CN109767035B - Analysis method for pipeline path of pipe-laying ship - Google Patents
Analysis method for pipeline path of pipe-laying ship Download PDFInfo
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Abstract
The invention belongs to the technical field of ship dynamic positioning control, and particularly relates to an analysis method for a pipeline path of a pipe-laying ship, which comprises the following steps: determining the position of a pipeline landing point according to the position and the contact distance of the pipe laying ship, and determining a sliding matrix according to the position of the pipeline landing point; judging the type of the curve path of the pipeline according to the sliding matrix; calculating an included angle between the straight paths according to the characteristics of the path types; calculating the distance from the tangent point to the middle point according to the radius of the arc and the included angle; calculating the position of the circle center and the tangent point 1 under the north-east coordinate system according to SF coordinate values of the circle center and the tangent point 1 relative to the 12-line path; calculating the position of the tangent point 2 in the north-east coordinate system according to the SF coordinate value of the tangent point 2 relative to the 23 linear path; the invention simplifies the preprocessing work of the waypoint table, and does not need to carry out complete calculation and analysis on the whole pipeline path in advance. And the whole path can be sequentially and comprehensively analyzed by circularly executing the pipeline path analysis method defined by the sliding matrix.
Description
Technical Field
The invention belongs to the technical field of ship dynamic positioning control, and particularly relates to an analysis method for a pipeline path of a pipe-laying ship.
Background
In the 21 st century, the ocean has become a critical area for global oil exploration. Foreign authorities have predicted that 44% of the total storage of future world oil and gas resources comes from the ocean. With the development of offshore oil industry, offshore oil and gas transportation becomes more and more busy, so that the underwater pipeline plays a crucial role in long-distance oil and gas transportation. Submarine pipelines are paved by adopting special engineering ships-pipe laying ships at present, in particular to deep water pipeline pavement, and about 75% of the world marine pipelines are constructed by the method. When a pipe laying ship performs pipeline laying operation, it is necessary to control the ship body to be positioned on the sea or to perform tracking along a predetermined path. When a conventional DP ship works, only a desired path is required to be directly set for the ship body, but the desired path is required to be set for laying pipelines in the pipe laying process, and the pipeline is indirectly laid on the set path through a DP system control ship.
The pipeline path of the pipelaying vessel is represented by a waypoint table. The form of the waypoint table is shown in table 1. The waypoint table comprises the distance between the pipeline landing point and the rotation center of the ship, namely the contact distance, besides the waypoint coordinates (under the north east coordinate system). Desired heading, desired speed and turning radius of the vessel. The pipeline path is divided into a straight path and a curve path by the track points and turning radii stored in the waypoint table, and the radius of each section of curve path is the size of the radius designated by the corresponding waypoint of the waypoint table. When the water depth in the sea area is a certain value, the contact distance is also a certain value. In the process of pipe laying, the water depth of the sea area in a certain range can be considered to be unchanged. Under this condition, it is made possible to estimate the ship path from the pipe path and the contact distance, which becomes the bridge of the connection between the pipe path and the ship path.
At present, research on the pipe laying operation of the dynamic positioning pipe laying ship at home and abroad mainly focuses on the aspects of the research on the positioning performance and the positioning capability analysis of the pipe laying ship, the path tracking control method of the pipe laying ship and the like. In the path tracking control of a pipelaying vessel, the tracking controller and the guiding strategy are mainly studied, but the pipeline path and the ship path are not studied in depth. A LOS line-of-sight guidance algorithm is commonly employed for path tracking of surface vessels. The line-of-sight guidance algorithm is applicable only to straight paths and not to curved paths. Therefore, the characteristics of the path types of the pipe-laying ship are researched, the characteristics of path change of the ship in the pipe-laying process are helped to be cleared, and a basis is provided for designing a guiding algorithm suitable for a curve path of the pipe-laying ship. The invention therefore proposes a method of pipeline path analysis for a pipe-laying vessel. Lays a foundation for calculating the expected path of the ship through the contact distance.
Disclosure of Invention
An analysis method for a pipelaying vessel pipeline path, comprising the steps of:
(1) Determining the position of a pipeline landing point according to the position and the contact distance of the pipe laying ship, and determining a sliding matrix according to the position of the pipeline landing point;
(2) Judging the type of the curve path of the pipeline according to the sliding matrix;
(3) Calculating an included angle between the straight paths according to the characteristics of the path types;
(4) Calculating the distance from the tangent point to the middle point according to the radius of the arc and the included angle;
(5) Calculating the position of the circle center and the tangent point 1 under the north-east coordinate system according to SF coordinate values of the circle center and the tangent point 1 relative to the 12-line path;
(6) Calculating the position of the tangent point 2 in the north-east coordinate system according to the SF coordinate value of the tangent point 2 relative to the 23 linear path;
(7) Calculating the track angle from the two tangent points to the circle center according to the tangent points and the circle center coordinates;
(8) And obtaining the coordinates of the start point and the end point of the linear path and the angle range of the arc path.
The method for determining the position of the pipeline landing point according to the position of the pipe laying ship and the contact distance, determining the sliding matrix according to the position of the pipeline landing point, and comprises the following steps:
the pipeline landing point is the first point in the waypoint table, and the sliding matrix consists of the 1 st, 2 nd and 3 rd points in the waypoint table; if the pipeline landing point is at the middle position, the sliding matrix consists of the tangent point of the last arc path and two navigation points after the tangent point.
The judging the type of the curve path of the pipeline according to the sliding matrix comprises the following steps:
the curve path types include the following 8 types:
type 1 path: the starting point is in the west, the end point is in the east, and the path is convex to the north;
type 2 path: the starting point is in the west, the end point is in the east, and the path is convex to the south;
3 rd path type: the starting point is east, the end point is west, and the path is northward convex;
type 4 path: the starting point is east, the end point is west, and the path is convex to the south;
type 5 path: the starting point is in the south, the end point is in the north, and the path is convex to the east;
type 6 path: the starting point is in the south, the end point is in the north, and the path is convex to the west;
path type 7: the starting point is north, the end point is south, and the path is convex to the east;
type 8 path: the starting point is north, the end point is south, and the path is convex to the west;
p for path type k The values are 1, 2, 3, 4, 5, 6, 7 and 8;
parameterization characteristics of the 1 st and 2 nd paths:
(1)E 3 >E 1 ；
(2)k 13 ＝(N 3 -N 1 )/(E 3 -E 1 )，k 13 is the slope of the line between 1 and 3 waypoints,
N′ 2 ＝N 1 +k 13 (E 2 -E 1 )，N′ 2 the projection point of the No. 2 waypoint on the connecting line of the 1 waypoint and the 3 waypoint;
(3) If N 2 >N′ 2 The path type formed by 1, 2 and 3 points of the sliding matrix is the first type;
if N 2 <N′ 2 The path type formed by 1, 2 and 3 points of the sliding matrix is the second type;
if N 2 ＝N′ 2 Then from 1 of the sliding matrix,2. 3 points form a straight line;
parameterization characteristics of the 3 rd and 4 th paths:
(1)E 3 <E 1 ；
(2)k 13 ＝(N 3 -N 1 )/(E 3 -E 1 )，k 13 is the slope of the line between 1 and 3 waypoints,
N′ 2 ＝N 1 +k 13 (E 2 -E 1 )，N′ 2 the projection point of the No. 2 waypoint on the connecting line of the 1 waypoint and the 3 waypoint;
(3) If N 2 ＞N' 2 The path type formed by 1, 2 and 3 points of the sliding matrix is the third type;
if N 2 ＜N' 2 The type of the path formed by the 1, 2 and 3 points of the sliding matrix is the fourth type;
if N 2 ＝N' 2 Then, forming a straight line by 1, 2 and 3 points of the sliding matrix;
parameterization characteristics of the 5 th and 6 th paths:
(1)E 3 ＝E 1 and N is 3 >N 1 ；
(2) If E 2 ＞E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is fifth;
if E 2 ＜E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is sixth;
if E 2 ＝E 1 Then, forming a straight line by 1, 2 and 3 points of the sliding matrix;
parameterization characteristics of the 7 th and 8 th paths:
(1)E 3 ＝E 1 and N is 3 <N 1 ；
(2) If E 2 ＞E 1 The path type formed by the 1, 2 and 3 points of the sliding matrix is a seventh type;
if E 2 ＜E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is eighth;
if E 2 ＝E 1 A straight line is formed by 1, 2, 3 points of the sliding matrix.
The calculating the included angle between the straight paths according to the characteristics of the path types comprises the following steps:
the method for calculating the included angle of each path comprises the following steps:
P k ＝1：a＝π-(c 23 -c 12 )
P k ＝2：a＝π-(c 12 -c 23 )
P k ＝3：a＝π-(c 12 -c 23 )
P k ＝4：a＝π-(c 23 -c 12 )
P k ＝5：a＝c 23 -c 12 -π
P k ＝6：a＝c 12 -c 23 -π
P k ＝7：a＝c 12 -(c 23 -π)
P k ＝8：a＝c 23 -(c 12 -π)
wherein C is 12 And C 23 The track angle representing the straight paths 12 and 23, i.e. the angle in clockwise direction with the true north axis; a represents the angle between two straight paths.
The calculating the distance from the tangent point to the middle point according to the radius of the arc and the included angle comprises the following steps:
distance l from tangent point to intermediate point 2q The calculation formula is as follows:
l 2q ＝R/tan(a/2)
wherein R is an arc radius, and a represents an included angle between two straight paths.
The calculating of the position of the tangent point 1 in the north-east coordinate system according to the SF coordinate values of the circle center and the tangent point relative to the 12 straight line path comprises the following steps:
in types 1, 4, 6, and 7, the center O is longitudinally spaced from the straight path 12 by a distance l 1q ＝(l 12 -l 2q ) The transverse distance is R, the coordinate of the circle center O is N O ,E O ]The following equation is satisfied with the 1-point coordinates:
wherein, [ N ] 1 ,E 1 ]Coordinates representing point number 1; c 12 Track angle of straight line path of 1, 2 point connection line;
solving the calculation formula for obtaining the center coordinates:
the longitudinal distance of the center O relative to the straight path 12 in types 2, 3, 5, 8 is l 1q ＝(l 12 -l 2q ) The transverse distance is-R, the coordinate of the circle center O is N O ,E O ]The following equation is satisfied with the 1-point coordinates:
wherein, [ N ] 1 ,E 1 ]Coordinates representing point number 1; c 12 Track angle of straight line path of 1, 2 point connection line;
solving the calculation formula for obtaining the center coordinates:
the longitudinal distance of the tangent point 1 relative to the 12 straight path is l 1q The lateral distance is 0, the coordinate [ N ] of the tangent point q1 q1 ,E q1 ]The coordinates satisfy the following equation:
the calculating the position of the tangent point 2 in the north-east coordinate system according to the SF coordinate values of the tangent point 2 relative to the 23 straight line path comprises the following steps:
the tangent point 2 has a longitudinal distance l relative to the 23 straight path 2q The transverse distance is 0, and the coordinate [ N ] of the tangent point 2 is obtained q2 ,E q2 ]The calculation formula is as follows:
wherein, [ N ] 2 ,E 2 ]Coordinates representing point No. 2; c 23 The track angle of a straight path representing a 2, 3 point link.
Calculating the track angle from the two tangent points to the circle center according to the tangent points and the circle center coordinates, wherein the calculating comprises the following steps:
if the path is 2, 4, 5, 6, 7 and 8, the calculated track angle is the real track angle;
for the path of type 1:
when c oq2 ＞c oq1 When the curve track angle is not zero crossing, namely the curve path is not the north axis;
c oq1 ＝c oq1
c oq2 ＝c oq2
wherein c oq1 And c oq2 The track angles respectively represent the connecting lines from the tangent point 1 and the tangent point 2 to the circle center;
when c oq2 ＜c oq1 When the curve is in the north-positive axis, the curve track angle zero crossing point is indicated;
c oq1 ＝c oq1 -2π
c oq2 ＝c oq2
for type 3 paths:
when c oq2 ＜c oq1 When the curve track angle is not zero crossing, namely the curve path is not the north axis;
c oq1 ＝c oq1 -2π
c oq2 ＝c oq2
when c oq2 ＞c oq1 When the curve is in the north-axis state, the curve track angle zero crossing point is shownAnd the direction of the arc path is anticlockwise;
c oq1 ＝c oq1
c oq2 ＝c oq2 -2π
wherein c oq1 C is the distance from the center of the circle to the tangent point 1 oq2 Is the distance from the center of the circle to the tangent point 2.
The obtaining the coordinates of the start point and the end point of the straight line path and the angle range of the arc path comprises the following steps:
the starting point of the straight line path is the first coordinate point [ N ] of the current sliding matrix 1 ,E 1 ]The end point is the coordinate [ N ] of the tangent point 1 q1 ,E q1 ]The method comprises the steps of carrying out a first treatment on the surface of the The angular range of the arc path is [ c ] oq1 ,c oq2 ]。
The invention has the beneficial effects that:
the invention simplifies the preprocessing work of the waypoint table, and does not need to carry out complete calculation and analysis on the whole pipeline path in advance. And the whole path can be sequentially and comprehensively analyzed by circularly executing the pipeline path analysis method defined by the sliding matrix.
Drawings
FIG. 1 is a path type diagram of type 1;
FIG. 2 is a 2 nd path type diagram;
FIG. 3 is a 3 rd path type diagram;
FIG. 4 is a 4 th path type diagram;
FIG. 5 is a 5 th path type diagram;
FIG. 6 is a 6 th path type diagram;
FIG. 7 is a 7 th path type diagram;
FIG. 8 is a path type diagram of the 8 th path;
FIG. 9 is a graph of path analysis based on a sliding matrix;
FIG. 10 is a path analysis flow diagram;
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention belongs to the technical field of ship dynamic positioning control, and particularly relates to an analysis method for a pipeline path of a pipe-laying ship.
In the 21 st century, the ocean has become a critical area for global oil exploration. Foreign authorities have predicted that 44% of the total storage of future world oil and gas resources comes from the ocean. With the development of offshore oil industry, offshore oil and gas transportation becomes more and more busy, so that the underwater pipeline plays a crucial role in long-distance oil and gas transportation. Submarine pipelines are paved by adopting special engineering ships-pipe laying ships at present, in particular to deep water pipeline pavement, and about 75% of the world marine pipelines are constructed by the method. When a pipe laying ship performs pipeline laying operation, it is necessary to control the ship body to be positioned on the sea or to perform tracking along a predetermined path. When a conventional DP ship works, only a desired path is required to be directly set for the ship body, but the desired path is required to be set for laying pipelines in the pipe laying process, and the pipeline is indirectly laid on the set path through a DP system control ship.
The pipeline path of the pipelaying vessel is represented by a waypoint table. The form of the waypoint table is shown in table 1. The waypoint table comprises the distance between the pipeline landing point and the rotation center of the ship, namely the contact distance, besides the waypoint coordinates (under the north east coordinate system). Desired heading, desired speed and turning radius of the vessel. The pipeline path is divided into a straight path and a curve path by the track points and turning radii stored in the waypoint table, and the radius of each section of curve path is the size of the radius designated by the corresponding waypoint of the waypoint table. When the water depth in the sea area is a certain value, the contact distance is also a certain value. In the process of pipe laying, the water depth of the sea area in a certain range can be considered to be unchanged. Under this condition, it is made possible to estimate the ship path from the pipe path and the contact distance, which becomes the bridge of the connection between the pipe path and the ship path.
At present, research on the pipe laying operation of the dynamic positioning pipe laying ship at home and abroad mainly focuses on the aspects of the research on the positioning performance and the positioning capability analysis of the pipe laying ship, the path tracking control method of the pipe laying ship and the like. In the path tracking control of a pipelaying vessel, the tracking controller and the guiding strategy are mainly studied, but the pipeline path and the ship path are not studied in depth. A LOS line-of-sight guidance algorithm is commonly employed for path tracking of surface vessels. The line-of-sight guidance algorithm is applicable only to straight paths and not to curved paths. Therefore, the characteristics of the path types of the pipe-laying ship are researched, the characteristics of path change of the ship in the pipe-laying process are helped to be cleared, and a basis is provided for designing a guiding algorithm suitable for a curve path of the pipe-laying ship. The invention therefore proposes a method of pipeline path analysis for a pipe-laying vessel. Lays a foundation for calculating the expected path of the ship through the contact distance.
The invention adopts the expression mode of a waypoint table aiming at the pipeline path of the pipe-laying ship, and firstly provides 8 basic pipeline path types by analyzing pipeline path types, wherein each path type consists of three waypoints. These 8 pipe path types cover all possible forms of pipe path. The form characteristics of the whole pipeline can be reflected and expressed by combining the path types in the step 8. The 8 pipe curve path types are shown in fig. 2. Because the pipeline path is formed by a straight line and an arc, only the starting point and the end point of the straight line path are needed to be known, and the arc path needs to know the information such as the position of the center of the circle besides the coordinates of the starting point and the end point. To facilitate analysis and calculation of the pipeline path, the concept of a sliding matrix is proposed. The form of the sliding matrix is shown in table 2, table 3. The sliding matrix is determined according to the position of the pipeline landing point, and the straight line path and the curve path of the pipeline to be paved next can be known through the calculation and the analysis of the sliding matrix. Therefore, preprocessing work of the waypoint table is simplified, and complete calculation and analysis of the whole pipeline path are not needed in advance. And the whole path can be sequentially and comprehensively analyzed by circularly executing the pipeline path analysis method defined by the sliding matrix. The sliding matrix is composed of points sequentially taken from the waypoint table. It should be noted that the first sliding matrix is the first three points in the waypoint table, and the last sliding matrix is composed of one tangential point and two waypoint coordinates. The sliding matrix is a 3×3 matrix, and includes position coordinates of three points and turning radius of a middle point, the first column is north coordinates, the second column is east coordinates, and the third column is turning radius.
The parameterization of each curve path is as follows:
it should be noted that E and N represent the east and north position coordinates of an waypoint. The coordinates of the points in fig. 2 are expressed as: 1 dot (N) 1 ,E 1 ) 2 points (N) 2 ,E 2 ) 3 points (N) 3 ,E 3 )。
Parameterization characteristics of the 1 st and 2 nd paths:
(1)E 3 ＞E 1 ；
(2)k 13 ＝(N 3 -N 1 )/(E 3 -E 1 )，k 13 is the slope of the line between 1 and 3 waypoints,
N' 2 ＝N 1 +k 13 (E 2 -E 1 )，N' 2 is the projection point of the No. 2 waypoint on the connecting line of the 1 and 3 waypoints.
(3) If N 2 ＞N' 2 The path type formed by 1, 2 and 3 points of the sliding matrix is the first type;
if N 2 ＜N' 2 The path type formed by 1, 2 and 3 points of the sliding matrix is the second type;
if N 2 ＝N' 2 A straight line is formed by 1, 2, 3 points of the sliding matrix.
Parameterization characteristics of the 3 rd and 4 th paths:
(1)E 3 ＜E 1 ；
(2)k 13 ＝(N 3 -N 1 )/(E 3 -E 1 )，k 13 is the slope of the line between 1 and 3 waypoints,
N' 2 ＝N 1 +k 13 (E 2 -E 1 )，N' 2 is the projection point of the No. 2 waypoint on the connecting line of the 1 and 3 waypoints.
(3) If N 2 ＞N' 2 The path type formed by 1, 2 and 3 points of the sliding matrix is the third type;
if N 2 ＜N' 2 Then from 1 of the sliding matrix,2. The type of the path formed by the 3 points is the fourth type;
if N 2 ＝N' 2 A straight line is formed by 1, 2, 3 points of the sliding matrix.
Parameterization characteristics of the 1 st and 6 th paths:
(1)E 3 ＝E 1 and N is 3 ＞N 1
(2) If E 2 ＞E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is fifth;
if E 2 ＜E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is sixth;
if E 2 ＝E 1 A straight line is formed by 1, 2, 3 points of the sliding matrix.
Parameterization characteristics of the 7 th and 8 th paths:
(1)E 3 ＝E 1 and N is 3 ＜N 1
(2) If E 2 ＞E 1 The path type formed by the 1, 2 and 3 points of the sliding matrix is a seventh type;
if E 2 ＜E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is eighth;
if E 2 ＝E 1 A straight line is formed by 1, 2, 3 points of the sliding matrix.
Path analysis based on sliding matrix as shown in fig. 4, the steps of the pipeline curve path analysis calculation based on the sliding matrix are as follows:
the first step: judging the type of the curve path of the pipeline according to the sliding matrix;
and a second step of: calculating an included angle between the straight paths according to the characteristics of the path types;
and a third step of: calculating the distance from the tangent point to the middle point according to the radius of the arc and the included angle;
fourth step: calculating the position of the circle center and the tangent point 1 under the north-east coordinate system according to SF coordinate values of the circle center and the tangent point 1 relative to the 12-line path;
fifth step: calculating the position of the tangent point 2 in the north-east coordinate system according to the SF coordinate value of the tangent point 2 relative to the 23 linear path;
sixth step: and calculating the track angle from the two tangent points to the circle center according to the tangent points and the circle center coordinates.
Seventh step: to the start and end coordinates of the straight path, and the angular extent of the arcuate path.
TABLE 1 representation of waypoint tables
TABLE 2 first sliding matrix
| 1 | N 1 | E 1 | 0 |
| 2 | N 2 | E 2 | R 2 |
| 3 | N 3 | E 3 | 0 |
TABLE 3 kth sliding matrix
| 1 | N q2 | E q2 | 0 |
| 2 | N k+1 | E k+1 | R k+1 |
| 3 | N k+2 | E k+2 | 0 |
The first step, determining the position of a pipeline landing point according to the position and the contact distance of the pipe laying ship, and determining a sliding matrix according to the position of the pipeline landing point, wherein if the pipeline landing point is the first point in the waypoint table, the sliding matrix consists of the 1 st, the 2 nd and the 3 rd points in the waypoint table. If the pipeline landing point is at the middle position, the sliding matrix consists of the tangent point of the last arc path and two navigation points after the tangent point.
And secondly, judging the type of the curve path according to the sliding matrix, wherein the parameterization characteristic of the type of the curve path in step 8 is given, so that the type of the curve path determined by the sliding matrix can be determined according to the position relation of three coordinate points in the sliding matrix. By P in combination k The values are 1, 2, 3, 4, 5, 6, 7, 8.
And thirdly, calculating the included angle between the straight paths according to the characteristics of the path types, wherein in the path analysis chart shown in fig. 4, the points 1, 2 and 3 are corresponding points in the sliding matrix respectively. The point O represents the center of the arc path, R represents the radius of the arc, and q1 and q2 represent the tangent points of the arc and the two straight lines. The method for calculating the included angle between the straight paths is related to the types of the paths, and the method for calculating the included angle of each path is as follows:
P k ＝1：a＝π-(c 23 -c 12 )
P k ＝2：a＝π-(c 12 -c 23 )
P k ＝3：a＝π-(c 12 -c 23 )
P k ＝4：a＝π-(c 23 -c 12 )
P k ＝5：a＝c 23 -c 12 -π
P k ＝6：a＝c 12 -c 23 -π
P k ＝7：a＝c 12 -(c 23 -π)
P k ＝8：a＝c 23 -(c 12 -π)
wherein C is 12 And C 23 The track angle representing the straight paths 12 and 23, i.e. the angle in clockwise direction with the true north axis; angle a represents the angle between two straight paths;
fourth, the distance from the tangent point to the intermediate point is calculated based on the radius and the included angle of the arc, and it is easy to derive from fig. 4 that the distances from the tangent points q1 and q2 to 2 are equal. And the tangent point to center distance (i.e., radius R) and path angle a are known. Thus the distance l from the tangent point to 2 2q The calculation formula is as follows:
l 2q ＝R/tan(a/2)
and fifthly, calculating the position of the tangent point 1 in the north-east coordinate system according to SF coordinate values of the circle center and the tangent point relative to the 12-straight-line path. The longitudinal distance of the circle center O relative to the straight path 12 is l 1q ＝(l 12 -l 2q ) The transverse distance is R. The coordinates of the circle center O [ N ] O ,E O ]The following equation is satisfied with the 1-point coordinates:
wherein: [ N ] 1 ,E 1 ]Coordinates representing point number 1; c 12 The track angle of the straight line path of the 1, 2 point link is shown.
Solving the above formula to obtain a calculation formula of the center coordinates;
it should be noted that in the 1, 4, 6, 7 types, the lateral distance of the center of the circle with respect to the path 12 is R, and in the 2, 3, 5, 8 types, the lateral distance of the center of the circle with respect to the path 12 is-R.
Similarly, the tangent point 1 has a longitudinal distance l relative to the 12 straight path 1q The lateral distance is 0. The coordinates N of the tangent point q1 q1 ,E q1 ]The coordinates satisfy the following equation:
and sixthly, calculating the position of the tangent point 2 in the north-east coordinate system according to the SF coordinate value of the tangent point 2 relative to the 23 straight-line path.
The tangent point 2 has a longitudinal distance l relative to the 23 straight path 2q The lateral distance is 0. The coordinates [ N ] of the tangent point 2 are obtained q2 ,E q2 ]A calculation formula;
wherein: [ N ] 2 ,E 2 ]Coordinates representing point No. 2; c 23 The track angle of a straight path representing a 2, 3 point link.
And seventhly, calculating the track angle from the two tangent points to the circle center according to the coordinates of the tangent points and the circle center. The track angle from the two tangent points to the center of the circle is calculated in order to determine the range of the arc path and provide for the calculation of the view point. For the 6 paths of 2, 4, 5, 6, 7 and 8, the calculated track angle is the real track angle. The paths of the two types 1 and 3 need to be determined according to the situation, because the angle area may pass through the 0 point. Track angles of two path types 1, 3 are described below.
In order to ensure the continuity of the zero-crossing arc line path track angle, the calculation formula from the arc line end point to the circle center track angle is as follows:
for the first type of arc path, when c oq2 ＞c oq1 When the curve is in the same direction, the curve track angle is not zero crossing, namely the curve path is not in the north-right axis.
c oq1 ＝c oq1
c oq2 ＝c oq2
Wherein c oq1 And c oq2 Representing the track angle of the line connecting the tangent point 1 and the tangent point 2 to the center of the circle, respectively.
When c oq2 ＜c oq1 And when the curve is in the north-positive axis, the curve track angle zero crossing point is indicated.
c oq1 ＝c oq1 -2π
c oq2 ＝c oq2
For the type 3 path, when c oq2 ＜c oq1 When the curve is in the same direction, the curve track angle is not zero crossing, namely the curve path is not in the north-right axis.
c oq1 ＝c oq1
c oq2 ＝c oq2
When c oq2 ＞c oq1 And when the curve is in the north-positive direction, the curve track angle zero crossing point is indicated, namely, the curve path crosses the north-positive axis, and the direction of the curve path is anticlockwise.
c oq1 ＝c oq1
c oq2 ＝c oq2 -2π
Eighth step, after analysis is completed, the coordinates of the start point and the end point of the straight line path and the angle of the arc path determined by the current sliding matrix can be obtainedA range of degrees. Wherein the start point of the straight line path is the first coordinate point [ N ] of the current sliding matrix 1 ,E 1 ]The end point is the coordinate [ N ] of the tangent point 1 q1 ,E q1 ]The method comprises the steps of carrying out a first treatment on the surface of the The angular range of the arc path is [ c ] oq1 ,c oq2 ]. The type and the range of the path of the ship can be calculated according to the path data, and preparation is made for track tracking control of the pipelaying ship.
Claims (8)
1. An analysis method for a pipeline path of a pipelaying vessel, comprising the steps of:
(1) Determining the position of a pipeline landing point according to the position and the contact distance of the pipe laying ship, and determining a sliding matrix according to the position of the pipeline landing point; the contact distance is the distance between the pipeline landing point and the rotation center of the ship; the pipeline path is divided into a straight path and a curve path by the track points and turning radii stored in the waypoint table, and the radius of each section of curve path is the size of the radius designated by the waypoint table corresponding to the waypoint; the sliding matrix is a 3×3 matrix, and comprises position coordinates of three points and turning radius of a middle point, wherein the first column is a north coordinate, the second column is an east coordinate, and the third column is a turning radius; if the pipeline landing point is the first point in the waypoint table, the sliding matrix consists of the 1 st, 2 nd and 3 rd points in the waypoint table; if the pipeline landing point is at the middle position, the sliding matrix consists of a tangent point of the last curve path and two navigation points after the tangent point; points 1, 2 and 3 are respectively corresponding points in the sliding matrix;
(2) Judging the type of the curve path of the pipeline according to the sliding matrix;
(3) Calculating an included angle between the straight paths according to the characteristics of the path types;
(4) Calculating the distance from the tangent points q1 and q2 to the intersection point of the two straight-line paths according to the curve radius and the included angle; the tangent points q1 and q2 represent the tangent points of the curve path and the two straight paths;
(5) Calculating the positions of the circle center and the tangent point q1 under a north-east coordinate system according to the circle center of the curve path and the SF coordinate values of the tangent point q1 relative to the 12-line path;
(6) Calculating the position of the tangent point q2 under the north-east coordinate system according to the SF coordinate value of the tangent point q2 relative to the 23 linear path;
(7) Calculating the track angle from the two tangent points to the circle center according to the tangent points and the circle center coordinates;
(8) And obtaining the coordinates of the start point and the end point of the straight line path and the angle range of the curve path.
2. An analysis method for a pipeline path of a pipelaying vessel according to claim 1, in which the determining of pipeline curve path type from a sliding matrix includes:
the curve path types include the following 8 types:
type 1 path: the starting point is in the west, the end point is in the east, and the path is convex to the north;
type 2 path: the starting point is in the west, the end point is in the east, and the path is convex to the south;
3 rd path type: the starting point is east, the end point is west, and the path is northward convex;
type 4 path: the starting point is east, the end point is west, and the path is convex to the south;
type 5 path: the starting point is in the south, the end point is in the north, and the path is convex to the east;
type 6 path: the starting point is in the south, the end point is in the north, and the path is convex to the west;
path type 7: the starting point is north, the end point is south, and the path is convex to the east;
type 8 path: the starting point is north, the end point is south, and the path is convex to the west;
p for path type k The values are 1, 2, 3, 4, 5, 6, 7 and 8; e and N represent the east position coordinates and the north position coordinates of each waypoint;
parameterization characteristics of the 1 st and 2 nd paths:
(1)E 3 >E 1 ；
(2)k 13 ＝(N 3 -N 1 )/(E 3 -E 1 )，k 13 is the slope of the line between 1 and 3 waypoints,
N' 2 ＝N 1 +k 13 (E 2 -E 1 )，N' 2 the projection point of the No. 2 waypoint on the connecting line of the 1 waypoint and the 3 waypoint;
(3) If N 2 >N' 2 The path type formed by 1, 2 and 3 points of the sliding matrix is 1 st;
if N 2 <N' 2 The path type formed by 1, 2 and 3 points of the sliding matrix is 2 nd;
if N 2 ＝N' 2 Then, forming a straight line by 1, 2 and 3 points of the sliding matrix;
parameterization characteristics of the 3 rd and 4 th paths:
(1)E 3 <E 1 ；
(2)k 13 ＝(N 3 -N 1 )/(E 3 -E 1 )，k 13 is the slope of the line between 1 and 3 waypoints,
N' 2 ＝N 1 +k 13 (E 2 -E 1 )，N' 2 the projection point of the No. 2 waypoint on the connecting line of the 1 waypoint and the 3 waypoint;
(3) If N 2 ＞N' 2 The path type formed by 1, 2 and 3 points of the sliding matrix is 3 rd;
if N 2 ＜N' 2 The path type formed by 1, 2 and 3 points of the sliding matrix is 4 th type;
if N 2 ＝N' 2 Then, forming a straight line by 1, 2 and 3 points of the sliding matrix;
parameterization characteristics of the 5 th and 6 th paths:
(1)E 3 ＝E 1 and N is 3 >N 1 ；
(2) If E 2 ＞E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is 5 th;
if E 2 ＜E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is 6 th;
if E 2 ＝E 1 Then, forming a straight line by 1, 2 and 3 points of the sliding matrix;
parameterization characteristics of the 7 th and 8 th paths:
(1)E 3 ＝E 1 and N is 3 <N 1 ；
(2) If E 2 ＞E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is 7 th;
if E 2 ＜E 1 The path type formed by 1, 2 and 3 points of the sliding matrix is 8 th;
if E 2 ＝E 1 A straight line is formed by 1, 2, 3 points of the sliding matrix.
3. An analysis method for a pipelaying vessel pipeline path according to claim 2, in which the calculating of the angle between the straight paths in dependence on path type characteristics includes:
the method for calculating the included angle of each path comprises the following steps:
P k ＝1：a＝π-(c 23 -c 12 )
P k ＝2：a＝π-(c 12 -c 23 )
P k ＝3：a＝π-(c 12 -c 23 )
P k ＝4：a＝π-(c 23 -c 12 )
P k ＝5：a＝c 23 -c 12 -π
P k ＝6：a＝c 12 -c 23 -π
P k ＝7：a＝c 12 -(c 23 -π)
P k ＝8：a＝c 23 -(c 12 -π)
wherein C is 12 And C 23 The track angle representing the straight paths 12 and 23, i.e. the angle between the straight paths 12 and 23 and the true north axis in the clockwise direction; a represents the angle between two straight paths.
4. An analysis method for a pipeline path of a pipelaying vessel according to claim 1, wherein the calculation of the distance from the tangent points q1 and q2 to the intersection of two straight paths from the curve radius and the included angle comprises:
distance l from tangent points q1 and q2 to the intersection of two straight paths 2q The calculation formula is as follows:
l 2q ＝R/tan(a/2)
wherein R is a curve radius, and a represents an included angle between two straight paths.
5. A method of analyzing a pipeline path of a pipelaying vessel according to claim 3, wherein calculating the position of the curved path in the north-east coordinate system based on the SF coordinate values of the center of the curved path and the tangent point q1 relative to the 12-straight path comprises:
in types 1, 4, 6, and 7, the center O is longitudinally spaced from the straight path 12 by a distance l 1q ＝(l 12 -l 2q ) The transverse distance is R, the coordinate of the circle center O is N O ,E O ]The following equation is satisfied with the 1-point coordinates:
wherein, [ N ] 1 ,E 1 ]Coordinates representing point number 1; c 12 Track angle of straight line path of 1, 2 point connection line;
solving the calculation formula for obtaining the center coordinates:
the longitudinal distance of the center O relative to the straight path 12 in types 2, 3, 5, 8 is l 1q ＝(l 12 -l 2q ) The transverse distance is-R, the coordinate of the circle center O is N O ,E O ]The following equation is satisfied with the 1-point coordinates:
wherein, [ N ] 1 ,E 1 ]Coordinates representing point number 1; c 12 Track angle of straight line path of 1, 2 point connection line;
solving the calculation formula for obtaining the center coordinates:
the tangent point q1 has a longitudinal distance l relative to the 12 straight path 1q The lateral distance is 0, the coordinate [ N ] of the tangent point q1 q1 ,E q1 ]The coordinates satisfy the following equation:
6. an analysis method for a piping path of a pipelaying vessel according to claim 1, wherein said calculating its position in the northeast coordinate system based on SF coordinate values of the tangent point q2 with respect to the 23 straight-line path includes:
the tangent point q2 has a longitudinal distance l relative to the 23 straight path 2q The transverse distance is 0, and the coordinate [ N ] of the tangent point q2 is obtained q2 ,E q2 ]The calculation formula is as follows:
wherein, [ N ] 2 ,E 2 ]Coordinates representing point No. 2; c 23 The track angle of a straight path representing a 2, 3 point link.
7. An analysis method for a pipeline path of a pipelaying vessel according to claim 2, wherein the calculating of the track angle from the two tangent points to the centre of the circle based on the coordinates of the tangent points and the centre of the circle comprises:
if the path is 2, 4, 5, 6, 7 and 8, the calculated track angle is the real track angle;
for type 1 paths:
when c oq2 ＞c oq1 When the curve track angle is zero-crossing, namely the curve path is north-crossing;
c oq1 ＝c oq1
c oq2 ＝c oq2
wherein c oq1 And c oq2 The track angles respectively represent the connecting lines from the tangent point q1 and the tangent point q2 to the circle center;
when c oq2 ＜c oq1 When the curve track angle zero crossing point is indicated, namely the curve path crosses the north axis;
c oq1 ＝c oq1 -2π
c oq2 ＝c oq2
for type 3 paths:
when c oq2 ＜c oq1 When the curve track angle is zero-crossing, namely the curve path is north-crossing;
c oq1 ＝c oq1 -2π
c oq2 ＝c oq2
when c oq2 ＞c oq1 When the curve track angle zero crossing point is indicated, namely the curve path crosses the north axis, and the direction of the curve path is anticlockwise;
c oq1 ＝c oq1
c oq2 ＝c oq2 -2π
wherein c oq1 C is the distance from the center of the circle to the tangent point q1 oq2 Is the distance from the center of the circle to the tangent point q 2.
8. The method of claim 7, wherein the obtaining the coordinates of the start and end points of the straight path and the angular range of the curved path comprises:
the starting point of the straight line path is the first coordinate point [ N ] of the current sliding matrix 1 ,E 1 ]The end point is cuttingCoordinates [ N ] of point q1 q1 ,E q1 ]The method comprises the steps of carrying out a first treatment on the surface of the The angular range of the curved path is [ c ] oq1 ,c oq2 ]。
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