that the unmanned ship can smoothly avoid unknown obstacles, and the function expression of the algorithm is as follows:
ζ is a self-correcting fuzzy factor, and specific values are shown in table 1:
the limiting conditions are as follows: OB * E { F, L, R, U }: relative positions of the obstacles to the USV, including front, left, right, and rear; d * E ∈ {1,2,3}: distance of obstacle from USV, d s Is the detection range of the unmanned ship, and when the distance of the obstacle is 0-0.5 d s Time corresponding to d 1 When the distance of the obstacle is 0.5-0.75 d s Time is corresponding to d 2 When the distance between the obstacles is 0.75-1.0 d s Time corresponding to d 3 (ii) a O, Y and Z are unmanned ship courses and respectively correspond to the straight linesThe values of zeta include 1.4, 1.2, 1.0, 0.8, 0.6, 0.4 and 0.2; rho 0 The maximum radius of the acting range of the repulsive force field of the obstacle; wherein, the repulsion force correction coefficient is adopted, the repulsion force of the obstacle to the unmanned ship is gradually reduced along with the action of two components of the repulsion force, the attraction force of the target point to the unmanned ship is gradually increased, and the lambda belongs to (0,1), k r And k a Is the thrust and attraction coefficients, ρ λ (p x ,p E ) The power of λ, ρ (p), representing the distance of the USV to the target point b ,p E )ρ(p b ,p obs ) The distances from the obstacle and the target point to the current position, respectively, are:
ρ(p x ,p * )＝||p x ,p * || 2
where ρ (p) x ,p obs ) The potential field direction of the barrier is that the barrier points to the unmanned ship. ρ (p) x ,p E ) Potential field of
The direction is as shown in fig. 7, that is, when the unmanned ship detects an obstacle, the unmanned ship is used as a starting point, a tangent line is made to the circular collision area of the obstacle, and a deviation angle beta smaller than the moving direction angle at the moment of the unmanned ship is formed 2 Direction is taken as rho (p) x ,p E ) The vector direction of (2). As shown in fig. 8, when the obstacle approaches the USV, or when the angle α between the obstacle and the direction of movement of the USV is small, the repelling effect of the obstacle should be increased appropriately.
In order to ensure that the unmanned ship can safely complete local collision avoidance and quickly return to a preset global course, the following three aspects are analyzed:
1) When the obstacle is not on the global path
When the unmanned ship is in the action range of the repulsive force field of the obstacle, the corrected repulsive force field is respectively opposite to rho (p) x ,p obs ) And ρ λ (p x ,p E ) Derivation to obtain two components of the correction repulsion
And &>
The expression form is as follows:
where ρ (p) x ,p obs ) Distance of obstacle to USV, ρ (p) x ,p E ) Is the distance from the target point to the USV, the specific direction is shown in FIG. 9, the vector component
In a direction in which the obstacle points toward the unmanned ship, the vector component &>
The direction of the unmanned ship is the motion direction of the unmanned ship and the safety area d s The tangential direction of (a);
the gravitational component is the negative gradient of its potential field, expressed as follows:
from this, the resultant force F h Is a repulsive force
And the gravitational force F a The sum of (1):
2) When the obstacle is on the global path
As shown in fig. 10, by the repulsive force component
And the repulsive force component->
By changing the resultant force F of the force applied by the potential field h The USV can successfully bypass the barrier to complete local path planning, and the problem that a target point in the traditional APF is inaccessible is solved. At the moment, the distance between the USV and the obstacle is gradually reduced, the self-correcting fuzzy factor zeta is increased, the repulsive force of the obstacle is increased, and the navigation safety of the USV is guaranteed.
3) Fast return to global path after collision avoidance
When unmanned ship safety range d s When no obstacle is detected in the unmanned ship, the dynamic collision avoidance is proved to be completed, at the moment, the potential field of the obstacle and a target point is closed, a course decision angle gamma is introduced, and the unmanned ship is enabled to quickly return to a preset global path by setting attraction points Q and K, specifically:
as shown in fig. 11, a ray with an included angle γ is made from the current position of the unmanned ship to the global path, the global path is intersected at a point Q, a point K is taken on the global path at a distance η in front of Q, and at this time, a gravitational potential field function is introduced at the point Q and the point K, which are defined as:
in the formula, k a Processing the negative gradient of the gravitational field to obtain the gravitational force F for the gravitational potential field gain factor psi ∈ { Q, K }, and obtaining the gravitational force F t (Ψ) is:
since the attractive force is proportional to the distance between the USV and the reference point Ψ, it is possible to ensure that the USV can safely and smoothly return to the global path, and since the distance between the USV and the point K is always greater than the point Q, and further, the direction of the attractive force is always biased toward the point K and directed toward the global path, the USV can pass through a point between the point Q and the point K, so that the return angle can be restricted from conforming to the movement characteristics of the USV.
Simulation example:
to demonstrate the effectiveness and superiority of the proposed hybrid path planning scheme, local and hybrid path planning simulations were performed in two real geographic areas, rubble gate and Zhou Gongdao, hong kong, china, with map preprocessing as shown in fig. 12-13. The simulation was performed in MATLAB R2018a simulation environment, with the simulation parameters shown in table 2:
example 1: global path
The AGA algorithm generates a continuous path from a starting point to an end point, and the continuous path is compared with a path generated after B spline interpolation fitting is carried out on discrete waypoints generated by the particle swarm optimization algorithm and the ant colony optimization algorithm respectively. As can be seen from table 2 and fig. 14, in the red stoneway environment, the length of the path obtained by using the AGA algorithm is similar to that of the PSO, but the path obtained by the PSO is closer to the obstacle, so that the navigation safety cannot be ensured. For the path generated by the ACO, too many waypoints are generated, so that the path finally obtained by the B-spline has too many inflection points, which does not conform to the motion characteristics of the USV. In the mondsand environment, the AGA algorithm is ideal in terms of both path length and path security. In addition, the adaptive genetic algorithm proposed by the patent is least time-consuming in terms of convergence speed and path length, and it can be seen in fig. 15 that 12 iterations or so converge in both environments. While the diversification of increments can cause small fluctuations, this is only a normal exploration of the environment. In summary, the proposed AGA path length is not necessarily the shortest, but can guarantee security.
Example 2: hybrid algorithm
Compared with the DWA algorithm, the proposed IAPF algorithm has enough safety performance in dealing with static obstacles that are not on the global path, although the IAPF algorithm has a slight difference in obstacle distance compared with the DWA. As shown in fig. 16 (a), a static obstacle exists in the global path, and both the IAPF algorithm and the DWA algorithm operate in the same and timely manner while avoiding the obstacle, but when returning to the global path, the DWA algorithm returns to the original path more quickly, and a large turning angle occurs, which is not in accordance with the unmanned ship motion characteristics. The proposed IAPF algorithm, though returning to the global path at a small angle by growing the local path, ensures that the USV path is smooth, avoiding large angle turns. The flight trajectories of the IAPF and DWA algorithms under dynamic obstacles are shown in fig. 16 (b). When a dynamic obstacle is encountered, the IAPF algorithm selects to sail downwards when the obstacle does not reach the global path, and when the obstacle reaches the global path and continues to move forwards, the IAPF algorithm selects to control the USV to detour from the rear of the dynamic obstacle. But the DWA still chooses to pass ahead of dynamic obstacles, with a longer trajectory than IAPF, increasing the risk of collision with the obstacle.
The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
In the above embodiments of the present invention, the description of each embodiment has its own emphasis, and reference may be made to the related description of other embodiments for parts that are not described in detail in a certain embodiment.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (2)
1. A method for hierarchical fuzzy-artificial potential field path planning is characterized by comprising the following steps:
s1, modeling an environment;
s2, executing an improved elite genetic algorithm, and planning a global path of the unmanned ship; in the step S2, an improved elite genetic algorithm is executed, and the method for planning the global path of the unmanned ship includes the following substeps:
s21, calculating the self-adaptive degree of the individual; the method for calculating the fitness of the individual in the step S21 includes:
adopting a fitness function containing B splines, wherein the fitness function is designed as follows:
wherein l, Δ are constants and Δ > 0;
is the control point of the basis function in the B-spline, <' > is>
Is the nth waypoint in the ith iteration;
L p is the path length:
l p is the closest distance between a certain path point and the obstacle, l p Expressed by euclidean distance as:
wherein the content of the first and second substances,
is the distance waypoint->
The nearest obstacle position of; />
Respectively showing the abscissa and ordinate of the nth barrier;
wherein the content of the first and second substances,
represents a positive integer set, and>
representing the set of path points in the ith iteration, p d,i (u)＝[x(u),y(u)] T ,/>
Represents a set of real numbers, and->
Vector of nodes
Cutting the raw materials into pieces; />
Denotes the Nth w + k +1 nodes, Ω θ Is a non-decreasing node sequence; n is a radical of i,k (u) is a B-spline basis function of order i k defined by the Boor-Cox recursive function, whose expressionThe following were used:
wherein the content of the first and second substances,
represents a sequence of nodes that is not decremented and->
S22, simplifying the complexity of global path planning through a genetic algorithm by adopting a coding mode of a decimal system;
s23, performing elite reservation operation; the method for performing the elite reservation operation in the step S23 includes:
calculating the fitness of all individuals according to a path length formula, wherein the fitness is more than 0 and less than P e :＝n e /N p (ii) an elite retention rate of < 1, sorting all individuals according to fitness and performing elite retention, wherein P is e Representing the elite retention, n e Indicates the number of Elite individuals retained, N p Represents the total number of individuals;
s24, executing diversified incremental operation; the method for performing diversified increment operations in the step S24 includes:
taking a value of 0 < P d :＝n d /N p A diversification increment ratio of < 1 from feasible region
In random generation of n d ·N w Orderly combination of candidate waypoints as n d An individual, wherein P d Denotes the diversity increment ratio, n d Represents an increased number of individuals;
s25, selecting, crossing and self-adapting mutation operations are executed; the method for performing the selection, crossover, and adaptive mutation operations in step S25 includes:
s251, perform selection operation, i.e.
Individuals with high fitness values are reserved in a wheel probability selection mode, and the individuals with high fitness values have higher selection probability to enter the next generation, so that the probability that the ith individual in the population is selected is as follows:
wherein, epsilon (p) d,i ) Calculating according to a formula of a fitness function;
s252, performing a crossover operation, i.e.
The process of gene recombination, i.e. generating new chromosome, of chromosome between different individuals is expressed by the following crossover operations:
a qj ＝a qj (1-b)a lj b
a lj ＝a lj (1-b)a kj b
wherein, a qj ,a lj Values representing the jth gene in the qth and the ith chromosome, respectively; b is E [0,1]The random number of (2);
s253, performing adaptive mutation operation, namely
And (3) adopting an adaptive mutation operation to determine the mutation probability of the individual through the adaptive value of the individual:
wherein, P m,max And P m,min Representing individual maximum and minimum, respectivelyThe mutation probability; epsilon (p) d,max ) And ε (p) d,avg ) Respectively representing the maximum and average fitness values in the population;
s3, executing a fuzzy-artificial potential field algorithm with fuzzy decision, and planning a local path of the unmanned ship; the function expression of the fuzzy-artificial potential field algorithm with fuzzy decision-making executed in the step S3 is as follows:
where ζ is a self-correcting blurring factor, ρ 0 The maximum radius of the acting range of the repulsive force field of the obstacle; wherein the repulsive force correction coefficient is the repulsive force correction coefficient, the repulsive force of the obstacle to the unmanned ship is gradually reduced along with the action of two components of the repulsive force, and the attractive force of the target point to the unmanned ship is gradually increased, so that lambda belongs to (0,1), k r And k a Is the coefficient of thrust and gravity, ρ λ (p x ,p E ) The power of λ, ρ (p), representing the distance of the USV to the target point b ,p E ) And ρ (p) b ,p obs ) The distances from the obstacle and the target point to the current position, respectively, are:
ρ(p x ,p * )＝||p x ,p * || 2
in order to ensure that the unmanned ship can safely complete local collision avoidance and quickly return to a preset global course, the following three aspects are analyzed:
1) When the obstacle is not on the global path
When the unmanned ship is in the action range of the repulsive force field of the obstacle, the corrected repulsive force field is respectively opposite to rho (p) x ,p obs ) And ρ λ (p x ,p E ) Derivation to obtain two components of the corrected repulsive force
And &>
The expression form is as follows:
where ρ (p) x ,p obs ) Distance of obstacle to USV, ρ (p) x ,p E ) Is the distance of the target point to the USV, vector component
In a direction in which the obstacle points toward the unmanned ship, the vector component &>
The direction of the unmanned ship is the motion direction of the unmanned ship and the safety area d s The tangential direction of (a);
the gravitational component is the negative gradient of its potential field, expressed as follows:
from this, the resultant force F h Is a repulsive force
And the gravitational force F a The sum of (1):
2) When the obstacle is on the global path
By component of repulsive force
And a repulsive force component>
By modifying the resultant force F of the force of the potential field h The USV can successfully bypass the barrier to complete local path planning, the distance between the USV and the barrier is gradually reduced, the self-correcting fuzzy factor zeta is increased, the repulsive force of the barrier is increased, and the navigation safety of the USV is ensured;
3) Fast return to global path after collision avoidance
When unmanned ship safety range d s When no obstacle is detected in the unmanned ship, the dynamic collision avoidance is proved to be completed, at the moment, the potential field of the obstacle and a target point is closed, a course decision angle gamma is introduced, and the unmanned ship is enabled to quickly return to a preset global path by setting attraction points Q and K, specifically:
making a ray with an included angle gamma from the current position of the unmanned ship to a global path, intersecting the global path at a point Q, taking a point K on the global path at a distance eta in front of the Q, and introducing a gravitational potential field function at the point Q and the point K respectively, wherein the gravitational potential field function is defined as:
in the formula, k a Processing the negative gradient of the gravitational field to obtain the gravitational force F for the gravitational potential field gain factor psi ∈ { Q, K }, and obtaining the gravitational force F t (Ψ) is:
because the attraction is in direct proportion to the distance between the USV and the reference point psi, the USV can be ensured to safely and smoothly return to the global path, and because the distance between the USV and the point K is always larger than the point Q, and in addition, the direction of the attraction is always deviated to the point K and points to the global path, the USV can pass through a certain point between the point Q and the point K, so that the return angle can be limited to accord with the motion characteristic of the USV;
and S4, inserting a virtual return point on the global path of the unmanned ship, and fusing the global path of the unmanned ship and the local path of the unmanned ship.
2. The method for hierarchical fuzzy-artificial potential field path planning according to claim 1, wherein said step S1 of environmental modeling, namely modeling the detection area of the unmanned ship, detecting the position of the obstacle by defining the detection area of the unmanned ship, and keeping the path of the unmanned ship away from the obstacle; specifically, the method comprises the following steps:
s11, defining a detection area of the unmanned ship, and as follows:
wherein d is s Radius of detection, p, for unmanned ships b ＝[x b ,y b ] T Is the position of the unmanned ship, p (t) = [ x, y =] T The position of the detected point in the environment; x is the number of b ,y b Respectively representing the horizontal coordinate and the vertical coordinate of the current unmanned ship, and x and y respectively representing the horizontal coordinate and the vertical coordinate of a detected point;
s12, setting a navigation area:
wherein it is present>
Is a feasible region>
Is an infeasible area;
is a detection area of an unmanned ship>
Is a navigation area;
s13, acquiring a starting point p in the set navigation area S ＝[x s ,y s ] T To the end point p E ＝[x E ,y E ] T A collision-free path of (a); x is the number of S ,y S Respectively representing the abscissa and ordinate of the origin, x E ,y E Respectively represent a horizontal coordinate and a vertical coordinate;
s14, distinguishing the no-passing area and the free-running area by using a formula h (p) =0.5R (p) +0.5G (p) +0B (p) to carry out grid binarization on the original color map, and thus obtaining a corresponding binary map
Wherein R (p), G (p) and B (p) are red, green and blue three-color values corresponding to the p points respectively, H (p) is the average value of the gray values in the surrounding 10 pixels, and G (p) s ) =0 denotes that the area is a feasible area, g (p) s ) =255 represents that the area is an infeasible area; finally obtaining feasible area
And an impracticable area->
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010538510.XA CN111610788B (en) | 2020-06-13 | 2020-06-13 | Hierarchical fuzzy-artificial potential field path planning method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010538510.XA CN111610788B (en) | 2020-06-13 | 2020-06-13 | Hierarchical fuzzy-artificial potential field path planning method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111610788A CN111610788A (en) | 2020-09-01 |
| CN111610788B true CN111610788B (en) | 2023-04-18 |
Family
ID=72204287
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010538510.XA Active CN111610788B (en) | 2020-06-13 | 2020-06-13 | Hierarchical fuzzy-artificial potential field path planning method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111610788B (en) |
Families Citing this family (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112882058B (en) * | 2021-01-08 | 2022-09-20 | 中国石油大学(华东) | Shipborne laser radar obstacle detection method based on variable-size grid map |
| CN113110424A (en) * | 2021-03-26 | 2021-07-13 | 大连海事大学 | Unmanned ship collision avoidance method based on chart information |
| CN113830108B (en) * | 2021-11-10 | 2023-07-28 | 苏州挚途科技有限公司 | Decision-making planning method and device for automatic driving vehicle |
| CN114355909A (en) * | 2021-12-22 | 2022-04-15 | 的卢技术有限公司 | Path planning method and device, computer equipment and storage medium |
| CN115328122B (en) * | 2022-08-02 | 2023-03-14 | 柳州城市职业学院 | Unmanned ship obstacle avoidance method and system based on multi-radar sensing |
| CN117093005B (en) * | 2023-10-16 | 2024-01-30 | 华东交通大学 | Autonomous obstacle avoidance method for intelligent automobile |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107368076A (en) * | 2017-07-31 | 2017-11-21 | 中南大学 | Robot motion's pathdepth learns controlling planning method under a kind of intelligent environment |
| CN110362089A (en) * | 2019-08-02 | 2019-10-22 | 大连海事大学 | A method of the unmanned boat independent navigation based on deeply study and genetic algorithm |
| CN110442135A (en) * | 2019-08-06 | 2019-11-12 | 南京赛沃夫海洋科技有限公司 | A kind of unmanned boat paths planning method and system based on improved adaptive GA-IAGA |
| CN110703752A (en) * | 2019-10-15 | 2020-01-17 | 哈尔滨工程大学 | Unmanned ship double-layer path planning method based on immune heredity-artificial potential field method |
| CN110887484A (en) * | 2019-10-14 | 2020-03-17 | 重庆邮电大学 | Mobile robot path planning method based on improved genetic algorithm and storage medium |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9436187B2 (en) * | 2015-01-15 | 2016-09-06 | The United States Of America As Represented By The Secretary Of The Navy | System and method for decentralized, multi-agent unmanned vehicle navigation and formation control |
-
2020
- 2020-06-13 CN CN202010538510.XA patent/CN111610788B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107368076A (en) * | 2017-07-31 | 2017-11-21 | 中南大学 | Robot motion's pathdepth learns controlling planning method under a kind of intelligent environment |
| CN110362089A (en) * | 2019-08-02 | 2019-10-22 | 大连海事大学 | A method of the unmanned boat independent navigation based on deeply study and genetic algorithm |
| CN110442135A (en) * | 2019-08-06 | 2019-11-12 | 南京赛沃夫海洋科技有限公司 | A kind of unmanned boat paths planning method and system based on improved adaptive GA-IAGA |
| CN110887484A (en) * | 2019-10-14 | 2020-03-17 | 重庆邮电大学 | Mobile robot path planning method based on improved genetic algorithm and storage medium |
| CN110703752A (en) * | 2019-10-15 | 2020-01-17 | 哈尔滨工程大学 | Unmanned ship double-layer path planning method based on immune heredity-artificial potential field method |
Non-Patent Citations (1)
| Title |
|---|
| Ning Wang 等.Dynamics-Constrained Global-Local Hybrid Path Planning of an Autonomous Surface Vehicle.IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.2020,全文. * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111610788A (en) | 2020-09-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111610788B (en) | Hierarchical fuzzy-artificial potential field path planning method | |
| CN106444740B (en) | Unmanned plane two dimension path planning method based on MB-RRT | |
| CN112462803B (en) | Unmanned aerial vehicle path planning method based on improved NSGA-II | |
| CN105512769A (en) | Unmanned aerial vehicle route planning system and unmanned aerial vehicle route planning method based on genetic programming | |
| CN110470306B (en) | Multi-robot formation navigation method capable of guaranteeing connectivity constraint and based on deep reinforcement learning | |
| CN110196598A (en) | A kind of dynamic collision prevention method of unmanned boat | |
| Zhang et al. | Receding horizon control for multi-UAVs close formation control based on differential evolution | |
| CN109931943B (en) | Unmanned ship global path planning method and electronic equipment | |
| CN111307158B (en) | AUV three-dimensional route planning method | |
| CN108413963A (en) | Bar-type machine people's paths planning method based on self study ant group algorithm | |
| CN112099501B (en) | Unmanned ship path planning method based on potential field parameter optimization | |
| Wang et al. | A novel hybrid map based global path planning method | |
| Li et al. | An improved differential evolution based artificial fish swarm algorithm and its application to AGV path planning problems | |
| CN110320907B (en) | Double-layer collision avoidance method for unmanned surface vessel based on improved ant colony algorithm and elliptic collision cone deduction model | |
| Peng et al. | A new fuzzy adaptive simulated annealing genetic algorithm and its convergence analysis and convergence rate estimation | |
| Zeng et al. | Robotic global path-planning based modified genetic algorithm and A* algorithm | |
| Xiao-Ting et al. | Flight path planning based on an improved genetic algorithm | |
| Wang et al. | An improved NSGA-II algorithm for UAV path planning problems | |
| Yuhang et al. | An adaptive evolutionary multi-objective estimation of distribution algorithm and its application to multi-UAV path planning | |
| Brintaki et al. | Coordinated UAV path planning using differential evolution | |
| CN117434950A (en) | Mobile robot dynamic path planning method based on Harris eagle heuristic hybrid algorithm | |
| Garip et al. | Path planning for multiple mobile robots in static environment using hybrid algorithm | |
| Sun et al. | Optimal UAV flight path planning using skeletonization and particle swarm optimizer | |
| CN114740873B (en) | Path planning method of autonomous underwater robot based on multi-target improved particle swarm algorithm | |
| Gong et al. | A path planning method based on improved particle swarm optimization algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |