CN107085427B - A kind of unmanned water surface ship formation control method following structure based on leader - Google Patents
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Abstract
The invention discloses a kind of unmanned water surface ship formation control methods that structure is followed based on leader, this method is directed to multiple unmanned water surface ship systems driven entirely, it proposes and solves the problems, such as that any follower and its leader prevent from colliding and keep to connect based on leader-follower formation control method, the described method comprises the following steps: establishing the dynamic model of unmanned water surface ship；Design the position output tracking error constraint condition of follower；Design tracking error transfer function；Using dynamic surface control Technology design Virtual Controller；Design the extraneous unknown disturbances such as disturbance observer compensation stormy waves stream；And constructivity design tracking formation control device.Formation control method proposed by the present invention ensures that any follower and its leader remain certain safe distance and be within the scope of the communication connection of its leader；Using dynamic surface control technology, the acceleration using leader is avoided, improves the practicability of design scheme.
Description
Technical field
The present invention relates to the formation control fields of unmanned water surface ship, and in particular to it is a kind of structure is followed based on leader nobody
Water surface ship formation control method.
Background technique
Unmanned water surface ship is a kind of ability with the autonomous navigation under practical marine environment, and can independently complete environment
The navigation unit by water of the tasks such as perception, target acquisition.Unmanned water surface ship has broad application prospects, and can be used for marine resources
Research, exploration, exploitation and transport, the detection and early warning of severe sea condition (such as Strong Breezes Over, billow, tropical storm), ocean
The exploration and monitoring of matter environment, the fields such as the observation of marine hydrology and maritime meteorology research.
For current unmanned water surface ship technical level, acquisition, processing and control of the single unmanned water surface ship in information
Ability etc. is limited.In face of complicated task and changeable ocean working environment, single unmanned water surface ship
Executive capability may seem insufficient.The population system formed using multiple unmanned water surface ships is divided complicated task
For solution at each simple subtask, multiple unmanned water surface ships are performed in parallel respective subtask, and pass through each unmanned water surface
Ship is in communication with each other, coordinates, cooperating to improve the efficiency entirely to work, and achievable single unmanned water surface ship can not or be difficult to complete
Work.By the inspiration of nature biotechnology group formation, unmanned boat formation control is that a typical coordinated movement of various economic factors control is asked
Topic.Multiple unmanned water surface ship formation controls refer to by designing suitable control strategy, so that the volume of multiple unmanned water surface ships composition
It is able to maintain a desired relative position and posture between each unmanned boat of team's system, and maintains the cooperative motion of formation,
Complete specific task.Unmanned water surface ship fleet system usually has superiority than single unmanned water surface ship system, can pass through
The formation cooperative cooperating of group makes up the deficiency of single unmanned boat ability, expands the limit of power of completion task, completes single
Unmanned water surface ship is difficult to the complex task completed.
The present invention proposes to be based on leader -- follower for the formation control problem of multiple full driving unmanned water surface ships
(Leader-Follower) formation control method, which solves any follower and its leader, to be prevented from colliding and keeping asking for connection
Topic.According to the safe distance and communication connection range of leader and follower, the position output tracking error of follower is designed about
Beam condition and tracking transfer function, and constructivity design formation control device, it is ensured that the position tracking of any unmanned water surface ship is missed
Difference does not violate position output tracking error constraint condition at any time, that is, ensure that any follower and its leader always
It keeps certain safe distance and is within the scope of the communication connection of its leader, to solve any in formation control follow
Person and its leader prevent from colliding and be kept for the problem of connecting.
Summary of the invention
The purpose of the present invention is in view of the above shortcomings of the prior art, provide it is a kind of structure is followed based on leader nobody
Water surface ship formation control method, this method prevent from colliding and keep connectivity problem in unmanned water surface ship formation control, will
Both of these problems are converted into the restricted problem of position tracking error, propose based on leader-follower's structure formation control side
Method, design formation control device make the position tracking error of any unmanned water surface ship not violate the constraint item at any time
Part solves the problems, such as to prevent from colliding and keep connection.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of unmanned water surface ship formation control method being followed structure based on leader, the described method comprises the following steps:
Step (1), the dynamic model for establishing multiple unmanned water surface ships；
Step (2), foundation leader-follower formation control mode, according to the safe distance of leader and follower
Carry out output tracking error constraint condition with the position of communication connection range design follower；
Step (3), design tracking error transfer function, are converted into equality constraint for tracking error inequality constraints；
Step (4), using dynamic surface control Technology design Virtual Controller: in conjunction with dynamic surface control technology and gradually pusher
Controller design technology avoids the derivation of Virtual Controller, so that the input of controller be avoided to believe comprising immesurable acceleration
Breath；
Step (5), design disturbance observer compensate extraneous unknown disturbances: using the method for disturbance observer, design disturbance
Observer estimates extraneous unknown disturbances, and designs corresponding feedforward disturbance compensation control device；
Step (6) designs formation tracking control unit using Lyapunov stability theory: design formation tracing control
Device using the stability of Lyapunov stability theory Strict Proof closed-loop system, and ensures any in formation control follow
Person and its leader remain certain safe distance and are within the scope of the communication connection of its leader.
Further, in step (1), the dynamic model of the multiple unmanned water surface ship are as follows:
Wherein, uiIndicate the longitudinal velocity of i-th of unmanned water surface ship, viIndicate the swaying speed of i-th of unmanned water surface ship,
riIndicate the steering angular velocity of i-th of unmanned water surface ship, ψiIt (t) is the course angle of i-th of unmanned water surface ship, i=1,2,3 ...
N,Indicate ψi(t) derivative,Indicate i-th of unmanned water surface ship in the speed of X-direction,Indicate i-th of unmanned water
Speed of the face ship in Y direction, MiIndicate the mass matrix of unmanned water surface ship,Indicate i-th of unmanned water surface ship in u, v, the side r
The vector that upward acceleration is constituted, C (vi) indicate coriolis force matrix, vi=[ui,vi,ri]T, D (vi) indicate damping matrix, τi
=[τui,τvi,τri]T, τuiIndicate the thrust of i-th of unmanned water surface ship longitudinal direction, τviIndicate i-th of unmanned water surface ship swaying direction
Thrust, τriIndicate the torque that i-th of unmanned water surface ship turns to, τwi=[τwui,τwvi,τwri]T, τwuiIndicate i-th of unmanned water
The external time-varying disturbance that face ship is subject in longitudinal direction, τwviWhen indicating the outside that i-th of unmanned water surface ship is subject in swaying direction
Become disturbance, τwriIndicate the external time-varying disturbance that i-th of unmanned water surface ship is subject in steering angular direction.
Further, the detailed process of the step (2) are as follows: by multiple unmanned water surface ship number consecutivelies are as follows: 1,2,3 ...
N, any unmanned water surface ship i are as the visual range of follower and its leader's unmanned water surface ship i-1Angle is?
Meet following constraint condition: d during entire motion controli,col<di(t)<di,con, so that leader and follower keep safety
Distance is simultaneously and within the scope of communication connection, and wherein the N of i=1,2,3 ... indicates first given unmanned water as i=0
The reference locus of face ship, (xi(t), yiIt (t)) is the position of i-th of unmanned water surface ship, (xi-1(t), yi-1It (t)) is (i-1)-th nothing
The position of people's water surface ship, di,col> 0 prevents the minimum safe distance of collision, d between unmanned water surface shipi,conFor unmanned water surface ship
Between keep in communication the maximum allowable range of connection, and di,con>di,col> 0, introduce any unmanned water surface ship i and its leader without
Desired distance d between people's water surface ship i-1i,des, and define leader's unmanned water surface ship i-1 of any unmanned water surface ship i and it
Tracking error edi(t)=di(t)-di,des, angular error eψi(t)=ψi-1(t)-ψi(t), wherein di,con>di,des>di,col
> 0, ψi-1It (t) is the course angle of (i-1)-th unmanned water surface ship, ψiIt (t) is the course angle of i-th of unmanned water surface ship, by follower
The distance between its leader constraints conversion is tracking error constraint: di,col-di,des<edi(t)<di,con-di,des。
Further, in step (2), the tracking error constraint condition design is as follows:
Wherein, edi(t) any unmanned water surface is indicated
The tracking error of ship i and its leader's unmanned water surface ship i-1, eψi(t) indicate any unmanned water surface ship i and its leader without
The angular error of people's water surface ship i-1,e di(t) e is indicateddi(t) lower bound performance function,Indicate edi(t) upper bound performance
Function,e ψi(t) e is indicatedψi(t) lower bound performance function,Indicate eψi(t) upper bound performance function, di,desIndicate any
Desired distance between unmanned water surface ship i and its leader's unmanned water surface ship i-1, di,colIt indicates to prevent from touching between unmanned water surface ship
The minimum safe distance hit,e di,∞Indicate performance functione di(t) steady-state value, κdiIndicate performance functione di(t) convergence speed
Degree, di,conIndicate the maximum allowable range of connection of keeping in communication between unmanned water surface ship,Indicate performance functionIt is steady
State value,e ψi,0Indicate performance functione ψi(t) initial value,e ψi,∞Indicate performance functione ψi(t) stationary value, κψiIndicate performance
Functione ψi(t) convergence rate.
Further, the error designed in step (3) tracks transfer function are as follows:
Wherein, zjiIndicate the transformed error of i-th of unmanned water surface ship, γjiIndicate i-th of unmanned water surface ship performance function
The upper bound divided by lower bound,Indicate the z of the nature truth of a matterjiPower,Indicate-the z of the nature truth of a matterjiPower,It indicates i-th
The lower bound of unmanned water surface ship performance function divided by the upper bound,And if only if zjiWhen=0,
Tji(zji,γji)=0；Tracking error inequality constraints is converted into following equality constraint:
Wherein:
Obtain following transformed error:
Further, it in step (4), introduces dynamic surface control technology and designs the firstorder filter of Virtual Controller are as follows:
Wherein, αfi=[αf1i,αf2i,αf3i]TTo filter virtual controlling input vector, αf1iIndicate α1iFiltering virtually control
System, αf2iIndicate α2iFiltering virtual controlling, αf3iIndicate α3iFiltering virtual controlling,Indicate αfiDerivative, αi=[α1i,
α2i,α3i]TFor virtual controlling input vector, α1iIndicate longitudinal velocity uiVirtual Controller, α2iIndicate swaying speed viIt is virtual
Controller, α3iIndicate steering angular velocity riVirtual Controller, μi=diag [μ1,μ2,μ3] it is filter time constant matrix, μ1
Indicate design filtering virtual controlling αf1iFilter time constant, μ2Indicate design filtering virtual controlling αf2iFilter temporal
Constant, μ3Indicate design filtering virtual controlling αf3iFilter time constant, i ∈ 1,2,3 ... N, j=d, ψ；αfi(0) it indicates
Filter virtual controlling αfiInitial value, αi(0) Virtual Controller α is indicatediInitial value, Virtual Controller αiIt designs as follows:
Wherein, ψiIt (t) is the course angle of i-th of unmanned water surface ship,Indicate the course of (i-1)-th unmanned water surface ship
The derivative at angle,For the visual angle between i-th of unmanned water surface ship and (i-1)-th unmanned water surface ship, kzdi> 0 indicates Virtual Controller
α1iDesign parameter, zdiIndicate i-th of unmanned water surface ship apart from transformed error,i∈
1,2,3 ... N, j=d, ψ；Indicate (i-1)-th unmanned water surface ship in the speed of X-direction,Indicate (i-1)-th nobody
Speed of the water surface ship in Y direction, kzψi> 0 indicates Virtual Controller α3iDesign parameter, zψiIndicate i-th of unmanned water surface ship
Angular transition error.
Further, the disturbance observer design in step (5) is as follows:
Wherein, eαi=αfi-αi, αfi=[αf1i,αf2i,αf3i]TTo filter virtual controlling input vector, αi=[α1i,α2i,
α3i]TFor virtual controlling input vector, z2i=vi-αfi=[z21i,z22i,z23i]T, vi=[ui,vi,ri]T, z21iIndicate longitudinal speed
Spend uiWith filtering virtual controlling αf1iDifference, z22iIndicate swaying speed viWith filtering virtual controlling αf2iDifference, z23iIndicate steering angle
Speed riWith filtering virtual controlling αf3iDifference, Kd1i=diag [kd11i,kd12i,kd13i] it is diagonal matrix, kd11iIndicate first
The design parameter of disturbance observer, kd12iIndicate the design parameter of second disturbance observer, kd13iIndicate third disturbance observation
The design parameter of device, MiIndicate the mass matrix of unmanned water surface ship, C (vi) indicate coriolis force matrix, D (vi) indicate damping matrix,
τi=[τui,τvi,τri]T, τuiIndicate the thrust of i-th of unmanned water surface ship longitudinal direction, τviIndicate i-th of unmanned water surface ship swaying side
To thrust, τriIndicate the torque that i-th of unmanned water surface ship turns to, μi=diag [μ1,μ2,μ3] it is filter time constant square
Battle array, μ1Indicate filtering virtual controlling αf1iFilter time constant, μ2Indicate filtering virtual controlling αf2iFilter temporal it is normal
Number, μ3Indicate filtering virtual controlling αf3iFilter time constant, ξ1i=[ξ11i,ξ12i,ξ13i]TIt is the state of disturbance observer
Variable, ξ11iIndicate the state variable of first disturbance observer, ξ12iIndicate the state variable of second disturbance observer, ξ13i
Indicate the state variable of third disturbance observer,For the estimated value of extraneous unknown disturbance.
Further, the formation tracking control unit designed in step (6) is as follows:
Wherein, K2i=diag [k21i,k22i,k23i] it is diagonal matrix, k21iIndicate formation control device τ1Design parameter,
k22iIndicate formation control device τ2Design parameter, k23iIndicate formation control device τ3Design parameter.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1, the present invention compensates the extraneous unknown disturbances such as stormy waves stream by disturbance observer, so that the design method is to the external world
Interference has stronger robustness.
2, the present invention tracks formation control device using dynamic surface control Technology design, avoids the acceleration using leader,
Improve the practicability of design scheme.
3, the controller design scheme that uses of the present invention so that the position tracking error of any unmanned water surface ship it is in office when
Quarter does not violate position output tracking error constraint condition, it is ensured that any follower and its leader remain certain peace
Full distance is simultaneously within the scope of the communication connection of its leader, to solve any follower and its leader in formation control
Prevent the problem of colliding and keeping connection.
Detailed description of the invention
Fig. 1 is leader-follower's formation structural schematic diagram of the multiple unmanned water surface ships of the embodiment of the present invention.
Fig. 2 is the multiple unmanned water surface ship formation control system structure diagrams of the embodiment of the present invention.
Fig. 3 is one group of unmanned water surface ship of the embodiment of the present invention and the visual range variation schematic diagram of its leader.
Fig. 4 is the course angle tracking error e of one group of unmanned water surface ship of the embodiment of the present inventionψi(t) schematic diagram.
Fig. 5 is the position output trajectory schematic diagram of one group of unmanned water surface ship formation control of the embodiment of the present invention.
Fig. 6 is the thrust τ of unmanned water surface of embodiment of the present invention ship longitudinal directionuiSchematic diagram.
Fig. 7 is the thrust τ in unmanned water surface of embodiment of the present invention ship swaying directionviSchematic diagram.
Fig. 8 is the torque τ that unmanned water surface of embodiment of the present invention ship turns toriSchematic 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:
A kind of unmanned water surface ship formation control method that structure is followed based on leader is present embodiments provided, this method is directed to
Connectivity problem is prevented from colliding and kept in unmanned water surface ship formation control, converts position tracking error for both of these problems
Restricted problem proposes that the leader-of multiple unmanned water surface ships follows based on leader-follower's structure formation control method
Person's formation structural schematic diagram as shown in Figure 1, multiple unmanned water surface ship formation control system structure diagrams as shown in Fig. 2, the side
Method specifically includes the following steps:
Step (1), the dynamic model for establishing multiple unmanned water surface ships；
The dynamic model of the multiple unmanned water surface ship are as follows:
Wherein, uiIndicate the longitudinal velocity of i-th of unmanned water surface ship, viIndicate the swaying speed of i-th of unmanned water surface ship,
riIndicate the steering angular velocity of i-th of unmanned water surface ship, ψiIt (t) is the course angle of i-th of unmanned water surface ship, i=1,2,3 ...
N,Indicate ψi(t) derivative,Indicate i-th of unmanned water surface ship in the speed of X-direction,Indicate i-th of unmanned water
Face ship Y direction speed,Indicate i-th of unmanned water surface ship in u, v, the vector that the acceleration on the direction r is constituted, vi=
[ui,vi,ri]T, τi=[τui,τvi,τri]T, τuiIndicate the thrust of i-th of unmanned water surface ship longitudinal direction, τviIndicate i-th of unmanned water
The thrust in face ship swaying direction, τriIndicate the torque that i-th of unmanned water surface ship turns to, τwi=[τwui,τwvi,τwri]T, τwuiIt indicates
The external time-varying disturbance that i-th of unmanned water surface ship is subject in longitudinal direction, τwviIndicate i-th of unmanned water surface ship in swaying direction
The external time-varying disturbance being subject to, τwriIndicate the external time-varying disturbance that i-th of unmanned water surface ship is subject in steering angular direction, MiTable
Show the mass matrix of unmanned water surface ship, C (vi) indicate coriolis force matrix, D (vi) indicate damping matrix, in which:
τwi=[2+4sin (0.05t), -3+2cos (0.05t), 2-5sin (0.05t)]T
In the present embodiment, 5 (i=1,2,3,4,5) identical unmanned water surface ship dynamic models are chosen, unmanned boat is
System parameter is respectively as follows:
m11i=25.8kg, m22i=33.8kg, m23i=m32i=1.0948kg,
m33i=2.76kg, c13(vi)=- m22ivi-m23iri,
d22(vi)=0.8612+36.2823* | vi|+0.805*|ri|,
d23(vi)=- 0.1079+0.845* | vi|+3.45*|ri|,
d32(vi)=- 0.1052-5.0437* | vi|-0.13*|ri|,
d33(vi)=1.9-0.08* | vi|+0.75*|ri|, i=1,2,3,4,5.
Hull length is Li=1.225m.
Step (2), foundation leader-follower formation control mode, according to the safe distance of leader and follower
Come output tracking error constraint condition, the neck of any unmanned water surface ship i and it with the position of communication connection range design follower
The visual range of the person's of leading unmanned water surface ship i-1 isAngle isMeet following constraint condition: d during entire motion controli,col<
di(t)<di,con, so that leader and follower keep safe distance simultaneously and within the scope of communication connection, as i=0, indicate
The reference locus of first given unmanned water surface ship, (xi(t), yiIt (t)) is the position of i-th of unmanned water surface ship, (xi-1(t),
yi-1It (t)) is the position of (i-1)-th unmanned water surface ship, di,col> 0 prevents the minimum safe distance of collision between unmanned water surface ship
From di,conKeep in communication the maximum allowable range of connection, and d between unmanned water surface shipi,con>di,col> 0, introduce it is any nobody
Desired distance d between water surface ship i and its leader's unmanned water surface ship i-1i,des, and define any unmanned water surface ship i and it
The tracking error e of leader's unmanned water surface ship i-1di(t)=di(t)-di,des, angular error eψi(t)=ψi-1(t)-ψi(t),
Wherein di,con>di,des>di,col> 0, ψi-1It (t) is the course angle of (i-1)-th unmanned water surface ship, ψiIt (t) is i-th of unmanned water surface
The distance between follower and its leader constraints conversion are tracking error constraint: d by the course angle of shipi,col-di,des<edi
(t)<di,con-di,des, in the present embodiment, di,con=6m, di,des=5m, di,col=4m, desired reference locus design are as follows:
As t≤60s, desired reference locus is linear motion: xd=3t, yd=ψd=0；
As t > 60s, desired reference locus is following circular motion:
xd=180+60sin (0.05 (t-60)),
yd=60 (1-cos (0.05 (t-60))),
ψd=0.05 (t-60).
With ηi=[xi(t),yi(t),ψi(t)]TIndicate the position (x of unmanned water surface shipi(t), yiAnd course angle ψ (t))i
(t), the initial position of unmanned water surface ship and course angle are respectively selected as η1(0)=[0,5,0]T, η2(0)=[0,10,0]T, η3
(0)=[0,15,0]T, η4(0)=[0,20,0]T, η5(0)=[0,25,0]T, initial velocity is selected as vi(0)=[0,0,0]T,
I=1,2,3,4,5；
The tracking error constraint condition of any unmanned water surface ship i followed and its leader's unmanned water surface ship i-1 design
It is as follows:
Wherein, edi(t) tracking error of any unmanned water surface ship i and its leader's unmanned water surface ship i-1, e are indicatedψi
(t) angular error of any unmanned water surface ship i and its leader's unmanned water surface ship i-1 are indicated, in the present embodiment
Step (3), design tracking error transfer function obtain following error equation after transfer function converts:
The visual range of any unmanned water surface ship i followed and its leader's unmanned water surface ship i-1 variation schematic diagram are such as
Shown in Fig. 3, the course angle tracking error e of any unmanned water surface shipψi(t) as shown in Figure 4.
Step (4), using dynamic surface control Technology design Virtual Controller, introduce dynamic surface control technology simultaneously design it is virtual
The firstorder filter of controller are as follows:
Wherein, αfi=[αf1i,αf2i,αf3i]TTo filter virtual controlling input vector, αi=[α1i,α2i,α3i]TVirtually to control
Input vector processed, the filter time constant matrix design in the present embodiment are μi=diag [0.1,0.1,0.1], virtual controlling
Device αiIt designs as follows:
Wherein,For the visual angle between i-th of unmanned water surface ship and (i-1)-th unmanned water surface ship, kzdi=kzψi=4, zdi
Indicate i-th of unmanned water surface ship apart from transformed error, Indicate (i-1)-th unmanned water surface ship in the speed of X-direction,Indicate speed of (i-1)-th unmanned water surface ship in Y direction, zψiIndicate the angular transition error of i-th of unmanned water surface ship.
Step (5), design disturbance observer compensate extraneous unknown disturbances, and disturbance observer design is as follows:
Wherein, eαi=αfi-αi, αfi=[αf1i,αf2i,αf3i]TTo filter virtual controlling input vector, αi=[α1i,α2i,
α3i]TFor virtual controlling input vector, z2i=vi-αfi=[z21i,z22i,z23i]T, vi=[ui,vi,ri]T, z21iIndicate longitudinal speed
Spend uiWith filtering virtual controlling αf1iDifference, z22iIndicate swaying speed viWith filtering virtual controlling αf2iDifference, z23iIndicate steering angle
Speed riWith filtering virtual controlling αf3iDifference, Kd1i=diag [6,6,6] is diagonal matrix, τi=[τui,τvi,τri]T, τuiIt indicates
The thrust of i-th of unmanned water surface ship longitudinal direction, τuiSchematic diagram as shown in fig. 6, τviIndicate i-th of unmanned water surface ship swaying direction
Thrust, τviSchematic diagram as shown in fig. 7, τriIndicate the torque that i-th of unmanned water surface ship turns to, τriSchematic diagram such as Fig. 8 institute
Show, ξ1i=[ξ11i,ξ12i,ξ13i]TIt is the state variable of disturbance observer, the state initial value of observer is ξ1i(0)=[0.5,
0.5,0.5]T,For the estimated value of extraneous unknown disturbance.
Step (6) designs formation tracking control unit using Lyapunov stability theory: design formation tracing control
Device using the stability of Lyapunov stability theory Strict Proof closed-loop system, and ensures any in formation control follow
Person and its leader remain within the scope of certain safe distance and communication connection in its leader, the formation of design with
Track controller is as follows:
Wherein, K2i=diag [6,6,6], position output trajectory schematic diagram such as Fig. 5 of one group of unmanned water surface ship formation control
It is shown.
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 (8)
1. a kind of unmanned water surface ship formation control method for following structure based on leader, which is characterized in that the method includes with
Lower step:
Step (1), the dynamic model for establishing multiple unmanned water surface ships；
Step (2), according to leader-follower formation control mode, according to the safe distance of leader and follower and lead to
Output tracking error constraint condition is carried out in the position of news join domain design follower；
Step (3), design tracking error transfer function, are converted into equality constraint for tracking error inequality constraints；
Step (4), using dynamic surface control Technology design Virtual Controller: controlled in conjunction with dynamic surface control technology and gradually pusher
Device designing technique avoids the derivation of Virtual Controller, so that avoiding the input of controller includes immesurable acceleration information；
Step (5), design disturbance observer compensate extraneous unknown disturbances: using the method for disturbance observer, designing disturbance observation
Device estimates extraneous unknown disturbances, and designs corresponding feedforward disturbance compensation control device；
Step (6) designs formation tracking control unit using Lyapunov stability theory: design formation tracking control unit is answered
With the stability of Lyapunov stability theory Strict Proof closed-loop system, and ensure in formation control any follower and its
Leader remains certain safe distance and is within the scope of the communication connection of its leader.
2. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, feature
It is, in step (1), the dynamic model of the multiple unmanned water surface ship are as follows:
Wherein, uiIndicate the longitudinal velocity of i-th of unmanned water surface ship, viIndicate the swaying speed of i-th of unmanned water surface ship, riTable
Show the steering angular velocity of i-th of unmanned water surface ship, ψiIt (t) is the course angle of i-th of unmanned water surface ship, the N of i=1,2,3 ...,Indicate ψi(t) derivative,Indicate i-th of unmanned water surface ship in the speed of X-direction,Indicate i-th of unmanned water surface
Speed of the ship in Y direction, MiIndicate the mass matrix of unmanned water surface ship,Indicate i-th of unmanned water surface ship in u, v, the direction r
On acceleration constitute vector, C (vi) indicate coriolis force matrix, vi=[ui,vi,ri]T, D (vi) indicate damping matrix, τi=
[τui,τvi,τri]T, τuiIndicate the thrust of i-th of unmanned water surface ship longitudinal direction, τviIndicate i-th of unmanned water surface ship swaying direction
Thrust, τriIndicate the torque that i-th of unmanned water surface ship turns to, τwi=[τwui,τwvi,τwri]T, τwuiIndicate i-th of unmanned water surface
The external time-varying disturbance that ship is subject in longitudinal direction, τwviIndicate the external time-varying that i-th of unmanned water surface ship is subject in swaying direction
Disturbance, τwriIndicate the external time-varying disturbance that i-th of unmanned water surface ship is subject in steering angular direction.
3. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, feature
It is, the detailed process of the step (2) are as follows: by multiple unmanned water surface ship number consecutivelies are as follows: 1,2,3 ... N, any unmanned water
Face ship i is as the visual range of follower and its leader's unmanned water surface ship i-1Angle is?
Meet following constraint condition: d during entire motion controli,col< di(t) < di,con, so that leader and follower keep pacifying
Full distance is simultaneously again within the scope of communication connection, the wherein N of i=1,2,3 ..., as i=0, indicate given first nobody
The reference locus of water surface ship, (xi(t), yiIt (t)) is the position of i-th of unmanned water surface ship, (xi-1(t), yi-(1It t)) is (i-1)-th
The position of unmanned water surface ship, di,col> 0 prevents the minimum safe distance of collision, d between unmanned water surface shipi,conFor unmanned water
Keep in communication the maximum allowable range of connection, and d between the ship of facei,con> di,col> 0 introduces any unmanned water surface ship i and leads with it
Desired distance d between the person's of leading unmanned water surface ship i-1i,des, and define leader's unmanned water surface of any unmanned water surface ship i and it
The tracking error e of ship i-1di(t)=di(t)-di,des, angular error eψi(t)=ψi-1(t)-ψi(t), wherein di,con>
di,des> di,col> 0, ψi-1It (t) is the course angle of (i-1)-th unmanned water surface ship, ψiIt (t) is the course of i-th of unmanned water surface ship
The distance between follower and its leader constraints conversion are tracking error constraint: d by anglei,col-di,des< edi(t) <
di,con-di,des。
4. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 3, feature
Be: in step (2), the tracking error constraint condition design is as follows:
Wherein, Indicate any unmanned water surface
The tracking error of ship i and its leader's unmanned water surface ship i-1, eψi(t) indicate any unmanned water surface ship i and its leader without
The angular error of people's water surface ship i-1,e di(t) e is indicateddi(t) lower bound performance function,Indicate edi(t) upper bound performance
Function,e ψi(t) e is indicatedψi(t) lower bound performance function,Indicate eψi(t) upper bound performance function, di,desIndicate any
Desired distance between unmanned water surface ship i and its leader's unmanned water surface ship i-1, di,colIt indicates to prevent from touching between unmanned water surface ship
The minimum safe distance hit,e di,∞Indicate performance functione di(t) steady-state value, κdiIndicate performance functione di(t) convergence speed
Degree, di,conIndicate the maximum allowable range of connection of keeping in communication between unmanned water surface ship,Indicate performance functionIt is steady
State value,e ψi,0Indicate performance functione ψi(t) initial value,e ψi,∞Indicate performance functione ψi(t) stationary value, κψiIndicate performance
Functione ψi(t) convergence rate.
5. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, feature
It is, the error designed in step (3) tracks transfer function are as follows:
Wherein, zjiIndicate the transformed error of i-th of unmanned water surface ship, γjiIndicate the upper bound of i-th of unmanned water surface ship performance function
Divided by lower bound,Indicate the z of the nature truth of a matterjiPower,Indicate-the z of the nature truth of a matterjiPower,Indicate i-th of unmanned water
The lower bound of face ship performance function divided by the upper bound,And if only if zjiWhen=0, Tji(zji,
γji)=0；Tracking error inequality constraints is converted into following equality constraint:
Wherein:
Obtain following transformed error:
6. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, feature
It is: in step (4), introduces dynamic surface control technology and design the firstorder filter of Virtual Controller are as follows:
Wherein, αfi=[αf1i,αf2i,αf3i]TTo filter virtual controlling input vector, αf1iIndicate α1iFiltering virtual controlling, αf2i
Indicate α2iFiltering virtual controlling, αf3iIndicate α3iFiltering virtual controlling,Indicate αfiDerivative, αi=[α1i,α2i,α3i]T
For virtual controlling input vector, α1iIndicate longitudinal velocity uiVirtual Controller, α2iIndicate swaying speed viVirtual Controller,
α3iIndicate steering angular velocity riVirtual Controller, μi=diag [μ1,μ2,μ3] it is filter time constant matrix, μ1Expression is set
Meter filtering virtual controlling αf1iFilter time constant, μ2Indicate design filtering virtual controlling αf2iFilter time constant, μ3
Indicate design filtering virtual controlling αf3iFilter time constant, i ∈ 1,2,3 ... N, j=d, ψ；αfi(0) indicate that filtering is empty
Quasi- control αfiInitial value, αi(0) Virtual Controller α is indicatediInitial value, Virtual Controller αiIt designs as follows:
Wherein, ψiIt (t) is the course angle of i-th of unmanned water surface ship,Indicate the course angle of (i-1)-th unmanned water surface ship
Derivative,For the visual angle between i-th of unmanned water surface ship and (i-1)-th unmanned water surface ship, kzdi> 0 indicates Virtual Controller α1i
Design parameter, zdiIndicate i-th of unmanned water surface ship apart from transformed error,i∈
1,2,3 ... N, j=d, ψ；Indicate (i-1)-th unmanned water surface ship in the speed of X-direction,Indicate (i-1)-th nobody
Speed of the water surface ship in Y direction, kzψi> 0 indicates Virtual Controller α3iDesign parameter, zψiIndicate i-th of unmanned water surface ship
Angular transition error, γjiIndicate the upper bound of i-th of unmanned water surface ship performance function divided by lower bound.
7. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, feature
It is, the disturbance observer design in step (5) is as follows:
Wherein, eαi=αfi- α,iαfi=[αf1i,αf2i,αf3i]TTo filter virtual controlling input vector, αi=[α1i,α2i,α3i]TFor
Virtual controlling input vector, z2i=vi-αfi=[z21i,z22i,z23i]T, vi=[ui,vi,ri]T, z21iIndicate longitudinal velocity uiWith
Filter virtual controlling αf1iDifference, z22iIndicate swaying speed viWith filtering virtual controlling αf2iDifference, z23iIndicate steering angular velocity ri
With filtering virtual controlling αf3iDifference, Kd1i=diag [kd11i,kd12i,kd13i] it is diagonal matrix, kd11iIndicate that first disturbance is seen
Survey the design parameter of device, kd12iIndicate the design parameter of second disturbance observer, kd13iIndicate setting for third disturbance observer
Count parameter, MiIndicate the mass matrix of unmanned water surface ship, C (vi) indicate coriolis force matrix, D (vi) indicate damping matrix, τi=
[τui,τvi,τri]T, τuiIndicate the thrust of i-th of unmanned water surface ship longitudinal direction, τviIndicate i-th of unmanned water surface ship swaying direction
Thrust, τriIndicate the torque that i-th of unmanned water surface ship turns to, μi=diag [μ1,μ2,μ3] it is filter time constant matrix, μ1
Indicate filtering virtual controlling αf1iFilter time constant, μ2Indicate filtering virtual controlling αf2iFilter time constant, μ3Table
Show filtering virtual controlling αf3iFilter time constant, ξ1i=[ξ11i,ξ12i,ξ13i]TIt is the state variable of disturbance observer,
ξ11iIndicate the state variable of first disturbance observer, ξ12iIndicate the state variable of second disturbance observer, ξ13iIndicate the
The state variable of three disturbance observers,For the estimated value of extraneous unknown disturbance.
8. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, feature
It is, the formation tracking control unit designed in step (6) is as follows:
Wherein, K2i=diag [k21i,k22i,k23i] it is diagonal matrix, k21iIndicate formation control device τ1Design parameter, k22iTable
Show formation control device τ2Design parameter, k23iIndicate formation control device τ3Design parameter, viIndicate i-th of unmanned water surface ship
Swaying speed, ψiFor the course angle of i-th of unmanned water surface ship, MiIndicate the mass matrix of unmanned water surface ship, C (vi) indicate Coriolis
Torque battle array, D (vi) indicate damping matrix,For the visual angle between i-th of unmanned water surface ship and (i-1)-th unmanned water surface ship, zdi
Indicate i-th of unmanned water surface ship apart from transformed error, zψiIndicate the angular transition error of i-th of unmanned water surface ship,It is outer
The estimated value of boundary's unknown disturbance.
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