CN107085427A - A kind of unmanned water surface ship formation control method for following structure based on leader - Google Patents
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Abstract
The invention discloses a kind of unmanned water surface ship formation control method for following structure based on leader, this method is directed to multiple unmanned water surface ship systems driven entirely, propose the formation control method based on leader follower and solve the problem of any follower prevents from colliding and keep being connected with its leader, the described method comprises the following steps：Set up the dynamic model of unmanned water surface ship；Design the position output tracking error constraints 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 are remained in certain safe distance and communication join domain in its leader；Using dynamic surface control technology, it is to avoid using the acceleration of leader, improve the practicality of design.
Description
Technical field
The present invention relates to the formation control field of unmanned water surface ship, and in particular to it is a kind of followed based on leader structure nobody
Water surface ship formation control method.
Background technology
Unmanned water surface ship is a kind of ability with the autonomous navigation under actual 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, available 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 fields such as the exploration and monitoring of matter environment, the observation of marine hydrology, and maritime meteorology research.
For current unmanned water surface ship technical merit, single unmanned water surface ship is in the acquisition of information, processing and controls
It is limited in terms of ability.In face of complicated task and changeable ocean working environment, single unmanned water surface ship
Executive capability may seem not enough.The population system constituted using multiple unmanned water surface ships, complicated task is divided
Solution is into each simple subtask, and multiple unmanned water surface ships are performed in parallel respective subtask, and pass through each unmanned water surface
Being in communication with each other, coordinate, cooperating with improving the efficiency entirely worked for ship, can complete single unmanned water surface ship and can not or be difficult to complete
Work.Inspired by nature biotechnology colony 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 ship compositions
Desired a relative position and posture can be kept between each unmanned boat of team's system, and maintain the cooperative motion of formation,
Complete specific task.Unmanned water surface ship fleet system generally has superiority than single unmanned water surface ship system, can pass through
The formation cooperative cooperating of colony 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 solves any follower to be prevented from colliding and keeps what is be connected to ask with its leader
Topic.According to the safe distance and communication join domain 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 constraints at any time, that is, ensure that any follower with its leader all the time
The certain safe distance of holding is simultaneously in the communication join domain of its leader, so as to solve any in formation control follow
The problem of person prevents from colliding and keeps being connected with its leader.
The content of the invention
The purpose of the present invention be for above-mentioned the deficiencies in the prior art there is provided it is a kind of followed based on leader structure nobody
Water surface ship formation control method, this method is directed to preventing in unmanned water surface ship formation control and collides and keep connectivity problem, will
The two problems are converted into the restricted problem of position tracking error, propose the formation control side based on leader-follower's structure
Method, design formation control device causes the position tracking error of any unmanned water surface ship not violate the constraint bar at any time
Part, solves the problem of preventing 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 for being followed structure based on leader, the described method comprises the following steps：
Step (1), the dynamic model for setting up multiple unmanned water surface ships；
Step (2), the formation control mode according to leader-follower, according to the safe distance of leader and follower
Carry out output tracking error constraints with the position of communication join domain design follower；
Step (3), design tracking error transfer function, equality constraint is converted into by tracking error inequality constraints；
Step (4), using dynamic surface control Technology design Virtual Controller：With reference to dynamic surface control technology and progressively pusher
Controller design technology avoids the derivation of Virtual Controller, so as to avoid the input of controller from believing comprising immesurable acceleration
Breath；
Step (5), the extraneous unknown disturbances of design disturbance observer compensation：Using the method for disturbance observer, design disturbance
Observer to external world estimated by unknown disturbances, and designs corresponding feedforward disturbance compensation control device；
Step (6), using Lyapunov stability theory design formation tracking control unit：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 are remained in certain safe distance and communication join domain in its leader.
Further, in step (1), the dynamic model of the multiple unmanned water surface ship is：
Wherein, uiRepresent the longitudinal velocity of i-th of unmanned water surface ship, viThe swaying speed of i-th of unmanned water surface ship is represented,
riRepresent the steering angular velocity of i-th of unmanned water surface ship, ψi(t) it is the course angle of i-th of unmanned water surface ship, i=1,2,3 ...
N,Represent ψi(t) derivative,Speed of i-th of unmanned water surface ship in X-direction is represented,Represent i-th of unmanned water surface
Ship is in the speed of Y direction, MiThe mass matrix of unmanned water surface ship is represented,Represent i-th of unmanned water surface ship in u, v, r directions
On acceleration constitute vector, C (vi) represent coriolis force matrix, vi=[ui,vi,ri]T, D (vi) represent damping matrix, τi=
[τui,τvi,τri]T, τuiRepresent the thrust of i-th of unmanned water surface ship longitudinal direction, τviRepresent i-th unmanned water surface ship swaying direction
Thrust, τriRepresent the torque that i-th of unmanned water surface ship is turned to, τwi=[τwui,τwvi,τwri]T, τwuiRepresent i-th of unmanned water surface
The outside time-varying disturbance that ship is subject in longitudinal direction, τwviRepresent the outside time-varying that i-th of unmanned water surface ship is subject in swaying direction
Disturbance, τwriRepresent that i-th of unmanned water surface ship is turning to the outside time-varying disturbance that angular direction is subject to.
Further, the detailed process of the step (2) is：It is by multiple unmanned water surface ship number consecutivelies：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 isWhole
Following constraints is met during individual motion control：di,col<di(t)<di,con, so that leader and follower keep safety away from
From communicating in join domain simultaneously again, the N of wherein i=1,2,3 ..., as i=0, represents first given unmanned water surface
The reference locus of ship, (xi(t), yi(t) it is) position of i-th of unmanned water surface ship, (xi-1(t), yi-1(t)) for the i-th -1 nobody
The position of water surface ship, di,col>0 be unmanned water surface ship between prevent collision minimum safe distance, di,conFor unmanned water surface ship it
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 nobody
Desired distance d between water surface ship i-1i,des, and define any unmanned water surface ship i and its leader's unmanned water surface ship i-1's
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-1(t) it is the course angle of the i-th -1 unmanned water surface ship, ψi(t) be the course angle of i-th unmanned water surface ship, by follower with
The distance between its leader constraints conversion constrains for tracking error：di,col-di,des<edi(t)<di,con-di,des。
Further, in step (2), the tracking error constraints design is as follows：
Wherein, edi(t) any unmanned water surface is represented
Ship i and its leader's unmanned water surface ship i-1 tracking error, eψi(t) represent any unmanned water surface ship i and its leader without
People's water surface ship i-1 angular error,e di(t) e is representeddi(t) lower bound performance function,Represent edi(t) upper bound performance
Function,e ψi(t) e is representedψi(t) lower bound performance function,Represent eψi(t) upper bound performance function, di,desRepresent any
Desired distance between unmanned water surface ship i and its leader's unmanned water surface ship i-1, di,colRepresent to prevent from touching between unmanned water surface ship
The minimum safe distance hit,e di,∞Represent performance functione di(t) steady-state value, κdiRepresent performance functione di(t) convergence speed
Degree, di,conThe maximum allowable range of connection of keeping in communication between unmanned water surface ship is represented,Represent performance functionIt is steady
State value,e ψi,0Represent performance functione ψi(t) initial value,e ψi,∞Represent performance functione ψi(t) stationary value, κψiRepresent performance
Functione ψi(t) convergence rate.
Further, the error tracking transfer function of design is in step (3)：
Wherein, zjiRepresent the transformed error of i-th of unmanned water surface ship, γjiRepresent i-th of unmanned water surface ship performance function
The upper bound divided by lower bound,Represent the z of the nature truth of a matterjiPower,Represent-the z of the nature truth of a matterjiPower,Represent 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, in step (4), introduce dynamic surface control technology and design the firstorder filter of Virtual Controller and be：
Wherein, αfi=[αf1i,αf2i,αf3i]TFor filtering virtual controlling input vector, αf1iRepresent α1iFiltering virtually control
System, αf2iRepresent α2iFiltering virtual controlling, αf3iRepresent α3iFiltering virtual controlling,Represent αfiDerivative, αi=[α1i,
α2i,α3i]TFor virtual controlling input vector, α1iRepresent longitudinal velocity uiVirtual Controller, α2iRepresent swaying speed viIt is virtual
Controller, α3iRepresent steering angular velocity riVirtual Controller, μi=diag [μ1,μ2,μ3] it is filter time constant matrix, μ1
Represent design filtering virtual controlling αf1iFilter time constant, μ2Represent design filtering virtual controlling αf2iFilter temporal
Constant, μ3Represent design filtering virtual controlling αf3iFilter time constant, i ∈ 1,2,3 ... N, j=d, ψ；αfi(0) represent
Filter virtual controlling αfiInitial value, αi(0) Virtual Controller α is representediInitial value, Virtual Controller αiDesign is as follows：
Wherein, ψi(t) it is the course angle of i-th of unmanned water surface ship,The derivative of the course angle of the i-th -1 unmanned water surface ship is represented,For the visual angle between i-th of unmanned water surface ship and the i-th -1 unmanned water surface ship, kzdi>0 represents Virtual Controller α1iDesign parameter,
zdiRepresent i-th unmanned water surface ship apart from transformed error,
I ∈ 1,2,3 ... N, j=d, ψ；Speed of the i-th -1 unmanned water surface ship in X-direction is represented,Represent the i-th -1 nothing
People's water surface ship is in the speed of Y direction, kzψi>0 represents Virtual Controller α3iDesign parameter, zψiRepresent i-th of unmanned water surface
The angular transition error of ship.
Further, the disturbance observer design in step (5) is as follows：
Wherein, eαi=αfi-αi, αfi=[αf1i,αf2i,αf3i]TFor filtering 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, z21iRepresent longitudinal direction speed
Spend uiWith filtering virtual controlling αf1iDifference, z22iRepresent swaying speed viWith filtering virtual controlling αf2iDifference, z23iRepresent steering angle
Speed riWith filtering virtual controlling αf3iDifference, Kd1i=diag [kd11i,kd12i,kd13i] it is diagonal matrix, kd11iRepresent first
The design parameter of disturbance observer, kd12iRepresent the design parameter of second disturbance observer, kd13iRepresent the 3rd disturbance observation
The design parameter of device, MiRepresent the mass matrix of unmanned water surface ship, C (vi) represent coriolis force matrix, D (vi) damping matrix is represented,
τi=[τui,τvi,τri]T, τuiRepresent the thrust of i-th of unmanned water surface ship longitudinal direction, τviRepresent i-th of unmanned water surface ship swaying side
To thrust, τriRepresent the torque that i-th of unmanned water surface ship is turned to, μi=diag [μ1,μ2,μ3] it is filter time constant square
Battle array, μ1Represent filtering virtual controlling αf1iFilter time constant, μ2Represent filtering virtual controlling αf2iFilter temporal it is normal
Number, μ3Represent filtering virtual controlling αf3iFilter time constant, ξ1i=[ξ11i,ξ12i,ξ13i]TIt is the state of disturbance observer
Variable, ξ11iRepresent the state variable of first disturbance observer, ξ12iRepresent the state variable of second disturbance observer, ξ13i
The state variable of the 3rd disturbance observer is represented,For the estimate of extraneous unknown disturbance.
Further, the formation tracking control unit of design is as follows in step (6)：
Wherein, K2i=diag [k21i,k22i,k23i] it is diagonal matrix, k21iRepresent formation control device τ1Design parameter,
k22iRepresent formation control device τ2Design parameter, k23iRepresent formation control device τ3Design parameter.
The present invention compared with prior art, has the following advantages that and beneficial effect：
1st, the present invention compensates the extraneous unknown disturbances such as stormy waves stream by disturbance observer so that the design method is to external world
Interference has stronger robustness.
2nd, the present invention is using dynamic surface control Technology design tracking formation control device, it is to avoid using the acceleration of leader,
Improve the practicality of design.
3rd, 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 constraints, it is ensured that any follower and its leader remain certain peace
Full distance is simultaneously in the communication join domain of its leader, so as to solve any follower and its leader in formation control
The problem of preventing from colliding and keep connection.
Brief description of the drawings
Fig. 1 is leader-follower's formation structural representation 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 architecture 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 change 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 ship swaying of embodiment of the present invention directionviSchematic diagram.
Fig. 8 is the torque τ that unmanned water surface of embodiment of the present invention ship is turned toriSchematic diagram.
Embodiment
With reference to embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited
In this.
Embodiment：
A kind of unmanned water surface ship formation control method for following structure based on leader is present embodiments provided, this method is directed to
Connectivity problem is collided and kept to preventing in unmanned water surface ship formation control, and the two problems are converted into position tracking error
Restricted problem, proposes the formation control method based on leader-follower's structure, the leader of multiple unmanned water surface ships-follow
Person's formation structural representation is as shown in figure 1, multiple unmanned water surface ship formation control system architecture diagrams are as shown in Fig. 2 the side
Method specifically includes following steps：
Step (1), the dynamic model for setting up multiple unmanned water surface ships；
The dynamic model of the multiple unmanned water surface ship is：
Wherein, uiRepresent the longitudinal velocity of i-th of unmanned water surface ship, viThe swaying speed of i-th of unmanned water surface ship is represented,
riRepresent the steering angular velocity of i-th of unmanned water surface ship, ψi(t) it is the course angle of i-th of unmanned water surface ship, i=1,2,3 ...
N,Represent ψi(t) derivative,Speed of i-th of unmanned water surface ship in X-direction is represented,Represent i-th of unmanned water
Face ship Y direction speed,I-th of unmanned water surface ship is represented in u, v, the vector that the acceleration on r directions is constituted, vi=
[ui,vi,ri]T, τi=[τui,τvi,τri]T, τuiRepresent the thrust of i-th of unmanned water surface ship longitudinal direction, τviRepresent i-th of unmanned water
The thrust in face ship swaying direction, τriRepresent the torque that i-th of unmanned water surface ship is turned to, τwi=[τwui,τwvi,τwri]T, τwuiRepresent
The outside time-varying disturbance that i-th of unmanned water surface ship is subject in longitudinal direction, τwviRepresent i-th of unmanned water surface ship in swaying direction
The outside time-varying disturbance being subject to, τwriRepresent that i-th of unmanned water surface ship is turning to the outside time-varying disturbance that angular direction is subject to, MiTable
Show the mass matrix of unmanned water surface ship, C (vi) represent coriolis force matrix, D (vi) damping matrix is represented, wherein：
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 be respectively：
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), the formation control mode according to leader-follower, according to the safe distance of leader and follower
Come output tracking error constraints, any unmanned water surface ship i and its neck with the position of communication join domain design follower
The person's of leading unmanned water surface ship i-1 visual range isAngle isFollowing constraints is met during whole motion control：di,col<
di(t)<di,con, so that leader keeps safe distance communicating in join domain with follower simultaneously again, as i=0, represent
The reference locus of first given unmanned water surface ship, (xi(t), yi(t) it is) position of i-th of unmanned water surface ship, (xi-1(t),
yi-1(t) it is) position of the i-th -1 unmanned water surface ship, di,col>0 be unmanned water surface ship between prevent collision minimum safe distance
From di,conFor the maximum allowable range for connection of being kept in communication between unmanned water surface ship, and di,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 with it
Leader's unmanned water surface ship i-1 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-1(t) it is the course angle of the i-th -1 unmanned water surface ship, ψi(t) it is i-th of unmanned water surface
The course angle of ship, the distance between follower and its leader constraints conversion is constrained for tracking error：di,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 is designed as：
As t≤60s, desired reference locus is linear motion：xd=3t, yd=ψd=0；
Work as t>During 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)]TRepresent the position (x of unmanned water surface shipi(t), yi) and course angle ψ (t)i
(t), the initial position and course angle of unmanned water surface ship are respectively chosen 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 selection is vi(0)=[0,0,0]T,
I=1,2,3,4,5；
Any unmanned water surface ship i followed and its leader's unmanned water surface ship i-1 tracking error constraints is designed
It is as follows：
Wherein, edi(t) any unmanned water surface ship i and its leader's unmanned water surface ship i-1 tracking error, e are representedψi
(t) represent in any unmanned water surface ship i and its leader's unmanned water surface ship i-1 angular error, the present embodiment
Step (3), design tracking error transfer function, after transfer function is converted, obtain following error equation：
Any unmanned water surface ship i followed and its leader's unmanned water surface ship i-1 visual range change schematic diagram is 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 and simultaneously design virtual
The firstorder filter of controller is：
Wherein, αfi=[αf1i,αf2i,αf3i]TFor filtering virtual controlling input vector, αi=[α1i,α2i,α3i]TFor virtual control
Filter time constant matrix design in input vector processed, the present embodiment is μi=diag [0.1,0.1,0.1], virtual controlling
Device αiDesign is as follows：
Wherein,For the visual angle between i-th of unmanned water surface ship and the i-th -1 unmanned water surface ship, kzdi=kzψi=4, zdi
Represent i-th unmanned water surface ship apart from transformed error, Speed of the i-th -1 unmanned water surface ship in X-direction is represented,Represent the i-th -1 unmanned water surface ship in the speed of Y direction, zψiRepresent the angular transition error of i-th of unmanned water surface ship.
Step (5), the extraneous unknown disturbances of design disturbance observer compensation, disturbance observer design are as follows：
Wherein, eαi=αfi-αi, αfi=[αf1i,αf2i,αf3i]TFor filtering 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, z21iRepresent longitudinal direction speed
Spend uiWith filtering virtual controlling αf1iDifference, z22iRepresent swaying speed viWith filtering virtual controlling αf2iDifference, z23iRepresent steering angle
Speed riWith filtering virtual controlling αf3iDifference, Kd1i=diag [6,6,6] is diagonal matrix, τi=[τui,τvi,τri]T, τuiRepresent
The thrust of i-th of unmanned water surface ship longitudinal direction, τuiSchematic diagram as shown in fig. 6, τviRepresent i-th of unmanned water surface ship swaying direction
Thrust, τviSchematic diagram as shown in fig. 7, τriRepresent the torque that i-th of unmanned water surface ship is turned to, τriSchematic diagram such as Fig. 8 institutes
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 estimate of extraneous unknown disturbance.
Step (6), using Lyapunov stability theory design formation tracking control unit：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 remained in certain safe distance and communication join domain 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.
It is described above, it is only patent preferred embodiment of the present invention, but the protection domain of patent of the present invention is not limited to
This, any one skilled in the art is in the scope disclosed in patent of the present invention, according to the skill of patent of the present invention
Art scheme and its patent of invention design are subject to equivalent substitution or change, belong to the protection domain of patent of the present invention.
Claims (8)
1. a kind of unmanned water surface ship formation control method for following structure based on leader, it is characterised in that methods described include with
Lower step：
Step (1), the dynamic model for setting up multiple unmanned water surface ships；
Step (2), the formation control mode according to leader-follower, according to the safe distance of leader and follower and lead to
Output tracking error constraints is carried out in the position of news join domain design follower；
Step (3), design tracking error transfer function, equality constraint is converted into by tracking error inequality constraints；
Step (4), using dynamic surface control Technology design Virtual Controller：Controlled with reference to dynamic surface control technology with progressively pusher
Device designing technique avoids the derivation of Virtual Controller, so as to avoid the input of controller from including immesurable acceleration information；
Step (5), the extraneous unknown disturbances of design disturbance observer compensation：Using the method for disturbance observer, disturbance observation is designed
Device to external world estimated by unknown disturbances, and designs corresponding feedforward disturbance compensation control device；
Step (6), using Lyapunov stability theory design formation tracking control unit：Formation tracking control unit is designed, should
With the stability of Lyapunov stability theory Strict Proof closed-loop system, and ensure in formation control any follower and its
Leader is remained in certain safe distance and communication join domain in its leader.
2. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, its feature
It is, in step (1), the dynamic model of the multiple unmanned water surface ship is：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mover>
<mi>x</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>u</mi>
<mi>i</mi>
</msub>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<msub>
<mi>&psi;</mi>
<mi>i</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<mo>-</mo>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<msub>
<mi>&psi;</mi>
<mi>i</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mi>y</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>u</mi>
<mi>i</mi>
</msub>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<msub>
<mi>&psi;</mi>
<mi>i</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<mo>+</mo>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<msub>
<mi>&psi;</mi>
<mi>i</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mi>&psi;</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>i</mi>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
<mo>=</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>M</mi>
<mi>i</mi>
</msub>
<msub>
<mover>
<mi>v</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>i</mi>
</msub>
<mo>=</mo>
<mo>-</mo>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>D</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>w</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, uiRepresent the longitudinal velocity of i-th of unmanned water surface ship, viRepresent 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, ψi(t) it is the course angle of i-th of unmanned water surface ship, the N of i=1,2,3 ...,Represent ψi(t) derivative,Speed of i-th of unmanned water surface ship in X-direction is represented,Represent i-th of unmanned water surface ship
In the speed of Y direction, MiThe mass matrix of unmanned water surface ship is represented,I-th of unmanned water surface ship is represented in u, v, on r directions
Acceleration constitute vector, C (vi) represent coriolis force matrix, vi=[ui,vi,ri]T, D (vi) represent damping matrix, τi=
[τui,τvi,τri]T, τuiRepresent the thrust of i-th of unmanned water surface ship longitudinal direction, τviRepresent i-th unmanned water surface ship swaying direction
Thrust, τriRepresent the torque that i-th of unmanned water surface ship is turned to, τwi=[τwui,τwvi,τwri]T, τwuiRepresent i-th of unmanned water surface
The outside time-varying disturbance that ship is subject in longitudinal direction, τwviRepresent the outside time-varying that i-th of unmanned water surface ship is subject in swaying direction
Disturbance, τwriRepresent that i-th of unmanned water surface ship is turning to the outside time-varying disturbance that angular direction is subject to.
3. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, it is characterised in that
The detailed process of the step (2) is：It is by multiple unmanned water surface ship number consecutivelies：1st, 2,3 ... N, any unmanned water surface ship i makees
Visual range for follower and its leader's unmanned water surface ship i-1 is
Angle isFollowing constraints is met during whole motion control：
di,col<di(t)<di,con, so that leader keeps safe distance communicating again in join domain simultaneously with follower, wherein i=
1st, 2,3 ... N, as i=0, represents the reference locus of first given unmanned water surface ship, (xi(t), yi(t)) it is i-th
The position of unmanned water surface ship, (xi-1(t), yi-1(t) it is) position of the i-th -1 unmanned water surface ship, di,col>0 is unmanned water surface ship
Between prevent collision minimum safe distance, di,conFor the maximum allowable range for connection of being kept in communication between unmanned water surface ship, and
di,con>di,col>0, the desired distance d introduced between any unmanned water surface ship i and its leader's unmanned water surface ship i-1i,des, and
Define any unmanned water surface ship i and its leader's unmanned water surface ship i-1 tracking error edi(t)=di(t)-di,des, angle
Spend error eψi(t)=ψi-1(t)-ψi(t), wherein di,con>di,des>di,col>0, ψi-1(t) it is the boat of the i-th -1 unmanned water surface ship
To angle, ψi(t) be the course angle of i-th unmanned water surface ship, by the distance between follower and its leader constraints conversion be with
Track error constraints：di,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, its feature
It is：In step (2), the tracking error constraints design is as follows：
<mrow>
<mo>-</mo>
<msub>
<munder>
<mi>e</mi>
<mo>&OverBar;</mo>
</munder>
<mrow>
<mi>d</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo><</mo>
<msub>
<mi>e</mi>
<mrow>
<mi>d</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo><</mo>
<msub>
<mover>
<mi>e</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>d</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>-</mo>
<msub>
<munder>
<mi>e</mi>
<mo>&OverBar;</mo>
</munder>
<mrow>
<mi>&psi;</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo><</mo>
<msub>
<mi>e</mi>
<mrow>
<mi>&psi;</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo><</mo>
<msub>
<mover>
<mi>e</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>&psi;</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
Wherein, edi(t) any unmanned water surface is represented
Ship i and its leader's unmanned water surface ship i-1 tracking error, eψi(t) represent any unmanned water surface ship i and its leader without
People's water surface ship i-1 angular error,e di(t) e is representeddi(t) lower bound performance function,Represent edi(t) upper bound performance
Function,e ψi(t) e is representedψi(t) lower bound performance function,Represent eψi(t) upper bound performance function, di,desRepresent any
Desired distance between unmanned water surface ship i and its leader's unmanned water surface ship i-1, di,colRepresent to prevent from touching between unmanned water surface ship
The minimum safe distance hit,e di,∞Represent performance functione di(t) steady-state value, κdiRepresent performance functione di(t) convergence speed
Degree, di,conThe maximum allowable range of connection of keeping in communication between unmanned water surface ship is represented,Represent performance functionIt is steady
State value,e ψi,0Represent performance functione ψi(t) initial value,e ψi,∞Represent performance functione ψi(t) stationary value, κψiRepresent 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, its feature
It is, the error tracking transfer function of design in step (3) is：
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>z</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>&gamma;</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<mi>e</mi>
<msub>
<mi>z</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
</msup>
<mo>-</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>z</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</msup>
</mrow>
<mrow>
<msup>
<mi>e</mi>
<msub>
<mi>z</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
</msup>
<mo>+</mo>
<msubsup>
<mi>&gamma;</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>z</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>,</mo>
<mi>i</mi>
<mo>&Element;</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>3</mn>
<mo>...</mo>
<mo>...</mo>
<mi>N</mi>
<mo>,</mo>
<mi>j</mi>
<mo>=</mo>
<mi>d</mi>
<mo>,</mo>
<mi>&psi;</mi>
</mrow>
Wherein, zjiRepresent the transformed error of i-th of unmanned water surface ship, γjiRepresent the upper bound of i-th of unmanned water surface ship performance function
Divided by lower bound,Represent the z of the nature truth of a matterjiPower,Represent-the z of the nature truth of a matterjiPower,Represent 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：
<mrow>
<msub>
<mi>z</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msubsup>
<mi>T</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>e</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
<msub>
<mi>&gamma;</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>ln</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<munder>
<mi>e</mi>
<mo>&OverBar;</mo>
</munder>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>&gamma;</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>e</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
6. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, its feature
It is：In step (4), introduce dynamic surface control technology and design the firstorder filter of Virtual Controller and be：
<mrow>
<msub>
<mi>&mu;</mi>
<mi>i</mi>
</msub>
<msub>
<mover>
<mi>&alpha;</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>f</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>f</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>f</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, αfi=[αf1i,αf2i,αf3i]TFor filtering virtual controlling input vector, αf1iRepresent α1iFiltering virtual controlling, αf2i
Represent α2iFiltering virtual controlling, αf3iRepresent α3iFiltering virtual controlling,Represent αfiDerivative, αi=[α1i,α2i,α3i]T
For virtual controlling input vector, α1iRepresent longitudinal velocity uiVirtual Controller, α2iRepresent swaying speed viVirtual Controller,
α3iRepresent 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, μ2Represent design filtering virtual controlling αf2iFilter time constant, μ3
Represent design filtering virtual controlling αf3iFilter time constant, i ∈ 1,2,3 ... N, j=d, ψ；αfi(0) represent that filtering is empty
Intend control αfiInitial value, αi(0) Virtual Controller α is representediInitial value, Virtual Controller αiDesign is as follows：
<mrow>
<msub>
<mi>&alpha;</mi>
<mrow>
<mn>3</mn>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>p</mi>
<mrow>
<mi>&psi;</mi>
<mi>i</mi>
</mrow>
</msub>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>k</mi>
<mrow>
<mi>z</mi>
<mi>&psi;</mi>
<mi>i</mi>
</mrow>
</msub>
<msub>
<mi>z</mi>
<mrow>
<mi>&psi;</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>q</mi>
<mrow>
<mi>&psi;</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mover>
<mi>&psi;</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
Wherein, ψ i (t) are the course angle of i-th of unmanned water surface ship, represent the derivative of the course angle of the i-th -1 unmanned water surface ship, are
Visual angle between i-th of unmanned water surface ship and the i-th -1 unmanned water surface ship, kzdi>0 represents Virtual Controller α 1i design parameter, and zdi is represented
I-th unmanned water surface ship apart from transformed error,
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>&lsqb;</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<munder>
<mi>e</mi>
<mo>&OverBar;</mo>
</munder>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mover>
<mi>e</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<mo>></mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>q</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>&lsqb;</mo>
<mfrac>
<mrow>
<msub>
<mover>
<munder>
<mi>e</mi>
<mo>&OverBar;</mo>
</munder>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<munder>
<mi>e</mi>
<mo>&OverBar;</mo>
</munder>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mover>
<mover>
<mi>e</mi>
<mo>&OverBar;</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>e</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
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<mo>&rsqb;</mo>
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I ∈ 1,2,3 ... N, j=d, ψ；Speed of the i-th -1 unmanned water surface ship in X-direction is represented, the i-th -1 nothing is represented
People's water surface ship is in the speed of Y direction, kz ψ i>0 represents Virtual Controller α 3i design parameter, and z ψ i represent i-th of unmanned water surface
The angular transition error of ship.
7. a kind of unmanned water surface ship formation control method for following structure based on leader according to claim 1, its feature
It is, the disturbance observer design in step (5) is as follows：
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Wherein, eαi=αfi-αi, αfi=[αf1i,αf2i,αf3i]TFor filtering 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, z21iRepresent longitudinal velocity uiWith
Filter virtual controlling αf1iDifference, z22iRepresent swaying speed viWith filtering virtual controlling αf2iDifference, z23iRepresent steering angular velocity ri
With filtering virtual controlling αf3iDifference, Kd1i=diag [kd11i,kd12i,kd13i] it is diagonal matrix, kd11iRepresent that first disturbance is seen
Survey the design parameter of device, kd12iRepresent the design parameter of second disturbance observer, kd13iRepresent setting for the 3rd disturbance observer
Count parameter, MiRepresent the mass matrix of unmanned water surface ship, C (vi) represent coriolis force matrix, D (vi) represent damping matrix, τi=
[τui,τvi,τri]T, τuiRepresent the thrust of i-th of unmanned water surface ship longitudinal direction, τviRepresent i-th unmanned water surface ship swaying direction
Thrust, τriRepresent the torque that i-th of unmanned water surface ship is turned to, μi=diag [μ1,μ2,μ3] it is filter time constant matrix, μ1
Represent filtering virtual controlling αf1iFilter time constant, μ2Represent 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,
ξ11iRepresent the state variable of first disturbance observer, ξ12iRepresent the state variable of second disturbance observer, ξ13iRepresent the
The state variable of three disturbance observers,For the estimate 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, its feature
It is, the formation tracking control unit of design is as follows in step (6)：
Wherein, K2i=diag [k21i,k22i,k23i] it is diagonal matrix, k21iRepresent formation control device τ1Design parameter, k22iTable
Show formation control device τ2Design parameter, k23iRepresent formation control device τ3Design parameter.
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| CN111506114A (en) * | 2020-05-25 | 2020-08-07 | 北京理工大学 | Aircraft formation control method |
| CN112034865A (en) * | 2020-08-12 | 2020-12-04 | 浙江大学 | Full-drive underwater vehicle track tracking control method based on optimization algorithm |
| CN112034865B (en) * | 2020-08-12 | 2021-10-08 | 浙江大学 | Full-drive underwater vehicle track tracking control method based on optimization algorithm |
| CN112666832A (en) * | 2020-12-23 | 2021-04-16 | 大连海事大学 | Non-periodic communication underwater glider cooperative controller structure and design method |
| CN112666832B (en) * | 2020-12-23 | 2022-08-30 | 大连海事大学 | Non-periodic communication underwater glider cooperative controller system and design method |
| CN112947462A (en) * | 2021-03-02 | 2021-06-11 | 广东省智能机器人研究院 | Unmanned ship group formation cooperative control method considering time-varying drift angle and attitude adjustment |
| CN113189979A (en) * | 2021-04-02 | 2021-07-30 | 大连海事大学 | Distributed queue finite time control method of unmanned ship |
| CN113189979B (en) * | 2021-04-02 | 2023-12-01 | 大连海事大学 | Finite time control method for distributed queue of unmanned ship |
| CN112987758A (en) * | 2021-04-29 | 2021-06-18 | 电子科技大学 | Multi-water-surface aircraft cooperative tracking formation control method |
| CN115453888A (en) * | 2022-10-10 | 2022-12-09 | 黄山学院 | Multi-mobile-robot formation control method based on equivalent input disturbance observer |
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