CN110262484A - Wheeled robot uniform rectilinear's formation control method based on adaptive event triggering - Google Patents
Wheeled robot uniform rectilinear's formation control method based on adaptive event triggering Download PDFInfo
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- G—PHYSICS
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- 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
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
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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
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle
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Abstract
The present invention relates to a kind of wheeled robot uniform rectilinear's formation control methods based on adaptive event triggering, the wheeled robot includes a leader robot and multiple follows robot, method includes the following steps: 1) expectation relative position when setting follows robot to form into columns with leader robot uniform rectilinear, the external signal observer based on event trigger mechanism is constructed, acquisition each follows robot with respect to the observation of leader robot；2) location error for following robot with leader robot is calculated, in conjunction with robot inearized model, obtains the normal place for following robot and standard control input；3) based on the normal place for following robot and standard control input, complete distributed self-adaption controller is constructed, acquisition follows the real time system control of robot to input.Compared with prior art, the present invention have the advantages that it is accurate and reliable, save the energy and more stable.
Description
Technical field
The present invention relates to a kind of complete distributed collaboration control methods of multiple agent based on adaptive event triggering, especially
It is to be related to a kind of wheeled robot uniform rectilinear's formation control method based on adaptive event triggering.
Background technique
With the development of multi-agent Technology, industry is higher and higher for being had based on the distributed AC servo system that event triggers
It is required that.Because single multiple agent can not know the global information of entire multi-agent system, simultaneously in certain complex environments
Because limited energy, environment complexity cannot achieve continuous communication between multiple agent.Therefore, in recent years, being touched based on event
The research of the complete distributed collaboration control of the multiple agent of hair receives the extensive concern of domestic and foreign scholars.
Wheeled robot formation control is a subdivision field of multiple agent Collaborative Control.And wheeled robot is at the uniform velocity
Straight line formation control problem is a subproblem of wheeled robot formation control problem, at present still without research or patent skill
Art, which can be realized, avoids the completely distributed uniform rectilinear's formation control of the wheeled robot of continuous communiction.It is well known that wheeled machine
The self-contained limited energy of device people, and communicating is the process extremely to consume energy.Simultaneously in some cases, due to environmental factor
Interference, the wheel type machine human world cannot achieve continuous communiction.Therefore intermittently communicating may be implemented by introducing event triggering technique,
Save the energy.According to the control mode of centralization, when core machine people when something goes wrong, entire form into columns will paralyse.In addition
It realizes that the communications cost of centerized fusion is excessively high, is not suitable for being applied in actual scene.Therefore it designs a kind of based on adaptive thing
The completely distributed uniform rectilinear's formation control device design method of the wheeled robot of part triggering is imperative.
Summary of the invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide one kind to be based on adaptive thing
Wheeled robot uniform rectilinear's formation control method of part triggering.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of wheeled robot uniform rectilinear's formation control method based on adaptive event triggering, the wheeled robot
Including a leader robot and it is multiple follow robot, method includes the following steps:
S1: expectation relative position when setting follows robot to form into columns with leader robot uniform rectilinear, building are based on thing
The external signal observer of part trigger mechanism, acquisition each follow robot with respect to the observation of leader robot；
S2: the location error for following robot with leader robot is calculated, in conjunction with robot inearized model, acquisition is followed
The normal place and standard of robot control input；
S3: based on the normal place for following robot and standard control input, constructing complete distributed self-adaption controller,
Acquisition follows the real time system control of robot to input.
Further, in the step S1, the expression formula of the event trigger mechanism of external signal observer is as follows:
In formula, ηi(t) follow robot i with respect to the observation of leader robot for the acquisition of external signal observer,I2For 2 × 2 unit matrix, aijIndicate robot i and the direct communication connection situation of robot j, For the l times event triggering moment for following robot i, in order to indicate easy, Zhi Houyong
kiTo represent ki(t), κiIt (t) is observer adaptive gain, initial value meets κi(0) >=1, ιi(t) it is triggered for event adaptive
Gain is answered, initial value meets ιi(0) >=1, ηei(t) it indicates to follow robot i self norms position and observation ηi(t) between
Error, a1For any positive real number, a2For any positive real number.
Selection liapunov function verifies state observer, the expression formula of liapunov function are as follows:
In formula, matrix For the Laplacian Matrix for following wheeled robot formation communication network topology,
Δ is the degree matrix for following wheeled robot formation communication network topology,With g2=g3λmax
(H)2It is constant.
To liapunov function derivation can prove designed leader's robotary observer can satisfy for
Arbitrary i,Requirement.
Further, in the step S2, the obtaining step of robot inearized model specifically:
S201: wheeled robot nonlinear model is established；
S202: building robotary vector linearizes robot nonlinear model.
Further, in the step S201, the expression formula of wheeled robot nonlinear model are as follows:
In formula, (xpi(t),ypiIt (t)) is position of the wheeled robot i in t moment cartesian coordinate system, viIt (t) is wheel
Linear velocity of the formula robot i in t moment cartesian coordinate system, θiIt (t) is wheeled robot i in t moment cartesian coordinate system
The angle of middle mass center, ωiIt (t) is angular speed of the wheeled robot i in t moment cartesian coordinate system, miFor wheeled robot i
Quality, JiFor the rotary inertia of wheeled robot i,uiIt (t) is wheeled robot i in t moment
System control input, fiIt (t) is size of the wheeled robot i in t moment input power, τi(t) defeated in t moment for wheeled robot i
Enter the size of torque.
Further, in the step S202, building robotary vector includes building leader's robotary vector
Robot transition vector, the expression formula of leader robotary vector v (t) are followed with building are as follows:
In formula, xp0(t) for leader robot in t moment along the coordinate of cartesian coordinate system x-axis direction, yp0(t) machine is led
Device people is in t moment along the coordinate in cartesian coordinate system y-axis direction, νx0(t) for leader robot in t moment along cartesian coordinate system
The speed of x-axis direction, vx0(t)=v0(t)cosθ0(t), v0(t) line for leader robot t moment in cartesian coordinate system
Speed, θ0It (t) is the angle of leader robot mass center in t moment cartesian coordinate system, νy0It (t) is leader robot in t
It carves along cartesian coordinate system y-axis direction speed, vy0(t)=v0(t)sinθ0(t)。
Further, the expression formula for following robotary vector are as follows:
xi(t)=[xpi-xp0-xdi,ypi-yp0-ydi,νxi,νyi]
X in formulaiIt (t) is to follow state vector of the robot i in t moment cartesian coordinate system, xpiTo follow robot i
Along the coordinate of cartesian coordinate system x-axis direction, xp0For the coordinate of leader's Robot cartesian coordinate system x-axis direction, ypiFor with
Coordinate of the random device people i along cartesian coordinate system y-axis direction, yp0For the seat in leader's Robot cartesian coordinate system y-axis direction
Mark, νxiTo follow robot i along the speed of cartesian coordinate system x-axis direction, vxi(t)=vi(t)cosθi(t), vi(t) for
Linear velocity of the random device people i in t moment cartesian coordinate system, θiIt (t) is to follow robot in t moment cartesian coordinate system
The angle of mass center, νyiTo follow robot i along the speed in cartesian coordinate system y-axis direction, vyi(t)=vi(t)sinθi(t)。Expectation relative position of the robot i with leader robot is followed when to ultimately form formation.
Further, in the step S202, the result of linearisation robot nonlinear model includes leader robot line
Property model and follow robot inearized model, the expression formula of leader's robot inearized model are as follows:
In formula,For leader robot inearized model,V (t) is leader's robotary
Vector.
Further, the expression formula for following robot inearized model are as follows:
In formula,For the inearized model for following robot i, xiIt (t) is that robot i is followed to sit in t moment Descartes
State vector in mark system, ui(t) to follow robot i to control input value in the system of t moment, v (t) is that robot is followed to exist
Linear velocity in cartesian coordinate system,Ei=04×4。
Further, in the step S2, location error expression formula of the robot with leader robot is followed are as follows:
ei(t)=pi(t)-p0(t)-pdi
ei(t)=Cixi(t)+Diui(t)+Fiv(t)
In formula, eiIt (t) is the location error for following robot i with leader robot, piIt (t) is to follow robot i in flute card
Position in your coordinate system,xpiIt (t) is to follow robot i in t moment along cartesian coordinate system x
The coordinate of axis direction, ypiIt (t) is to follow coordinate of the robot i in t moment along cartesian coordinate system y-axis direction, p0It (t) is leader
Robot t moment in the position of cartesian coordinate system,pdiTo follow robot i and leader's machine
Expectation relative position when people uniform rectilinear forms into columns,xdiIt is expectation relative position in cartesian coordinate system x-axis
The coordinate in direction, ydiCoordinate for expectation relative position in cartesian coordinate system y-axis direction,Di=04×4,
Further, in the step S2, the normal place of robot and the acquisition of standard control input are followed specifically:
The location error for following robot with leader robot is established, and follows the equation group of robot inearized model, solves institute
It states equation group and obtains the normal place for following robot and standard control input, the expression formula of the equation group are as follows:
XiS=AiXi+BiUi+Ei
0=CiXi+DiUi+Fi
In formula, XiFor the normal place for following robot i, UiTo follow the standard of robot i to control input.
Further, in the step S3, the expression formula of complete distributed self-adaption controller is as follows:
ui(t)=K1ixi(t)+K2iηi(t)
K2i=Ui-K1iXi
In formula, ui(t) to follow the real time system control of robot to input, K1iFor feedback gain matrix, value makes square
Battle array Ai+BiK1iTie up hereby stable, K in Hull2iFor feedforward gain matrix.
Compared with prior art, the invention has the following advantages that
(1) external signal observer of the present invention, which uses, is based on event trigger mechanism, avoids the company between wheeled robot
Continuous communication, realizes intermittently communicating, saves the energy.
(2) present invention combines the characteristics of wheeled robot uniform rectilinear formation control, to wheeled robot nonlinear model
It is linearized, so that wheeled robot uniform rectilinear formation control method of the present invention is more accurate and reliable.
(3) auto-adaptive parameter is introduced in controller of the present invention, follows robot to each respectively and have corresponding controller
It is controlled, realizes complete distributed self-adaption control, avoid wheeled robot during formation control to global information
Dependence, increase the stability of system.
Detailed description of the invention
Fig. 1 is that the process of the wheeled robot uniform rectilinear's formation control method triggered the present invention is based on adaptive event is shown
It is intended to；
Fig. 2 is position view of the wheeled robot in cartesian coordinate system；
Fig. 3 is the communication network topology schematic diagram that wheeled robot is formed into columns in the embodiment of the present invention；
Fig. 4 is wheeled robot formation error in the embodiment of the present invention with the result figure of time change；
Fig. 5 is wheeled robot formation trajectory diagram in the embodiment of the present invention.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention
Premised on implemented, the detailed implementation method and specific operation process are given, but protection scope of the present invention is not limited to
Following embodiments.
Embodiment 1
As shown in Figure 1, the present embodiment is a kind of wheeled robot uniform rectilinear formation control based on adaptive event triggering
Method processed, wheeled robot include a leader robot and it is multiple follow robot, method includes the following steps:
S1: expectation relative position when setting follows robot to form into columns with leader robot uniform rectilinear, building are based on thing
The external signal observer of part trigger mechanism, acquisition each follow robot with respect to the observation of leader robot；
S2: the location error for following robot with leader robot is calculated, in conjunction with robot inearized model, acquisition is followed
The normal place and standard of robot control input；
S3: based on the normal place for following robot and standard control input, constructing complete distributed self-adaption controller,
Acquisition follows the real time system control of robot to input.
Above-mentioned steps circulation executes, and current time is input with the result that last moment obtains.
1, expectation relative position when setting follows robot to form into columns with leader robot uniform rectilinear
Design ultimately forms the expectation relative position that robot i is followed when formation with leader robot
In the present embodiment, it enables
2, external signal observer event trigger mechanism is designed
External signal observer of the design based on event trigger mechanism not needing continuous communiction between wheeled robot,
Follow robot that can observe leader robotary v (t) simultaneously, i.e., for arbitrary i,External signal
The expression formula of the event trigger mechanism of observer is as follows:
In formula, ηi(t) follow robot i with respect to the observation of leader robot for the acquisition of external signal observer,I2For 2 × 2 unit matrix, aijIndicate robot i and the direct communication connection situation of robot j,
The a if the observation that robot i can obtain jij> 0, otherwise aij=0, For with random device
The l times event triggering moment of people i uses k to indicate easy lateriTo represent ki(t), κi(t) adaptively increase for observer
Benefit, initial value meet κi(0) >=1, ιi(t) adaptive gain is triggered for event, initial value meets ιi(0) >=1, ηei(t) table
Show and follows robot i self norms position and observation ηi(t) error between, a1For any positive real number, a2It is any positive real
Number.
Selection liapunov function verifies state observer, the expression formula of liapunov function are as follows:
In formula, matrix For the Laplacian Matrix for following wheeled robot formation communication network topology,
Δ is the degree matrix for following wheeled robot formation communication network topology,With g2=g3λmax
(H)2It is constant.
To liapunov function derivation can be found that designed leader's robotary observer can satisfy for
Arbitrary i,Requirement.
In the present embodiment, the communication network topology between wheeled robot formation is as shown in figure 3, so corresponding Laplce
MatrixSpend matrix Δ and H-matrix are as follows:
The present embodiment leads robotary observer and complete distributed self-adaption controller parameter as shown in table 1.
Table 1 leads robotary observer and complete distributed self-adaption controller parameter
3, robot inearized model is obtained
The obtaining step of robot inearized model specifically:
S201: wheeled robot nonlinear model, coordinate of the wheeled robot in cartesian coordinate system such as Fig. 2 institute are established
Show, the expression formula of wheeled robot nonlinear model are as follows:
In formula, (xpi(t),ypiIt (t)) is position of the wheeled robot i in t moment cartesian coordinate system, viIt (t) is wheel
Linear velocity of the formula robot i in t moment cartesian coordinate system, θiIt (t) is wheeled robot i in t moment cartesian coordinate system
The angle of middle mass center, ωiIt (t) is angular speed of the wheeled robot i in t moment cartesian coordinate system, miFor wheeled robot i
Quality, JiFor the rotary inertia of wheeled robot i,uiIt (t) is wheeled robot i in t moment
System control input, fiIt (t) is size of the wheeled robot i in t moment input power, τi(t) defeated in t moment for wheeled robot i
Enter the size of torque.
S202: linearisation leader's robot nonlinear model.
In conjunction with the characteristics of uniform rectilinear's formation control, wheeled robot model is linearized.Wheeled robot is at the uniform velocity
Straight line is formed into columns follows wheeled robot to form by 1 leader's wheeled robot and N-1.Wherein lead the mark of wheeled robot
It number is 0, and the robot remains linear uniform motion during formation control, then the nonlinear model of the robot
Are as follows:
I.e. leader robot remains linear velocity v during formation control0(t), mass center angle, θ0(t) when not becoming 0
Initial value is carved, while keeping angular velocity omega0It (t) is 0.Definition leader Robot cartesian coordinate system x-axis direction speed be
vx0(t)=v0(t)cosθ0(t), speed along the y-axis direction is vy0(t)=v0(t)cosθ0(t), then leading the non-of robot
Linear model can be converted to following form:
Lead the expression formula of robotary vector v (t) are as follows:
The nonlinear model of leader robot can be converted into following linear model:
In formula,For leader robot inearized model,V (t) is leader's robotary
Vector.
In the present embodiment, the original state for leading robot is
S203: linearisation follows robot nonlinear model
The same speed for following robot i along cartesian coordinate system x-axis direction that defines is vxi(t)=vi(t)cosθi(t),
Speed along the y-axis direction is vyi(t)=vi(t)cosθi(t), then following the nonlinear model of robot i can convert are as follows:
WhereinIt is the control input after conversion.
That constructs follows the expression formula of robotary vector are as follows:
xi(t)=[xpi-xp0-xdi,ypi-yp0-ydi,νxi,νyi]
Following linear model can be converted by following the nonlinear model of robot:
In formula,For the inearized model for following robot i, xiIt (t) is that robot i is followed to sit in t moment Descartes
State vector in mark system, uiIt (t) is that the system for following robot i controls input value, v (t) is to follow robot in Descartes
Linear velocity in coordinate system,Ei=04×4。
4, the normal place for following robot and standard control input are obtained
Follow the normal place of robot and the acquisition of standard control input specifically: foundation follows robot and leader's machine
The location error of device people, and the equation group of robot inearized model is followed, it solves the equation group acquisition and follows robot
Normal place and standard control input.
Follow location error expression formula of the robot with leader robot are as follows:
ei(t)=pi(t)-p0(t)-pdi
ei(t)=Cixi(t)+Diui(t)+Fiv(t)
In formula, eiIt (t) is the location error for following robot i with leader robot, piIt (t) is to follow robot i in flute card
Position in your coordinate system,xpiIt (t) is to follow robot i in t moment along cartesian coordinate system x
The coordinate of axis direction, ypiIt (t) is to follow coordinate of the robot i in t moment along cartesian coordinate system y-axis direction, p0It (t) is leader
Robot t moment in the position of cartesian coordinate system,pdiTo follow robot i and leader's machine
Expectation relative position when people uniform rectilinear forms into columns,xdiIt is expectation relative position in cartesian coordinate system x-axis
The coordinate in direction, ydiCoordinate for expectation relative position in cartesian coordinate system y-axis direction,Di=04×4,
The expression formula of equation group are as follows:
XiS=AiXi+BiUi+Ei
0=CiXi+DiUi+Fi
In formula, XiFor the normal place for following robot i, UiTo follow the standard of robot i to control input.
In the present embodiment, wheeled robot formation follows wheeled robot by 1 leader's wheeled robot and 4 altogether
Composition, four original states for following wheeled robot are
5, complete distributed self-adaption controller is constructed
The expression formula of complete distributed self-adaption controller is as follows:
ui(t)=K1ixi(t)+K2iηi(t)
K2i=Ui-K1iXi
In formula, ui(t) to follow the real time system control of robot to input, K1iFor feedback gain matrix, value makes square
Battle array Ai+BiK1iTie up hereby stable, K in Hull2iFor feedforward gain matrix.
6, result
Carrying out emulation experiment to above-mentioned wheeled robot fleet system can obtain.Fig. 4 gives formation error with the time
Change as a result, formation error restrains rapidly as time increases.Fig. 5 gives the formation track of wheeled robot, can be with
Find out and ultimately forms right angle formation.
The preferred embodiment of the present invention has been described in detail above.It should be appreciated that those skilled in the art without
It needs creative work according to the present invention can conceive and makes many modifications and variations.Therefore, all technologies in the art
Personnel are available by logical analysis, reasoning, or a limited experiment on the basis of existing technology under this invention's idea
Technical solution, all should be within the scope of protection determined by the claims.
Claims (9)
1. a kind of wheeled robot uniform rectilinear's formation control method based on adaptive event triggering, the wheeled robot packet
It includes a leader robot and multiple follows robot, which is characterized in that method includes the following steps:
S1: expectation relative position when setting follows robot to form into columns with leader robot uniform rectilinear, building are touched based on event
The external signal observer of hair mechanism, acquisition each follow robot with respect to the observation of leader robot；
S2: calculating the location error for following robot with leader robot, in conjunction with robot inearized model, obtains with random device
The normal place and standard of people controls input；
S3: based on the normal place for following robot and standard control input, complete distributed self-adaption controller is constructed, is obtained
The real time system control of robot is followed to input.
2. a kind of wheeled robot uniform rectilinear formation control side based on adaptive event triggering according to claim 1
Method, which is characterized in that in the step S1, the expression formula of the event trigger mechanism of external signal observer is as follows:
In formula, ηi(t) follow robot i with respect to the observation of leader robot for the acquisition of external signal observer,I2For 2 × 2 unit matrix, aijIndicate that the direct communication connection situation of robot i and robot j is joined
Number, For the l times event triggering moment for following robot i, in order to indicate easy, later
Use kiTo represent ki(t), κiIt (t) is observer adaptive gain, initial value meets κi(0) >=1, ιi(t) certainly for event triggering
Gain is adapted to, initial value meets ιi(0) >=1, ηei(t) it indicates to follow robot i self norms position and observation ηi(t) it
Between error, a1For any positive real number, a2For any positive real number.
3. a kind of wheeled robot uniform rectilinear formation control side based on adaptive event triggering according to claim 1
Method, which is characterized in that in the step S2, the obtaining step of robot inearized model specifically:
S201: wheeled robot nonlinear model is established；
S202: building robotary vector linearizes robot nonlinear model.
4. a kind of wheeled robot uniform rectilinear formation control side based on adaptive event triggering according to claim 3
Method, which is characterized in that in the step S202, the result for linearizing robot nonlinear model is linearized including leader robot
Model and follow robot inearized model, the expression formula of leader's robot inearized model are as follows:
In formula,For leader robot inearized model, v (t) is leader's robotary vector.
5. a kind of wheeled robot uniform rectilinear formation control side based on adaptive event triggering according to claim 4
Method, which is characterized in that the expression formula of leader robotary vector v (t) are as follows:
In formula, xp0(t) for leader robot in t moment along the coordinate of cartesian coordinate system x-axis direction, yp0(t) robot is led
In t moment along the coordinate in cartesian coordinate system y-axis direction, νx0(t) for leader robot in t moment along cartesian coordinate system x-axis
The speed in direction, vx0(t)=v0(t)cosθ0(t), v0(t) linear speed for leader robot t moment in cartesian coordinate system
Degree, θ0It (t) is the angle of leader robot t moment mass center in cartesian coordinate system, νy0It (t) is leader robot in t moment
Along cartesian coordinate system y-axis direction speed, vy0(t)=v0(t)sinθ0(t)。
6. a kind of wheeled robot uniform rectilinear formation control side based on adaptive event triggering according to claim 4
Method, which is characterized in that the expression formula for following robot inearized model are as follows:
In formula,For the inearized model for following robot i, xiIt (t) is to follow robot i in t moment cartesian coordinate system
State vector, ui(t) to follow robot i to control input value in the system of t moment, v (t) is to follow robot in Descartes
Linear velocity in coordinate system,Ei=04×4。
7. a kind of wheeled robot uniform rectilinear formation control side based on adaptive event triggering according to claim 6
Method, which is characterized in that the expression formula for following robotary vector are as follows:
xi(t)=[xpi-xp0-xdi,ypi-yp0-ydi,νxi,νyi]
X in formulaiIt (t) is to follow state vector of the robot i in t moment cartesian coordinate system, xpiTo follow robot i along flute
The coordinate of karr coordinate system x-axis direction, xp0For the coordinate of leader's Robot cartesian coordinate system x-axis direction, ypiFor with random
Coordinate of the device people i along cartesian coordinate system y-axis direction, yp0For the coordinate in leader's Robot cartesian coordinate system y-axis direction,
νxiTo follow robot i along the speed of cartesian coordinate system x-axis direction, vxi(t)=vi(t)cosθi(t), vi(t) for random
Linear velocity of the device people i in t moment cartesian coordinate system, θiIt (t) is to follow robot mass center in t moment cartesian coordinate system
Angle, νyiTo follow robot i along the speed in cartesian coordinate system y-axis direction, vyi(t)=vi(t)sinθi(t)。Expectation relative position of the robot i with leader robot is followed when to ultimately form formation.
8. a kind of wheeled robot uniform rectilinear formation control side based on adaptive event triggering according to claim 1
Method, which is characterized in that in the step S2, follow the normal place of robot and the acquisition of standard control input specifically: build
The vertical location error for following robot with leader robot, and the equation group of robot inearized model is followed, solve the party
Journey group obtains the normal place for following robot and standard control input, the expression formula of the equation group are as follows:
XiS=AiXi+BiUi+Ei
0=CiXi+DiUi+Fi
In formula, XiFor the normal place for following robot i, UiTo follow the standard of robot i to control input,Di=04×4,
9. a kind of wheeled robot uniform rectilinear formation control side based on adaptive event triggering according to claim 1
Method, which is characterized in that in the step S3, the expression formula of complete distributed self-adaption controller is as follows:
ui(t)=K1ixi(t)+K2iηi(t)
K2i=Ui-K1iXi
In formula, ui(t) to follow the real time system control of robot to input, K1iFor feedback gain matrix, value makes matrix Ai+
BiK1iTie up hereby stable, K in Hull2iFor feedforward gain matrix.
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