CN112947086A - Self-adaptive compensation method for actuator faults in formation control of heterogeneous multi-agent system consisting of unmanned aerial vehicle and unmanned vehicle - Google Patents
Self-adaptive compensation method for actuator faults in formation control of heterogeneous multi-agent system consisting of unmanned aerial vehicle and unmanned vehicle Download PDFInfo
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Abstract
The invention discloses a self-adaptive compensation method for actuator faults in formation control of a heterogeneous multi-agent system consisting of an unmanned aerial vehicle and an unmanned vehicle, which comprises the following steps: the multi-agent system comprises an unmanned aerial vehicle and an unmanned vehicle, wherein the unmanned vehicle model adopts a two-wheeled mobile robot, and the unmanned aerial vehicle model adopts a four-rotor unmanned aerial vehicle, so that the unmanned aerial vehicle model is respectively modeled and simplified. And respectively modeling an XOY plane model of the unmanned ground vehicle and the unmanned aerial vehicle position subsystem of the system after the fault occurs and a Z-axis model of the unmanned aerial vehicle position subsystem, so as to realize unmanned aerial vehicle-unmanned vehicle formation control. And determining the communication topology of the multi-agent system as a strong communication graph. And designing a control law under the condition that the self-adaptive law updates the fault estimation parameters by using a backstepping method to realize formation control. And designing a control law under the condition that the self-adaptive law updates fault estimation parameters by a backstepping method for the Z-axis model of the quad-rotor unmanned aerial vehicle with the fault of the actuator, so as to realize consistency. The invention can ensure that the multi-agent system can smoothly realize formation control under the condition of unknown fault.
Description
Technical Field
The invention belongs to the technical field of formation control of aerospace heterogeneous multi-agent systems, and particularly relates to a self-adaptive compensation method for actuator faults in formation control of a heterogeneous multi-agent system formed by an unmanned aerial vehicle and an unmanned vehicle.
Background
A multi-agent system refers to a system in which a certain number of agents cooperate with each other to accomplish a specific task. Compared with a single intelligent agent, the multi-intelligent-agent system can complete more complex and arduous work and has wider application scenes, such as wireless sensor networks, robot formation, multi-manipulator cooperative assembly and the like. Therefore, more and more researchers are beginning to focus on the issue of cooperative control of multi-agent systems. Cooperative control means that in a certain communication network environment, a group of intelligent agents can reach an agreement according to a specific requirement by designing a proper control algorithm. At present, most researches on cooperative control of multi-agent systems are focused on isomorphic multi-agent systems, and researches on cooperative control of heterogeneous multi-agent systems are relatively few, such as cooperative control of unmanned aerial vehicles and unmanned ground vehicles.
In modern control systems, as the systems scale up and the task complexity increases, the probability of system failure increases. However, failure of either system can severely reduce the stability of the system. Therefore, fault-tolerant cooperative control of the multi-agent system is very important.
The faults can be classified into topology faults and component faults according to the location where the fault occurs. Topology faults are faults occurring between agents that affect the communication topology, such as packet loss and communication interruption, while component faults are faults occurring inside a single node, such as actuator faults, controlled object faults, sensor faults, and the like.
Fault tolerant control can be broadly divided into two categories according to different design considerations: passive fault-tolerant control and active fault-tolerant control. In passive fault-tolerant control, the parameters and structure of the controller are generally fixed, the controller is designed to be robust against a specific type of fault, online detection of fault information is not required, and common control methods include adaptive control, sliding mode control, fuzzy control and the like. Unlike passive fault-tolerant control methods, active fault-tolerant control combines fault detection and identification by reconfiguring controller actions to actively respond to a fault.
In the context of "Time-varying formatting control of a scalable heterologous multi-agent system" (R.Rahimi et al/Robotics and Autonomous Systems 62(2014) 1799-1805), authors have investigated the problem of queuing control of multi-agent Systems in a Time-varying queuing environment. For special applications of rescue and surveillance, a set of systems consisting of drones and unmanned vehicles is considered. Because the degrees of freedom of unmanned aerial vehicles and unmanned vehicles are different, cooperative control between intelligent agents faces many problems. The Lyapunov-based controller is provided, and adopts a distributed control method to stabilize bee colonies, so that the system forms a rigid formation. However, this approach does not take into account the case of unknown failure of the multi-agent system. If the system fails, the result of the failure of the formation control may occur.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a self-adaptive compensation method for actuator faults in formation control of a heterogeneous multi-agent system consisting of an unmanned aerial vehicle and an unmanned vehicle, and can ensure that the multi-agent system can still smoothly realize formation control under the condition of unknown faults.
The present invention adopts the following technical solutions to solve the above technical problems.
A self-adaptive compensation method for actuator faults in formation control of a heterogeneous multi-agent system consisting of an unmanned aerial vehicle and an unmanned vehicle comprises the following steps:
the method comprises the following steps that step 1, a multi-agent system comprises M unmanned vehicles and (N-M) unmanned aerial vehicles, wherein a two-wheel mobile robot is adopted as an unmanned vehicle model, a four-rotor unmanned aerial vehicle is adopted as an unmanned aerial vehicle model, modeling and simplification are respectively carried out on the unmanned aerial vehicle model, and a second-order unmanned vehicle model and a second-order unmanned aerial vehicle model are obtained;
step 2, considering that the actuator of the multi-agent system has partial failure fault, respectively modeling an XOY plane model of the unmanned ground vehicle and the unmanned plane position subsystem after the fault and a Z-axis model of the unmanned plane position subsystem, and simultaneously realizing unmanned plane-unmanned vehicle formation control;
step 4, aiming at an XOY plane model of the unmanned ground vehicle and the unmanned aerial vehicle position subsystem with the actuator fault, designing a control law under the condition that the fault estimation parameters are updated by a self-adaptive law by using a backstepping method to realize formation control;
and 5, designing a control law under the condition that the fault estimation parameters are updated by the self-adaptive law by utilizing a backstepping method aiming at the Z-axis model of the quad-rotor unmanned aerial vehicle with the fault of the actuator, so as to realize consistency.
Further, in step 1, it is assumed that the direction of each unmanned vehicle is fixed and the same, namely χi(t) ═ χ; then the angular velocity omegai(t) ═ 0; the simplified kinetic equation of the ith two-wheeled mobile robot model is as follows:
wherein,
the coordinates of the front end point are represented,
Ldiis the distance between the hand point and the middle point of the two wheels, Fi(t),τi(t) input force and input moment, Mgi,JgiRespectively representing the mass and the moment of inertia of the ith unmanned vehicle;
because the model of the quad-rotor unmanned aerial vehicle is complex, the coupling problem exists, and if disturbance is considered, the model becomes more complex; here wind disturbances are ignored, while assuming that the attitude of each drone is fixed and the same, i.e., #i(t)＝φ,θi(t)＝θ,ψi(t) ═ ψ; the motion of the ith unmanned aerial vehicle modelThe mechanical equation is as follows:
wherein p isi(t)＝[pxi(t),pyi(t),pzi(t)]TIn the state of the position, the position of the mobile phone is changed,
Maiindicating the quality of the ith drone,
represents a control input;
meanwhile, the unmanned aerial vehicle and the unmanned ground vehicle XOY two-dimensional model are considered to be cooperatively formed and controlled, and the unmanned aerial vehicle Z-axis model is independently controlled.
Further, in step 2, considering the XOY plane model of the simplified unmanned ground vehicle and drone location subsystem in case of a multiplicative actuator failure, the following second order system may be represented:
wherein x isi(t)∈R2,vi(t)∈R2,ui(t)∈R2Respectively representing position information, velocity information and control input, 0<ρi≤1；
The simplified Z-axis model of the unmanned aerial vehicle position subsystem can be represented by the following second-order system when an actuator multiplicative fault occurs:
wherein x isi(t)∈R,vi(t)∈R,ui(t) E.R represents position information, speed information and control input, respectively; 0<ρi≤1；
Expected time-varying formation of
Wherein h isi(t)＝[hxi(t),hvi(t)]T(ii) a A multi-agent system may be considered to implement formation control if the following two equations can hold:
further, in step 3, consider the multi-agent communication topology as a strongly connected graph of the following properties:
1) the Laplace matrix L of the strong connection graph has one eigenvalue of 0, and the real parts of the other eigenvalues are positive;
2) a positive definite vector can be found
Satisfy the requirement of
Wherein
Further, in step 4, to simplify the analysis process, assume xi(t),vi(t),ui(t) is one-dimensional, and the two-dimensional model result can be obtained by popularizing the kronecker product;
suppose that
At the same time order zi(t)＝xi(t)-hxi(t)，mi(t)＝vi(t)-hvi(t), herein defined
If it is not
Can obtain
Namely, the multi-agent system realizes formation control;
definition of
ξ(t)＝[ξ1(t),ξ2(t),...,ξN(t)]TError variables can be obtained
And ξ (t) are:
wherein, P ═ diag { ρ ═ P1,ρ2,…,ρN}；
ξ (t) can be considered as a virtual control signal in the first expression; first, a dummy control signal α is designed to ensure when ξ (t) ═ α
Then designing a control signal u (t) to ensure the required system performance; design α is:
wherein k is1If the value is more than 0, the validity of the virtual control signal alpha can be verified;
in addition, the definition G ═ P-1At the same time define
Is an estimate of G; designing a reference nominal control signal, wherein the design control signal u (t) is:
in order to realize the control signal shown in the above formula, the following adaptive law pair is designed
Updating:
thus, the effectiveness of the control law u (t) under the adaptive law update can be proved.
Further, in step 5, a reference position signal x is givend(t) and a reference velocity signal vd(t) definition of
The following error dynamics equations are obtained for the position tracking error and the velocity tracking error, respectively:
consider that
Can be regarded as a virtual control signal in the first formula; firstly, a virtual control signal beta is designediTo ensure when
When the temperature of the water is higher than the set temperature,
then the control input signal u is designedi(t) to ensure
Designing a virtual control signal betaiComprises the following steps:
wherein k is1i> 0 is a given normal number, the dummy control signal beta can be verifiediThe effectiveness of (a);
definition of
Definition of
Is λiEstimation of (2), estimation error
Is defined as
Designed control signal ui(t) and for updating
The adaptation law of (1) is as follows:
wherein k is2i＞0，γi> 0 is two given normal numbers; thus proving the control law u under the adaptive law updatei(t) effectiveness.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. aiming at the heterogeneous multi-agent system consisting of the unmanned aerial vehicle and the unmanned vehicle, the invention solves the formation control problem of the multi-agent system under the failure of the actuator, and can ensure the stability of the system when the failure occurs. The unmanned aerial vehicle-unmanned vehicle air-ground combined formation can realize the complementation of the unmanned aerial vehicle and the unmanned vehicle in the aspects of load, perception, communication and the like through mutual cooperation, and improves the flexibility of the whole system and the adaptability to an unknown environment, thereby completing tasks which are difficult to complete by independent unmanned aerial vehicle formation or unmanned vehicle formation, such as large-scale area investigation, geographical survey, tracking pursuit and evasion, cooperative navigation, rescue, map drawing and the like. Meanwhile, under the corresponding fault-tolerant control strategy, the working task can be still completed even under the condition that the partial actuator of the unmanned aerial vehicle-unmanned vehicle system has a fault.
2. According to the invention, a backstepping control method is adopted to obtain a control law for formation control of the two-dimensional models of the unmanned aerial vehicle and the unmanned vehicle and a control law for solving consistency of the Z-axis model of the unmanned aerial vehicle. Meanwhile, the uncertainty of the fault matrix is solved by adopting an adaptive direct compensation scheme. The method is ideal in rapidity and effectiveness when unmanned aerial vehicle and unmanned vehicle formation control is achieved and direct self-adaptive fault compensation is achieved, high in feasibility and easy to achieve.
3. The invention can effectively compensate the problem of actuator faults in the formation control of the heterogeneous multi-agent system formed by unmanned vehicles of the unmanned aerial vehicle, ensures the expected system stability and asymptotic tracking performance, and has important significance for the reliable control of the formation of the multi-agent system and the completion of tasks. Specifically, the method mainly comprises the following points:
1) the environmental information is efficiently and accurately acquired. A plurality of unmanned aerial vehicles and an unmanned vehicle form an expected formation, so that local environment information in different ranges can be obtained, and overall environment information can be obtained through a certain local information integration method.
2) The parallel work is realized, and the work efficiency is higher. Because a single unmanned aerial vehicle has limited task execution capacity, the time consumption is high when the task with larger workload is completed, and a plurality of unmanned aerial vehicles can complete the task more quickly by executing the task in parallel.
3) The system robustness is higher. The multiple unmanned aerial vehicle formation internally has certain formation constraint, and if the behavior of a certain unmanned aerial vehicle in the formation has errors or dead weight, the constraint of the whole formation can be eliminated.
4) The system fault tolerance is strong. Under the proposed fault-tolerant control strategy, even if an actuator of the multi-unmanned aerial vehicle system fails, the multi-unmanned aerial vehicle system can still complete preset work tasks under an adaptive direct compensation scheme and keep formation.
Drawings
FIG. 1 is a flow chart of one embodiment of the method of the present invention.
FIG. 2 is a multi-agent system communication topology diagram of one embodiment of the present invention.
FIG. 3 is an embodiment of the invention of an unmanned vehicle-unmanned aerial vehicle X-axis model position error signal
Graph is shown.
FIG. 4 is an embodiment of the present invention of an unmanned vehicle-unmanned aerial vehicle X-axis model speed error signal xie(t) graph.
FIG. 5 is a diagram of an unmanned vehicle-unmanned aerial vehicle Y-axis model position error signal according to an embodiment of the present invention
Graph is shown.
FIG. 6 is a speed error signal xi of a Y-axis model of an unmanned vehicle-unmanned aerial vehicle according to an embodiment of the inventione(t) graph.
Fig. 7 is a diagram of a position state of a Z-axis model of an unmanned aerial vehicle according to an embodiment of the invention.
Fig. 8 is a diagram of a Z-axis model speed state of an unmanned aerial vehicle according to an embodiment of the invention.
Detailed Description
The invention designs an adaptive compensation method for actuator faults in formation control of a heterogeneous multi-agent system consisting of unmanned aerial vehicles and unmanned vehicles. First, the unmanned aerial vehicle and the unmanned ground vehicle are simplified to a second order model. Aiming at the problem of formation control of XOY two-dimensional models of unmanned aerial vehicles and unmanned ground vehicles, a self-adaptive direct fault compensation control scheme is provided. Meanwhile, a corresponding self-adaptive direct fault compensation control protocol is provided for the consistency of the Z-axis model of the unmanned aerial vehicle.
The technical scheme of the invention is further explained in detail by combining the attached drawings:
FIG. 1 is a flow chart of one embodiment of the method of the present invention. As shown in fig. 1, the method of this embodiment includes the following steps:
step 1.1) considering the kinetic equation of the ith two-wheeled mobile robot model as follows:
wherein p isi(t)＝[pxi(t),pyi(t)]TIndicating the position state,. chii(t) represents a direction. Vi(t),ωi(t) represents linear velocity and angular velocity, respectively. Fi(t),τi(t) is the input force and the input torque. Mgi,JgiRespectively representing the mass and the rotational inertia of the ith unmanned vehicleAmount of the compound (A).
Consider that the front end point of the robot can be defined as a hand point, whose formula is as follows:
wherein L isdiIs the distance between the hand point and the middle point of the two wheels.
Representing the coordinates of the front end point.
Assuming that the direction of each unmanned vehicle is fixed and the same, i.e. χi(t) ×. Then the angular velocity omegai(t) is 0. By applying the derivation of equation (18) and the substitution of equation (17), the following can be obtained:
wherein,
step 1.2) the model of the quad-rotor unmanned aerial vehicle is complex, and the coupling problem exists. If perturbations are considered, the model becomes more complex. Ignoring wind disturbances here, consider the kinetic equation for the ith unmanned aerial vehicle model as:
wherein p isi(t)＝[pxi(t),pyi(t),pzi(t)]TIndicates the position state, ζi(t)＝[φi(t),θi(t),ψi(t)]TShowing the roll angle of the ith unmanned plane,Pitch angle and yaw angle. I isx,Iy,IzIs the moment of inertia. Mai,Jai,laiRespectively representing the mass, the inertia matrix and the length of the ith drone.
Representing a control input.
To simplify the problem and achieve cooperative control of drones and unmanned ground vehicles, it is assumed that the attitude of each drone is already fixed and the same, i.e., #i(t)＝φ,θi(t)＝θ,ψiAnd (t) ═ ψ. Then equation (20) can be converted to:
wherein,
in the invention, the cooperative formation control of the unmanned aerial vehicle and the unmanned ground vehicle XOY two-dimensional model is realized, and the unmanned aerial vehicle Z-axis model is controlled independently.
And 2, considering partial failure faults of actuators of the multi-agent system, respectively modeling an XOY plane model of the unmanned ground vehicle and the unmanned plane position subsystem after the faults occur and a Z-axis model of the unmanned plane position subsystem, and simultaneously realizing unmanned plane-unmanned vehicle formation control. The method comprises the following specific steps:
step 2.1) in case of a multiplicative actuator failure, the simplified XOY plane model of the unmanned ground vehicle and unmanned aerial vehicle position subsystem can be represented by the following second order system:
wherein x isi(t)∈R2,vi(t)∈R2,ui(t)∈R2Respectively, position information, velocity information, and control inputs. Note 0<ρi≤1。
The simplified Z-axis model of the unmanned aerial vehicle position subsystem can be represented by the following second-order system when an actuator multiplicative fault occurs:
wherein x isi(t)∈R,vi(t)∈R,ui(t) ∈ R indicates position information, speed information, and control input, respectively. Note 0<ρi≤1。
Step 2.2) the control objective of the invention is to design a proper control algorithm to ensure that the unmanned aerial vehicle-unmanned vehicle heterogeneous multi-agent system can keep stability and realize formation control under the condition of multiplication actuator failure.
Expected time-varying formation of
Wherein h isi(t)＝[hxi(t),hvi(t)]T. A multi-agent system can be considered to achieve formation control if the following two equations can be established.
in general, the communication topology between multi-agent systems can be represented by an undirected graph or a directed graph. Consider the structure of a graph denoted by G ═ (V, E, a), where V ═ {1,2, …, N } is a set of nodes,
for sets of edges between nodes, A ═ aij]N×NIs a contiguous matrix whose elements are all non-negative. If (j, i) E E, it means that node i can receive the state information of node j, and the element a in the adjacency matrixijIs greater than 0; otherwise
At this time, the node i cannot receive the state information of the node j, aij0. In multi-agent system research, the communication topology is also generally represented by a Laplacian matrix. When the communication topology adjacency matrix is a, the Laplacian matrix thereof can be expressed as: l ═ B-a. Wherein B ═ diag { B ═ B1,b2,…,bN}，
FIG. 2 is a multi-agent system communication topology diagram of one embodiment of the present invention. The invention considers the multi-agent communication topology as a strong communication graph. The nature of the strong connectivity graph is briefly described here: 1) the Laplace matrix L of the strong connection graph has one eigenvalue of 0, and the real parts of the other eigenvalues are positive. 2) A positive definite vector can be found
Satisfy the requirement of
Wherein
Step 4, aiming at an XOY plane model of the unmanned ground vehicle and the unmanned aerial vehicle position subsystem with the actuator fault, designing a control law under the condition that the fault estimation parameters are updated by a self-adaptive law by using a backstepping method to realize formation control; the method comprises the following steps:
and 4.1) designing a controller of an XOY plane model of the unmanned ground vehicle and the unmanned aerial vehicle position subsystem in consideration. To simplify the analysis process, assume xi(t),vi(t),ui(t) is one-dimensional, and two-dimensional model results can thus be generalized by the kronecker product.
Suppose that:
let zi(t)＝xi(t)-hxi(t)，mi(t)＝vi(t)-hvi(t) of (d). The following intermediate error equation can be derived:
are defined herein
It is easy to find if
Can obtain
According to equation (29), the multi-agent system achieves formation control.
Definition of
ξ(t)＝[ξ1(t),ξ2(t),…,ξN(t)]T. Can obtain error variable
And ξ (t) are:
wherein, P ═ diag { ρ ═ P1,ρ2,…,ρN}。
Step 4.2) designing an intermediate virtual control signal alpha, specifically:
considering (32), ξ (t) may be considered a virtual control signal. First, a dummy control signal α can be designed to ensure when ξ (t) ═ α
The control signal u (t) is then designed to ensure the desired system performance. Here, α is designed to be:
wherein k is1> 0 is a normal number.
First, the control performance of the virtual control signal α is analyzed. Defining a tracking error xie(t) ═ ξ (t) - α. Selecting a positive definite Lyapunov function V1(t) the following:
from equations (32) and (35), it is possible to obtain:
xi is not difficult to finde(t) is 0, then
The control signal u (t) is then designed to ensure limt→∞And xi (t) -alpha is 0, so that the system achieves the expected system performance.
Step 4.3) here the uncertainty P of the system is assumed first-1It is known that the topology of simultaneous multi-agent systems is strongly connected. The nominal control signal of the control signal in design formula (33) is as follows:
applying the nominal control signal shown in equation (37) to equation (27) ensures that the multi-agent system remains stable in the event of actuator failure, and
the validity of the nominal control signal (37) is demonstrated below. The following positive definite Lyapunov function was chosen:
by substituting formula (33) and formula (36) for formula (38), it is possible to obtain:
let u (t) be u*(t), it is not difficult to obtain:
formula (40) shows
According to Barbalt's introductionIt can be obtained that the multi-agent system can still be kept stable and formation can be realized in the case of actuator failure of the system, and
step 4.4) definition of G ═ P-1At the same time define
Is an estimate of G. Referring to the design of the nominal control signal in equation (37), the design control signal u (t) of the present invention is:
in order to realize the control signal represented by the formula (41), the following adaptive law pair is designed
Updating:
the validity of the control law u (t) of equation (41) updated by the adaptive law (42) is demonstrated next.
Defining estimation error
It can be easily found that the method can be used,
the following positive definite Lyapunov function was chosen:
wherein, γgIs an arbitrary given normal number.
By deriving equation (43) and substituting equation (33), equation (36) and equation (42), we can obtain:
formula (44) shows
According to the Barbalt theorem, the multi-agent system can still keep stable and realize formation under the condition that the system has actuator failure, and
and 5, designing an adaptive fault compensation method aiming at the Z-axis model of the quadrotor unmanned aerial vehicle with the actuator fault, and designing a control law under the condition that the fault estimation parameters are updated by the adaptive law by utilizing a backstepping method to realize consistency. The method comprises the following specific steps:
and 5.1) designing a controller of the Z-axis model of the quad-rotor unmanned aerial vehicle. The Z-axis of the simplified position subsystem of the drone can be represented by equation (23). Given a reference position signal xd(t) and a reference velocity signal vd(t) of (d). Definition of
Position tracking error and velocity tracking error, respectively. The following error kinetics equation can be obtained:
step 5.2) design of intermediate virtual control signal betaiSpecifically:
in view of the equation (45),
may be considered a virtual control signal. Firstly, a virtual control signal beta is designediTo ensure when
When the temperature of the water is higher than the set temperature,
the control input signal u is then designedi(t) to ensure
The dummy control signal beta is designed hereiComprises the following steps:
wherein k is1i> 0 is a given normal number.
First of all the virtual control signal beta is analyzediThe control performance of (2). Defining tracking error
The following positive definite Lyapunov function was chosen:
by deriving equation (48) from equations (45) and (47), it is possible to obtain:
it is easy to find if
Then
Next, the present invention will focus on the control signal ui(t) to realize
Thereby enabling the system to achieve the desired performance.
Step 5.3) definition
Definition of
Is λiEstimation of (2), estimation error
Is defined as
Designed control signal ui(t) and for updating
The adaptation law of (1) is as follows:
wherein k is2i＞0，γi> 0 is two given normal numbers.
Next, the control signal u under the adaptive update law (51) is demonstratedi(t) effectiveness. The following positive definite Lyapunov function was chosen:
by taking the derivative of equation (52), we can obtain:
by substituting formula (51) for formula (53), it can be estimated that:
therefore, the temperature of the molten metal is controlled,
thereby can obtain
The Z axis of the position subsystem after the unmanned aerial vehicle is simplified can realize second-order consistency.
The following description of the simulation verification of the method of the present invention:
aiming at the simulation of the self-adaptive compensation method for the faults of the actuators in the formation control of the unmanned aerial vehicle-unmanned vehicle heterogeneous multi-agent system, the method comprises the following steps:
step 1: selecting the composition of an unmanned aerial vehicle-unmanned aerial vehicle heterogeneous multi-agent system and a communication topological graph of the system, and setting the initial state of each agent.
Step 2: and selecting a desired unmanned aerial vehicle-unmanned vehicle time-varying formation and a simplified unmanned aerial vehicle Z-axis model desired height and desired speed.
And step 3: and selecting the fault degree of each agent and injecting the fault degree into the multi-agent system.
And 4, step 4: constructing a middle virtual control signal alpha of the simplified unmanned aerial vehicle-unmanned vehicle XOY two-dimensional model according to the formula (34), constructing a control law u (t) according to the formula (41), and further constructing a control law t according to the formula (42)Estimating new parameters, setting parameter information including k1,k2,γg。
And 5: intermediate virtual control signal beta of simplified unmanned aerial vehicle Z-axis model built according to formula (47)iA control law u is constructed according to the formula (50)i(t) and updating the parameter estimates according to equation (51) and setting parameter information including k1i,k2i,γi。
Step 6: and building a corresponding system in Matlab/Simulink, and setting related parameters and system initial values to obtain a final simulation result.
The invention relates to a self-adaptive compensation method for actuator faults in formation control of an unmanned aerial vehicle-unmanned vehicle heterogeneous multi-agent system, which comprises the following specific implementation processes:
1. consider a heterogeneous multi-agent system consisting of three drones and three drones, whose communication topology is a strongly connected graph, as shown in fig. 2. Wherein the multi-agents 1,2, 3 represent three unmanned aerial vehicles, and the agents 4, 5, 6 represent three unmanned vehicles. The initial state of each agent is set as follows:
x1(0)＝[10,14,11]T,v1(0)＝[1,2,2]T；x2(0)＝[8,4,5]T,v2(0)＝[1,3,-5]T；
x3(0)＝[4,5,-8]T,v3(0)＝[-2,-2,-2]T；x4(0)＝[15,9]T,v4(0)＝[-1,-8]T；
x5(0)＝[-15,-8]T,v5(0)＝[2,2]T；x6(0)＝[-8,-12]T,v6(0)＝[3,3]T。
2. selecting a desired UAV-UAV time-varying formation model as a rotary formation tracking model, which can be specifically expressed as:
selected simplified Z-axis model expectation of unmanned aerial vehicleHeight xd(t) 10 and desired speed vd(t)＝0。
3. The failure levels of the selected agents are as follows:
ρ1＝0.8,ρ2＝0.6,ρ3＝1,ρ4＝0.6,ρ5＝0.5,ρ6＝1 (56)
4. constructing a middle virtual control signal alpha of the simplified unmanned aerial vehicle-unmanned vehicle XOY two-dimensional model according to the formula (34), constructing a control law u (t) according to the formula (41), updating parameter estimation according to the formula (42), and setting parameter information k1＝10，k2＝50，γg＝0.1。
5. Intermediate virtual control signal beta of simplified unmanned aerial vehicle Z-axis model built according to formula (47)iA control law u is constructed according to the formula (50)i(t) and updating the parameter estimation according to equation (51), setting parameter information, k1i＝10，k2i＝50，γi＝0.1，i＝1,2,3。
6. The algorithm of the invention is simulated according to the parameters to obtain the position error signal of the X axis of the unmanned aerial vehicle-unmanned vehicle
Curve, unmanned aerial vehicle-unmanned vehicle X-axis speed error signal xie(t) curve, unmanned aerial vehicle-unmanned vehicle Y axis position error signal
Curve, unmanned aerial vehicle-unmanned vehicle Y-axis speed error signal xie(t) curve, unmanned aerial vehicle Z axle position state curve and unmanned aerial vehicle Z axle speed state curve. As shown in fig. 3, 4, 5, 6, 7 and 8, respectively.
The method can effectively compensate the problem of actuator faults in the formation control of the heterogeneous multi-agent system formed by unmanned vehicles of the unmanned aerial vehicle, and ensures the expected system stability and asymptotic tracking performance, which has important significance for the reliable control of the formation of the multi-agent system and the completion of tasks.
The embodiments of the present invention have been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.
Claims (6)
1. A self-adaptive compensation method for actuator faults in formation control of a heterogeneous multi-agent system consisting of an unmanned aerial vehicle and an unmanned vehicle is characterized by comprising the following steps:
the method comprises the following steps that step 1, a multi-agent system comprises M unmanned vehicles and (N-M) unmanned aerial vehicles, wherein a two-wheel mobile robot is adopted as an unmanned vehicle model, a four-rotor unmanned aerial vehicle is adopted as an unmanned aerial vehicle model, modeling and simplification are respectively carried out on the unmanned aerial vehicle model, and a second-order unmanned vehicle model and a second-order unmanned aerial vehicle model are obtained;
step 2, considering that the actuator of the multi-agent system has partial failure fault, respectively modeling an XOY plane model of the unmanned ground vehicle and the unmanned plane position subsystem after the fault and a Z-axis model of the unmanned plane position subsystem, and simultaneously realizing unmanned plane-unmanned vehicle formation control;
step 3, determining the communication topology of the multi-agent system as a strong communication graph;
step 4, aiming at an XOY plane model of the unmanned ground vehicle and the unmanned aerial vehicle position subsystem with the actuator fault, designing a control law under the condition that the fault estimation parameters are updated by a self-adaptive law by using a backstepping method to realize formation control;
and 5, designing a control law under the condition that the fault estimation parameters are updated by the self-adaptive law by utilizing a backstepping method aiming at the Z-axis model of the quad-rotor unmanned aerial vehicle with the fault of the actuator, so as to realize consistency.
2. The adaptive compensation method for actuator failure in formation control of heterogeneous multi-agent system consisting of unmanned aerial vehicle and unmanned vehicle according to claim 1, wherein in step 1, assuming that the direction of each unmanned vehicle is fixed and the same, χi(t) ═ χ; then the angular velocity omegai(t) ═ 0; the simplified kinetic equation of the ith two-wheeled mobile robot model is as follows:
wherein,
the coordinates of the front end point are represented,
Ldiis the distance between the hand point and the middle point of the two wheels, Fi(t),τi(t) input force and input moment, Mgi,JgiRespectively representing the mass and the moment of inertia of the ith unmanned vehicle;
because the model of the quad-rotor unmanned aerial vehicle is complex, the coupling problem exists, and if disturbance is considered, the model becomes more complex; here wind disturbances are ignored, while assuming that the attitude of each drone is fixed and the same, i.e., #i(t)＝φ,θi(t)＝θ,ψi(t) ═ ψ; the kinetic equation of the ith unmanned aerial vehicle model is:
wherein p isi(t)＝[pxi(t),pyi(t),pzi(t)]TThe status of the position is indicated,
Maiindicating the quality of the ith drone,
represents a control input;
meanwhile, the unmanned aerial vehicle and the unmanned ground vehicle XOY two-dimensional model are considered to be cooperatively formed and controlled, and the unmanned aerial vehicle Z-axis model is independently controlled.
3. The adaptive compensation method for actuator failure in formation control of heterogeneous multi-agent system consisting of unmanned aerial vehicle and unmanned vehicle according to claim 1, wherein in step 2, considering that in case of multiplicative actuator failure, the XOY plane model of simplified unmanned ground vehicle and unmanned aerial vehicle position subsystem can be represented by the following second order system:
wherein x isi(t)∈R2,vi(t)∈R2,ui(t)∈R2Respectively representing position information, velocity information and control input, 0<ρi≤1；
The simplified Z-axis model of the unmanned aerial vehicle position subsystem can be represented by the following second-order system when an actuator multiplicative fault occurs:
wherein x isi(t)∈R,vi(t)∈R,ui(t) E.R represents position information, speed information and control input, respectively; 0<ρi≤1；
Expected time-varying formation of
Wherein h isi(t)＝[hxi(t),hvi(t)]T(ii) a A multi-agent system may be considered to implement formation control if the following two equations can hold:
4. the adaptive compensation method for actuator failure in formation control of heterogeneous multi-agent system consisting of unmanned aerial vehicle and unmanned vehicle according to claim 1, wherein in step 3, the multi-agent communication topology is considered as a strong communication graph with the following properties:
1) the Laplace matrix L of the strong connection graph has one eigenvalue of 0, and the real parts of the other eigenvalues are positive;
2) a positive definite vector can be found
Satisfy the requirement of
Wherein
5. The method for adaptively compensating actuator faults in formation control of heterogeneous multi-agent system consisting of unmanned aerial vehicle and unmanned aerial vehicle according to claim 1, wherein in step 4, for simplifying analysis process, x is assumedi(t),vi(t),ui(t) is one-dimensional, and the two-dimensional model result can be obtained by popularizing the kronecker product;
suppose that
At the same time order zi(t)＝xi(t)-hxi(t)，mi(t)＝vi(t)-hvi(t), herein defined
If it is not
Can obtain
Namely, the multi-agent system realizes formation control;
definition of
ξ(t)＝[ξ1(t),ξ2(t),...,ξN(t)]TError variables can be obtained
And ξ (t) are:
wherein, P ═ diag { ρ ═ P1,ρ2,...,ρN}；
ξ (t) can be considered as a virtual control signal in the first expression; first, a dummy control signal α is designed to ensure when ξ (t) ═ α
Then designing a control signal u (t) to ensure the required system performance; design α is:
wherein k is1If the value is more than 0, the validity of the virtual control signal alpha can be verified;
in addition, the definition G ═ P-1At the same time define
Is an estimate of G; designing a reference nominal control signal, wherein the design control signal u (t) is:
in order to realize the control signal shown in the above formula, the following adaptive law pair is designed
Updating:
thus, the effectiveness of the control law u (t) under the adaptive law update can be proved.
6. The adaptive compensation method for actuator failure in formation control of heterogeneous multi-agent system consisting of unmanned aerial vehicle and unmanned aerial vehicle according to claim 1, wherein in step 5, reference position signal x is givend(t) and a reference velocity signal vd(t) definition of
The following error dynamics equations are obtained for the position tracking error and the velocity tracking error, respectively:
consider that
Can be regarded as a virtual control signal in the first formula; firstly, a virtual control signal beta is designediTo ensure when
When the temperature of the water is higher than the set temperature,
then the control input signal u is designedi(t) to ensure
Designing a virtual control signal betaiComprises the following steps:
wherein k is1i> 0 is a given normal number, the dummy control signal beta can be verifiediThe effectiveness of (a);
definition of
Definition of
Is λiEstimation of (2), estimation error
Is defined as
Designed control signal ui(t) and for updating
The adaptation law of (1) is as follows:
wherein k is2i＞0，γi> 0 is two given normal numbers; thus proving the control law u under the adaptive law updatei(t) effectiveness.
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