CN116820101A - Under-actuated unmanned ship formation control method under condition of distance information loss - Google Patents
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Abstract
The application relates to an underactuated unmanned ship formation control method under the condition of distance information deficiency. The application relates to the technical field of unmanned ship formation control, and provides formation control of an underactuated unmanned ship by means of azimuth information measured by an optical sensor under the condition of not depending on a sight distance instrument. The algorithm can effectively realize track tracking of the formation of the underactuated unmanned ship, and the requirement on system resources can be reduced by reducing the online calculated amount through a minimum learning parameter algorithm. Firstly, establishing an underactuated unmanned ship formation kinematic dynamics model, and carrying out model conversion on a gesture subsystem; then, constructing a target formation of the unmanned ship and determining a control target; and finally, designing a formation controller of the leading-following structure, and verifying the stability and the robustness of the unmanned ship formation system. The application can effectively realize track tracking control of unmanned ship formation under the condition of communication distance loss, and proves that error signals of a control system can be converged rapidly.
Description
Technical Field
The application relates to the technical field of unmanned ship formation control, in particular to an underactuated unmanned ship formation control method under the condition of distance information loss.
Background
In recent years, with the development of science and technology, world-wide countries are increasingly competing for ocean resources. The unmanned surface vessel plays a role in the middle of the intelligent offshore platform. With the continuous deep exploration of the ocean, the ocean operation environment is gradually complex, and the unmanned surface vehicle cooperative formation control is widely applied to the military and civil fields due to the characteristics of high system reliability, high task completion rate, flexible maneuver and the like.
The unmanned vessels on the water surface form a cluster which is composed of two or more unmanned vessels and can finish the directional task, the overall advantage of the formation can be furthest exerted, and the close cooperation among vessels and the overall command of the formation are facilitated by changing the formation shape in real time. The main advantages of unmanned ship formation include: (1) And each boat in the formation is distributed in different areas, the respective tasks are respectively executed, and after the tasks of each boat are organically combined, the whole unmanned boat formation can complete relatively complex and huge tasks. (2) When some unmanned boats lose the capacity of executing tasks, the tasks can still be distributed to other boats, so that the formation fault tolerance performance is improved, and the smooth completion of the tasks is ensured.
However, to enable the above tasks to be efficiently accomplished, there is also a great deal of reliance on unmanned craft formation control techniques. There are a number of problems currently in existence for unmanned ship formation systems. For internal factors of the unmanned ship formation system, the problems of nonlinearity, strong coupling, multiple inputs and multiple outputs, uncertainty, strong disturbance, underactuation, multiple constraints and the like are included; external conditions of the unmanned ship comprise communication delay, data packet loss, topology switching, spoofing attack, denial of service attack, malicious node attack, event triggering, game theory and the like.
The main content of the application is to design a leader-follower structure unmanned ship formation control scheme under the condition of distance information deficiency. In an actual task scene, the on-board stadia are high in cost, and large-scale unmanned ships can not be listed in a large quantity for formation.
Disclosure of Invention
In order to overcome the defects of the prior art, in order to realize the underactuated unmanned ship formation control method based on the leader-follower structure under the condition of distance information deficiency, the unmanned ship formation and the formation controller are designed to enable the unmanned ship formation to change the formation so as to adapt to different working conditions, and when the unmanned ship formation is in a communication limited state as a whole, pose information of adjacent ships cannot be acquired or directly utilized among ships, so that unmanned ship formation control failure is caused. According to the method, the inter-adjacent information of each boat in the formation is acquired by means of the on-board sensor, and under the condition that distance information cannot be acquired, under-actuated unmanned boat formation control can be successfully realized only by means of the acquired azimuth information.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
The application provides an underactuated unmanned ship formation control method under the condition of distance information deficiency, which provides the following technical scheme:
an under-actuated unmanned ship formation control method under the condition of distance information loss, comprising the following steps:
step 1: establishing an underactuated unmanned ship formation kinematic dynamics model, and carrying out model conversion on a gesture subsystem;
step 2: constructing a target formation of the unmanned ship, and determining a control target;
step 3: and a formation controller of the leading following structure is established to control unmanned ship formation.
Preferably, the step 1 model building process specifically includes:
considering the two-dimensional plane motion of the three-degree-of-freedom underactuated unmanned ship under a geodetic coordinate system and a satellite coordinate system, the kinematic equation of the unmanned ship is represented by the following formula:
wherein ,pi ＝(x i ,y i )，p i Representing the position of the ith unmanned ship under the geodetic coordinate system; psi phi type i Representing the heading of an ith unmanned ship under a geodetic coordinate system; u (u) i ,v i ,r i Respectively representing the corresponding speed or angular speed of longitudinal direction, horizontal drift and bow swing under a satellite coordinate system;
establishing a kinetic equation corresponding to the unmanned ship, wherein the kinetic equation is expressed by the following formula:
wherein ,miu ,m iv ,m ir Representing the inertial mass of the ith unmanned boat; nonlinear function f iu ,f iv ,f ir Representing a set of uncertainty terms consisting of a centripetal force term, a coriolis force term, and a hydrodynamic damping force term; external disturbance forces/moments caused by wind, waves, currents are denoted as tau iud ,τ ivd ,τ ird The method comprises the steps of carrying out a first treatment on the surface of the The control forces/moments corresponding to longitudinal and bow movements are denoted as tau respectively iu ,τ ir 。
Preferably, the step 1 model conversion process is specifically:
setting upFor the synthesis speed of the unmanned ship, the kinematic equation of the unmanned ship is simplified into the following formula:
wherein ,ψiw As the heading angle, ψ iw ＝ψ i +β i ；β i Is sideslip angle beta i ＝atan(v i /u i ) The method comprises the steps of carrying out a first treatment on the surface of the The underactuated unmanned ship lacks transverse thrust, and drift force can cause the unmanned ship to generate sideslip angle beta i The following formula can be obtained:
the above formula is based on u i ＝U i cos(β i ) Derived; when u is i At=0, the unmanned boat is stationary; the kinetic equation of the under-actuated unmanned boat is rewritten as:
dividing the unmanned aerial vehicle system into a position subsystem and a posture subsystem, wherein the position subsystem is represented by the following formula:
wherein ,is a nonlinear term related to the unmanned ship state, and comprises the model uncertainty and the exposed outside of the unmanned shipA disturbance force/moment;
setting p i ＝col(x i ,y i ),ξ iψ ＝col(cosψ iw ,sinψ iw ) Respectively representing coordinates and conversion vectors of the unmanned ship; for the gesture subsystem, there are:
wherein ,nonlinear term->Satisfy->
Preferably, the step 2 specifically includes:
defining leader follower formation configuration asUndirected graph->Comprises a finite set of m sides and n points>Is provided with->Is a layout;
definition ψ= [ ψ ] 1 ,...,ψ n ] T, wherein ψi For the heading angle of the ith unmanned ship, respectively defining and />The layout p and heading angle ψ can in turn be written as p= [ p ] as a set of points of the leader and follower l ,p f ] T Psi= [ psi ] l ,ψ f ] T ；
The azimuth vector is g= [ g ] 1 ,...,g m ] T Wherein each vector element in the set is paired with an undirected graphOne-to-one correspondence of the edges of (a); acquiring azimuth vector g by on-board sensor k K e 1..m, the azimuth vector is written in the form:
wherein ,is an edge vector, an azimuth vector g ij Represents p j Relative to p i Unlike conventional measurement methods, this expression regards orientation as a two-dimensional real vector space +.>An angle in and e ij ＝-e ij ,g ij ＝-g ij ；
For target formation, an azimuthal Laplace matrix is definedThe method comprises the following steps:
when the head of the kth edge is the ith vertex, then there isWhen the tail of the kth edge is the ith vertex, then there is
The azimuth laplace matrix is divided into the following forms:
wherein , and />Target position following boat->Is denoted as->The desired heading angle of each following boat +.>Is denoted as-> wherein />A desired location for an ith unmanned boat;
the formula for preventing collision among boats is given as follows: order theThen there is a minimum distance l to satisfyTo ensure that when delta (0) satisfies +.>At the time, there areFor->All are true.
Preferably, the targets are as follows:
based on the azimuth measurement, a formation control law is designed for the unmanned ship to satisfy the conditions:
(1) The adjacent azimuth angle satisfies
(2) The heading angle satisfies wherein /> Indicating the desired heading angle.
Preferably, the step 3 specifically includes:
unmanned ship formation controller based on leading-following structure is designed as follows:
the tracking error is defined as follows:
wherein ,
according toConsidering the directed graph, then the azimuth constraint +.>Is rewritten to +.>Order the
Setting the auxiliary variable asThe virtual control law is designed as follows:
wherein ,
setting the virtual tracking errors as respectivelyIs->The derived unmanned ship dynamic system equation is as follows:
the derivatives of the relevant adaptive law are respectively:
α ζu ,β ζu ,α ζr beta and beta ζr Is positive gain, input vector isThe unmanned ship formation control input based on the azimuth information is set as:
stable unmanned ship formation error U ie and rie The upper part plays the leading role.
Preferably, since the ith unmanned boat only needs to measure its azimuth angle relative to the interproximal boatThe virtual control law is designed to be distributed;
due toThe designed virtual control laws are always bounded, i.e
From the geometrical relationship, due toThen->And g is equal to ij Is vertical, and the virtual control law keeps the distance between boats and continuously reduces the azimuth angle g ij Is a function of the error of (a).
An underactuated unmanned ship formation control system under the condition of distance information loss is characterized in that: the system comprises:
the model building module is used for building an underactuated unmanned ship formation kinematic dynamics model and carrying out model conversion on the attitude subsystem;
the formation module is used for constructing a target formation of the unmanned ship and determining a control target;
the control module establishes a formation controller of the leading following structure to control unmanned ship formation
A computer readable storage medium having stored thereon a computer program for execution by a processor for implementing a method of underactuated unmanned aerial vehicle formation control in the absence of distance information
A computer device comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes an underactuated unmanned aerial vehicle formation control method under the condition of distance information loss when executing the computer program
The application has the following beneficial effects:
compared with the prior art, the application has the advantages that:
compared with the prior art, the unmanned ship formation control can be completed only by the relative azimuth measurement value and the hull speed measurement value, less measurement information is needed by the control method, and meanwhile, the complex coupling relation between the dynamic part, the position and the attitude subsystem of the control object in the actual engineering is correctly considered, so that the control architecture is effectively simplified, and the unmanned ship formation track tracking is realized under the conditions of external interference and uncertain model parameters and has strong robustness.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present application, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of an unmanned ship formation controller method based on a lead following structure in accordance with the present application;
FIG. 2 is a two-dimensional plan trajectory of an unmanned boat;
FIG. 3 is a plot of azimuth error variation for unmanned ship formation;
FIG. 4 is a control signal response graph;
FIG. 5 is a graph of position error versus heading angle error versus longitudinal speed error versus yaw rate error;
FIG. 6 is a graph of the time response of the adaptive law;
fig. 7 is an unmanned boat formation communication topology.
Detailed Description
The following description of the embodiments of the present application will be made apparent and fully in view of the accompanying drawings, in which some, but not all embodiments of the application are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
In the description of the present application, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present application. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present application, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present application will be understood in specific cases by those of ordinary skill in the art.
In addition, the technical features of the different embodiments of the present application described below may be combined with each other as long as they do not collide with each other.
The present application will be described in detail with reference to specific examples.
First embodiment:
according to the embodiments shown in fig. 1 to 7, the specific optimization technical scheme adopted by the present application to solve the above technical problems is as follows: the application relates to an under-actuated unmanned ship formation control method under the condition of distance information deficiency, which considers the complex coupling relation between the dynamic part and the position and posture subsystem of a control object in actual engineering, effectively simplifies the control architecture, realizes the track tracking of unmanned ship formation under the conditions of external interference and uncertain model parameters, and has strong robustness.
An under-actuated unmanned ship formation control method under the condition of distance information loss, comprising the following steps:
step 1: establishing an underactuated unmanned ship formation kinematic dynamics model, and carrying out model conversion on a gesture subsystem;
step 2: constructing a target formation of the unmanned ship, and determining a control target;
step 3: and a formation controller of the leading following structure is established to control unmanned ship formation.
The application provides an underactuated unmanned ship formation control method aiming at the condition of distance information deficiency. In recent years, the technology of unmanned ships on water surface is rapidly developed, the working environment is complex and changeable, in the actual task scene, the on-board stadia are expensive, and large-scale unmanned ships can not be listed in large quantity for formation, so that the application provides that the formation control of the underactuated unmanned ships is realized by means of azimuth information measured by an optical sensor under the condition of not depending on the stadia. The algorithm can effectively realize track tracking of the formation of the underactuated unmanned ship, and the requirement on system resources can be reduced by reducing the online calculated amount through a minimum learning parameter algorithm. Firstly, establishing an underactuated unmanned ship formation kinematic dynamics model, and carrying out model conversion on a gesture subsystem; then, constructing a target formation of the unmanned ship and determining a control target; and finally, designing a formation controller of the leading-following structure, and verifying the stability and the robustness of the unmanned ship formation system. The application can effectively realize track tracking control of unmanned ship formation under the condition of communication distance loss, and proves that error signals of a control system can be converged rapidly.
Specific embodiment II:
the second embodiment of the present application differs from the first embodiment only in that:
the step 1 model building process specifically comprises the following steps:
considering the two-dimensional plane motion of the three-degree-of-freedom underactuated unmanned ship under a geodetic coordinate system and a satellite coordinate system, the kinematic equation of the unmanned ship is represented by the following formula:
wherein ,pi ＝(x i ,y i )，p i Representing the position of the ith unmanned ship under the geodetic coordinate system; psi phi type i Representing the heading of an ith unmanned ship under a geodetic coordinate system; u (u) i ,v i ,r i Respectively represent under the satellite coordinate systemSpeed or angular speed corresponding to longitudinal, transverse and bow;
establishing a kinetic equation corresponding to the unmanned ship, wherein the kinetic equation is expressed by the following formula:
wherein ,miu ,m iv ,m ir Representing the inertial mass of the ith unmanned boat; nonlinear function f iu ,f iv ,f ir Representing a set of uncertainty terms consisting of a centripetal force term, a coriolis force term, and a hydrodynamic damping force term; external disturbance forces/moments caused by wind, waves, currents are denoted as tau iud ,τ ivd ,τ ird The method comprises the steps of carrying out a first treatment on the surface of the The control forces/moments corresponding to longitudinal and bow movements are denoted as tau respectively iu ,τ ir 。
Third embodiment:
the difference between the third embodiment and the second embodiment of the present application is that:
the step 1 model conversion process specifically comprises the following steps:
setting upFor the synthesis speed of the unmanned ship, the kinematic equation of the unmanned ship is simplified into the following formula:
wherein ,ψiw As the heading angle, ψ iw ＝ψ i +β i ；β i Is sideslip angle beta i ＝atan(v i /u i ) The method comprises the steps of carrying out a first treatment on the surface of the The underactuated unmanned ship lacks transverse thrust, and drift force can cause the unmanned ship to generate sideslip angle beta i The following formula can be obtained:
the above formula is based on u i ＝U i cos(β i ) Derived; when u is i At=0, the unmanned boat is stationary; the kinetic equation of the under-actuated unmanned boat is rewritten as:
dividing the unmanned aerial vehicle system into a position subsystem and a posture subsystem, wherein the position subsystem is represented by the following formula:
wherein ,the method is a nonlinear term related to the state of the unmanned ship, and comprises the uncertainty of a model of the unmanned ship and external disturbance force/moment received by the model;
setting p i ＝col(x i ,y i ),ξ iψ ＝col(cosψ iw ,sinψ iw ) Respectively representing coordinates and conversion vectors of the unmanned ship; for the gesture subsystem, there are:
wherein ,nonlinear term->Satisfy->
Fourth embodiment:
the fourth embodiment of the present application differs from the third embodiment only in that:
the step 2 specifically comprises the following steps:
defining leader follower formation configuration asUndirected graph->Comprises a finite set of m sides and n points>Is provided with->Is a layout;
definition ψ= [ ψ ] 1 ,...,ψ n ] T, wherein ψi For the heading angle of the ith unmanned ship, respectively defining and />The layout p and heading angle ψ can in turn be written as p= [ p ] as a set of points of the leader and follower l ,p f ] T Psi= [ psi ] l ,ψ f ] T ；
The azimuth vector is g= [ g ] 1 ,...,g m ] T Wherein each vector element in the set is paired with an undirected graphOne-to-one correspondence of the edges of (a); acquiring azimuth vector g by on-board sensor k K e 1..m, the azimuth vector is written in the form:
wherein ,is an edge vector, an azimuth vector g ij Represents p j Relative to p i Unlike conventional measurement methods, this expression regards orientation as a two-dimensional real vector space +.>An angle in and e ij ＝-e ij ,g ij ＝-g ij ；
For target formation, an azimuthal Laplace matrix is definedThe method comprises the following steps:
when the head of the kth edge is the ith vertex, then there isWhen the tail of the kth edge is the ith vertex, then there is
The azimuth laplace matrix is divided into the following forms:
wherein , and />Target position following boat->Is denoted as->The desired heading angle of each following boat +.>Is denoted as-> wherein />A desired location for an ith unmanned boat;
the formula for preventing collision among boats is given as follows: order theThen there is a minimum distance l to satisfyTo ensure that when delta (0) satisfies +.>At the time, there areFor->All are true.
Fifth embodiment:
the fifth embodiment of the present application differs from the fourth embodiment only in that:
based on the azimuth measurement, a formation control law is designed for the unmanned ship to satisfy the conditions:
(1) The adjacent azimuth angle satisfies
(2) The heading angle satisfies wherein /> Indicating the desired heading angle.
Specific embodiment six:
the difference between the sixth embodiment and the fifth embodiment of the present application is that:
the step 3 specifically comprises the following steps:
unmanned ship formation controller based on leading-following structure is designed as follows:
the tracking error is defined as follows:
wherein ,
according toConsidering the directed graph, then the azimuth constraint +.>Is rewritten to +.>Order the
Setting auxiliaryThe auxiliary variable isThe virtual control law is designed as follows:
wherein ,
setting the virtual tracking errors as respectivelyIs->The derived unmanned ship dynamic system equation is as follows:
the derivatives of the relevant adaptive law are respectively:
α ζu ,β ζu ,α ζr beta and beta ζr Is positive gain, input vector isThe unmanned ship formation control input based on the azimuth information is set as:
stable unmanned ship formation error U ie and rie The upper part plays the leading role.
Specific embodiment seven:
the seventh embodiment of the present application differs from the sixth embodiment only in that:
because the ith unmanned ship only needs to measure the azimuth angle of the ith unmanned ship relative to the adjacent shipsThe virtual control law is designed to be distributed;
due toThe designed virtual control laws are always bounded, i.e
From the geometrical relationship, due toThen->And g is equal to ij Is vertical, and the virtual control law keeps the distance between boats and continuously reduces the azimuth angle g ij Is a function of the error of (a).
Specific embodiment eight:
the eighth embodiment of the present application differs from the seventh embodiment only in that:
the application provides an underactuated unmanned ship formation control system under the condition of distance information deficiency, which comprises the following components:
the model building module is used for building an underactuated unmanned ship formation kinematic dynamics model and carrying out model conversion on the attitude subsystem;
the formation module is used for constructing a target formation of the unmanned ship and determining a control target;
and the control module establishes a formation controller of the leading following structure to control unmanned ship formation.
Specific embodiment nine:
the difference between the embodiment nine and the embodiment eight of the present application is that:
the present application provides a computer-readable storage medium having stored thereon a computer program for execution by a processor for implementing an under-actuated unmanned aerial vehicle formation control method, such as in the absence of distance information
The purpose of the application is realized in the following way: the underactuated unmanned ship formation control method under the condition of the lack of distance information is designed, and comprises the following steps:
(1) Establishing an underactuated unmanned ship formation kinematic dynamics model, and carrying out model conversion on a gesture subsystem;
(2) Constructing a target formation of the unmanned ship and determining a control target;
(3) A formation controller of a leading-following structure is designed;
(4) And verifying the stability and the robustness of the unmanned ship formation system.
1. In the step 1, unmanned ship formation kinematics and dynamics models are established, and model conversion is carried out on a gesture subsystem, wherein the model conversion is as follows:
considering the two-dimensional plane motion of the three-degree-of-freedom underactuated unmanned ship under the geodetic coordinate system and the satellite coordinate system, the kinematic equation of the first unmanned ship can be expressed as follows:
definition p i ＝(x i ,y i )，p i And (5) representing the position of the ith unmanned ship in the geodetic coordinate system. Psi phi type i And (5) representing the heading of the ith unmanned ship under the geodetic coordinate system. u (u) i ,v i ,r i Respectively representing the corresponding speeds or angular speeds of longitudinal, transverse and bow in the satellite coordinate system. Next, a kinetic equation corresponding to the unmanned boat is given, expressed as:
wherein ,miu ,m iv ,m ir Representing the inertial mass of the ith unmanned boat. Nonlinear function f iu ,f iv ,f ir Representing a set of uncertainty terms consisting of a centripetal force term, a coriolis force term, and a hydrodynamic damping force term. In addition, the external disturbance force/moment caused by wind, wave, current is denoted as τ iud ,τ ivd ,τ ird . The control forces/moments corresponding to longitudinal and bow movements are denoted as tau respectively iu ,τ ir . In addition, due to the underactuated nature of the unmanned boat in the present chapter, no relevant control force is applied to the lateral float motion of the unmanned boat.
Further, defineFor the synthesis speed of the unmanned ship, the kinematic equation of the unmanned ship can be simplified as follows:
wherein ,ψiw As the heading angle, ψ iw ＝ψ i +β i 。β i Is sideslip angle beta i ＝atan(v i /u i ). Due to underactuated unmannedThe lack of lateral thrust and drift force can lead to the generation of sideslip angle beta by unmanned boats i . The following formula can be obtained:
the above formula is based on u i ＝U i cos(β i ) Derived from the above. When u is i At=0, the drone is stationary. Accordingly, the kinetic equation of the under-actuated unmanned boat can be rewritten as:
for ease of description, the unmanned boat system is divided into a position subsystem and a posture subsystem, wherein the position subsystem may be expressed as:
wherein ,is a nonlinear term related to the unmanned ship state, and comprises the model uncertainty of the unmanned ship and the external disturbance force/moment. />
Let p be i ＝col(x i ,y i ),ξ iψ ＝col(cosψ iw ,sinψ iw ) Representing the coordinates and conversion vectors of the unmanned aerial vehicle, respectively. For the gesture subsystem, there are:
wherein ,nonlinear term->Satisfy->
2. Subsequently, in step 2, a target formation of the unmanned ship is constructed and a control target is determined as follows:
a formation definition based on the leader follower configuration, an azimuth constraint definition, and a target formation definition are now given.
Defining leader-follower formation configuration asUndirected graph->Comprises a finite set of m sides and n points>Is provided with->Is a layout.
Furthermore, since the control object is an unmanned boat, the control problem related to the heading angle must also be taken into consideration. For this, define ψ= [ ψ = 1 ,...,ψ n ] T, wherein ψi For the heading angle of the ith unmanned ship, since the proposed distributed formation control scheme is designed in the formation configuration of the leader-follower, for convenience, the following is defined respectively and />The layout p and heading angle ψ can in turn be written as p= [ p ] as a set of points of the leader and follower l ,p f ] T Psi= [ psi ] l ,ψ f ] T 。
The azimuth vector is g= [ g ] 1 ,...,g m ] T Wherein each vector element in the set is paired with an undirected graphOne-to-one correspondence of the edges of (a). The azimuth vector g can be obtained by a boat-mounted sensor (such as radar, laser radar and the like) k K.epsilon.1..m. Here, to facilitate theoretical analysis, the azimuth vector is generally written in the form of:
wherein ,eij p j -p i Is an edge vector, an azimuth vector gi j Represents p j Relative to p i Unlike conventional measurement methods, this expression treats the orientation as a two-dimensional real vector spaceAn angle in and e ij ＝-e ij ,g ij ＝-g ij 。
For target formation, an azimuthal Laplace matrix is definedThe method comprises the following steps:
if the head of the kth edge is the ith vertex, then there isIf the tail of the kth edge is the ith vertex, then there is
For ease of analysis, the azimuth laplace matrix is divided into the following forms:
wherein , and />Suppose target formation +.>Is infinitely stiff in a small orientation and has at least two leaders in the formation, so the matrix +.>Is nonsingular, then follows the target position of the boat +.>Can be expressed as +.>Thus, each following the desired heading angle of the boat +.>Can be expressed as +.> wherein />Is the desired location of the ith unmanned boat.
Considering the possible collision problem of members in the formation and formation holding process in the formation of unmanned ships, the collision prevention formula among ships is given as follows: order theThen there is a minimum distance l to satisfyTo ensure that when delta (0) satisfies +.>At the time, there areFor->All are true.
The control targets are as follows:
based on the azimuth measurement, a formation control law is designed for the unmanned ship to satisfy the conditions:
(1) The adjacent azimuth angle satisfies
(2) The heading angle satisfies wherein /> Indicating the desired heading angle.
3. Further, the unmanned ship formation controller based on the lead-following structure is designed in step 3 as follows:
the tracking error is defined as follows:
wherein ,
due toConsidering the directed graph, then the azimuth constraint +.>Can be rewritten to +.>Order theFor this purpose, the auxiliary variable is defined as +.>The virtual control law is designed as follows:
wherein ,first, since the ith unmanned boat only needs to measure its azimuth angle +.>The virtual control laws are designed to be distributed. Furthermore, due to->The designed virtual control law is always bounded, i.e. +.>Finally, as can be seen from the geometrical relationship, due toThen->With gi j Is vertical. Thus, the virtual control law keeps the inter-boat distance and continuously reduces the azimuth gi j Is a function of the error of (a).
Defining virtual tracking errors as respectivelyIs->Accordingly, the unmanned boat dynamic system equation can be deduced as follows: />
The derivatives of the relevant adaptive law are respectively:
α ζu ,β ζu ,α ζr beta and beta ζr Is positive gain, input vector isThe unmanned ship formation control input based on the azimuth information is set as:
the scheme stabilizes unmanned ship formation errors U ie and rie The upper part plays the leading role. Meanwhile, except for azimuth information, each unmanned ship in the formation in the control scheme cannot interact with other state information of the neighbor ships. Design parameter k introduced in the control scheme u and kr So that in analysis U e The process is clearer when the convergence is improved. In addition, k u and kr The larger the value of (c), the higher the convergence speed of the unmanned aerial vehicle formation system, and the higher the demand for control signals.
4. In step 4, the stability and robustness of the unmanned ship formation system are verified:
since unmanned aerial vehicle formation will eventually converge to target formation, the bearing error must converge to zero. So for the position part of unmanned ship formation, a suitable lyapunov function is designed as follows:
deriving Lyapunov function and substituting virtual control law into the Lyapunov function
Due toThen all of the values of [ delta (t) ] are not more than [ delta (0) ] for all of the values of [ t ] > 0. Due to->/>
Finally can get
V can be seen as 1 Is exponentially converging.
Similarly, the Lyapunov function is selectedIt can also prove V 2 Is exponentially converging.
In order to theoretically verify the errors of unmanned ship formation systems and the stability of the designed adaptive parameters, a Lyapunov function is constructed as follows:
will V 3 The derivative is obtained by combining a tracking error dynamics formula:
wherein
The effectiveness of the proposed control strategy is verified by the lyapunov correlation theory. By adopting the minimum learning parameter method, the excessive loss of the calculation resources of the unmanned ship formation control system is effectively reduced. Through the analysis, under the control scheme, the state quantity and the error of all unmanned ships formation can be finally consistent and stable.
The performance of the controller will be demonstrated and verified by the simulation example.
The unmanned ship formation comprises two virtual leaders and four real following ships. In the simulation, the mass m of each unmanned ship is 23.8kg, the length L is 1.255m, the width B is 0.29m, and the mathematical model parameters and the external disturbance parameters of the unmanned ships are all international standard values, as shown in the table 1:
table 1 unmanned ship model parameter table
All hydrodynamic parameters not listed in the table are assumed to be zero.
Establishing a target formationThe communication topology of (2) is shown in figure 7. The number 1 and the number 4 are selected as virtual leading boats, and the initial states of all unmanned boats in the formation are as follows:
p 1 (0)＝[10m,10m,π/4]
p 2 (0)＝[0m,7m,π/2]
p 3 (0)＝[15m,0m,π/9]
p 4 (0)＝[10m,-10m,π/4]
p 5 (0)＝[-3m,1m,π/7]
p 6 (0)＝[-8m,10m,π/8]
further, virtual pilot control parameters and neural network parameters are shown in table 2:
table 2 control parameter table
The detailed simulation results are shown in fig. 2-6.
FIG. 2 is a two-dimensional flat of unmanned ship formationThe face track diagram shows that the unmanned ship forms an isosceles right triangle formation after a certain time in formation and keeps the formation running all the time, and the designed unmanned ship formation control scheme can ensure that the following ship in formation can timely track the corresponding expected track given by the virtual pilot ship; FIG. 3 shows azimuth errors for unmanned aerial vehicle formationA graph changing along with time, wherein the azimuth angle error gradually converges to be near 0 along with the formation of unmanned ship formation alignment; fig. 4 (a) (b) are schematic diagrams of output control forces and moments corresponding to the unmanned ship position subsystem and the attitude subsystem, respectively, and the control forces/moments of each unmanned ship are limited to 350N and 400n×m respectively, so that the control forces/moments of the unmanned ships can be found to fluctuate sharply at the initial moment, and the rapid response to the state quantity errors is ensured; FIG. 5 (a) (b) is position error +.>And the heading angle error is +.>According to the change graph with time, the heading angle errors of all following boats are converged to 0 at about 12 s; FIG. 5 (c) (d) is a graph of the longitudinal speed error and the yaw rate error of the unmanned aerial vehicle formation over time, respectively, and it can be found that the unmanned aerial vehicle formation position error, the heading error, and the longitudinal speed error and the yaw rate error can all be converged to a tight set at about 12s, and remain stable all the time after that, that is, the errors of the two are finally consistent and bounded; FIG. 6 (a) (b) are adaptive parameters +.> and />Because of introducing the minimum parameter learning method, only the two adaptive parameters are updated in the formation control processNot the entire weight matrix.
Specific embodiment ten:
the tenth embodiment of the present application differs from the ninth embodiment only in that:
the application provides computer equipment, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes an underactuated unmanned ship formation control method under the condition of distance information loss when executing the computer program.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or N embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction. Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present application, "N" means at least two, for example, two, three, etc., unless specifically defined otherwise. Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more N executable instructions for implementing specific logical functions or steps of the process, and further implementations are included within the scope of the preferred embodiment of the present application in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the embodiments of the present application. Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or N wires, a portable computer cartridge (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer readable medium may even be paper or other suitable medium on which the program is printed, as the program may be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory. It is to be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the N steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. As with the other embodiments, if implemented in hardware, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
The above-mentioned preferred implementation manner of the under-actuated unmanned aerial vehicle formation control method under the condition of the lack of distance information is not limited to the above-mentioned embodiment, and all technical solutions under the concept belong to the protection scope of the present application. 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 application, which is also considered to be within the scope of the present application.
Claims (10)
1. An underactuated unmanned ship formation control method under the condition of distance information loss is characterized by comprising the following steps: the method comprises the following steps:
step 1: establishing an underactuated unmanned ship formation kinematic dynamics model, and carrying out model conversion on a gesture subsystem;
step 2: constructing a target formation of the unmanned ship, and determining a control target;
step 3: and a formation controller of the leading following structure is established to control unmanned ship formation.
2. The method according to claim 1, characterized in that: the step 1 model building process specifically comprises the following steps:
considering the two-dimensional plane motion of the three-degree-of-freedom underactuated unmanned ship under a geodetic coordinate system and a satellite coordinate system, the kinematic equation of the unmanned ship is represented by the following formula:
wherein ,pi ＝(x i ,y i )，p i Representing the position of the ith unmanned ship under the geodetic coordinate system; psi phi type i Representing the heading of an ith unmanned ship under a geodetic coordinate system; u (u) i ,v i ,r i Respectively representing the corresponding speed or angular speed of longitudinal direction, horizontal drift and bow swing under a satellite coordinate system;
establishing a kinetic equation corresponding to the unmanned ship, wherein the kinetic equation is expressed by the following formula:
wherein ,miu ,m iv ,m ir Representing the inertial mass of the ith unmanned boat; nonlinear function f iu ,f iv ,f ir Representing a set of uncertainty terms consisting of a centripetal force term, a coriolis force term, and a hydrodynamic damping force term; external disturbance forces/moments caused by wind, waves, currents are denoted as tau iud ,τ ivd ,τ ird The method comprises the steps of carrying out a first treatment on the surface of the The control forces/moments corresponding to longitudinal and bow movements are denoted as tau respectively iu ,τ ir 。
3. The method according to claim 2, characterized in that: the step 1 model conversion process specifically comprises the following steps:
setting upFor the synthesis speed of the unmanned ship, the kinematic equation of the unmanned ship is simplified into the following formula:
wherein ,ψiw As the heading angle, ψ iw ＝ψ i +β i ；β i Is sideslip angle beta i ＝atan(v i /u i ) The method comprises the steps of carrying out a first treatment on the surface of the The underactuated unmanned ship lacks transverse thrust, and drift force can cause the unmanned ship to generate sideslip angle beta i The following formula can be obtained:
the above formula is based on u i ＝U i cos(β i ) Derived; when u is i At=0, the unmanned boat is stationary; the kinetic equation of the under-actuated unmanned boat is rewritten as:
dividing the unmanned aerial vehicle system into a position subsystem and a posture subsystem, wherein the position subsystem is represented by the following formula:
wherein ,the method is a nonlinear term related to the state of the unmanned ship, and comprises the uncertainty of a model of the unmanned ship and external disturbance force/moment received by the model;
setting p i ＝col(x i ,y i ),ξ iψ ＝col(cosψ iw ,sinψ iw ) Respectively representing coordinates and conversion vectors of the unmanned ship; for the gesture subsystem, there are:
wherein ,nonlinear term->Satisfy->
4. A method according to claim 3, characterized in that: the step 2 specifically comprises the following steps:
defining leader follower formation configuration asUndirected graph->Comprises a finite set of m sides and n points>Is provided with->Is a layout;
definition ψ= [ ψ ] 1 ,...,ψ n ] T, wherein ψi For the heading angle of the ith unmanned ship, respectively defining and />The layout p and heading angle ψ can in turn be written as p= [ p ] as a set of points of the leader and follower l ,p f ] T Psi= [ psi ] l ,ψ f ] T ；
The azimuth vector is g= [ g ] 1 ,…,g m ] T Wherein each vector element pair in the set corresponds to an edge in the undirected graph G one by one; acquiring azimuth vector g by on-board sensor k K e 1, …, m, the azimuth vector is written as follows:
wherein ,is an edge vector, an azimuth vector g ij Represents p j Relative to p i Unlike conventional measurement methods, this expression regards orientation as a two-dimensional real vector space +.>An angle in and e ij ＝-e ij ,g ij ＝-g ij ；
For target formation, an azimuthal Laplace matrix is definedThe method comprises the following steps:
when the head of the kth edge is the ith vertex, then there isWhen the tail of the kth edge is the ith vertex, there is +.>
The azimuth laplace matrix is divided into the following forms:
wherein , and />Target position following boat->Is denoted as->The desired heading angle of each following boat +.>Is denoted as-> wherein />A desired location for an ith unmanned boat;
the formula for preventing collision among boats is given as follows: order theThere is a minimum distance +>Satisfy->To ensure that when delta (0) satisfies +.>There is->For->All are true.
5. The method according to claim 4, characterized in that: the control targets are as follows:
based on the azimuth measurement, a formation control law is designed for the unmanned ship to satisfy the conditions:
(1) The adjacent azimuth angle satisfies
(2) The heading angle satisfies wherein />Indicating the desired heading angle.
6. The method according to claim 5, characterized in that: the step 3 specifically comprises the following steps:
unmanned ship formation controller based on leading-following structure is designed as follows:
the tracking error is defined as follows:
wherein ,
according toConsidering the directed graph, then the azimuth constraint +.>Is rewritten to +.>Order the
Setting the auxiliary variable asThe virtual control law is designed as follows:
wherein ,
setting the virtual tracking errors as respectivelyIs->The derived unmanned ship dynamic system equation is as follows:
the derivatives of the relevant adaptive law are respectively:
α ζu ,β ζu ,α ζr beta and beta ζr Is positive gain, input vector isThe unmanned ship formation control input based on the azimuth information is set as:
stable unmanned ship formation error U ie and rie The upper part plays the leading role.
7. The method according to claim 6, characterized in that:
because the ith unmanned ship only needs to measure the azimuth angle of the ith unmanned ship relative to the adjacent shipsThe virtual control law is designed to be distributed;
due toThe designed virtual control laws are always bounded, i.e
From the geometrical relationship, due toThen->And g is equal to ij Is vertical, and the virtual control law keeps the distance between boats and continuously reduces the azimuth angle g ij Is a function of the error of (a).
8. An underactuated unmanned ship formation control system under the condition of distance information loss is characterized in that: the system comprises:
the model building module is used for building an underactuated unmanned ship formation kinematic dynamics model and carrying out model conversion on the attitude subsystem;
the formation module is used for constructing a target formation of the unmanned ship and determining a control target;
and the control module establishes a formation controller of the leading following structure to control unmanned ship formation.
9. A computer readable storage medium having stored thereon a computer program, characterized in that the program is executed by a processor for implementing the method according to claims 1-7.
10. A computer device comprising a memory and a processor, the memory storing a computer program, characterized by: the processor, when executing the computer program, implements the method of claims 1-7.
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| CN117369267A (en) * | 2023-10-31 | 2024-01-09 | 东海实验室 | Method and system for controlling underwater helicopter surrounding formation under event triggering frame |
| CN117784619A (en) * | 2024-02-26 | 2024-03-29 | 广东海洋大学 | Under-actuated unmanned ship fault-tolerant control method based on zero and differential game |
| CN117784619B (en) * | 2024-02-26 | 2024-05-31 | 广东海洋大学 | Under-actuated unmanned ship fault-tolerant control method based on zero and differential game |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117369267A (en) * | 2023-10-31 | 2024-01-09 | 东海实验室 | Method and system for controlling underwater helicopter surrounding formation under event triggering frame |
| CN117369267B (en) * | 2023-10-31 | 2024-04-30 | 东海实验室 | Method and system for controlling underwater helicopter surrounding formation under event triggering frame |
| CN117784619A (en) * | 2024-02-26 | 2024-03-29 | 广东海洋大学 | Under-actuated unmanned ship fault-tolerant control method based on zero and differential game |
| CN117784619B (en) * | 2024-02-26 | 2024-05-31 | 广东海洋大学 | Under-actuated unmanned ship fault-tolerant control method based on zero and differential game |
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