CN110196599A - A kind of collision prevention with connect the unmanned boat distribution formation control method kept under constraint - Google Patents

A kind of collision prevention with connect the unmanned boat distribution formation control method kept under constraint Download PDF

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CN110196599A
CN110196599A CN201910560210.9A CN201910560210A CN110196599A CN 110196599 A CN110196599 A CN 110196599A CN 201910560210 A CN201910560210 A CN 201910560210A CN 110196599 A CN110196599 A CN 110196599A
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unmanned boat
error
function
virtual
formation
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CN110196599B (en
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戴诗陆
袁佳
董超
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South China Sea Survey Technology Center Of State Oceanic Administration (south China Sea Buoy Center Of State Oceanic Administration)
South China University of Technology SCUT
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South China Sea Survey Technology Center Of State Oceanic Administration (south China Sea Buoy Center Of State Oceanic Administration)
South China University of Technology SCUT
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/0206—Control of position or course in two dimensions specially adapted to water vehicles

Abstract

The invention discloses a kind of collision prevention with connect the unmanned boat distribution formation control method for keeping constraint lower, comprising steps of constructing the kinematics and dynamics modeling of unmanned boat；Information exchange in unmanned boat fleet system between each individual is described with undirected topological diagram；Establish the range error equation, virtual course angle error equation and azimuth angle error equation of adjacent unmanned boat on kth side, and by collision prevention with connect the restricted problem for keeping constraint specification formation error in pairs；Ensure that formation error meets the constraint condition of default transient performance using logarithm obstacle liapunov function, and carries out the design of Virtual Controller for the virtual course angle error system, range error system and azimuth angle error system of i-th of unmanned boat with backstepping technique method；Formation control device design in dynamic surface control technology avoid to Virtual Controller repeatedly derivation problem with solve the problems, such as that acceleration can not be surveyed；Design the distributed formation control device based on disturbance observer.

Description

A kind of collision prevention with connect the unmanned boat distribution formation control method kept under constraint
Technical field
The present invention relates to the formation control field of unmanned boat, in particular to a kind of collision prevention with connect keep constraint under nobody Ship distribution formation control method.
Background technique
Formation motion control is a typical problem of more unmanned boat cooperative systems, is the pass for realizing unmanned boat work compound One of key technology.Unmanned boat with certain formation structure compares single unmanned boat efficiency when completing certain complicated risky operation It is higher, exploration in water, target homing, sea chart drafting, resources survey etc..
Compared with the Trajectory Tracking Control of single unmanned boat, one of the difficult point of formation motor control problems is reference locus (usually being generated as virtual pilotage people) can not be acquired in all follower.Therefore, the follower in fleet system mainly according to By backfence information exchange, using from neighbours local message and self information local computing oneself control signal, I.e. each unmanned boat plans that itself is acted in next step using distributed formation control device strategy, to reach the system of forming and keeping The purpose of pattern formation.
When unmanned boat fleet system navigates by water under complicated sea situation, unknown outside extraneous stormy waves, ocean current etc. disturb will receive Dynamic influence, it is easy to deviate preset ideal trajectory, enter the transient process of adjustment trajector deviation.Although using traditional Quadratic form Li Yapu love Theory of Stability can guarantee the stability of system, but system is unable to satisfy preset transitory Energy (overshoot and convergence rate that refer mainly to error).Therefore, another difficult point of formation motion control is how to combine The transient state and steady-state performance of system.
Unmanned boat fleet system can encounter many problems during real navigation, for example adjacent unmanned boat enters each other Safe distance within the scope of, be just easy to happen the danger of collision, so as to cause system penalty even collapse；If mutual Relative position too far, since the short haul connection of wireless device in practical application is restricted communication link, in communication capacity In the case where topically effective, and adjacent unmanned boat can be made not receive the signal of other side's transmission, weaken communication quality.Cause This, collision avoids keeping with communication connection being also problem in need of consideration.
In addition, the variable that is difficult to handle and be unable to measure is usually contained in the derivative of Virtual Controller, external unknown time-varying Disturbance can also impact system performance, and these problems all bring huge challenge to unmanned boat distribution formation control.
Summary of the invention
The purpose of the present invention is being directed to the problems of the prior art, a kind of collision prevention is provided and the nothing that connect under holding constrains People's ship distribution formation control method, the method design distributed formation control device for the unmanned boat that model determines, it is ensured that The distance and angle of adjacent unmanned boat are in a preassigned distance range always in entire movement of forming into columns, and are formed into columns and are missed Difference meets preassigned steady-state performance and transient performance, and can be avoided communication connection when collision occurs, remains initial State and the desired formation mode of formation.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of collision prevention with connect the unmanned boat distribution formation control method kept under constraint, the method includes following steps It is rapid:
Step (1): the kinematics and dynamics modeling of unmanned boat in fleet system is established；
Step (2): Associative algcbra graph theoretic approach uses non-directed graphTo describe the information in unmanned boat fleet system between each individual Interaction；
Step (3): the range error equation of adjacent unmanned boat on kth side is establishedVirtual course angle error equation And azimuth angle error equationWhereinM is non-directed graphIn all different sides total quantity, It communicates to connect to avoid collision and keeping, is described as collision prevention with the restricted problem kept is connect in conjunction with default capabilities control technology To the restricted problem of formation error；
Step (4): logarithmic barrier function is introduced in Li Yapu love Function Synthesis design method, and construction is corresponding right Number obstacle Li Yapu love function, it is ensured that after formation error is no more than preset transient performance constraint condition, and utilization The virtual course angle error system, range error system and azimuth angle error system that design method is pushed away for i-th of unmanned boat carry out The design of Virtual Controller, wherein i ∈ { 1,2 ... n }, n are the total number of unmanned boat in fleet system；
Step (5): dynamic surface control technology is introduced, on the basis of step (4) utilize backstepping technique method to avoid appearance Virtual Controller repeatedly derivation the problem of and controller in the problem of including the acceleration information of neighbours' unmanned boat；
Step (6): based on step (3) to algebraic graph theory method, the default capabilities control technology, logarithm obstacle in step (5) Li Yapu love function, backstepping technique method and dynamic surface control technology, and unknown external disturbance is carried out using disturbance observer Estimation and compensation are to design suitable distributed formation control device.
Further, in step (1), the kinematics and dynamics modeling of i-th of unmanned boat are as follows:
First three items in above formula are the kinematical equations of system, wherein (xi,yi) indicate i-th of unmanned boat in geodetic coordinates It is (OeXeYe) under position；ψiFor the course angle under earth coordinates；In each component corresponding to body sit Mark system (obxbyb) under forward speed ui, swaying speed υiWith steering angular velocity ri；Last in above formula is the dynamic of system Mechanical equation, wherein Mi> 0 is inertial matrix；For total coriolis force and centripetal acceleration matrix；To damp square Battle array；τiIndicate the control input of unmanned boat；τωi(t) the external unknown time-varying due to caused by the natural causes such as stormy waves, ocean current is indicated Disturbance；Matrix Mi,WithConcrete form difference it is as follows:
Wherein
In above formula, miIt is the quality of i-th of unmanned boat；IziIt is the rotary inertia on steering angular velocity direction； WithIt is additional mass；xgiIt is i-th of unmanned boat in xbCenter of gravity on coordinate；X(·), Y(·)And N(·)It is to advance respectively Linear and a secondary fluid dynamics damped coefficient on directional velocity, swaying directional velocity and steering angular velocity direction.
Further, in step (2), non-directed graph is usedTo describe in unmanned boat fleet system between each individual Information exchange,It is finite nonempty set conjunction, referred to as vertex set, wherein the vertex correspondence that number is 0 is virtually led Boat person, each vertex correspondence in set { 1,2, ..., N } have the follower of identical number； It is finite aggregate, referred to as side collection, each edge are corresponding with the identical adjacent unmanned boat numbered and can communicated with each other；Non-directed graph's Adjacency matrix A=(aij)(N+1)×(N+1)Element aij∈ { 0,1 }, when the information of the available unmanned boat j of unmanned boat i, j at this time Referred to as tail portion, i are known as head, aij=1, otherwise aij=0；The neighbours of vertex i collect is defined as:
To avoid error defined in step (3) from producing ambiguity, non-directed graph is given in advanceIn each edge specify a side To introducing incidence matrix B=(bij)(N+1)×M, wherein M beIn all different sides total quantity, each element definition in matrix Are as follows:
It usesIndicate kth side, wherein
Further, the adjacent unmanned boat i in step (3), on kth sidekAnd jkRelative positionAzimuthWith virtual course angleIt is specifically defined are as follows:
Wherein
Communication connection is kept: radius isBorder circular areas indicate unmanned boat ikThe region that information can be received, when every When the communication range of a unmanned boat is limited, to guarantee stable and reliable communication, adjacent unmanned boat ikAnd jkDistance must be positioned at Vertex i in communication zone, i.e., on kth sidek、jkBetween distance must meet
Wherein,For the radius of the communication zone on preset kth side；
Collision avoids: radius isBorder circular areas indicate unmanned boat ikHull radius, when any pair it is adjacent nobody Ship can just prevent collision, i.e., adjacent unmanned boat i outside mutual default safety zonekAnd jkBetween distance must meet
Wherein,dk,conIt is avoided collision on preset kth side Least radius；
Azimuth-limited: adjacent unmanned boat ik、jkCentral point obBetween line be known as central point line, azimuthFor unmanned boat ikCourse angle and ik、jkAngle between central point line, the angle is counterclockwise, and value is positive, clockwise Value is negative, to guarantee the safety and communication quality when the navigation of unmanned boat fleet system, it is necessary to ensure that
Wherein θk,conMeet 0 < θ of inequalityk,con<π/2；
The formation position error being defined as followsFormation angular errorWith
Wherein, dk,des、θk,desAnd ψk,desIt is opposite to respectively indicate ideal distance on kth side, desirable orientation angle and ideal Course angle, usually their value are constant, and 0 < d of inequalityk,col<dk,des<dk,conWith | θk,des|<θk,con< pi/2 assembly It is vertical, it is clear that if errorWithMeet following inequality, then communicate to connect holding, collision avoid with azimuth by Limit just can be guaranteed:
Wherein, WithThe quality of fleet system performance is affected since transient performance is serious, using pre- performance function as mistake The boundary function of difference, to formation errorWithIt is constrained, specific constraint is as follows
Wherein, nk=dk,θk,ψk；WithBe specified by designer, it is smooth, bounded and decline with the time The function subtracted, it is contemplated that it is just elected to be boundary function by the characteristic of exponential functionWithI.e.WithConcrete form For
In above formula,WithThe also referred to as default capabilities function of monotone decreasing；Initial value Parameter WithBe greater than zero can design parameter, and relationship must be met:WithIts InWithIndicate the maximum steady state error amount allowed.Reasonable above-mentioned parameter of choosing can make errorMeet Preset transient performance (referring mainly to convergence rate and overshoot) and steady-state performance (referring mainly to steady-state error).
Further, in step (4), due under the conditions of not violating default transient state and steady state constraint, using traditional two Secondary type Li Yapu love function design controller, which is one, very has the problem of challenge, therefore introduces logarithmic barrier function and solve Restricted problem.Formation angular errorCorresponding logarithmic barrier functionConcrete form it is as follows
In above formula,Ln () indicates natural logrithm, can from above formula Know, ifValue always in the opener comprising zero pointFluctuation, function in rangeBounded always is incited somebody to action, only Following two situation is occurred,Value just can be infinitely great or infinitely small: whenWhen,WhenWhen,Therefore it can be achieved by ensuring that functionBoundedness guarantee errorAlways not The preset transient state of violation formula and steady state constraint；DefinitionDue to functionIt is not a positive definite letter Number, therefore reconfigure a kind of nonnegative function that control design case is carried out based on Li Yapu love function, referred to as logarithm obstacle Li Ya General love function, specific as follows:
Virtual Controller design is carried out for virtual course angle error system with backstepping technique method, then i-th of unmanned boat Virtual Controller αriAre as follows:
Wherein
kriBe greater than zero can design parameter；It indicates the side of connection vertex i and vertex j, i.e.,It is equivalent toThis literary style, to have WithMeet following relationship: when vertex, i is side kijHead when, Δ (i, kij)=1；When vertex, i is side kijTail portion when, Δ (i, kij)=- 1；Otherwise Δ (i, kij)=0；
Similarly, logarithmic barrier function is introducedWithGuarantee formation position error respectivelyWith formation angular errorPreset transient state and steady state constraint are not violated, and limitation problem is converted into boundedness problem, considers such as minor function
Wherein χ=d, θ；Construction as follows aboutWithNon-negative logarithm obstacle Li Yapu love Function
For range error system and azimuth angle error system, the Virtual Controller α obtained with backstepping technique methoduiWith αυiFor
Wherein
kuiAnd kυiBe greater than zero can design parameter；AngleVariableRespectively indicate adjacent unmanned boat i on kth sidekAnd jkRelative position, azimuth and virtual course Angle；WithRespectively correspond unmanned boat j on kth sidekForward speed and swaying speed；Unmanned boat on corresponding kth side ikSteering angular velocity；WithForm it is as follows
Further, in step (5), to avoid Virtual Controller, derivation (asks second order or higher derivative to will increase meter repeatedly Calculation amount) and prevent from including acceleration item in designed controller, dynamic surface control technology is introduced, using dynamic surface control When technology, Virtual Controller α is allowedθi, wherein θ=u, υ, filter Virtual Controller by obtaining after a low-pass first order filter αθfi, to offset some coupling terms, selection allows αθmiBy filter to obtain αθfi, specific as follows shown
Wherein, μui> 0 and μυi> 0 is programmable time constant filter；YuiAnd YυiForm difference it is as follows
Wherein, angleVariableIt respectively indicates adjacent on kth side Unmanned boat ikAnd jkRelative position, azimuth and virtual course angle；WithIt is logarithmic barrier function；With? It is the function about system state variables.
Further, in step (6), skill is controlled to algebraic graph theory method, the default capabilities in step (5) based on step (3) Art, logarithm obstacle Li Yapu love function, backstepping technique method and dynamic surface control technology, and use following disturbance observer pair Unknown external disturbance τωiEstimated and is compensated
Wherein, Kdi=diag { kd1i,kd2i,kd3iBe by greater than zero can the positive definite matrix that constitutes of design parameter；For τωiEstimated value；For the state vector of three-dimensional observation device；Then distributed formation control device τiIt can design are as follows:
Wherein
Diagonal matrix Kτi=diag { kτ1i,kτ2i,kτ3iIt is by can the positive definite matrix that constitutes of design parameter；MiFor inertial matrix；For total coriolis force and centripetal acceleration matrix；For damping matrix；Qi(pij,ψij) be system state variables letter Number；Error vector ei=[eui,eυi,eri]T, wherein eui、eυiAnd eriRespectively indicate the forward speed u of i-th of unmanned boatiWith filter Wave Virtual Controller αufiDifference, swaying speed υiWith filtering Virtual Controller αυfiDifference, steering angular velocity riWith Virtual Controller αriDifference:
eui=ui-αufi
eυi=υi-αυfi
eri=ri-αri
VectorWherein eαuiAnd eαui For level error, the filtering Virtual Controller α of i-th of unmanned boat is respectively indicatedufiWith Virtual Controller αuiDifference, filtering it is virtual Controller αυfiWith Virtual Controller αυiDifference:
Compared with the prior art, the invention has the following advantages and beneficial effects:
1, the formation control device designed by the present invention is distributed formation control device.Since reference locus is (usually by virtual Pilotage people generates) not acquired in all follower, therefore the follower in fleet system are mainly using reception from neighbour For the local message and self information in residence in the control signal of local computing oneself, i.e., it is designed out that each unmanned boat is based on graph theoretic approach Distributed formation control device come plan itself in next step act, to achieve the purpose that form and keep system pattern formation.
2, the stable state of formation control system and transient performance are important indicators in need of consideration in controller design.The present invention In conjunction with default capabilities control technology, make in formation error convergence to a preset allowed band, and guarantees error The transient performances such as convergence rate and overshoot meet certain preset values, that is, require transient state and steady-state performance while being expired Foot.
3, the present invention introduces logarithmic barrier function in Li Yapu love Function Synthesis design method, and construction is corresponding right Number type obstacle Li Yapu love function, it is ensured that formation error is no more than preset restriction range, so that adjacent unmanned boat It does not collide, the desired ideal formation mode of the communication connection status and realization when remaining initial.
Detailed description of the invention
Fig. 1 is the basic formation structural schematic diagram in working region of the embodiment of the present invention.
Fig. 2 is the undirected communication topology figure of unmanned boat of embodiment of the present invention fleet system.
Fig. 3 is the whole control block diagram of the formation control of unmanned boat of the embodiment of the present invention.
Fig. 4 is the phase-plane diagram of unmanned boat of embodiment of the present invention formation movement.
Fig. 5 is tail clearance of embodiment of the present invention variable analogous diagram.
Fig. 6 (a) is that the embodiment of the present invention is formed into columns the azimuthal variations analogous diagram on the 1st article of side, and Fig. 6 (b) is that the present invention is implemented The azimuthal variations analogous diagram on the 2nd and the 4th article of side of example formation, Fig. 6 (c) are the side on the 3rd and the 5th article of side of formation of the embodiment of the present invention Parallactic angle variable analogous diagram.
Fig. 7 is formation of embodiment of the present invention virtual course angle error variable analogous diagram.
Fig. 8 is formation control of embodiment of the present invention device τuiExport analogous diagram.
Fig. 9 is formation control of embodiment of the present invention device τυiExport analogous diagram.
Figure 10 is formation control of embodiment of the present invention device τriExport analogous diagram.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited In this.
Embodiment:
Collision prevention keeps the distributed formation control of the unmanned boat under constraint with connecting, and altogether includes a virtual neck in formation Boat person and five follower.Fig. 1 is the basic formation structural schematic diagram in working region, and Fig. 2 is the undirected communication of fleet system Topological diagram.
It is illustrated in figure 3 the whole controller chassis of collision prevention with the distributed formation control for the unmanned boat connecting under keeping constraining Figure, the detailed implementation process of control method include the following steps:
Step (1): the kinematics and dynamics modeling of i-th of unmanned boat, vector form are established are as follows:
First item in above formula is the kinematical equation of system.Wherein, ηi=[xi,yi,ψi]TIndicate that i-th of unmanned boat exists Earth coordinates (OeXeYe) under position (xi,yi) and course angle ψi；Indicate that i-th of unmanned boat is sat in body Mark system (obxbyb) under corresponding forward speed (ui), swaying speed (υi) and steering angular velocity (ri).Section 2 in above formula is The kinetics equation of system.Wherein, Mi> 0 is inertial matrix；C(νi) it is total coriolis force and centripetal acceleration matrix；D(νi) be Damping matrix；τiIndicate the control input of unmanned boat；τωi(t) indicate outer due to caused by the natural causes such as sea wind, wave, ocean current The unknown time-varying disturbance in portion.Matrix J (ψi), Mi, C (νi) and D (νi) concrete form are as follows:
Wherein
In above formula, miIt is the quality of i-th of unmanned boat；IziIt is the rotary inertia on steering angular velocity direction； WithIt is additional mass；xgiIt is i-th of unmanned boat in xbCenter of gravity on coordinate；X(·), Y(·)And N(·)It is to advance respectively Linear and a secondary fluid dynamics damped coefficient on directional velocity, swaying directional velocity and steering angular velocity direction.
In the present embodiment, the system parameter difference of unmanned boat is as shown in table 1 below.
1 unmanned boat model parameter of table
In this example, the setting of the position of five follower's unmanned boats of initial time, course angle and speed is respectively η1 (0)=[- 3.4,0.6,0]T、η2(0)=[- 6.828,2.828,0.1]T、η3(0)=[- 6.828, -2.828, -0.1]T、η4 (0)=[- 9.657,5.657,0.2]T、η5(0)=[- 9.657,5.657,0.2]T；The speed of initial time is νi(0)= [0,0,0]T。
In this example, the form of external disturbance is
τωi(t)=[4sin (ω ' t), 5sin (ω ' t), 6cos (ω ' t)]T
Wherein, ω '=0.06rad/s.It is by the reference locus that virtual pilotage people generates
η0=[R ω sin (ω t), R ω (1-cos (ω t)), ω t]T
Wherein, ω=0.02rad/s, R=60m, i.e. reference locus are a circle, radius 60m.
Step (2): non-directed graphFor describing the information exchange in unmanned boat fleet system between each individual. It is that finite nonempty set is closed, referred to as vertex set is gathered wherein numbering the virtual pilotage people of vertex correspondence for being 0 1,2, ..., N in each vertex correspondence have follower's unmanned boat of identical number；It is to have Limit set, referred to as side collection, the adjacent unmanned boat that each edge is corresponding with identical number and can communicate with each other.Non-directed graphAdjoining Matrix A=(aij)(N+1)×(N+1)It has the property that
Above formula explanation, (j is known as tail portion at this time, and i is known as head), a when the information of the available unmanned boat j of unmanned boat iij =1, otherwise aij=0.Since communication topology figure is non-directed graph, i.e., can be in communication with each other between two vertex connected by same side, Therefore adjacency matrix is symmetrical matrix.The neighbours of vertex i collect is defined as:
To avoid error defined in step (3) from producing ambiguity, non-directed graph is given in advanceIn each edge specify a side To.Although the direction of each edge can arbitrarily be chosen, when topological diagram is one tree, general default makees upper one layer of node For the tail portion on side, head of next layer of the node as side.Introduce incidence matrix B=(bij)(N+1)×M, wherein M beIn own The total quantity on different sides.Each element in matrix is defined as:
It usesIndicate kth side, wherein
This example is as shown in Figure 2.Wherein,Five sides are all referred in figure Direction is determined, and the desirable orientation angle on five sides is respectively θ1,des=0, θ2,des=θ4,des=-π/4 and θ3,des=θ5,des=π/ 4.The neighbours of five follower collect WithAs shown in Fig. 4 unmanned boat fleet system is in phase plane Actual path figure.
Step (3): the adjacent unmanned boat i on kth sidekAnd jkRelative position, azimuth and virtual course angle definition It is as follows
Wherein
Communication connection is kept: radius di,conBorder circular areas indicate that unmanned boat i can receive the region of information.When each When the communication range of unmanned boat is limited, to guarantee stable and reliable communication, adjacent unmanned boat ikAnd jkDistance must be positioned at it is logical Believe in region, i.e., the vertex i on kth sidek、jkBetween distance must meet
Wherein,For the radius of the communication zone on preset kth side.
Collision avoids: radius RiBorder circular areas indicate unmanned boat i hull radius.When the unmanned boat position of arbitrary neighborhood In outside default safety zone, collision, i.e., adjacent unmanned boat i can be just preventedkAnd jkBetween distance must meet
Wherein,dk,conIt is avoided collision on preset kth side Least radius.
Azimuth-limited: adjacent unmanned boat ik、jkCentral point obBetween line be known as central point line, azimuthFor unmanned boat ikCourse angle and ik、jkAngle between central point line, the angle is counterclockwise, and value is positive, clockwise Value is negative.To guarantee the safety and communication quality when the navigation of unmanned boat fleet system, it is necessary to ensure that
Wherein θk,conMeet 0 < θ of inequalityk,con<π/2。
The formation position error being defined as followsFormation angular errorWith
Wherein, dk,des、θk,desAnd ψk,desIt is opposite to respectively indicate ideal distance on kth side, desirable orientation angle and ideal Course angle, usually their value are constant, and 0 < d of inequalityk,col<dk,des<dk,conWith | θk,des|<θk,con< pi/2 assembly It is vertical.Obviously, if errorWithMeet following inequality, then communicate to connect holding, collision avoid with azimuth by Limit just can be guaranteed.
Wherein, WithThe quality of fleet system performance is affected since transient performance is serious, using pre- performance function as mistake The boundary function of difference, to formation errorWithIt is constrained.Specific constraint is as follows
Wherein, nk=dk,θk,ψk；WithBe specified by designer, it is smooth, bounded and decline with the time The function subtracted.In view of the characteristic of exponential function, it is just elected to be boundary functionWithI.e.WithConcrete form For
In above formula,WithThe also referred to as default capabilities function of monotone decreasing；Initial value Parameter WithBe greater than zero can design parameter, and relationship must be met:WithIts InWithIndicate the maximum steady state error amount allowed.Reasonable above-mentioned parameter of choosing can make errorIt is full The preset transient performance (referring mainly to convergence rate and overshoot) of foot and steady-state performance (referring mainly to steady-state error).
In the present embodiment, the safe distance of five groups of adjacent unmanned boats, communication radius, ideal relative position distance, side Parallactic angle range and the value at ideal virtual course angle are set to: dk,col=dcol=3m, dk,con=dcon=5m, dk,des =ddes=4m, θk,con=θcon=pi/2-0.2 and ψk,des=ψdes=0.
Default capabilities functionWithConcrete form be respectively
The actual range d of i.e. adjacent unmanned boatijConstraint section be
It is illustrated in figure 5 tail clearance variable dijChange with time figure, Cong Tuzhong dijChange procedure knows that ship spacing is most All it is intended to ideal spacing d eventuallydesNear.Moreover, the transient swing process of ship spacing does not cross the upper following of setting always Boundary.This analogous diagram illustrates that control program can preferably solve the problems, such as that collision avoids and communicate to connect holding.
As Fig. 6 (a), Fig. 6 (b), Fig. 6 (c) show formation azimuthal variations θijChange with time figure, it is known that θijBegin Eventually in the constraint section of angular field of viewInterior variation, and finally all converge to theorem Think azimuth angle thetak,desNear.This analogous diagram illustrates that control program can preferably solve the problems, such as azimuth-limited.
Fig. 7 show formation virtual course angle error variableChange with time figure.ErrorAlways constrain in In fixed boundary, meet preset transient state and steady-state performance, that is, there is lesser overshoot, faster convergence rate and errorZero crossings can finally be converged to.
Step (4): it introduces logarithmic barrier function and solves restricted problem.Formation angular errorCorresponding logarithm obstacle FunctionConcrete form it is as follows
In above formula,Ln () indicates natural logrithm.It can from above formula Know, ifValue always in the opener comprising zero pointFluctuation, function in rangeTo bounded always.Only Following two situation is occurred,Value just can be infinitely great or infinitely small: whenWhen,WhenWhen,It therefore can be by ensuring functionBoundedness guarantee errorAlways not The preset transient state of violation formula and steady state constraint.DefinitionDue to functionIt is not a positive definite letter Number, therefore reconfigure a kind of nonnegative function that control design case is carried out based on Li Yapu love function, referred to as logarithm obstacle Li Ya General love function, it is specific as follows
Virtual Controller design is carried out for virtual course angle error system with backstepping technique method, then i-th of unmanned boat Virtual Controller αriAre as follows:
Wherein
kriBe greater than zero can design parameter；It indicates the side of connection vertex i and vertex j, i.e.,It is equivalent toThis literary style, to have WithΔ(i,kij) meet following relationship: when vertex, i is side kijHead when, Δ (i, kij)=1；When vertex, i is side kijTail portion when, Δ (i, kij)=- 1；Otherwise Δ (i, kij)=0.
Similarly, logarithmic barrier function is introducedWithGuarantee formation position error respectivelyWith formation angular errorPreset transient state and steady state constraint are not violated, and limitation problem is converted into boundedness problem.Consider such as minor function
Wherein χ=d, θ；Construction as follows aboutWithNon-negative logarithm obstacle Li Yapu love Function
For range error system and azimuth angle error system, the Virtual Controller α obtained with backstepping technique methoduiWith αυiFor
Wherein
kuiAnd kυiBe greater than zero can design parameter；AngleVariableRespectively indicate adjacent unmanned boat i on kth sidekAnd jkRelative position, azimuth and virtual course Angle；WithRespectively correspond unmanned boat j on kth sidekForward speed and swaying speed；Unmanned boat on corresponding kth side ikSteering angular velocity；WithForm it is as follows
Step (5): to avoid derivation repeatedly (second order or higher derivative is asked to will increase calculation amount) and preventing designed Include acceleration item in controller, introduces dynamic surface control technology.When using dynamic surface control technology, general way It is to allow Virtual Controller αθi(θ=u, υ) is by obtaining filtering Virtual Controller α θ after a low-pass first order filterfi.To offset The selection of some coupling terms allows αθmiBy filter to obtain αθfi, specific as follows shown
Wherein μui> 0 and μυi> 0 is programmable time constant filter, in the present embodiment, chooses μui=0.8, μυi= 0.1；
YuiAnd YυiForm difference it is as follows
Step (6): based on step (3) to algebraic graph theory method, the default capabilities control technology, logarithm obstacle in step (5) Li Yapu love function, backstepping technique method and dynamic surface control technology, and unknown outside is disturbed using following disturbance observer Dynamic τωiEstimated and is compensated
Wherein, Kdi=diag { kd1i,kd2i,kd3iBe by greater than zero can the positive definite matrix that constitutes of design parameter, in this reality It applies in example, chooses Kdi=diag { 1.2,1.2,1.2 }；For τωiEstimated value；For the state vector of three-dimensional observation device, Initial value is taken asThen distributed formation control device τiIt may be designed as:
Wherein
Diagonal matrix Kτi=diag { kτ1i,kτ2i,kτ3iIt is by can the positive definite matrix that constitutes of design parameter；MiFor inertial matrix；For total coriolis force and centripetal acceleration matrix；For damping matrix；Qi(pij,ψij) be system state variables letter Number；Error vector ei=[eui,eυi,eri]T, wherein eui、eυiAnd eriRespectively indicate the forward speed u of i-th of unmanned boatiWith filter Wave Virtual Controller αufiDifference, swaying speed υiWith filtering Virtual Controller αυfiDifference, steering angular velocity riWith Virtual Controller αriDifference:
eui=ui-αufi
eυi=υi-αυfi
eri=ri-αri
VectorWherein eαuiAnd eαui For level error, the filtering Virtual Controller α of i-th of unmanned boat is respectively indicatedufiWith Virtual Controller αuiDifference, filtering it is virtual Controller αυfiWith Virtual Controller αυiDifference:
eαui=αufi-αui
eαυi=αυfi-αυi
In the present embodiment, K is chosenτi=diag { 4,1,4 }.Fig. 8 to Figure 10 show the control input of fleet system τui、τυiAnd τriChange curve, it is known that their continuous boundeds and more smooth.
The distributed formation control device of the present embodiment can make each of unmanned boat fleet system individual merely with neighbours Local message can plan itself next step track, to realize desired formation mode, while maintaining initial time Communication connection quality prevents collision generation, azimuth from constraining always in the visible range, and formation error meets preset transitory It can and finally converge in a sufficiently small neighborhood of equalization point zero point.
Present invention combination default capabilities control technology introduces logarithm barrier in Li Yapu love Function Synthesis design method Hinder function, and constructs corresponding logarithm obstacle Li Yapu love function.By ensuring logarithm obstacle Li Yapu love function Boundedness guarantee that formation error changes in the restriction range of the performance function of the bound exponential decrease of setting always, i.e., The convergence rate of formation error is greater than the convergence rate of performance function and overshoot does not exceed the preset overshoot of performance function. Change the limitation of the adjustable transient performance to error of design parameter of performance function.By establishing each pair of adjacent unmanned boat Range error equation, virtual course angle error equation and azimuth angle error equation, and collision prevention is retouched with the constraint kept is connect After the restricted problem for stating pairs of error, if guaranteeing, error changes in the boundary as defined in performance function always, just not only can solve Collision avoids the problem that, communicates to connect holding and azimuth-limited, it can also be ensured that the transient performance of error meets preset requirement.
Time-varying and reluctant immeasurablel variable are usually contained in the derivative of Virtual Controller.To avoid utilizing Occur in the design process of backstepping technique method Virtual Controller repeatedly derivation the problem of, present invention combination dynamic surface control technology mentions Go out suitable distributed formation control method to produce easy-to-handle to reduce the computational complexity of control design case Succinct distributed director.In addition, when unmanned boat fleet system navigates by water under complicated sea situation, it can be inevitably by the external world The external unknown disturbance such as stormy waves, ocean current influence.The present invention by design disturbance observer to unknown disturbances carry out estimation and Compensation guarantees that closed loop formation error system is stablized.
The above, only the invention patent preferred embodiment, but the scope of protection of the patent of the present invention is not limited to This, anyone skilled in the art is in the range disclosed in the invention patent, according to the present invention the skill of patent Art scheme and its patent of invention design are subject to equivalent substitution or change, belong to the scope of protection of the patent of the present invention.

Claims (7)

1. a kind of collision prevention with connect keep constraint under unmanned boat distribution formation control method, which is characterized in that the method The following steps are included:
Step (1): the kinematics and dynamics modeling of unmanned boat in fleet system is established；
Step (2): Associative algcbra graph theoretic approach uses non-directed graphTo describe the information exchange in unmanned boat fleet system between each individual；
Step (3): the range error equation of adjacent unmanned boat on kth side is establishedVirtual course angle error equationAnd Azimuth angle error equationWhereinM is non-directed graphIn all different sides total quantity, to keep away Exempt to collide and keep communication connection, is described as collision prevention to volume with the restricted problem kept is connect in conjunction with default capabilities control technology The restricted problem of team's error；
Step (4): introducing logarithmic barrier function in Li Yapu love Function Synthesis design method, and constructs corresponding logarithm barrier Hinder Li Yapu love function, it is ensured that formation error is no more than preset transient performance constraint condition, and sets with pusher Meter method carries out virtual for the virtual course angle error system, range error system and azimuth angle error system of i-th of unmanned boat The design of controller, wherein i ∈ { 1,2 ... n }, n are the total number of unmanned boat in fleet system；
Step (5): introducing dynamic surface control technology on the basis of step (4) utilize backstepping technique method, virtual to avoid occurring Controller repeatedly derivation the problem of and controller in the problem of including the acceleration information of neighbours' unmanned boat；
Step (6): based on step (3) to algebraic graph theory method, the default capabilities control technology, logarithm obstacle Li Ya in step (5) General love function, backstepping technique method and dynamic surface control technology, and unknown external disturbance is estimated using disturbance observer With compensation to design suitable distributed formation control device.
2. a kind of collision prevention according to claim 1 with connect keep constraint under unmanned boat distribution formation control method, It is characterized in that, in step (1), the kinematics and dynamics modeling of i-th of unmanned boat are as follows:
First three items in above formula are the kinematical equations of system, wherein (xi,yi) indicate i-th of unmanned boat in earth coordinates (OeXeYe) under position；ψiFor the course angle under earth coordinates；In each component correspond to body coordinate It is (obxbyb) under forward speed ui, swaying speed υiWith steering angular velocity ri；Last in above formula is the power of system Learn equation, wherein Mi> 0 is inertial matrix；For total coriolis force and centripetal acceleration matrix；For damping matrix； τiIndicate the control input of unmanned boat；τωi(t) the external unknown time-varying disturbance due to caused by natural cause is indicated；Matrix Mi,WithConcrete form difference it is as follows:
Wherein
In above formula, miIt is the quality of i-th of unmanned boat；IziIt is the rotary inertia on steering angular velocity direction； WithIt is additional mass；xgiIt is i-th of unmanned boat in xbCenter of gravity on coordinate；X(·), Y(·)And N(·)It is in forward speed respectively Linear and a secondary fluid dynamics damped coefficient on direction, swaying directional velocity and steering angular velocity direction.
3. a kind of collision prevention according to claim 1 with connect keep constraint under unmanned boat distribution formation control method, It is characterized in that, using non-directed graph in step (2)It is handed over to describe the information in unmanned boat fleet system between each individual Mutually,It is that finite nonempty set is closed, referred to as vertex set collects wherein numbering the virtual pilotage people of vertex correspondence for being 0 Close 1,2, ..., N in each vertex correspondence have the follower of identical number； It is finite aggregate It closes, referred to as side collection, the adjacent unmanned boat that each edge is corresponding with identical number and can communicate with each other；Non-directed graphAdjacency matrix A =(aij)(N+1)×(N+1)Element aij∈ { 0,1 }, when the information of the available unmanned boat j of unmanned boat i, j is known as tail portion at this time, I is known as head, aij=1, otherwise aij=0；The neighbours of vertex i collect is defined as:
To avoid error defined in step (3) from producing ambiguity, non-directed graph is given in advanceIn each edge specify a direction, Introduce incidence matrix B=(bij)(N+1)×M, wherein M beIn all different sides total quantity, each element in matrix is defined as:
Use (jk,ik) ∈ ε indicates kth side, wherein ik、
4. a kind of collision prevention according to claim 3 with connect keep constraint under unmanned boat distribution formation control method, It is characterized in that, the adjacent unmanned boat i in step (3), on kth sidekAnd jkRelative positionAzimuthAnd phase To course angleIt is specifically defined are as follows:
Wherein
Communication connection is kept: radius isBorder circular areas indicate unmanned boat ikThe region that information can be received, when each nothing When the communication range of people's ship is limited, to guarantee stable and reliable communication, adjacent unmanned boat ikAnd jkDistance must be positioned at communication Vertex i in region, i.e., on kth sidek、jkBetween distance must meet
Wherein,For the radius of the communication zone on preset kth side；
Collision avoids: radius isBorder circular areas indicate unmanned boat ikHull radius, when any pair of adjacent unmanned boat exists Outside mutual default safety zone, collision, i.e., adjacent unmanned boat i can be just preventedkAnd jkBetween distance must meet
Wherein,dk,conFor the most smaller part avoided collision on preset kth side Diameter；
Azimuth-limited: adjacent unmanned boat ik、jkCentral point obBetween line be known as central point line, azimuthFor Unmanned boat ikCourse angle and ik、jkAngle between central point line, the angle is counterclockwise, and value is positive, and value clockwise is It is negative, to guarantee the safety and communication quality when the navigation of unmanned boat fleet system, it is necessary to ensure that
Wherein θk,conMeet 0 < θ of inequalityk,con<π/2；
The formation position error being defined as followsFormation angular errorWith
Wherein, dk,des、θk,desAnd ψk,desRespectively indicate ideal distance, desirable orientation angle and the ideal virtual course on kth side Angle, their value are constant, and 0 < d of inequalityk,col<dk,des<dk,conWith | θk,des|<θk,con< pi/2 is always set up, it is clear that if ErrorWithMeet following inequality, then communicates to connect holding, collision avoids just to obtain with azimuth-limited To guarantee:
Wherein,-θk,con-θk,des<0、θk,con-θk,des>0、WithThe quality of fleet system performance is affected since transient performance is serious, using pre- performance function as error Boundary function, to formation errorWithIt is constrained, specific constraint is as follows
Wherein, nk=dk,θk,ψk；WithBe specified by designer, it is smooth, bounded and decay with the time Function, it is contemplated that it is just elected to be boundary function by the characteristic of exponential functionWithI.e.WithConcrete form be
In above formula,WithThe also referred to as default capabilities function of monotone decreasing；Initial value Parameter WithBe greater than zero can design parameter, and relationship must be met:WithIts InWithIndicate the maximum steady state error amount allowed.
5. a kind of collision prevention according to claim 4 with connect keep constraint under unmanned boat distribution formation control method, It is characterized by: in step (4), formation angular errorCorresponding logarithmic barrier functionConcrete form it is as follows
In above formula,Ln () indicate natural logrithm, if from above formula it is found that IfValue always in the opener comprising zero pointFluctuation, function in rangeBounded always is incited somebody to action, is only gone out Existing following two situation,Value just can be infinitely great or infinitely small: whenWhen,WhenWhen,Therefore it can be achieved by ensuring that functionBoundedness guarantee error
Always the preset transient state of formula and steady state constraint are not violated；DefinitionDue to functionIt is not One positive definite integral form, therefore a kind of nonnegative function that control design case is carried out based on Li Yapu love function is reconfigured, referred to as pair Number obstacle Li Yapu love function, specific as follows:
Virtual Controller design is carried out for virtual course angle error system with backstepping technique method, then the void of i-th of unmanned boat Quasi- controller αriAre as follows:
Wherein
kriBe greater than zero can design parameter；It indicates the side of connection vertex i and vertex j, i.e.,Deng Valence in(jk,ik) this literary style of ∈ ε, to have WithΔ(i,kij) meet following relationship: when vertex, i is side kijHead when, Δ (i, kij)=1；Work as top Point i is side kijTail portion when, Δ (i, kij)=- 1；Otherwise Δ (i, kij)=0；
Similarly, logarithmic barrier function is introducedWithGuarantee formation position error respectivelyWith formation angular errorNo Preset transient state and steady state constraint are violated, limitation problem is converted into boundedness problem, considers such as minor function
Wherein χ=d, θ；Construction as follows aboutWithNon-negative logarithm obstacle Li Yapu love function
For range error system and azimuth angle error system, the Virtual Controller α obtained with backstepping technique methoduiAnd αviFor
Wherein
kuiAnd kviBe greater than zero can design parameter；AngleVariable Respectively indicate adjacent unmanned boat i on kth sidekAnd jkRelative position, azimuth and virtual course angle；WithIt is right respectively Answer unmanned boat j on kth sidekForward speed and swaying speed；Unmanned boat i on corresponding kth sidekSteering angular velocity； ζχkAnd lχkForm it is as follows
6. a kind of collision prevention according to claim 5 with connect keep constraint under unmanned boat distribution formation control method, It is characterized by: in step (5), for avoid Virtual Controller repeatedly derivation and prevent include in designed controller plus Speed term introduces dynamic surface control technology, when using dynamic surface control technology, allows Virtual ControllerWhereinIt is logical Filtering Virtual Controller is obtained after crossing a low-pass first order filterTo offset some coupling terms, selection is allowedPass through Filter is to obtainShown in specific as follows
Wherein, μui> 0 and μυi> 0 is programmable time constant filter；YuiAnd YυiForm difference it is as follows
Wherein, angleVariableRespectively indicate on kth side it is adjacent nobody Ship ikAnd jkRelative position, azimuth and virtual course angle；WithIt is logarithmic barrier function；WithIt is to close In the function of system state variables.
7. a kind of collision prevention according to claim 6 with connect keep constraint under unmanned boat distribution formation control method, It is characterized by: in step (6), based on step (3) to algebraic graph theory method, the default capabilities control technology, logarithm in step (5) Obstacle Li Yapu love function, backstepping technique method and dynamic surface control technology, and using following disturbance observer to unknown outer Portion disturbs τωiEstimated and is compensated
Wherein, Kdi=diag { kd1i,kd2i,kd3iBe by greater than zero can the positive definite matrix that constitutes of design parameter；For τωi's Estimated value；For the state vector of three-dimensional observation device；Then distributed formation control device τiIt can design are as follows:
Wherein
Diagonal matrix Kτi=diag { kτ1i,kτ2i,kτ3iIt is by can the positive definite matrix that constitutes of design parameter；MiFor inertial matrix； For total coriolis force and centripetal acceleration matrix；For damping matrix；Qi(pij,ψij) be system state variables function；Accidentally Difference vector ei=[eui,eυi,eri]T, wherein eui、eυiAnd eriRespectively indicate the forward speed u of i-th of unmanned boatiIt is virtual with filtering Controller αufiDifference, swaying speed υiWith filtering Virtual Controller αυfiDifference, steering angular velocity riWith Virtual Controller αriIt Difference:
eui=ui-αufi
eυi=vi-αυfi
eri=ri-αri
VectorWherein eαuiAnd eαuiFor layer Surface error respectively indicates the filtering Virtual Controller α of i-th of unmanned boatufiWith Virtual Controller αuiDifference, filtering virtual controlling Device αυfiWith Virtual Controller αυiDifference:
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