CN107525509B - Open water area sailing ship path planning method based on genetic algorithm - Google Patents
Open water area sailing ship path planning method based on genetic algorithm Download PDFInfo
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- 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
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Abstract
The invention relates to the field of modern triangular sailing boat intelligent control, and provides a novel sailing boat path planning method using a genetic algorithm in an open water area, so that automatic planning of a sailing boat path is realized, and a sailing boat path turning point list is finally generated. Converting the geographic coordinates into plane coordinates according to a coordinate conversion formula by using the electronic chart as a base chart to simplify the calculation process; calculating wind vector data of the whole wind field by an interpolation method, and visualizing the wind vector data into a wind field image; the sailing boat speed table is used as a calculation basis for sailing boat speed, and the boat wind is taken into consideration to calculate more accurate windward angle and apparent wind speed of the sailing boat; sequencing randomly generated turning points to improve the effectiveness of an initial population; calculating the time of sailing on each section of air route by adopting an integral method; finally, the coding, selecting, crossing and mutation processes of the genetic algorithm are modified to adapt to the problems to be solved by the invention.
Description
Technical Field
The invention relates to the field of intelligent control of modern triangular sailing ships, in particular to a sailing ship path planning method using a genetic algorithm in an open water area.
Background
Sailing boats are popular to more and more people as green and fashionable gentleman sports. Normally, the sailing path of the sailing ship is planned by the crew according to the received marine weather information. However, the wind field on the sea surface is variable and uneven, the optimal path cannot be obtained only by experience, and the long-distance sailing path cannot be completed by only once planning. Automatic path planning is a very critical step to achieve automatic driving of sailing ships. Since the power of the sailing boat comes from wind and has a non-sailing area of about 90 degrees, the route planning of the sailing boat becomes complicated, and multi-section dynamic planning is needed to keep the sailing boat on the optimal route all the time.
The previous research on sailing ship path planning mainly solves the problem that sailing ship competition is in navigation around a landmark and adopts a sectional and fuzzy comprehensive method. For example, relevant papers published by chenchen li, geyan and the like, "sailing ship sailing around-standard optimal path planning method", "sailing ship sailing around-standard path dynamic simulation based on a zoning optimization method", and "sailing ship driving optimal path planning method based on fuzzy comprehensive evaluation" have the following disadvantages: firstly, only the path planning during close-range sailing competition is solved, but the long-range sailing line planning of sailing ships in open water areas is not very suitable, and secondly, the sailing ships have ship wind during sailing, and the windward size and angle of the sailing ships can be changed due to the existence of the ship wind.
Disclosure of Invention
The method realizes automatic planning of the sailing ship path by using the sailing ship path planning method based on the genetic algorithm, and finally generates a sailing ship path turning point list. The technical scheme of the invention is explained by the following aspects:
first, in order to make the method and apparatus of the present invention more comprehensible, the related concepts and definitions are as follows:
1. the wind vector refers to wind data with both direction and magnitude.
2. The wind field refers to a sea surface space with uneven distribution of local wind speed and wind direction in a certain range, and can acquire detailed wind vector data.
3. Path planning, i.e. route planning, is the same meaning in this context.
4. The invention relates to a meteorological station, wherein the area related to the meteorological station is the sea surface, the meteorological station refers to a ship station, a marine meteorological buoy and other devices for acquiring meteorological data, and the devices for acquiring the meteorological data are replaced by a meteorological station.
5. The key position points refer to positions of a weather station, a starting point and an end point.
Secondly, the open water area sailing ship path planning method based on the genetic algorithm mainly comprises the following steps:
step one, preparing a sailing boat speed table (table 1) and a sailing boat speed chart, wherein each section of wind corresponds to one sailing boat speed table, the sailing boat speed table lists maximum speeds corresponding to different wind bulwarks, the sailing boat speed chart is a diagram of the sailing boat speed table, and the sailing boat speed tables with different wind levels can be drawn on one sailing boat speed chart.
TABLE 1 sailing boat speedometer (all data available)
| Wind side angle | Speed of |
| 0 | 0 |
| 1 | 0 |
| 2 | 0 |
| 3 | 0 |
| … | … |
| 45 | 0 |
| … | … |
| 90 | -45 |
| … | … |
| 180 | -90 |
| -180 | 90 |
| … | … |
| -90 | 45 |
| … | … |
| -45 | 0 |
| 0 | 0 |
And step two, preparing a chart of the water area to be navigated, wherein the chart of the larger navigation area is obtained by the projection of the mercator, has no angle deformation and has the characteristics of a straight line with an equiangular course, and the like, so the navigation map adopts the chart commonly used for navigation.
Inputting data of all weather stations in the navigation area, wherein coordinates and data of the weather stations are shown in the following table, and the table lists different weather station numbers and corresponding longitudes, latitudes, wind directions and wind speeds:
TABLE 2 weather station coordinates and wind vector data
| Weather station numbering | Longitude (G) | Latitude | Wind direction | Wind |
| 1 | α1 | β1 | ang1 | vol1 |
| 2 | α2 | β2 | ang2 | vol2 |
| … | … | … | … | … |
| k | αk | βk | angk | volk |
Inputting the positions of a navigation starting point and a navigation ending point, wherein the coordinates of the starting point and the ending point are shown in a table, and the longitude and the latitude of the starting point and the ending point are listed in the table:
TABLE 3 weather station coordinates and wind vector data
And step five, performing digital processing on the chart in the step two (the digital processing can be completed through auxiliary software such as Surfer, ArcGis, MapGis, lead adjustment and the like) to obtain the plane coordinates of key position points in the chart, as shown in table 4, and listing the geographical coordinates and the plane coordinates of the key position points in the chart. The geographic coordinates in the chart and the plane coordinates in the digital chart are converted into the following formulas:
(a,b)＝f(α,β)
wherein, the relationship among a, b, alpha and beta is as follows:
(α0，β0) Is the geographic coordinate of any point in the chart, (a)0，b0) The corresponding plane coordinates are obtained; that is, the ratio of the difference between the geographical longitude and the geographical latitude of any two points in the chart width range is equal to the ratio of the difference between the abscissa and the ordinate of the corresponding plane coordinate in the digitized chart.
Generally, the transverse amplitude and the longitudinal amplitude of a chart are not more than 1500 units, namely, the digitalized chart is not more than 225 ten thousand square units.
TABLE 4 Key location point coordinates within a navigation area
| Key location point | Longitude (G) | Latitude | Abscissa of the circle | Ordinate of the |
| Weather station | ||||
| 1 | α1 | β1 | a1 | b1 |
| Weather station 2 | α2 | β2 | a2 | b2 |
| … | … | … | … | … |
| Weather station k | αk | βk | ak | bk |
| Starting point | αm | βn | m | n |
| Terminal point | αr | βs | r | s |
Combining the collected data of each meteorological station and the corresponding coordinates of the meteorological stations to respectively generate a meteorological station wind direction matrix and a meteorological station wind speed matrix;
weather station wind direction matrix:
a weather station wind speed matrix:
and seventhly, respectively carrying out gridding processing on the wind direction matrix and the wind speed matrix of the meteorological station to obtain the wind direction matrix and the wind speed matrix of the whole wind field, and obtaining wind vector data of any point in the chart amplitude range by inquiring the wind direction matrix and the wind speed matrix of the wind field. The invention adopts an inverse distance weighting interpolation method to find the weather station closest to the point to be interpolated, and interpolates the data of the weather stations according to the area size in proportion, wherein the specific formula is as follows:
wherein the content of the first and second substances,
are points (x, y) to (x)j,yj) The horizontal distance of points, j 1,2, k, p is a constant greater than 0, called the weighted power exponent, and in the present invention p 1 is taken for the wind vector interpolation.
Wind field wind direction matrix:
wind field wind speed matrix:
and step eight, the modeling of the invention is simplified and comprises the following basic assumptions and constraint conditions:
1. the method has the advantages that the method has no limitation of channel width, path range and obstacles in open water;
2. sailing ships sail strictly according to a set course when sailing on each section of air route, and the sailing ships cannot yaw;
3. sailboats cannot be headed backwards because conventional sailboat routes do not take a backward route even if the target is in a positive windward position. Therefore, the effectiveness of randomly generating the route to the destination can be improved, a plurality of invalid paths are prevented from being generated, and the model solving efficiency is improved;
4. setting the number of turning points (number of genes) as C, the number of populations (number of chromosomes) as N, wherein each turning point is a gene, and each path is a chromosome;
step nine, generating an initial population:
according to the number of turning points determined in the last step, in the range of the digitized chart, N routes (namely chromosomes) are randomly generated, wherein each chromosome is provided with C turning points, and the initial population and the chromosome gene sequences are as follows:
initial population: p0＝{P1 0,2 0,,i 0,,N 0In which P is0Denotes the 0 th generation population, Pi 0Is the ith chromosome of generation 0;
turning point of ith route: pi 0＝[p0i 1,0i 2,,p0i j…,p0i C]Wherein p is0i jIs the jth turning point of the ith chromosome of the 0 th generation and has the coordinate of (c)0i j,d0i j)。
Step ten, determining the binary encoding bit number:
because the transverse amplitude and the longitudinal amplitude of one chart do not exceed 1500 units, the distance between the east-west direction and the south-north direction is 10 units during the gridding processing of the five charts in the step, the coordinate value of the turning point does not exceed 150, and 2 is used for solving the problem that the coordinate value of the turning point is not larger than 1507＜150＜28Therefore, the coding is just an 8-bit binary number.
Step eleven, sorting turning points:
since randomly generated turning points are cluttered, the effectiveness of the route is low if there is a random connection from the starting point to the destination point, and therefore the coordinates need to be arranged first when they are encoded into chromosomes. In general, even if the target is in a positive windward position, the conventional sailing ship route does not adopt a backward route, so the arrangement sequence rule of the randomly generated C steering points in the chromosome is as follows: according to the projection size sequence of the vectors from the starting point to the end point of the turning point, the calculation formula is as follows:
wherein the content of the first and second substances,
a vector representing the distance from the starting point to the end point,
represents from the starting point toA unit vector of the endpoint;
C′jthe projection size of a vector which represents that the jth turning point falls on the starting point to the end point;
to obtain { C'1,C′2,…,C′j,…,C′CAfter that, arranging the steering points in the order from small to large, and then arranging the corresponding coordinates in the order to obtain a new steering point ordered set: pi 0′＝[p0i′ 1,p0i′ 2,…,p0i′ j…,p0i′ C]. And connecting the starting point to the end point in sequence according to rules to generate a reasonable route map.
Step twelve, encoding: sequentially sequencing each turning point p after the last step0i′ jThe abscissa and ordinate of the graph are converted into binary form and arranged in a row to form a 16 × C bit binary sequence
I.e. the encoding of the chromosome is completed.
Step thirteen, calculate each chromosome (each route) Pi 0Length of time from starting point to end point TiThe calculation formula is as follows:
wherein, tjRepresenting the slave steering point p0i′ jSailing to a turning point p0i′ j+1The time taken;
due to p0i′ jTo p0i′ j+1The size and direction of the true wind may be changed and uneven, and the windward size and direction of the sailing boat are changed due to the existence of the boat wind during sailing, so that the time on the section of the air route is difficult to directly calculate, therefore, the invention adopts an integral method to calculate, and the calculation formula is as follows:
the true wind vector data of the sailing area can be directly searched from the wind direction matrix and the wind speed matrix of the wind field. The apparent wind is the vector sum of the true wind and the ship wind, and the apparent wind calculation formula is as follows:
wherein v, theta respectively represent the size and direction of the apparent wind;
v1，θ1respectively representing the navigation speed and the navigation direction;
v2，θ2respectively representing the size and the direction of the true wind;
step fourteen, setting an evaluation function: the purpose of path planning is to minimize the time from the starting point to the end point of the sailing ship, and the evaluation function is eval (P)i) Representation, for each chromosome P in the populationi nSetting a probability, Pi nExpressing the ith chromosome of the nth generation so that the probability of the chromosome being selected is proportional to the fitness of other chromosomes in the population, the stronger the fitness of the chromosome, the greater the probability of the chromosome being selected, and the calculation formula is as follows:
step fifteen, selecting operation, wherein the selecting method of the invention using roulette specifically comprises the following operations:
1. for each chromosome PiCalculating the cumulative probability qiThe formula is as follows:
2. from (0, q)C]Generating a random number r;
3. if q isi-1＜r≤qiThen, the ith chromosome P is selectedi，i＝1,2,…,C；
4. Repeating 2) and 3) for C times, so as to obtain C copied chromosomes
Sixthly, cross operation, wherein single-point cross is adopted in the invention, and the specific operation is as follows:
1. firstly, defining the cross probability in the population as RCWith the expected value of NxR in the populationCThe individual chromosomes will be subject to a crossover operation,
2. to define the parent individuals of the crossover operation, the following process is repeated from i-1 to i-N:
3. from [0,1 ]]If r is generated as a random number r<RCThen P is selectedi n′As a parent, with P1 n′，P2 n′… represent the parents chosen above and group them randomly, such as:
(P1 n′，P2 n′),(P3 n′，P4 n′),(P5 n′，P6 n′),…
4. when the number of parents is odd, one chromosome is randomly removed to ensure pairwise pairing, and then (P'1,P′2) How the above groups are interleaved is explained for the purpose of example.
5. Due to the fact thatThe invention adopts single-point crossing, randomly generates 1 crossing point r between 1 and k, and carries out chromosome P exchange1 n′And P2 n′To form two offspring, chromosome P1 n′＝(pn1 1,pn1 2,…,pn1 C)，P2 n′＝(pn2 1,pn2 2,…,pn2 C) Namely:
X＝(pn1 1,pn1 2,…,pn2 r,…,pn2 C)
Y＝(pn2 1,pn2 2,…,pn1 r,…,pn1 C)
seventhly, performing mutation operation, wherein the specific steps are as follows:
1. defining a parameter RmIs the probability of variation of the genetic system, which indicates that there will be an expectation value of NxR in the populationmEach chromosome is used for mutation operation.
2. Similar to the process of selecting a parent in a crossover operation, the following process is repeated from i-1 to i-C:
3. from the interval [0,1]If r is generated as a random number r<RmThen chromosome P is selectedi nAs parents of the mutation, p is used for each selected parenti n＝(pni 1,pni 2,…,pni j,…,pni C) The mutation was performed in the following manner
4. Firstly, a variation point s between 1 and k is selected, if the point gene is 0, the gene is replaced by 1, if the point gene is 1, the gene is replaced by 0, and the genotype of the formed offspring is as follows:
Pi n＝(pni 1,ni 2,…,pni s-1,pni′ s,pni s+1,…,pni C)
wherein p isni′ sRepresents a gene block at the mutation point s after gene conversion;
eighteen step convergence criteria
After the above selection, crossing and mutation operations, a new population is obtained, the original population is replaced by the population formed by the new generation, and the above selection, crossing and mutation processes are repeated until the time T of chromosome (route)iThe calculation is terminated upon convergence to a more stable solution.
Generally, the maximum iteration number can be selected as a convergence criterion of the algorithm, and in order to obtain a global optimal solution, if the maximum iteration number is set to be large, the corresponding calculation time is long. In practice, a more suitable maximum number of iterations can be determined as a convergence criterion by trial and error, thereby reducing the calculation time.
Nineteenth step, route decoding:
respectively will use time TiShortest Pi nCorresponding binary digits
Conversion to a decimal plane coordinate set:
Pi n＝[pni 1,pni 2,…,pni j…,pni C]
wherein p isni jIs the j-th turning point of the ith chromosome of the nth generation and has the coordinate of (c)ni j,dni j)。
Twenty, converting the decimal plane coordinate in the previous step into a geographical coordinate according to the following formula, and generating a sailing ship path turning point list, wherein the list comprises a starting point, an end point, and the plane coordinate and the geographical coordinate of each turning point:
(α,β)＝f-1(a,b)
wherein the relationship among a, b, alpha and beta is the same as that in the fifth step.
TABLE 5 list of turning points
| Turning point | Horizontal coordinate of plane | Longitudinal coordinate of plane | Geographic longitude | Geographical latitude |
| Starting point | m | n | αm | βn |
| 1 | cni 1 | dni 1 | λ1 | μ1 |
| 2 | cni 2 | dni 2 | λ2 | μ2 |
| … | … | … | … | … |
| j | cni j | dni j | λj | μj |
| … | … | … | … | … |
| C | cnC C | dni C | λC | μC |
| Terminal point | r | s | αr | βs |
And twenty one, connecting the generated steering points into a line, and generating the optimal path of the sailing boat.
Thirdly, the invention has the following effects and advantages:
the sailing ship path planning method is based on the electronic chart, and after digital processing, the process and the result can be displayed on the chart, so that the route planning calculation and the process visualization are more visual; the sailing speed table is used as a calculation basis for sailing speed of the sailing boat, so that the boat speed at any wind bulwark angle and wind speed can be obtained, and more accurate windward angle and apparent wind speed of the sailing boat can be obtained by taking the boat wind into consideration, so that the calculation process can be more accurate; the wind vector data of the whole wind field is obtained by adopting an inverse distance weighting interpolation method, only less wind data of meteorological sites are needed, the actual measurement on a large scale is not needed, and the visualization is a wind field image, so that the navigation environment is more vivid.
The randomly generated turning points are sequenced according to the projection size sequence of the vectors from the turning points to the starting point and the end point, so that the reasonability of the randomly generated route is improved, and a more excellent initial value is provided for model solution; because the wind vectors of different sea areas are different, the time of each flight is difficult to directly solve, and the time of sailing ships sailing on each section of air route and the time of the total flight are calculated by adopting an integral method, so that the calculation result is more accurate; and finally, modifying the encoding, selection, hybridization and variation of the genetic algorithm, converting the plane coordinates of the turning points into binary systems respectively to form a line as a chromosome gene, and taking the time for the chromosome to reach the end point as a selection basis so as to adapt to the problems to be solved by the invention.
Drawings
FIG. 1 is a plot of the speed of a 23-foot conventional keel sail boat;
FIG. 2 is a sea chart of a water area to be sailed in a sea area of the east sea;
FIG. 3 is a schematic view of a wind farm;
FIG. 4 is a randomly generated initial population;
FIG. 5 is a diagram of a route arbitrarily drawn from a starting point to an ending point;
FIG. 6 is a schematic diagram of a steering point ranking calculation rule;
FIG. 7 is a diagram of a route from a starting point to an ending point according to a rule;
FIG. 8 is a schematic view of apparent wind calculation;
FIG. 9 is a schematic illustration of a wind farm local wind speed value;
FIG. 10 is a sailing route of a sailing vessel that has been optimized by the method of the present invention;
Detailed Description
The structure of the sailboat of the present invention will be described in further detail below with reference to the accompanying drawings.
Fig. 1 is a diagram of the sailing speed of a 23-foot conventional keel sail sailing boat, which is a polar diagram, and because the polar diagram is symmetrical, only a semicircle of 180 degrees can be drawn. The numbers on the left axis represent the sailing speed, and the sailing speed which can be achieved by the sailing boat under different levels of wind speed and different wind bulwark angles is respectively drawn in the figure.
FIG. 2 is a diagram of a water area to be navigated in a sea area of the east China sea, wherein the diagram of the larger navigation area is obtained by projection of a mercator, has no angular deformation and has the characteristic that an equiangular course is a straight line, so that the navigation map of the invention adopts the diagram of the sea which is commonly used for navigation, wherein "#" represents a meteorological site and "#" represents a starting point or an end point.
FIG. 3 is a schematic diagram of a wind field, in which wind vector data of any point within the amplitude range of a chart can be obtained by querying a wind direction matrix and a wind speed matrix of the wind field, wherein arrows in the diagram represent wind vectors, angles of the arrows represent wind directions, and lengths of the arrows represent wind speeds.
FIG. 4 is a diagram of randomly generated initial populations, with 20 routes from start to end and 8 turning points per route, from which it can be seen that a randomly generated route is difficult to meet the requirements of a sailing ship route without passing through a certain regular turn point ranking.
Fig. 5 is a schematic diagram of a route randomly connecting from a start point to an end point, where "" indicates a turning point.
Fig. 6 is a schematic diagram of a steering point sorting calculation rule, in which randomly generated steering points are arranged in the order of the projection size of a vector falling from a start point to an end point.
Fig. 7 is a route map in which a start point is connected to an end point in a regular manner, and the rationality of the route is increased by arranging randomly generated turning points in the order of the size of the projection of a vector falling from the start point to the end point and then connecting the turning points in the order from the start point to the end point.
FIG. 8 is a schematic view of the calculation of apparent wind, which is the composite wind of true wind and ship wind, the direction of ship wind is opposite to the heading direction, and the size of ship wind is the size of navigational speed. True wind is natural wind, i.e. wind relative to the sea surface. It is necessary to take the sailing boat into account that the angle of the sailing boat facing the wind changes as the speed increases, which has an important influence on the selection and planning of the sailing boat route.
FIG. 9 is a schematic diagram of a local wind speed value of a wind field, the magnitude and direction of a true wind in each voyage are generally unevenly distributed, and the voyage time of each voyage can be calculated by an integral method.
FIG. 10 shows the sailing route of the sailing boat processed and optimized by the method of the present invention, and a relatively suitable number of turning points can be found by a test method, too many turning points increase the labor intensity of sailing boat driving, and too few turning points make it impossible to find the optimal route.
A method for planning the sailing ship path in open water area based on genetic algorithm mainly comprises the following steps:
step one, preparing a sailing boat speed table (table 1) and a sailing boat speed chart (figure 1), wherein each section of wind corresponds to one sailing boat speed table, the sailing boat speed table is listed with maximum speeds corresponding to different wind bulwark angles, the sailing boat speed chart is a diagram of the sailing boat speed table, and the sailing boat speed tables with different wind levels can be drawn on one sailing boat speed chart. Generally, if the wind speed exceeds 33 knots (seven grades of wind), it is not suitable for sailing ships, otherwise there is a danger.
TABLE 1 sailing boat speedometer (all data available)
Step two, preparing a chart of the water area to be navigated, wherein the chart of the larger navigation area is obtained by projection of the mercator, has no angle deformation and has the characteristics that the equiangular course is a straight line, and the like, so the navigation map of the invention adopts the chart commonly used for navigation, and a certain sea area in the east China sea is taken as an example below, as shown in fig. 2.
Inputting data of all weather stations in the navigation area, wherein the positions of the weather stations in the chart are shown in fig. 2, the coordinates and the data of the weather stations are shown in the following table, and the table lists different weather station numbers and corresponding longitudes, latitudes, wind directions and wind speeds:
TABLE 2 weather station coordinates and wind vector data
| Weather station numbering | Longitude (G) | Latitude | Wind | Wind speed | |
| 1 | α1 | β1 | ang1 | vol1 | |
| 2 | α2 | β2 | ang2 | vol2 | |
| … | … | … | … | … | |
| k | αk | βk | angk | volk |
Inputting the positions of a navigation starting point and a navigation ending point, wherein the positions of the starting point and the ending point in the chart are shown in FIG. 2, the coordinates of the starting point and the ending point are shown in the following table, and the longitude and the latitude of the starting point and the ending point are listed in the table:
TABLE 3 weather station coordinates and wind vector data
And step five, performing digital processing on the chart in the step two (the digital processing can be completed through auxiliary software such as Surfer, ArcGis, MapGis, lead adjustment and the like) to obtain the plane coordinates of key position points in the chart, as shown in table 4, and listing the geographical coordinates and the plane coordinates of the key position points in the chart. The geographic coordinates in the chart and the plane coordinates in the digital chart are converted into the following formulas:
. The geographic coordinates in the chart and the plane coordinates in the digital chart are converted into the following formulas:
(a,b)＝f(α,β)
wherein, the relationship among a, b, alpha and beta is as follows:
(α0，β0) Is the geographic coordinate of any point in the chart, (a)0，b0) The corresponding plane coordinates are obtained; that is, the ratio of the difference between the geographical longitude and the geographical latitude of any two points in the chart width range is equal to the ratio of the difference between the abscissa and the ordinate of the corresponding plane coordinate in the digitized chart.
Generally, the transverse amplitude and the longitudinal amplitude of a chart are not more than 1500 units, namely, the digitalized chart is not more than 225 ten thousand square units.
TABLE 4 Key location point coordinates within a navigation area
| Key location point | Longitude (G) | Latitude | Abscissa of the circle | Ordinate of the |
| Weather station | ||||
| 1 | α1 | β1 | a1 | b1 |
| Weather station 2 | α2 | β2 | a2 | b2 |
| … | … | … | … | … |
| Weather station k | αk | βk | ak | bk |
| Starting point | αm | βn | m | n |
| Terminal point | αr | βs | r | s |
Combining the collected data of each meteorological station and the corresponding coordinates of the meteorological stations to respectively generate a meteorological station wind direction matrix and a meteorological station wind speed matrix;
weather station wind direction matrix:
a weather station wind speed matrix:
and seventhly, respectively carrying out gridding processing on the wind direction matrix and the wind speed matrix of the meteorological station to obtain the wind direction matrix and the wind speed matrix of the whole wind field, and obtaining wind vector data of any point in the chart amplitude range by inquiring the wind direction matrix and the wind speed matrix of the wind field, as shown in fig. 3. The invention adopts an inverse distance weighting interpolation method to find the weather station closest to the point to be interpolated, and interpolates the data of the weather stations according to the area size in proportion, wherein the specific formula is as follows:
wherein the content of the first and second substances,
are points (x, y) to (x)j,yj) The horizontal distance of points, j 1,2, k, P is a constant greater than 0, called the weighted power exponent, and in the present invention P1 is taken for the wind vector interpolation.
Wind field wind direction matrix:
wind field wind speed matrix:
and step eight, the modeling of the invention is simplified and comprises the following basic assumptions and constraint conditions:
1. the method has the advantages that the method has no limitation of channel width, path range and obstacles in open water;
2. sailing ships sail strictly according to a set course when sailing on each section of air route, and the sailing ships cannot yaw;
3. sailboats cannot be headed backwards because conventional sailboat routes do not take a backward route even if the target is in a positive windward position. Therefore, the effectiveness of randomly generating the route to the destination can be improved, a plurality of invalid paths are prevented from being generated, and the model solving efficiency is improved;
4. setting the number of turning points (number of genes) as C, the number of populations (number of chromosomes) as N, each turning point being a gene, and the total path being a chromosome;
step nine, generating an initial population:
according to the number of turning points determined in the last step, in the range of the digitized chart, N routes (namely chromosomes) are randomly generated, wherein each chromosome has C turning points, and as shown in FIG. 4, the initial population and the chromosome gene sequence are as follows:
initial population: p0＝{P1 0,P2 0,…,Pi 0,…,PN 0In which P is0Denotes the 0 th generation population, Pi 0Is the ith chromosome of generation 0;
turning point of ith route: pi 0＝[p0i 1,p0i 2,…,p0i j…,p0i C]Wherein p is0i jIs the jth turning point of the ith chromosome of the 0 th generation and has the coordinate of (c)0i j,d0i j)。
Step ten, determining the binary encoding bit number:
because the transverse amplitude and the longitudinal amplitude of one chart do not exceed 1500 units, the distance between the east-west direction and the south-north direction is 10 units during the gridding processing of the five charts in the step, the coordinate value of the turning point does not exceed 150, and 2 is used for solving the problem that the coordinate value of the turning point is not larger than 1507＜150＜28Therefore, the coding is just an 8-bit binary number.
Step eleven, sorting turning points:
since randomly generated turning points are cluttered, if there is a random connection from the starting point to the ending point, as shown in fig. 5, the route is less efficient and therefore the coordinates need to be arranged first when encoded into a chromosome. In general, even if the target is in a positive windward position, the conventional sailing ship route does not adopt a backward route, so the arrangement sequence rule of the randomly generated C steering points in the chromosome is as follows: according to the projection size sequence of the vector of the turning point falling from the starting point to the end point, as shown in fig. 6, the calculation formula is as follows:
wherein the content of the first and second substances,
a vector representing the distance from the starting point to the end point,
a unit vector representing a point from a start point to an end point;
C′jthe projection size of a vector which represents that the jth turning point falls on the starting point to the end point;
to obtain { C'1,C′2,…,C′j,…,C′CAfter that, arranging the steering points in the order from small to large, and then arranging the corresponding coordinates in the order to obtain a new steering point ordered set: pi 0′＝[p0i′ 1,p0i′ 2,…,p0i′ j…,p0i′ C]. The starting point is connected with the end point in sequence according to rules to generate a reasonable routeAs shown in fig. 7.
Step twelve, encoding: sequentially sequencing each turning point p after the last step0i′ jThe abscissa and ordinate of the graph are converted into binary form and arranged in a row to form a 16 × C bit binary sequence
I.e. the encoding of the chromosome is completed.
Step thirteen, calculate each chromosome (each route) Pi 0Length of time from starting point to end point TiThe calculation formula is as follows:
wherein, tjIndicating a slave steering point P0i′ jSailing to a turning point p0i′ j+1The time taken;
due to p0i′ jTo p0i′ j+1The size and direction of the true wind may be changed and uneven, as shown in fig. 9, and the windward size and direction of the sailing boat may be changed due to the existence of the wind of the sailing boat during sailing, so that it is difficult to directly find the time on the section of the sailing line, therefore, the invention adopts an integral method to calculate, and the calculation formula is as follows:
the true wind vector data of the sailing area can be directly searched from the wind direction matrix and the wind speed matrix of the wind field. The apparent wind is the vector sum of the true wind and the ship wind, and as shown in fig. 8, the apparent wind calculation formula is as follows:
wherein v, theta respectively represent the size and direction of the apparent wind;
v1，θ1respectively representing the navigation speed and the navigation direction;
v2，θ2respectively representing the size and the direction of the true wind;
step fourteen, setting an evaluation function: the purpose of path planning is to minimize the time from the starting point to the end point of the sailing ship, and the evaluation function is eval (P)i) Representation, for each chromosome P in the populationi nSetting a probability, Pi nExpressing the ith chromosome of the nth generation so that the probability of the chromosome being selected is proportional to the fitness of other chromosomes in the population, the stronger the fitness of the chromosome, the greater the probability of the chromosome being selected, and the calculation formula is as follows:
step fifteen, selecting operation, wherein the selecting method of the invention using roulette specifically comprises the following operations:
1. for each chromosome PiCalculating the cumulative probability qiThe formula is as follows:
2. from (0, q)C]Generating a random number r;
3. if q isi-1＜r≤qiThen, the ith chromosome P is selectedi，i＝1,2,…,C；
4. Repeating 2) and 3) for C times, so as to obtain C copied chromosomes
Sixthly, cross operation, wherein single-point cross is adopted in the invention, and the specific operation is as follows:
1. firstly, defining the cross probability in the population as RCIn the population, there is a desireValue of N RCThe individual chromosomes will be subject to a crossover operation,
2. to define the parent individuals of the crossover operation, the following process is repeated from i-1 to i-N:
3. from [0,1 ]]If r is generated as a random number r<RCThen P is selectedi n′As a parent, with P1 n′，P2 n′… represent the parents chosen above and group them randomly, such as:
(P1 n′，P2 n′),(P3 n′，P4 n′),(P5 n′，P6 n′),…
4. when the number of parents is odd, one chromosome is randomly removed to ensure pairwise pairing, and then (P'1,P′2) How the above groups are interleaved is explained for the purpose of example.
5. As the invention adopts single-point crossing, 1 crossing point r between 1 and k is randomly generated, and the chromosome P is exchanged1 n′And P2 n′To form two offspring, chromosome P1 n′＝(pn1 1,pn1 2,…,pn1 C)，P2 n′＝(pn2 1,pn2 2,…,pn2 C) Namely:
X＝(pn1 1,pn1 2,…,pn2 r,…,pn2 C)
Y＝(pn2 1,pn2 2,…,pn1 r,…,pn1 C)
seventhly, performing mutation operation, wherein the specific steps are as follows:
1. defining a parameter RmIs the probability of variation of the genetic system, which indicates that there will be an expectation value of NxR in the populationmEach chromosome is used for mutation operation.
2. Similar to the process of selecting a parent in a crossover operation, the following process is repeated from i-1 to i-C:
3. from the interval [0,1]If r is generated as a random number r<RmThen chromosome P is selectedi nAs parents of the mutation, P is used for each selected parenti n＝(pni 1,pni 2,…,pni j,…,pni C) The mutation was performed in the following manner
4. Firstly, a variation point s between 1 and k is selected, if the point gene is 0, the gene is replaced by 1, if the point gene is 1, the gene is replaced by 0, and the genotype of the formed offspring is as follows:
Pi n＝(pni 1,pni 2,…,pni s-1,pni′ s,pni s+1,…,pni C)
wherein p isni′ sRepresents a gene block at the mutation point s after gene conversion;
eighteen step convergence criteria
After the above selection, crossing and mutation operations, a new population is obtained, the original population is replaced by the population formed by the new generation, and the above selection, crossing and mutation processes are repeated until the time T of chromosome (route)iThe calculation is terminated upon convergence to a more stable solution.
Generally, the maximum iteration number can be selected as a convergence criterion of the planning algorithm, and in order to obtain a global optimal solution, if the maximum iteration number is set to be large, the corresponding calculation time is long. In practice, a more suitable maximum number of iterations can be determined as a convergence criterion by trial and error, thereby reducing the calculation time.
Nineteenth step, route decoding:
respectively will use time TiShortest Pi nCorresponding binary digits
Conversion to a decimal plane coordinate set:
Pi n＝[pni 1,pni 2,…,pni j…,pni C]
wherein p isni jIs the j-th turning point of the ith chromosome of the nth generation and has the coordinate of (c)ni j,dni j)。
Twenty, converting the decimal plane coordinate in the previous step into a geographical coordinate according to the following formula, and generating a sailing ship path turning point list, wherein the list comprises a starting point, an end point, and the plane coordinate and the geographical coordinate of each turning point:
(α,β)＝f-1(a,b)
wherein the relationship among a, b, alpha and beta is the same as that in the fifth step
TABLE 5 list of turning points
| Turning point | Horizontal coordinate of plane | Longitudinal coordinate of plane | Geographic longitude | Geographical latitude |
| Starting point | m | n | αm | βn |
| 1 | cni 1 | dni 1 | λ1 | μ1 |
| 2 | cni 2 | dni 2 | λ2 | μ2 |
| … | … | … | … | … |
| j | cni j | dni j | λj | μj |
| … | … | … | … | … |
| C | cni C | dni C | λC | μC |
| Terminal point | r | s | αr | βs |
Twenty one, the generated turning points are connected into a line, and an optimal path of the sailing boat is generated, as shown in fig. 10.
Claims (1)
1. A method for planning a sailing ship path in an open water area based on a genetic algorithm is characterized by comprising the following steps:
preparing a sailing boat speed table and a sailing boat speed chart, wherein each section of wind corresponds to one sailing boat speed table, and the sailing boat speed table is listed with maximum speeds corresponding to different wind bulwarks;
preparing a chart of the water area to be sailed;
inputting data of all weather stations in the navigation area into a table, wherein the table is listed with numbers of different weather stations and corresponding longitude, latitude, wind direction and wind speed;
inputting the positions of the navigation starting point and the navigation ending point into a table, wherein the longitude and the latitude of the starting point and the ending point are listed in the table:
step five, carrying out digital processing on the chart obtained in the step two to obtain the plane coordinates of the key position points in the chart, wherein the conversion formula of the geographic coordinates and the plane coordinates in the chart is as follows: (a, b) ═ f (α, β), where the relationship between a, b, α, β is:
a and alpha are respectively the abscissa of the geographic coordinate and the planar coordinate, b and beta are respectively the ordinate of the geographic coordinate and the planar coordinate, a0And alpha0Respectively the geographical and the horizontal coordinates of the plane coordinates of the arbitrary point, b0And beta0Respectively being the geographic coordinate of any point and the vertical coordinate of the plane coordinate;
combining the collected data of each meteorological station and the corresponding coordinates of the meteorological stations to respectively generate a meteorological station wind direction matrix and a meteorological station wind speed matrix;
step seven, finding the meteorological station closest to the point to be interpolated by adopting an inverse distance weighted interpolation method, and carrying out gridding processing on the wind direction matrix and the wind speed matrix of the meteorological station to obtain the wind direction matrix and the wind speed matrix of the whole wind field, wherein the calculation formula is as follows:
wherein z isjIs a point (x)j,yj) The vertical height in the horizontal plane, here taken as constant 1,
are points (x, y) to (x)j,yj) The horizontal distance of points, j 1,2, · · k, P is a constant greater than 0, called the weighted power exponent, taking P1;
and step eight, simplifying the following modeling:
1) no restrictions of channel width, path extent and obstructions in open waters;
2) sailing the sailing ship according to a set course strictly when the sailing ship sails on each section of air route, and not yawing;
3) the sailing boat cannot course backwards, and even if the target is in a positive windward position, the conventional sailing boat route cannot adopt a backward route, so that the effectiveness of randomly generating the route to reach the end point can be improved, a plurality of invalid paths are prevented from being generated, and the model solving efficiency is improved;
4) setting the number of turning points as C, namely the number of genes as C, the number of populations as N, namely the number of chromosomes as N, wherein each turning point is a gene, and the total path is a chromosome;
step nine, generating an initial population according to the number of the turning points determined in the previous stepRandomly generating N routes, namely N routes, in the range of the graph amplitude of the digitized chart, wherein each chromosome is provided with C turning points and an initial population P0＝{P1 0,P2 0,…,Pi 0,…,PN 0In which P is0Denotes the 0 th generation population, Pi 0Is the ith chromosome of generation 0; turning point of ith route: pi 0＝[p0i 1,p0i 2,…,p0i j…,p0i C]Wherein p is0i jIs the jth turning point of the ith chromosome of the 0 th generation and has the coordinate of (c)0i j,d0i j)；
Step ten, because the transverse amplitude and the longitudinal amplitude of one chart do not exceed 1500 units, the distance between the east-west direction and the south-north direction is 10 units during the gridding processing of the chart in the step five, the coordinate value of the turning point does not exceed 150, and because 27<150<28Therefore, the gene coding adopts 8-bit binary number;
sorting the randomly generated turning points according to the projection size of the vector of the turning points from the starting point to the end point, wherein the calculation formula is as follows:
wherein the content of the first and second substances,
a vector representing the distance from the starting point to the end point,
a unit vector representing the unit from the start point to the end point,
representing the vector formed by the starting point and the jth turning point, thetajTo represent
And
is included angle C'jThe projection size of a vector of the jth steering point falling from the starting point to the end point is represented, wherein m and r are respectively horizontal coordinates of a starting point coordinate and an end point coordinate, and n and s are respectively vertical coordinates of the starting point coordinate and the end point coordinate;
step twelve, sequentially sequencing each steering point p sequenced in the previous step0i′jThe abscissa and ordinate of the graph are converted into binary form and arranged in a row to form a 16 × C bit binary sequence
Namely, the coding of the chromosome is completed;
step thirteen, calculating each chromosome Pi 0Length of time from starting point to end point TiThe calculation formula is
Wherein, tjRepresenting the slave steering point p0i′ jSailing to a turning point p0i′ j+1The time taken; calculating p by integration0i′ jTo p0i′ j+1The time on the route is calculated by the formula
The apparent wind is the vector sum of true wind and ship wind, and the apparent wind calculation formula is
Wherein v, theta respectively represent the size and direction of the apparent wind, v1，θ1Respectively representing the magnitude and direction of the speed, v2，θ2Respectively representing the size and the direction of the true wind, and s represents the linear distance between turning points;
step fourteen, setting evaluation function eval (P) according to time from starting point to end point of sailing boati) For each chromosome P in the populationi nSetting a probability, Pi nExpressing the ith chromosome of the nth generation so that the probability of the chromosome being selected is proportional to the fitness of other chromosomes in the population, the stronger the fitness of the chromosome, the greater the probability of the chromosome being selected, and the formula
Step fifteen, the selection method using roulette specifically operates as follows:
1) for each chromosome PiCalculating the cumulative probability qiThe formula is as follows:
2) from (0, q)C]Generating a random number r;
3) if q isi-1<r≤qiThen, the ith chromosome P is selectedi，i＝1,2,…,C；
4) Repeat 2) and 3) a total of C times, so that C copies of the chromosome are obtained
Sixthly, adopting single-point crossing in a crossing mode, and specifically operating as follows:
1) first, define the cross probability in the population as RCWith the expected value of NxR in the populationCThe individual chromosomes will be subject to a crossover operation,
2) to define the parent individuals of the crossover operation, the following process is repeated from i-1 to i-N:
3) from [0,1 ]]If r is generated as a random number r<RCThen P is selectedi n' As a parent, with P1 n′，P2 n' … denotes the parents selected above and groups them randomly;
4) when the number of parents is odd, randomly removing a chromosome to ensure pairwise pairing;
5. for point (P'1,P′2) Randomly generating 1 crossover point r between 1 and k by exchanging chromosome P1 n' and P2 n' to the r-th to C-th genes to form two offspring, chromosome P1 n′＝(pn1 1,pn1 2,…,pn1 C)，P2 n′＝(pn2 1,pn2 2,…,pn2 C) Namely:
X＝(pn1 1,pn1 2,…,pn2 r,…,pn2 C)
Y＝(pn2 1,pn2 2,…,pn1 r,…,pn1 C)
seventhly, the specific steps of the mutation operation are as follows:
1) define the parameter RmIs the probability of variation of the genetic system, which indicates that there will be an expectation value of NxR in the populationmEach chromosome is used for carrying out mutation operation;
2) similar to the process of selecting a parent in a crossover operation, the following process is repeated from i-1 to i-C:
3) from the interval [0,1 ]]If r is generated as a random number r<RmThen chromosome P is selectedi nAs parents of the mutation, P is used for each selected parenti n＝(pni 1,pni 2,…,pni j,…,pni C) The mutation was performed in the following manner
4) First, a mutation point s between 1 and k is selected, if the point gene is 0, the gene is replaced with 1, if the point gene is 1, the gene is replaced with 0, and the genotype of the formed offspring is:
Pi n＝(pni 1,pni 2,…,pni s-1,pni′s,pni s+1,…,pni C)
wherein p isni′sRepresents a gene block at the mutation point s after gene conversion;
eighteen, after the selection, crossing and mutation, a new population is obtained, the original population is replaced by the new generation, the selection, crossing and mutation processes are repeated until the time T of the chromosomeiConverging to a relatively stable solution, and terminating the calculation; the maximum iteration times can also be selected as a convergence criterion of the evolutionary programming algorithm, and in order to obtain a global optimal solution, if the maximum iteration times are set to be large, the corresponding calculation time is long; in practice, a more appropriate maximum iteration number can be determined as a convergence criterion through trial, so that the calculation time is reduced;
nineteenth decoding operation is that the elapsed time T is respectively usediShortest Pi nCorresponding binary digits
Conversion to a decimal plane coordinate set, Pi n＝[pni 1,pni 2,…,pni j…,pni C]Wherein p isni jIs the j-th turning point of the ith chromosome of the nth generation and has the coordinate of (c)ni j,dni j)；
Twenty, converting the decimal plane coordinate of the previous step into a geographic coordinate:
and twenty one, connecting the generated steering points into a line, and generating the optimal path of the sailing boat.
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