CN114967692A - System and method for generating autopilot continuous path based on ship stability - Google Patents
System and method for generating autopilot continuous path based on ship stability Download PDFInfo
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Abstract
The invention relates to the field of ship motion control, in particular to an automatic rudder continuous path generating system and a method based on ship stability. The invention uses the two-dimensional coefficient of the polynomial curve as the execution track as the input signal of the autopilot, can realize the accurate control of the ship course, and simultaneously keeps the actual rudder angle of the ship motion not to exceed the maximum rudder angle limit range.
Description
Technical Field
The invention relates to the field of ship motion control, in particular to an automatic rudder continuous path generating system and method based on ship stability.
Background
The prosperity of global economy promotes the increase of navigation demand, the automation degree of ships is higher and higher in order to ensure the accuracy of directions and the safety of navigation when the ships navigate on the sea, and the planning and the execution of navigation paths can be carried out through an autopilot. According to the functional division, the autopilot can be divided into a Heading autopilot (following control system) which can realize tracking and keeping control of a Heading and a Track autopilot (Track control system) which includes Track deviation control and steering control.
For example, patent document No. CN101872195A discloses a method for analyzing deviation of marine navigation track of a ship, comprising the steps of: (1) inputting longitude and latitude coordinates Q (xq, yq, zq) of a departure place and longitude and latitude coordinates M (xm, ym, zm) of a destination; (2) calculating an expected optimal track; (3) correcting the expected track in a segmented manner; (4) calculating the deviation of the ship and the track section; (5) judging whether the ship is in the current track section; (6) if yes, repeating the step (4), otherwise, entering the next track segment calculation, repeating the step (4), and finally, directly sending the calculated track to the autopilot for execution.
The existing method is used for generating the autopilot flight path, when the ship is switched into the set flight path from the current position, the limit of the ship stability control quantity is not considered, and if the ship speed is high enough, the ship stability control quantity exceeds the allowable value, serious consequences can be caused.
Disclosure of Invention
The invention aims to provide a method for generating an autopilot continuous path based on ship stability, which is used for generating the autopilot continuous path under the premise of considering the ship stability and improving the safety of changing the ship course by the autopilot by keeping the stability.
The method for generating the autopilot continuous path based on the ship stability comprises the following steps:
step 3, calculating the tangent direction of the terminal point, the punctuation coordinates of the terminal point and the tangent length of the terminal point after sailing according to the acquired course change angle value, the minimum allowable curvature radius, the point coordinates of the starting point and the tangent direction of the starting point, and determining boundary parameters according to the point coordinates of the starting point, the tangent direction of the starting point, the tangent length of the starting point, the point coordinates of the terminal point, the tangent direction of the terminal point and the tangent length of the terminal point;
and 4, calculating a polynomial two-dimensional coefficient according to the boundary parameters in the step 3, and taking the set of the polynomial two-dimensional coefficient as a path for executing the flight path.
The beneficial effect of this scheme is:
when the path of the ship during navigation is automatically generated, the rudder angle during navigation is set not to exceed the maximum rudder angle limit value, the execution flight path of the autopilot is optimized, the navigation path is set on the premise of ship stability, and the safety of the autopilot for changing the course of the ship can be improved on the premise of keeping stable ship navigation. And the calculation generation of the navigation path is carried out by using the input maximum rudder angle limit value and the course change angle value, and compared with the existing learning algorithm, the path generation speed is high.
Further, in the step 1, the heading change angle value is expressed as: delta phi; the absolute value of the vessel speed is expressed as: u ═ v 0 L, |; the maximum rudder angle limit value that guarantees stability of the ship when the speed of the ship is U is expressed as: delta max (ii) a Micro-model of longitudinal motion of shipThe subformulation is: f (δ, ω), where ω is the steering angular velocity of the hull in the horizontal plane and δ is the actual rudder angle of the ship;
quintic bernstein polynomial curve P with zero curvature at starting and ending points 5 (u) is expressed as:
Setting the ship speed U when the ship sails along a preset curve as a preset value, wherein in a Cartesian coordinate system, a basic polynomial curve is uniquely determined by the following parameters: { r 0 ,α 0 ,d 0 ,c 0 ,r 1 ,α 1 ,d 1 ,c 1 }, wherein:
r 0 and r 1 Coordinates of start and end points of the polynomial curve, α 0 And alpha 1 Tangential to the start and end of the polynomial curve, d 0 And d 1 Tangent lengths of the starting and ending points of the polynomial curve, c 0 And c 1 Curvature values at the start and end of the polynomial curve, and a 1 ＝α 0 +Δφ，α 0 ＝arctg(ν 0x /v 0y )，c 0 ＝0，c 1 ＝0。
The beneficial effects are that: and by defining and representing each parameter, subsequent calculation is facilitated.
Further, in step 1, the optimal polynomial curve is d in the determined basic polynomial curve 0 、r 1 、d 1 The absolute value U of the ship speed and the maximum rudder angle limit value delta max Setting the point coordinates of the end point to be known, and assigning a basic polynomialThe tangent length d of the starting point and the end point is determined by setting the curve to have axial symmetry 0 ＝d 1 Solving the minimum curvature radius R of the transition path from the ship to the new course m And a minimum radius of curvature R m Not less than the value of the differential equation of the ship longitudinal motion model, and calculating r 1 To obtain an optimal polynomial curve.
The beneficial effects are that: by generating a continuous path for the definition of the optimal polynomial curve, too large a curvature of the generated ship path can be avoided.
Further, in the step 1, the optimal polynomial curve of the ship with the course changing into the angle delta phi is defined as an allowable optimal polynomial curve, and the given circle radius of the ship along the route from the starting point to the end point is set as R sc The given circle is a circle passing through the starting point and the end point of the optimal polynomial curve, and three constructors are constructed by fitting an empirical data table, wherein the three constructors are respectively as follows: f. of cl (Δφ)、r sc (Δφ)、d 1 (Δ φ), and defines R m A basic polynomial curve constructor of 1.
The beneficial effects are that: by allowing the definition of the optimal polynomial curve, the curvature of the ship navigation path is further considered, and the stability of the ship navigation is improved.
Further, in the step 2, the first curvature radius is represented as R m_b At the curve boundary of the optimal polynomial curve, due to the curvature c 0 ＝c 1 0, angular velocity ω of the ship 0 ＝ω 1 0, the first formula is:
expressing the second radius of curvature as R m_c When the optimal polynomial curve is in the curve, the derivative of the angular velocity of the ship is zero, and the differential equation of the ship longitudinal motion model is as follows: f (δ, ω) is 0, and the second formula is:
minimum allowable radius of curvature R m Expressed as: r is m ＝max(R m_b ,R m_c )。
The beneficial effects are that: and calculating the minimum allowable curvature radius by combining the constructor obtained by fitting the empirical data table, thereby improving the accuracy of the generated path.
Further, in the step 3, the boundary parameter is determined according to the following sub-steps:
substep 3.1, calculating the tangential direction of the end point according to the point coordinate of the starting point and the course change angle value, alpha 1 ＝α 0 +Δφ；
Substep 3.2, calculating a given circle radius from the minimum allowable radius of curvature and the constructor, of sc ＝R m r sc (Δφ)；
Substep 3.3, calculating the point coordinates of the end point according to the point coordinates of the start point, the given circle radius, the course change angle value and the constructor, in order,
substep 3.4, calculating the tangent length from the minimum allowable radius of curvature and the constructor as: d ═ R m d 1 (Δ φ), we obtain the parameters that allow the optimal polynomial curve boundary to be { r } 0 ,α 0 ,d 0 ,r 1 ,α 1 ,d 1 }。
The beneficial effects are that: and calculating the plurality of parameters in sequence to obtain boundary parameters allowing the optimal polynomial curve, and providing boundary information generated by the path.
Further, in the step 4, the allowed polynomial two-dimensional coefficients of the optimal polynomial curve are calculated according to the following formula:
A 0 ＝r 0 ；
A 2 ＝2·A 1 +A 0 ；
A 3 ＝r 1 ；
A 5 ＝2·A 4 +A 3 ；
obtain a set of polynomial two-dimensional coefficients as { A } 0 ,A 1 ,A 2 ,A 3 ,A 4 ,A 5 }。
The beneficial effects are that: and calculating a polynomial two-dimensional coefficient according to the boundary parameter, and applying the boundary parameter of the generated path to actual track control to improve the accuracy of track control.
The automatic rudder continuous path generating system based on ship stability comprises a setting module, a sensing module and a processing module;
the setting module is used for inputting a maximum rudder angle limit value and a course change value;
the sensing module is used for detecting the speed of the ship, the point coordinate of the gravity center of the ship and the course angle when the ship navigates;
the processing module is used for acquiring a maximum rudder angle limit value and a course change value from the setting module, acquiring the speed, point coordinates and a course angle of the ship from the sensing module, calculating a minimum allowable curvature radius according to the course change value, the maximum rudder angle limit value and the speed of the ship, calculating a boundary parameter of a changed track of the ship according to the course change value, the minimum allowable curvature radius, the point coordinates and the course angle, and calculating a two-dimensional coefficient of a polynomial curve according to the boundary parameter to serve as an execution track of the ship.
The beneficial effect of this scheme is:
parameters are input through a setting module, parameters detected by a ship sensor are combined, the path generation of ship navigation is carried out, the range of track change is limited through the input parameters, the stability of the ship in the path conversion process during navigation is guaranteed, and the safety of ship navigation is improved.
Further, the setting module comprises a first setter and a second setter, wherein the first setter is used for inputting a maximum rudder angle limit value, and the second setter is used for inputting a course change value;
the sensing module comprises a first sensor, a second sensor and a third sensor, wherein the first sensor is used for detecting the speed of the ship when the ship navigates, the second sensor is used for detecting the point coordinate of the gravity center of the ship, and the third sensor is used for detecting the course angle when the ship navigates;
the processing module comprises a first processor, a second processor and a third processor, wherein the first processor is used for calculating a minimum allowable curvature radius according to a course change value, a maximum rudder angle limit value and the speed of the ship, the second processor is used for calculating boundary parameters of a changed track of the ship according to the course change value, the minimum allowable curvature radius, point coordinates and a course angle, and the third processor is used for calculating a two-dimensional coefficient of a polynomial curve according to the boundary parameters to serve as the execution track of the ship.
The beneficial effects are that: the single parameter is input through the independent setting device, the independent sensor respectively detects different parameters, and the independent processor is utilized to carry out corresponding calculation operation, so that the acquisition of multiple parameters of the ship in the marine navigation process is more accurate and direct, the calculation processes of different parameters are faster, and the real-time performance of control according to the calculation parameters is improved.
Drawings
Fig. 1 is a schematic block diagram of an autopilot continuous path generation system based on ship stability according to a first embodiment of the present invention;
fig. 2 is a flow chart of a rudder continuous path generating method based on ship stability according to a second embodiment of the present invention;
fig. 3 is a parameter definition schematic diagram of an autopilot continuous path generation method based on ship stability according to a second embodiment of the present invention;
FIG. 4 shows an optimal polynomial curve end point r in the rudder continuous path generating method based on ship stability according to the second embodiment of the present invention 1 Calculating a schematic diagram of the coordinates;
fig. 5 is a graph of an allowed optimal polynomial in an autopilot continuous path generation method based on ship stability according to a second embodiment of the present invention;
FIG. 6 shows a constructor f in an autopilot continuous path generation method based on ship stability according to a second embodiment of the present invention cl (Δ φ) expression scheme;
FIG. 7 shows a constructor r in an autopilot continuous path generation method based on ship stability according to a second embodiment of the present invention sc (Δ φ) expression scheme;
FIG. 8 is a structural function d in the method for generating an autopilot continuous path based on ship stability according to the second embodiment of the present invention 1 (Δ φ) expression scheme;
fig. 9 is a comparison graph of the track simulation results of the autopilot continuous path generation method based on ship stability in the second embodiment of the present invention;
fig. 10 is a ship stability change rule diagram of an autopilot continuous path generation method based on ship stability in the second embodiment of the present invention.
Detailed Description
The following is a more detailed description of the present invention by way of specific embodiments.
Example one
An automatic rudder continuous path generating system based on ship stability is shown in figure 1: the device comprises a setting module, a sensing module and a processing module.
The setting module is used for inputting the maximum rudder angle limit value and the course change value, the setting module comprises a first setter and a second setter, the first setter is used for inputting the maximum rudder angle limit value, the second setter is used for inputting the course change value, and the first setter and the second setter can be existing input keys or a man-machine interaction display screen.
The sensing module is used for detecting the speed of a ship, the point coordinate and the course angle of the gravity center of the ship when the ship navigates, and comprises a first sensor, a second sensor and a third sensor, wherein the first sensor is used for detecting the speed of the ship when the ship navigates, the first sensor can use the existing ship speed sensor, the second sensor is used for detecting the point coordinate of the gravity center of the ship, the second sensor can use the existing ship gravity center position coordinate sensor, the third sensor is used for detecting the course angle of the ship when the ship navigates, and the third sensor can use the existing ship course sensor.
The processing module is used for acquiring a maximum rudder angle limit value and a course change value from the setting module, the processing module comprises a first processor, a second processor and a third processor, the processing module acquires the speed, the point coordinate and the course angle of the ship from the sensing module, the processing module calculates a minimum allowable curvature radius according to the course change value, the maximum rudder angle limit value and the speed of the ship, the processing module calculates a boundary parameter of a changed track of the ship according to the course change value, the minimum allowable curvature radius, the point coordinate and the course angle, and the processing module calculates a two-dimensional coefficient of a polynomial curve as an execution track of the ship according to the boundary parameter; the first processor is used for calculating the minimum allowable curvature radius according to the course change value, the maximum rudder angle limit value and the ship speed, the second processor is used for calculating the boundary parameter of the ship changing track according to the course change value, the minimum allowable curvature radius, the point coordinate and the course angle, the third processor is used for calculating the two-dimensional coefficient of the polynomial curve according to the boundary parameter to serve as the execution track of the ship, and the first processor, the second processor and the third processor can use the existing PC computer.
Example two
On the basis of the first embodiment, as shown in fig. 2, the method for generating an autopilot continuous path based on ship stability includes the following steps:
The heading change angle value is expressed as: delta phi; the absolute value of the vessel speed is expressed as: u ═ v 0 L, |; the maximum rudder angle limit value that guarantees stability of the ship when the speed of the ship is U is expressed as: delta max (ii) a The differential equation of the ship longitudinal motion model is as follows: and ω' is F (δ, ω), where ω is the steering angular velocity of the hull in the horizontal plane and δ is the actual rudder angle of the ship.
Defining two-dimensional coefficients of a polynomial from a Bernstein polynomial curve, i.e. a quintic-fold Bernstein polynomial curve P with zero curvature at the starting and ending points 5 (u) is expressed as:
For a continuous path, a flight path is composed of several polynomial curves, where the polynomial curves refer to general names of categories, and the curvatures of the boundary points of the polynomial curves on different curves are equal when the flight path transits from one curve to another curve. Defining a basic polynomial curve in a Cartesian coordinate system according to the absolute value of the speed of the ship when the ship navigates along the curve, setting the speed U of the ship when the ship navigates along a preset curve as a preset value, wherein in the Cartesian coordinate system, the X axis points to the east and the Y axis points to the north, and the basic polynomial curve is formed by the following parametersOne of the determinations is: { r 0 ,α 0 ,d 0 ,c 0 ,r 1 ,α 1 ,d 1 ,c 1 }, wherein: r is a radical of hydrogen 0 And r 1 Coordinates of start and end points of the polynomial curve, alpha 0 And alpha 1 Tangential to the start and end of the polynomial curve, d 0 And d 1 Tangent lengths of the starting and ending points of the polynomial curve, c 0 And c 1 Curvature values at the start and end of the polynomial curve, and a 1 ＝α 0 +Δφ，α 0 ＝arctg(ν 0x /v 0y )，c 0 ＝0，c 1 ＝0，ν 0x And v 0y Is the projection of the ship speed vector at the starting point of the track in a Cartesian coordinate system.
As shown in fig. 4, an optimal polynomial curve is defined according to a basic polynomial curve that the maximum rudder angle of the ship does not exceed the maximum rudder angle limit value when the new sailing path is generated, and the optimal polynomial curve is d in the determined basic polynomial curve 0 、r 1 、d 1 The absolute value U of the ship speed and the maximum rudder angle limit value delta max Assuming that the coordinates of the point of the end point are known, and the basic polynomial curve is set to have axial symmetry, the tangent length d of the start point and the end point 0 ＝d 1 Solving the minimum curvature radius R of the transition path from the ship to the new course m And a minimum radius of curvature R m Not less than the differential equation value of the ship longitudinal motion model, i.e. the absolute value U and the maximum rudder angle limit value delta max Substituting into the differential equation of the ship longitudinal motion model to solve and calculate r 1 To obtain an optimal polynomial curve. The track is a polynomial curve, and the course is the tangential direction of a certain point. Transitioning to a new heading means a curve and a radius of curvature needs to be calculated.
As shown in FIG. 5, an optimal polynomial curve allowing for the change of the ship's course is defined according to the ship's course change angle, that is, the optimal polynomial curve allowing for the change of the ship's course to be delta phi is defined as an optimal polynomial curve, and the radius of a given circle of the ship's course from the starting point to the end point is set as R sc Given the circle is by the optimum numberThe circles of the start and end points of the polynomial curve, a given circle may also be determined with the chord length of the straight line length between the start and end points, i.e. R sc Is a curve r 0 Ar 1 Given the radius of the circle, R m Is a curve r 0 Ar 1 The three constructors are constructed by fitting an empirical data table, and are respectively as follows: f. of cl (Δφ)、r sc (Δφ)、d 1 (Δ φ), and defines R m The basic polynomial curve of 1 is constructed to solve a series of given extreme value problems with Δ Φ in the range of 1 ° to 180 °, i.e. to calculate an optimal polynomial curve. Constructor f cl (Δ φ) As shown in FIG. 6, the constructor r sc (Δ φ) As shown in FIG. 7, the function d is constructed 1 (Δ φ) as shown in FIG. 8, the abscissa of the graph of each constructor is the value of the heading change angle and the ordinate is the value of the constructor function.
Expressing the first radius of curvature as R m_b At the curve boundary of the optimal polynomial curve, due to the curvature c 0 ＝c 1 0, angular velocity ω of the ship 0 ＝ω 1 0, the first formula is:
expressing the second radius of curvature as R m_c When the optimal polynomial curve is inside, the derivative of the angular velocity of the ship is zero, and the differential equation of the longitudinal motion model of the ship is as follows: f (δ, ω) is 0, and the second formula is:
minimum allowable radius of curvature R m Expressed as: r is m ＝max(R m_b ,R m_c )。
Step 3, calculating the tangent direction of the terminal point, the punctuation coordinates of the terminal point and the tangent length of the terminal point after sailing according to the acquired course change angle value, the minimum allowable curvature radius, the point coordinates of the starting point and the tangent direction of the starting point, determining boundary parameters according to the point coordinates of the starting point, the tangent direction of the starting point, the tangent length of the starting point, the point coordinates of the terminal point, the tangent direction of the terminal point and the tangent length of the terminal point, and determining the boundary parameters according to the following substeps:
substep 3.1, calculating the tangential direction of the end point according to the point coordinate of the starting point and the course change angle value, alpha 1 ＝α 0 +Δφ；
Substep 3.2, calculating a given radius of the circle from the minimum allowable radius of curvature and the constructor, in that, R sc ＝R m r sc (Δ φ), the minimum allowable radius of curvature in the formula is represented by the formula R m ＝max(R m_b ,R m_c ) Calculating to obtain;
substep 3.3, calculating the point coordinates of the end point according to the point coordinates of the start point, the given circle radius, the course change angle value and the constructor, in order,
substep 3.4, calculating the tangent length from the minimum allowable radius of curvature and the constructor as: d ═ R m d 1 (Δ φ), the minimum allowable radius of curvature in the equation is given by the equation R m ＝max(R m_b ,R m_c ) Calculating to obtain the boundary parameter of the allowable optimal polynomial curve as r 0 ,α 0 ,d 0 ,r 1 ,α 1 ,d 1 }。
A 0 ＝r 0 ；
A 2 ＝2·A 1 +A 0 ；
A 3 ＝r 1 ；
A 5 ＝2·A 4 +A 3 ；
taking the set of the polynomial two-dimensional coefficients as a path for executing a flight path to obtain a set of the polynomial two-dimensional coefficients as { A } 0 ,A 1 ,A 2 ,A 3 ,A 4 ,A 5 }。
The method of the embodiment is utilized to generate the autopilot continuous path to obtain the simulation result graphs as shown in fig. 9 and fig. 10, the designed parameters in the simulation process are not disclosed based on confidentiality, and the simulation results on the graphs show that the flight path error deviation obtained by the method is small, the course can be accurately controlled, the actual rudder angle does not exceed the maximum rudder angle limit, and good ship stability is always kept in the autopilot flight path control process.
In the embodiment, the rudder angle does not exceed the maximum rudder angle limit value during navigation, the execution track of the autopilot is optimized, the navigation track is set on the premise of ship stability, and the safety of the autopilot for changing the ship course can be improved on the premise of keeping the ship navigation stable. And the calculation generation of the navigation path is carried out by using the input maximum rudder angle limit value and the course change angle value, and compared with the existing learning algorithm, the path generation speed is high. And the accurate control of the ship course can be realized, and the actual rudder angle of the ship movement can not exceed the maximum rudder angle limit range.
The foregoing is merely an example of the present invention and common general knowledge of known specific structures and features of the embodiments is not described herein in any greater detail. It should be noted that, for those skilled in the art, without departing from the structure of the present invention, several changes and modifications can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicability of the patent. The scope of the claims of the present application shall be determined by the contents of the claims, and the description of the embodiments and the like in the specification shall be used to explain the contents of the claims.
Claims (9)
1. The method for generating the continuous path of the autopilot based on ship stability is characterized by comprising the following steps of:
step 1, defining a polynomial two-dimensional coefficient according to a Bernstein polynomial curve, defining a basic polynomial curve in a Cartesian coordinate system according to an absolute value of a speed of a ship when the ship navigates along the curve, defining an optimal polynomial curve according to the basic polynomial curve of which the maximum rudder angle of the ship does not exceed a maximum rudder angle limit value when a new navigation path is generated, and defining an allowed optimal polynomial curve according to a course change angle of the ship;
step 2, acquiring parameters: the maximum rudder angle limit value, the course change angle value and the absolute value of the ship speed are calculated according to the parameters and a first formula, a first curvature radius of the ship sailing on the curve boundary of the optimal polynomial curve is calculated, a second curvature radius of the ship sailing in the optimal polynomial curve is calculated according to the parameters and a second formula, and the maximum value of the first curvature radius and the second curvature radius is taken as the minimum allowable curvature radius;
step 3, calculating the tangent direction of the terminal point, the punctuation coordinates of the terminal point and the tangent length of the terminal point after sailing according to the acquired course change angle value, the minimum allowable curvature radius, the point coordinates of the starting point and the tangent direction of the starting point, and determining boundary parameters according to the point coordinates of the starting point, the tangent direction of the starting point, the tangent length of the starting point, the point coordinates of the terminal point, the tangent direction of the terminal point and the tangent length of the terminal point;
and 4, calculating a polynomial two-dimensional coefficient according to the boundary parameters in the step 3, and taking the set of the polynomial two-dimensional coefficient as a path for executing the flight path.
2. The system and method for generating an autopilot continuous path based on vessel stability of claim 1 wherein: in the step 1, the heading change angle value is expressed as: delta phi; the absolute value of the vessel speed is expressed as: u ═ v 0 L, |; the maximum rudder angle limit value that guarantees stability of the ship when the speed of the ship is U is expressed as: delta max (ii) a The differential equation of the ship longitudinal motion model is as follows: f (δ, ω), where ω is the steering angular velocity of the hull in the horizontal plane and δ is the actual rudder angle of the ship;
quintic bernstein polynomial curve P with zero curvature at starting and ending points 5 (u) is expressed as:
Setting the ship speed U when the ship sails along a preset curve as a preset value, wherein in a Cartesian coordinate system, a basic polynomial curve is uniquely determined by the following parameters: { r 0 ,α 0 ,d 0 ,c 0 ,r 1 ,α 1 ,d 1 ,c 1 }, wherein:
r 0 and r 1 Coordinates of start and end points of the polynomial curve, alpha 0 And alpha 1 Tangential to the start and end of the polynomial curve, d 0 And d 1 Tangent lengths of the starting and ending points of the polynomial curve, c 0 And c 1 Curvature values at the start and end of the polynomial curve, and a 1 ＝α 0 +Δφ，α 0 ＝arctg(ν 0x /v 0y )，c 0 ＝0，c 1 ＝0。
3. The rudder continuous path generating method based on ship stability according to claim 2, wherein: in the step 1, the optimal polynomial curve is d in the determined basic polynomial curve 0 、r 1 、d 1 The absolute value U of the ship speed and the maximum rudder angle limit value delta max Assuming that the coordinates of the point of the end point are known, and the basic polynomial curve is set to have axial symmetry, the tangent length d of the start point and the end point 0 ＝d 1 Solving the minimum curvature radius R of the transition path from the ship to the new course m And a minimum radius of curvature R m Not less than the value of the differential equation of the ship longitudinal motion model, and calculating r 1 To obtain an optimal polynomial curve.
4. The rudder continuous path generating method based on ship stability according to claim 3, wherein: in the step 1, the optimal polynomial curve of the ship with the course changing into the angle delta phi is defined as an allowable optimal polynomial curve, and the given circle radius of the ship along the track from the starting point to the end point is set as R sc The given circle is a circle passing through the starting point and the end point of the optimal polynomial curve, and three constructors are constructed by fitting an empirical data table, wherein the three constructors are respectively as follows: f. of cl (Δφ)、r sc (Δφ)、d 1 (Δ φ) and defines R m A basic polynomial curve constructor of 1.
5. The rudder continuous path generating method based on ship stability according to claim 4, wherein: in the step 2, the first curvature radius is represented as R m_b At the curve boundary of the optimal polynomial curve, due to the curvature c 0 ＝c 1 0, angular velocity ω of the ship 0 ＝ω 1 0, the first formula is:
expressing the second radius of curvature as R m_c When the optimal polynomial curve is inside, the derivative of the angular velocity of the ship is zero, and the differential equation of the longitudinal motion model of the ship is as follows: f (δ, ω) is 0, and the second formula is:
minimum allowable radius of curvature R m Expressed as: r m ＝max(R m_b ,R m_c )。
6. The rudder continuous path generating method based on ship stability according to claim 5, wherein: in the step 3, the boundary parameter is determined according to the following substeps:
substep 3.1, calculating the tangential direction of the end point according to the point coordinate of the starting point and the course change angle value, alpha 1 ＝α 0 +Δφ；
Substep 3.2, calculating a given radius of the circle from the minimum allowable radius of curvature and the constructor, in that, R sc ＝R m r sc (Δφ)；
Substep 3.3, calculating the point coordinates of the end point according to the point coordinates of the start point, the given circle radius, the course change angle value and the constructor, in order,
substep 3.4, calculating the tangent length from the minimum allowable radius of curvature and the constructor as: d ═ R m d 1 (Δ φ), we obtain the parameters that allow the optimal polynomial curve boundary to be { r } 0 ,α 0 ,d 0 ,r 1 ,α 1 ,d 1 }。
7. The rudder continuous path generating method based on ship stability according to claim 6, characterized in that: in the step 4, the allowable polynomial two-dimensional coefficient of the optimal polynomial curve is calculated according to the following formula:
A 0 ＝r 0 ；
A 2 ＝2·A 1 +A 0 ；
A 3 ＝r 1 ；
A 5 ＝2·A 4 +A 3 ；
obtain a set of polynomial two-dimensional coefficients as { A } 0 ,A 1 ,A 2 ,A 3 ,A 4 ,A 5 }。
8. Automatic rudder continuous path generating system based on ship stability, its characterized in that: the device comprises a setting module, a sensing module and a processing module;
the setting module is used for inputting a maximum rudder angle limit value and a course change value;
the sensing module is used for detecting the speed of the ship, the point coordinate of the gravity center of the ship and the course angle when the ship navigates;
the processing module is used for acquiring a maximum rudder angle limit value and a course change value from the setting module, acquiring the speed, point coordinates and a course angle of the ship from the sensing module, calculating a minimum allowable curvature radius according to the course change value, the maximum rudder angle limit value and the speed of the ship, calculating a boundary parameter of a changed track of the ship according to the course change value, the minimum allowable curvature radius, the point coordinates and the course angle, and calculating a two-dimensional coefficient of a polynomial curve according to the boundary parameter to serve as an execution track of the ship.
9. The rudder continuous path generating system based on ship stability according to claim 8, wherein: the setting module comprises a first setter and a second setter, wherein the first setter is used for inputting a maximum rudder angle limit value, and the second setter is used for inputting a course change value;
the sensing module comprises a first sensor, a second sensor and a third sensor, wherein the first sensor is used for detecting the speed of the ship when the ship navigates, the second sensor is used for detecting the point coordinate of the gravity center of the ship, and the third sensor is used for detecting the course angle when the ship navigates;
the processing module comprises a first processor, a second processor and a third processor, wherein the first processor is used for calculating a minimum allowable curvature radius according to a course change value, a maximum rudder angle limit value and the speed of the ship, the second processor is used for calculating a boundary parameter of a changed track of the ship according to the course change value, the minimum allowable curvature radius, a point coordinate and a course angle, and the third processor is used for calculating a two-dimensional coefficient of a polynomial curve according to the boundary parameter to serve as an execution track of the ship.
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