CN114035565B - Sea surface ship formation control method based on adsorption behavior - Google Patents
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Abstract
The invention relates to a sea surface ship formation control method based on adsorption behavior. According to the invention, a virtual structure is built according to the expected formation, a formation driving distance matrix is built, the optimal allocation is solved by utilizing a Hungary algorithm based on formation of the shortest distance, and the ship reaches the expected position according to the optimal allocation. And secondly, adjusting the adjusting parameters controlled by the output speed of the controller by establishing output feedback control, so that the follower adjusts the pose of the follower, and the follower maintains the convergence of the relative distance and angle. Finally, a plurality of adsorption areas are arranged near the navigator, so that when the movement process of the navigator is too fast, the follower is attracted to directly move to the vicinity of the navigator, and meanwhile, the adsorption areas are formed, so that the stability of the formation is maintained, and the method can be applied to formation of larger scale.
Description
Technical Field
The invention relates to the technical field of ship formation control, in particular to a sea surface ship formation control method based on adsorption behavior.
Background
Formation control technology plays an increasingly important role in the fields of commerce, science and military, and related applications are now available everywhere; offshore, terrestrial, airborne and space. The marine formation control is always important, the ship formation control is widely applied in the military field, the warships form formations rapidly and stably in different tactics, the safety and the fight force of the warships are increased, the two world war is embodied, and specific applications comprise formation guard of guard ships, marine formation patrol and the like. Due to the fact that resources are poor, ocean resources are detected greatly, tasks such as ocean exploration, offshore rescue, submarine resource exploration and offshore replenishment are conducted by ship formation, and automation level can be improved greatly, manpower and material resources are saved, and working efficiency is improved.
There are many examples in nature, migration of birds, ants looking for food, etc. Sea surface ship formation control refers to the problem that a ship system moves towards a target while keeping a preset formation and adapting to the environment, and compared with a single ship, the ship has the advantages of flexibility, robustness, efficiency and the like in terms of processing tasks through a formation mode. With the development of economy, formation becomes more and more intelligent under the promotion of new sensors, communication technologies and computer technologies, and has wider application prospect and high practical value. Aiming at the existing autonomous ship cooperative system in China, the intelligent ship is quickened, and the development of the marine industry in China is quickened to be the next stage target.
The existing formation control method mainly comprises the following steps: pilot-follower method, virtual structure method, behavior-based method, etc. The leader-follower approach is widely used due to its simplicity and scalability, but without explicit feedback. First, the existing research at home and abroad mainly focuses on the traditional problems of formation maintenance, obstacle avoidance and the like, and an important process of formation in formation control is omitted. In the formation stage, the existing method moves to a specific position according to a certain control rule. The formation strategy with the shortest total distance is not considered, resulting in additional energy consumption. Secondly, the research on how to keep the formation stable, form feedback and the like is less, particularly when the speed of a navigator is high, the formation can be caused to diverge, the formation is difficult to maintain by the existing method, and the formation can be destroyed.
Disclosure of Invention
The invention designs a ship formation scheme by utilizing output feedback control, and a plurality of adsorption areas are arranged near a pilot, so that the problem of formation divergence of a pilot following algorithm is solved. The invention provides a sea surface ship formation control method based on adsorption behavior, which provides the following technical scheme:
a sea surface ship formation control method based on adsorption behavior comprises the following steps:
step 1: establishing expected formation modeling to obtain expected formations of positive n-side shapes with the node spacing d;
step 2: setting an objective function F, wherein the sum of the travelling routes of ships participating in formation to the corresponding formation nodes is changed by changing the travelling path of the ships, so that the objective function F obtains the minimum value, and the minimum value is expressed by the following formula:
Wherein S i (i=1, 2,., n) represents a travel distance of the ship i from the initial position to the apex of the formation;
Step 3: establishing a formation travel distance matrix D, determining and obtaining the formation travel distance matrix D according to the initial position P 0 and the virtual structure vertex position P k of each ship in the ship system, and expressing the matrix by the following formula:
Wherein d ij denotes the distance of the vessel i to the virtual structure vertex j,
Step 4: establishing an allocation matrix A, and searching n independent elements positioned in different rows and columns in the allocation matrix A, wherein the combination result is the optimal solution of the assignment problem, and the allocation matrix A is expressed as follows:
step 5: solving an optimal solution by using a Hungary algorithm;
Step 6: designing a formation control scheme by utilizing output feedback control; the actual relative distance and angle are obtained by determining the position between the follower and the navigator, then the controller outputs the adjusting parameters controlled by the speed according to the set relative distance and angle, so that the follower adjusts the pose of the follower, even if the follower moves along with the navigator, and the convergence of the relative distance and angle is kept, namely l-l d,
Step 7: establishing a pilot following algorithm formation control motion model;
step 8: taking any point on the same axis with the rotation center point as a reference point The pose relationship of the reference point and the rotation center point is expressed by the following formula:
Wherein d represents the displacement between the rotation center and the reference point, the positive direction of the displacement represents the advancing direction of the ship, and an included angle between the positive direction of l and the positive direction of the x axis is set as beta;
the kinematic equation of the follower is expressed by:
wherein, Representing the euclidean distance between the pilot and follower,Representing the relative angle between the pilot and the follower;
step 9: determining an expression based on output feedback control:
Wherein, alpha 1、α2 is a proportional control coefficient;
the follower's control output (ω 2,v2) is represented by:
According to the control output of the follower, the control input of the controlled object at the moment of the next period t+T is (v 2(t+T),ω2 (t+T)) through the pilot pose related information and the follower pose related information, and the formation task is completed through changing the current motion state of the follower, so that l and l are the same Convergence and maintenance of system settings l d and/>
Step 10: stability analysis was performed based onIn the formation control of the closed-loop control law, when the navigator makes uniform linear motion or uniform circular motion, the formation will converge to a fixed formation (l=l d,/>) The initial states of the formation and the follower do not affect the fixed formation; ship formation motion pair l and/>The method is stable gradually, when the movement speed of the navigator is too high, the follower is difficult to keep up, and the movement track of the follower is in a divergent state relative to the navigator, namely the formation is destroyed.
Preferably, the step 1 specifically includes: the initial positions of n ships are distributed as P 0＝{(xi0,yi0) I=1, 2, the number n is equal to the number n, each ship is uniformly distributed, and a regular n-sided polygon is adopted as an expected formation; taking the center point C (x c,yc) of the expected formation as a reference point, the relative coordinate distribution of each vertex is expressed by the following formula:
Pk＝{(xk,yk)|k＝1,2,...,n}；
For a positive n-sided polygon, the first vertex P 1 is set to a direction angle θ relative to the center point C of the formation, and the other nodes rotate counterclockwise about the center point with P 1 and θ as control variables.
Preferably, the step 5 specifically includes:
step 5.1: searching the maximum value of all elements of the distance matrix D, and setting the element to 0; when only one non-zero element appears in a certain row or column in the matrix, setting the non-zero element to 1, and setting the row and column where the element is positioned to 0;
Step 5.2: until the distance matrix D becomes composed of only two elements, 0 and 1, and the rows and columns where element 1 is located are unique, the number of elements 1 is also equal to the matrix dimension n;
Step 5.3: searching a position a min ij where an element 1 in the optimal allocation matrix A is located, namely, an optimal solution of the allocation matrix A; the element D min ij at the corresponding position of the distance matrix D is also the optimal solution of the matrix, i.e. the shortest travel distance S i＝dmin ij from the ship i to the virtual structure node j.
Preferably, the step 7 specifically includes: defining the pose of the ship i as (x i,yi,θi) by taking the rotation center as a reference, wherein the pose represents the x coordinate, the y coordinate and the heading of the ith ship; v i、ωi denotes the speed at the centre of rotation, l denotes the euclidean distance between the pilot and the follower, y denotes the relative azimuth of the follower at its reference point,Representing the relative angle between the pilot and the follower; d represents the displacement between the rotation center and the reference point, and its positive direction represents the ship advancing direction.
Preferably, the method further comprises: step 11: by arranging a plurality of adsorption areas near the navigator, the follower is attracted to directly move to the vicinity of the navigator, and the adsorption areas are formed by the follower, so that the method is applied to larger-scale formation.
Preferably, the step 11 specifically includes: establishing an adsorption area for a follower by taking the coordinate (x 0,y0) of a pilot as a center, wherein the adsorption area is expressed by the following formula:
wherein, Θ 0 is the angle of attack of the navigator, i=1, 2,..;
the ith follower moves towards the adsorption area of the navigator in a shorter time and reaches the vicinity of the stable point; when (when) When the follower successfully reaches the optimal position of the adsorption area, the formation system keeps the formation for formation movement; after the fusion adsorption behavior, the motion trail of the formation members is smoother and has no oscillation, and the motion trail of the follower is converged to the motion trail of the navigator.
The invention has the following beneficial effects:
The invention selects the total distance from the angle of minimum energy consumption as an important index for measuring the ship formation system, namely the accumulation of the distances required by each ship in the ship system from the initial position to the formation position. The shortest total path of the system is the optimal formation. Based on a virtual structure method and a Hungary algorithm, providing a formation forming strategy based on the shortest distance; and secondly, designing a ship formation scheme by utilizing output feedback control, and arranging a plurality of adsorption areas near a pilot to solve the problem of formation divergence of a pilot following algorithm formation.
Drawings
FIG. 1 is a schematic diagram of formation modeling based on a virtual structure method;
FIG. 2 is a schematic diagram of an output feedback control scheme;
FIG. 3 is a schematic diagram of a pilot-following algorithm formation control motion model;
FIG. 4 is an overall flow chart;
FIG. 5 is a regular trilateral formation;
FIG. 6 is a comparative simulation of three algorithms;
FIG. 7 is a simulation example effect diagram;
fig. 8 is a simulation comparison chart.
Detailed Description
The present invention will be described in detail with reference to specific examples.
First embodiment:
According to the invention, as shown in fig. 1 to 8, the total distance is selected from the angle of minimum energy consumption as an important index for measuring the ship formation system, namely the sum of the distances required by each ship in the ship system to reach the formation position from the initial position. The shortest total path of the system is the optimal formation.
Step 1: formation modeling is desired. The initial position distribution of n vessels is P 0＝{(xi0,yi0) i=1, 2. The relative coordinate distribution of each vertex is P k＝{(xk,yk) k=1, 2, n with the center point C (x c,yc) of the desired formation as a reference point. For the regular n-sided figure, setting the direction angle theta of the first vertex P 1 relative to the center point C of the figure, and rotating other nodes anticlockwise around the center point by taking P 1 and theta as control variables to obtain the expected figure, namely the virtual structure, of the regular n-sided figure with the node interval d.
Step 2: an objective function F is set. Setting an objective function F to represent the sum of the traveling routes of ships participating in formation to corresponding formation nodes respectively, and changing the traveling distance by changing the traveling path of the ships so as to obtain the minimum value of the objective function F:
where S i (i=1, 2,., n) represents a travel distance of the ship i from the initial position to the apex of the formation.
Step 3: and establishing a formation driving distance matrix D. The value of the objective function F is closely related to the assignment mode of the ship reaching the virtual structure vertex, and the invention can obtain a formation driving distance matrix D according to the initial position P 0 of each ship in the ship system and the virtual structure vertex position P k:
Wherein d ij denotes the distance of the vessel i to the virtual structure vertex j,
Step 4: an allocation matrix a is established. Since subtracting or adding the same constant to all elements of a certain row (column) of the distance matrix D does not change the optimal allocation. By looking up n independent elements in the allocation matrix a in different rows and columns, their combined result is the optimal solution to the assignment problem. The allocation matrix a is:
Step 5: and solving an optimal solution by using a Hungary algorithm. Firstly, searching the maximum value of all elements of the distance matrix D, and setting the element to 0; if only one non-zero element appears in a certain row (column) in the matrix, setting the non-zero element to 1, and setting the row and column where the element is positioned to 0; secondly, until the distance matrix D is changed to contain only two elements of 0 and 1, and the row and the column where the element 1 is located are unique, the number of the elements 1 is equal to the dimension n of the matrix; and finally, searching the position a min ij of the element 1 in the optimal allocation matrix A, namely the optimal solution of the allocation matrix A. The element D min ij at the corresponding position of the distance matrix D is also the optimal solution of the matrix, i.e. the shortest travel distance S i＝dmin ij from the ship i to the virtual structure node j.
Ship formation based on adsorption behavior
Only one navigator is needed to be arranged in the piloting following algorithm, and the followers move according to the relative distance and the angle, so that formation control of the expected formation is realized, and the formation mode is more flexible. But the formation has no explicit feedback and lacks robustness due to the presence of the leader.
Step 6: the formation control scheme is designed using output feedback control as shown in fig. 3. The follower obtains the actual relative distance and angle by calculating the position between the follower and the navigator, and then the controller outputs the speed-controlled adjustment parameters according to the relative distance and angle set by the system, so that the follower adjusts the pose of the follower, even if the follower moves along with the navigator, and the convergence of the relative distance and angle is kept, namely l-l d,
Step 7: the pilot-following algorithm formation control motion model is established as shown in fig. 4. Defining the pose of the ship i as (x i,yi,θi) by taking the rotation center as a reference, wherein the pose represents the x coordinate, the y coordinate and the heading of the ith ship; v i、ωi denotes the speed at the centre of rotation, l denotes the euclidean distance between the pilot and the follower, y denotes the relative azimuth of the follower at its reference point,Representing the relative angle between the pilot and the follower. d represents the displacement between the rotation center and the reference point, and its positive direction represents the ship advancing direction.
Step 8: solving the kinematic equation of the follower: taking any point on the same axis with the rotation center point as a reference pointThe pose relation between the reference point and the rotation center point is as follows:
in equation 4, d represents a displacement between the rotation center and the reference point, and the positive direction thereof represents the ship advancing direction. Let the included angle between the positive direction of the l and the positive direction of the x-axis be beta.
The kinematic equation of the follower:
In the formula 5, the components are, Representing the euclidean distance between the pilot and follower,
Representing the relative angle between the pilot and the follower.
Step 9: and solving follower control output.
An expression based on output feedback control:
In equation 6, α 1、α2 is a proportional control coefficient.
Control output of follower (ω 2,v2):
in the formula 7, the components are,
According to the control output of the follower, the control input of the controlled object (follower) at the moment of the next period t+T is (v 2(t+T),ω2 (t+T)) is obtained through the pilot pose related information and the follower pose related information, and the formation task is completed by changing the current motion state of the follower, so that l and l are the same as each otherConvergence and maintenance of system settings l d and/>
Step 10: stability analysis. According to Lyapunov theory, stability of the formation system is analyzed. Based onIn the formation control of the closed-loop control law, if the pilot makes uniform linear motion or uniform circular motion, the formation will converge to a fixed formation (l=l d,/>) And the initial states of the formation and follower do not affect the fixed formation. Ship formation motion pair l and/>Is gradually stable, if the movement speed of the navigator is too high, the follower is difficult to keep up, and the movement track of the follower is in a divergent state relative to the navigator, namely, the formation is destroyed.
Step 11: an adsorption behavior and a pilot-following method formation are combined, and a pilot following algorithm based on the adsorption behavior is provided. By arranging a plurality of adsorption areas near the navigator, the follower is attracted to directly move to the vicinity of the navigator, and the adsorption areas are formed by the follower, so that the method can be applied to larger-scale formation.
Establishing an adsorption area for a follower by taking the coordinate (x 0,y0) of a navigator as a center, and defining as follows:
In the formula 8, the components are, For the adsorption zone of the pilot (which is essentially a potential point for attracting the follower to move), θ 0 is the angle of attack of the pilot, i=1, 2.
The i th follower moves towards the adsorption zone of the navigator in a shorter time and reaches the vicinity of the stable point; when (when)And when the level theta i-θi||＜εθ indicates that the follower successfully reaches the optimal position of the adsorption area, the formation system keeps the formation for formation movement. After the fusion adsorption behavior, the motion trail of the formation members is smoother and has no oscillation, and the motion trail of the follower is converged to the motion trail of the navigator.
Specific embodiment II:
shortest path based allocation policy formation
(Initial position of vessel to desired formation node members input control Components on X-axis and Y-axis)
In order to enable members of a formation to reach a desired formation node in the shortest path, the members are made to reach the target in the shortest path by controlling the magnitude and direction of the respective components (forces) of the X-axis and the Y-axis. After a period of time, the control input on the X axis and the Y axis of each ship is 0, namely the target point is reached, and the formation of the expected formation is completed.
Taking a regular triangle (side length of 1.5 m) as an example, the result of counting the total distance from the initial node to the target node by three methods is shown in table 1.
Table 1 total distance comparison of four methods
In the formation process, the total distance based on the virtual structure method is minimum, and the shortest distance is obtained because the objective function of the total distance is optimized by using the Hungary method in this section.
(1) Ship formation based on adsorption behavior
In a matrix region with a simulation environment of 1500×1500, the initial pose of 5 vessels was ：q1＝[250 250 0]Τ,q2＝[200 300 0]Τ,q3＝[300 200 0]Τ,q4＝[150 250 0]Τ,q5＝[350 100 0]Τ. navigator speeds of 35km/h, respectively. Taking the navigator as a reference standard, the absolute value of the distance between the follower and the navigator is i/12||＝||l13 I=70 and i/14||＝||l15 I=140, absolute value of relative angle is
When the speed of the navigator is greater than 35km/h, the whole formation is diffused, namely the formation is destroyed; after the adsorption behavior is fused, the motion trail of the formation member is smoother and has no oscillation, and the motion trail of the follower is converged to the motion trail of the navigator, so that the formation system of the navigator following algorithm based on the adsorption behavior can reach a stable state quickly.
When the pilot speed is greater than 35km/h. The relative distances and angles between the members under the ABLF algorithm stabilize at the set point (i.e. l=l d,) Thus, stable formation motion is formed, and higher stability and accuracy of the improved pilot following algorithm based on adsorption behavior are demonstrated.
The above is only a preferred implementation manner of the sea surface ship formation control method based on the adsorption behavior, and the protection scope of the sea surface ship formation control method based on the adsorption behavior is not limited to the above embodiment, and all technical schemes under the concept belong to the protection scope of the invention. It should be noted that modifications and variations can be made by those skilled in the art without departing from the principles of the present invention, which is also considered to be within the scope of the present invention.
Claims (6)
1. A sea surface ship formation control method based on adsorption behavior is characterized by comprising the following steps: the method comprises the following steps:
step 1: establishing expected formation modeling to obtain expected formations of positive n-side shapes with the node spacing d;
step 2: setting an objective function F, wherein the sum of the travelling routes of ships participating in formation to the corresponding formation nodes is changed by changing the travelling path of the ships, so that the objective function F obtains the minimum value, and the minimum value is expressed by the following formula:
Wherein S i, i=1, 2,..n, n represents the travel distance of the vessel i from the initial position to the apex of the formation;
Step 3: establishing a formation travel distance matrix D, determining and obtaining the formation travel distance matrix D according to the initial position P 0 and the virtual structure vertex position P k of each ship in the ship system, and expressing the matrix by the following formula:
Wherein d ij denotes the distance of the vessel i to the virtual structure vertex j,
Step 4: establishing an allocation matrix A, and searching n independent elements positioned in different rows and columns in the allocation matrix A, wherein the combination result is the optimal solution of the assignment problem, and the allocation matrix A is expressed as follows:
step 5: solving an optimal solution by using a Hungary algorithm;
Step 6: designing a formation control scheme by utilizing output feedback control; the actual relative distance and angle are obtained by determining the position between the follower and the navigator, then the controller outputs the adjusting parameters controlled by the speed according to the set relative distance and angle, so that the follower adjusts the pose of the follower, even if the follower moves along with the navigator, and the convergence of the relative distance and angle is kept, namely l-l d,
Step 7: establishing a pilot following algorithm formation control motion model;
step 8: taking any point on the same axis with the rotation center point as a reference point The pose relationship of the reference point and the rotation center point is expressed by the following formula:
Wherein d represents the displacement between the rotation center and the reference point, the positive direction of the displacement represents the advancing direction of the ship, and an included angle between the positive direction of l and the positive direction of the x axis is set as beta;
the kinematic equation of the follower is expressed by:
wherein, Representing Euclidean distance between pilot and follower,/>Representing the relative angle between the pilot and the follower;
step 9: determining an expression based on output feedback control:
Wherein, alpha 1、α2 is a proportional control coefficient;
The follower's control output ω 2,v2 is represented by:
According to the control output of the follower, the control input v 2(t+T),ω2 (t+T) of the controlled object at the moment of the next period t+T is obtained through the pilot pose related information and the follower pose related information, and the formation task is completed by changing the current motion state of the follower, so that l and l are the same Convergence and maintenance of system settings l d and/>
Step 10: stability analysis was performed based onIn the formation control of the closed-loop control law, when the navigator makes uniform linear motion or uniform circular motion, the formation is converged into a fixed formation l=l d,/>The initial states of the formation and the follower do not affect the fixed formation; ship formation motion pair l and/>The method is stable gradually, when the movement speed of the navigator is too high, the follower is difficult to keep up, and the movement track of the follower is in a divergent state relative to the navigator, namely the formation is destroyed.
2. The sea surface ship formation control method based on the adsorption behavior according to claim 1, wherein the sea surface ship formation control method is characterized by comprising the following steps: the step 1 specifically comprises the following steps: the initial positions of n ships are distributed as P 0＝{(xi0,yi0) I=1, 2, the number n is equal to the number n, each ship is uniformly distributed, and a regular n-sided polygon is adopted as an expected formation;
Taking the center point C (x c,yc) of the expected formation as a reference point, the relative coordinate distribution of each vertex is expressed by the following formula:
Pk＝{(xk,yk)|k＝1,2,...,n}；
For a positive n-sided polygon, the first vertex P 1 is set to a direction angle θ relative to the center point C of the formation, and the other nodes rotate counterclockwise about the center point with P 1 and θ as control variables.
3. The sea surface ship formation control method based on the adsorption behavior according to claim 2, wherein the sea surface ship formation control method is characterized by comprising the following steps: the step 5 specifically comprises the following steps:
step 5.1: searching the maximum value of all elements of the distance matrix D, and setting the element to 0; when only one non-zero element appears in a certain row or column in the matrix, setting the non-zero element to 1, and setting the row and column where the element is positioned to 0;
Step 5.2: until the distance matrix D becomes composed of only two elements, 0 and 1, and the rows and columns where element 1 is located are unique, the number of elements 1 is also equal to the matrix dimension n;
Step 5.3: searching a position a min ij where an element 1 in the optimal allocation matrix A is located, namely, an optimal solution of the allocation matrix A; the element D min ij at the corresponding position of the distance matrix D is also the optimal solution of the matrix, i.e. the shortest travel distance S i＝dmin ij from the ship i to the virtual structure node j.
4. The sea surface ship formation control method based on the adsorption behavior according to claim 3, wherein the sea surface ship formation control method is characterized by comprising the following steps of: the step 7 specifically comprises the following steps: defining the pose of the ship i as (x i,yi,θi) by taking the rotation center as a reference, wherein the pose represents the x coordinate, the y coordinate and the heading of the ith ship; v i、ωi denotes the speed at the centre of rotation, l denotes the euclidean distance between the pilot and the follower, y denotes the relative azimuth of the follower at its reference point,Representing the relative angle between the pilot and the follower; d represents the displacement between the rotation center and the reference point, and its positive direction represents the ship advancing direction.
5. The sea surface ship formation control method based on the adsorption behavior according to claim 4, wherein the sea surface ship formation control method is characterized in that: the method further comprises the steps of: step 11: by arranging a plurality of adsorption areas near the navigator, the follower is attracted to directly move to the vicinity of the navigator, and the adsorption areas are formed by the follower, so that the method is applied to larger-scale formation.
6. The sea surface ship formation control method based on the adsorption behavior according to claim 4, wherein the sea surface ship formation control method is characterized in that: the step 11 specifically comprises the following steps: establishing an adsorption area for a follower by taking the coordinate (x 0,y0) of a pilot as a center, wherein the adsorption area is expressed by the following formula:
wherein, Θ 0 is the angle of attack of the navigator, i=1, 2,..;
the ith follower moves towards the adsorption area of the navigator in a shorter time and reaches the vicinity of the stable point; when (when) When the follower successfully reaches the optimal position of the adsorption area, the formation system keeps the formation for formation movement; after the fusion adsorption behavior, the motion trail of the formation members is smoother and has no oscillation, and the motion trail of the follower is converged to the motion trail of the navigator.
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