CN112947086B - 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 PDF

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CN112947086B
CN112947086B CN202110256086.4A CN202110256086A CN112947086B CN 112947086 B CN112947086 B CN 112947086B CN 202110256086 A CN202110256086 A CN 202110256086A CN 112947086 B CN112947086 B CN 112947086B
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马亚杰
王娟
姜斌
冒泽慧
陆宁云
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Nanjing University of Aeronautics and Astronautics
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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 the formation control of the unmanned aerial vehicles and the unmanned aerial vehicles. 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. For a Z-axis model of the quad-rotor unmanned aerial vehicle with actuator faults, a backstepping method is used for designing a control law under the condition that the self-adaptive law updates fault estimation parameters, and consistency is achieved. The invention can ensure that the multi-agent system can smoothly realize formation control under the condition of unknown fault.

Description

Self-adaptive compensation method for actuator faults in formation control of heterogeneous multi-agent system consisting of unmanned aerial vehicle and unmanned vehicle
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 refers to that in a certain communication network environment, a group of intelligent agents can reach an agreement according to specific requirements 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 likelihood of system failure increases. However, failure of either system can severely reduce the stability of the system. Therefore, the fault-tolerant cooperative control of the multi-agent system is very important.
Depending on the location where the fault occurs, the fault can be classified into a topology fault and a component fault. 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 text "Time-varying formation control of a organized multiple agent system" (R.Rahimi et al/Robotics and Autonomous Systems 62 (2014) 1799-1805), the authors investigated the problem of formation control of multi-agent Systems in a Time-varying formation 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 a system forms 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 formation control failure 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-intelligent-system consisting of an unmanned aerial vehicle and an unmanned vehicle, and can ensure that the multi-intelligent-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 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.
Further, in step 1, it is assumed that the direction of each unmanned vehicle is fixed and the same, namely χ i (t) = χ; then the angular velocity omega i (t) =0; the simplified dynamic equation of the ith two-wheeled mobile robot model is as follows:
Figure GDA0003712282490000021
wherein the content of the first and second substances,
Figure GDA0003712282490000022
the coordinates of the front end point are represented,
Figure GDA0003712282490000023
Figure GDA0003712282490000024
L di is the distance between the hand point and the middle point of the two wheels, F i (t),τ i (t) input force and input moment, M gi ,J gi Respectively 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, coupling problems exist, 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,θ i (t)＝θ,ψ i (t) = ψ; the kinetic equation of the ith unmanned aerial vehicle model is:
Figure GDA0003712282490000031
Figure GDA0003712282490000032
wherein p is i (t)＝[p xi (t),p yi (t),p zi (t)] T In the state of the position, the position of the mobile phone is changed,
Figure GDA0003712282490000033
Figure GDA0003712282490000034
M ai indicating the quality of the ith drone,
Figure GDA0003712282490000035
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:
Figure GDA0003712282490000036
wherein x is i (t)∈R 2 ,v i (t)∈R 2 ,u i (t)∈R 2 Respectively representing position information, velocity information and control input, 0<ρ i ≤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:
Figure GDA0003712282490000037
wherein x is i (t)∈R,v i (t)∈R,u i (t) E R represents position information, speed information and control input respectively; 0<ρ i ≤1；
Expected time-varying formation of
Figure GDA0003712282490000038
Wherein h is i (t)＝[h xi (t),h vi (t)] T (ii) a A multi-agent system may be considered to implement formation control if the following two equations can hold:
Figure GDA0003712282490000039
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 a characteristic value of 0, and the real parts of the other characteristic values are positive;
2) A positive definite vector can be found
Figure GDA0003712282490000041
Satisfy the requirement of
Figure GDA0003712282490000042
Wherein
Figure GDA0003712282490000043
Further, in step 4, to simplify the analysis process, assume x i (t),v i (t),u i (t) is one-dimensional, and the two-dimensional model result can be obtained by popularizing the kronecker product;
suppose that
Figure GDA0003712282490000044
At the same time order z i (t)＝x i (t)-h xi (t)，m i (t)＝v i (t)-h vi (t), herein defined
Figure GDA0003712282490000045
If it is not
Figure GDA0003712282490000046
Can obtain
Figure GDA0003712282490000047
Namely, the multi-agent system realizes formation control;
definition of
Figure GDA0003712282490000048
ξ(t)＝[ξ 1 (t),ξ 2 (t),...,ξ N (t)] T Error variables can be obtained
Figure GDA0003712282490000049
And ξ (t) are:
Figure GDA00037122824900000410
Figure GDA00037122824900000411
wherein P = diag { ρ } 1 ,ρ 2 ,...,ρ N }；
ξ (t) can be considered as a virtual control signal in the first expression; first, a dummy control signal α is designed to ensure that when ξ (t) = α
Figure GDA00037122824900000412
Then designing a control signal u (t) to ensure the required system performance; design α is:
Figure GDA00037122824900000413
wherein k is 1 If the value is more than 0, the validity of the virtual control signal alpha can be verified;
in addition, G = P is defined -1 At the same time define
Figure GDA00037122824900000414
Is an estimate of G; design of the reference nominal control signal, the design control signal u (t) is:
Figure GDA00037122824900000415
in order to realize the control signal shown in the above formula, the following adaptive law pair is designed
Figure GDA00037122824900000416
And (3) updating:
Figure GDA00037122824900000417
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 given d (t) and a reference velocity signal v d (t) definition of
Figure GDA0003712282490000051
The following error dynamics equations are obtained for the position tracking error and the velocity tracking error, respectively:
Figure GDA0003712282490000052
Figure GDA0003712282490000053
consider that
Figure GDA0003712282490000054
Can be regarded as a virtual control signal in the first formula; firstly, a virtual control signal beta is designed i To ensure when
Figure GDA0003712282490000055
When the utility model is used, the water is discharged,
Figure GDA0003712282490000056
then the control input signal u is designed i (t) to ensure
Figure GDA0003712282490000057
Designing a virtual control signal beta i Comprises the following steps:
Figure GDA0003712282490000058
wherein k is 1i Greater than 0 is oneTo determine the norm, the virtual control signal β can be verified i The effectiveness of (a);
definition of
Figure GDA0003712282490000059
Definition of
Figure GDA00037122824900000510
Is λ i Estimation of (2), estimation error
Figure GDA00037122824900000511
Is defined as
Figure GDA00037122824900000512
Designed control signal u i (t) and for updating
Figure GDA00037122824900000513
The adaptation law of (1) is as follows:
Figure GDA00037122824900000514
Figure GDA00037122824900000515
wherein k is 2i ＞0，γ i More than 0 is two given normal numbers; thus proving the control law u under the adaptive law update i (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 improve the flexibility of the whole system and the adaptability to an unknown environment, thereby completing tasks which are difficult to be completed by the unmanned aerial vehicle formation or the unmanned vehicle formation, such as large-scale region investigation, geographic survey, tracking pursuit and escape, 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 has a certain formation constraint inside, and if the behavior of a certain unmanned aerial vehicle in the formation has errors or is dead, the actions can be eliminated through the constraint of the whole formation.
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
Figure GDA0003712282490000061
A graph.
FIG. 4 is an embodiment of the present invention of an unmanned vehicle-unmanned aerial vehicle X-axis model speed error signal xi e (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
Figure GDA0003712282490000062
A graph.
FIG. 6 is a Y-axis model speed error signal ξ for an unmanned vehicle-UAV according to an embodiment of the invention e (t) graph.
Fig. 7 is a diagram of a model position state of the unmanned aerial vehicle Z axis according to an embodiment of the present invention.
Fig. 8 is a diagram of the velocity state of the model Z-axis of the drone according to one 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, consider a heterogeneous multi-agent system including M unmanned vehicles and (N-M) unmanned vehicles. The two-wheel mobile robot is adopted as the unmanned vehicle model, the four-rotor unmanned aerial vehicle is adopted as the unmanned vehicle model, modeling and simplification are respectively carried out on the two-wheel mobile robot model, and a second-order unmanned vehicle model are obtained. Determining a model of a heterogeneous multi-agent system, comprising the steps of:
step 1.1) considering the kinetic equation of the ith two-wheeled mobile robot model as follows:
Figure GDA0003712282490000071
wherein p is i (t)＝[p xi (t),p yi (t)] T Indicating the position state,. Chi i (t) represents a direction. V i (t),ω i (t) represents linear velocity and angular velocity, respectively. F i (t),τ i (t) is the input force and the input torque. M is a group of gi ,J gi Respectively representing the mass and the moment of inertia of the ith unmanned vehicle.
Considering that the front end point of the robot can be defined as a hand point, the formula is as follows:
Figure GDA0003712282490000072
wherein L is di Is the distance between the hand point and the middle point of the two wheels.
Figure GDA0003712282490000073
Representing the coordinates of the front end point.
Assuming that the direction of each unmanned vehicle is fixed and the same, i.e. χ i (t) = χ. Then the angular velocity omega i (t) =0. By applying the derivation of equation (18) and the substitution of equation (17), the following can be obtained:
Figure GDA0003712282490000074
wherein the content of the first and second substances,
Figure GDA0003712282490000075
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 the wind disturbances here, consider the kinetic equation for the ith model of the unmanned aerial vehicle as:
Figure GDA0003712282490000076
Figure GDA0003712282490000081
wherein p is i (t)＝[p xi (t),p yi (t),p zi (t)] T Indicates the position state, ζ i (t)＝[φ i (t),θ i (t),ψ i (t)] T Representing the roll, pitch and yaw of the ith drone. I is x ,I y ,I z Is the moment of inertia. M ai ,J ai ,l ai Respectively representing the mass, the inertia matrix and the length of the ith drone.
Figure GDA0003712282490000082
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., phi i (t)＝φ,θ i (t)＝θ,ψ i (t) = ψ. Then equation (20) can be converted to:
Figure GDA0003712282490000083
Figure GDA0003712282490000084
wherein the content of the first and second substances,
Figure GDA0003712282490000085
Figure GDA0003712282490000086
Figure GDA0003712282490000087
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:
Figure GDA0003712282490000088
wherein x is i (t)∈R 2 ,v i (t)∈R 2 ,u i (t)∈R 2 Respectively, position information, velocity information, and control inputs. Note 0<ρ i ≤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:
Figure GDA0003712282490000091
wherein x is i (t)∈R,v i (t)∈R,u i (t) ∈ R indicates position information, speed information, and control input, respectively. Note 0<ρ i ≤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
Figure GDA0003712282490000092
Wherein h is i (t)＝[h xi (t),h vi (t)] T . A multi-agent system can be considered to achieve formation control if the following two equations can be established.
Figure GDA0003712282490000093
Step 3, determining the communication topology of the multi-agent system as a strong communication graph;
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,
Figure GDA0003712282490000094
for a set of edges between nodes, A = [ a = ij ] N×N Is a contiguous matrix whose elements are all non-negative. If (j, i) ∈ E, it indicates that node i can receive the state information of node j, at this time, the element a in the adjacency matrix ij Is greater than 0; otherwise
Figure GDA0003712282490000099
At this time, the node i cannot receive the state information of the node j, a ij And =0. General in multi-agent system researchThe signal topology is also typically 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 } 1 ,b 2 ,...,b N }，
Figure GDA0003712282490000095
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 introduced 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
Figure GDA0003712282490000096
Satisfy the requirements of
Figure GDA0003712282490000097
Wherein
Figure GDA0003712282490000098
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 x i (t),v i (t),u i (t) is one-dimensional, and two-dimensional model results can thus be generalized by the kronecker product.
Suppose that:
Figure GDA0003712282490000101
let z i (t)＝x i (t)-h xi (t)，m i (t)＝v i (t)-h vi (t) of (d). Can push awayThe following intermediate error equation is derived:
Figure GDA0003712282490000102
are defined herein
Figure GDA0003712282490000103
It is easy to find if
Figure GDA0003712282490000104
Can obtain
Figure GDA0003712282490000105
According to equation (29), the multi-agent system achieves formation control.
Definition of
Figure GDA0003712282490000106
ξ(t)＝[ξ 1 (t),ξ 2 (t),...,ξ N (t)] T . Can obtain error variable
Figure GDA0003712282490000107
And ξ (t) as:
Figure GDA0003712282490000108
Figure GDA0003712282490000109
wherein P = diag { ρ } 1 ,ρ 2 ,...,ρ N }。
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
Figure GDA00037122824900001010
The control signal u (t) is then designed to ensure the desired system performance. Here, α is designed to be:
Figure GDA00037122824900001011
wherein k is 1 > 0 is a normal number.
First, the control performance of the virtual control signal α is analyzed. Defining a tracking error xi e (t) = ξ (t) - α. Selecting a positive definite Lyapunov function V 1 (t) the following:
Figure GDA0003712282490000111
from equations (32) and (35), it is possible to obtain:
Figure GDA0003712282490000112
xi is not difficult to find e (t) =0, then
Figure GDA0003712282490000113
The control signal u (t) will be designed next to guarantee lim t→∞ (ξ (t) - α) =0, thereby causing the system to achieve desired system performance.
Step 4.3) here the uncertainty P of the system is assumed first -1 It 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:
Figure GDA0003712282490000114
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
Figure GDA0003712282490000115
the validity of the nominal control signal (37) is demonstrated below. The following positive definite Lyapunov function was chosen:
Figure GDA0003712282490000116
by substituting equation (33) and equation (36) into equation (38), the following can be obtained:
Figure GDA0003712282490000117
let u (t) = u * (t), it is not difficult to obtain:
Figure GDA0003712282490000118
formula (40) shows
Figure GDA0003712282490000119
ξ e (t)∈L 2 ∩L ∞ . 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
Figure GDA00037122824900001110
step 4.4) define G = P -1 Simultaneously define
Figure GDA00037122824900001111
Is an estimate of G. Referring to the design of the nominal control signal in equation (37), the control signal u (t) is designed according to the present invention as follows:
Figure GDA0003712282490000121
in order to realize the control signal represented by the formula (41), the following adaptive law is designedTo pair
Figure GDA0003712282490000122
Updating:
Figure GDA0003712282490000123
the validity of the control law u (t) of equation (41) updated by the adaptive law (42) is demonstrated next.
Defining an estimation error
Figure GDA0003712282490000124
It can be easily found that the method can be used,
Figure GDA0003712282490000125
the following positive definite Lyapunov function was chosen:
Figure GDA0003712282490000126
wherein, γ g Is an arbitrary given normal number.
By applying the derivative of equation (43) and substituting equation (33), equation (36) and equation (42), the following can be obtained:
Figure GDA0003712282490000127
formula (44) shows
Figure GDA0003712282490000128
ξ e (t)∈L 2 ∩L ∞ . 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
Figure GDA0003712282490000129
Figure GDA00037122824900001210
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 x d (t) and a reference velocity signal v d (t) of (d). Definition of
Figure GDA00037122824900001211
Figure GDA00037122824900001212
Position tracking error and velocity tracking error, respectively. The following error kinetics equation can be obtained:
Figure GDA00037122824900001213
Figure GDA00037122824900001214
step 5.2) design of intermediate virtual control signal beta i Specifically:
in view of the formula (45),
Figure GDA00037122824900001215
may be considered a virtual control signal. Firstly, a virtual control signal beta is designed i To ensure when
Figure GDA00037122824900001216
When the utility model is used, the water is discharged,
Figure GDA00037122824900001217
the control input signal u is then designed i (t) to ensure
Figure GDA00037122824900001218
The dummy control signal beta is designed here i Comprises the following steps:
Figure GDA0003712282490000131
wherein k is 1i > 0 is a given normal number.
First of all the virtual control signal beta is analyzed i The control performance of (2). Defining tracking error
Figure GDA0003712282490000132
The following positive definite Lyapunov function was chosen:
Figure GDA0003712282490000133
by deriving equation (48) from equations (45) and (47), it is possible to obtain:
Figure GDA0003712282490000134
it is easy to find that
Figure GDA0003712282490000135
Then
Figure GDA0003712282490000136
Next, the present invention will focus on the study of the control signal u i (t) to realize
Figure GDA0003712282490000137
Thereby enabling the system to achieve the desired performance.
Step 5.3) definition
Figure GDA0003712282490000138
Definition of
Figure GDA0003712282490000139
Is λ i Estimation of (2), estimation error
Figure GDA00037122824900001310
Is defined as
Figure GDA00037122824900001311
Designed control signal u i (t) and for updating
Figure GDA00037122824900001312
The adaptation law of (1) is as follows:
Figure GDA00037122824900001313
Figure GDA00037122824900001314
wherein k is 2i ＞0，γ i > 0 is two given normal numbers.
Next, the control signal u under the adaptive update law (51) is demonstrated i (t) effectiveness. The following positive definite Lyapunov function was chosen:
Figure GDA00037122824900001315
by taking the derivative of equation (52), we can obtain:
Figure GDA0003712282490000141
by substituting equation (51) into equation (53), it can be estimated that:
Figure GDA0003712282490000142
therefore, the number of the first and second electrodes is increased,
Figure GDA0003712282490000143
thereby can obtain
Figure GDA0003712282490000144
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-intelligent-agent system, which is designed by the invention, 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 intelligent agent and injecting the fault degree into the multi-intelligent-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 a formula (34), constructing a control law u (t) according to a formula (41), updating parameter estimation according to a formula (42), and setting parameter information comprising k 1 ,k 2 ,γ g 。
And 5: intermediate virtual control signal beta of simplified unmanned aerial vehicle Z-axis model built according to formula (47) i A 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 k 1i ,k 2i ,γ i 。
And 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-intelligent-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 and 3 represent three unmanned planes, and the agents 4,5 and 6 represent three unmanned vehicles. The initial state of each agent is set as follows:
x 1 (0)＝[10,14,11] T ,v 1 (0)＝[1,2,2] T ；x 2 (0)＝[8,4,5] T ,v 2 (0)＝[1,3,-5] T ；
x 3 (0)＝[4,5,-8] T ,v 3 (0)＝[-2,-2,-2] T ；x 4 (0)＝[15,9] T ,v 4 (0)＝[-1,-8] T ；
x 5 (0)＝[-15,-8] T ,v 5 (0)＝[2,2] T ；x 6 (0)＝[-8,-12] T ,v 6 (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:
Figure GDA0003712282490000151
selected simplified unmanned aerial vehicle Z-axis model expected height x d (t) =10 and desired speed v d (t)＝0。
3. The failure levels of the selected agents are as follows:
ρ 1 ＝0.8,ρ 2 ＝0.6,ρ 3 ＝1,ρ 4 ＝0.6,ρ 5 ＝0.5,ρ 6 ＝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 k 1 ＝10，k 2 ＝50，γ g ＝0.1。
5. Intermediate virtual control signal beta of simplified unmanned aerial vehicle Z-axis model built according to formula (47) i A control law u is constructed according to the formula (50) i (t) and updating the parameters according to equation (51)Estimating, setting parameter information, k 1i ＝10，k 2i ＝50，γ i ＝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
Figure GDA0003712282490000152
Curve, unmanned aerial vehicle-unmanned vehicle X-axis speed error signal xi e (t) curve, unmanned aerial vehicle-unmanned vehicle Y axis position error signal
Figure GDA0003712282490000153
Curve and Y-axis speed error signal xi of unmanned aerial vehicle-unmanned vehicle e (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 (5)

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, the unmanned aerial vehicle model is respectively modeled and simplified, 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;
step 5, aiming at a Z-axis model of the quad-rotor unmanned aerial vehicle 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, and realizing consistency;
in the step 1, the direction of each unmanned vehicle is assumed to be fixed and the same, namely chi i (t) = χ; then the angular velocity omega i (t) =0; the simplified dynamic equation of the ith two-wheeled mobile robot model is as follows:
Figure FDA0003712282480000011
wherein the content of the first and second substances,
Figure FDA0003712282480000012
the coordinates of the front end point are represented,
Figure FDA0003712282480000013
Figure FDA0003712282480000014
L di is the distance between the hand point and the middle point of the two wheels, F i (t),τ i (t) input force and input moment, M gi ,J gi Respectively 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, such as disturbance is considered,the model will become 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,θ i (t)＝θ,ψ i (t) = ψ; the kinetic equation of the ith unmanned aerial vehicle model is:
Figure FDA0003712282480000015
Figure FDA0003712282480000016
wherein p is i (t)＝[p xi (t),p yi (t),p zi (t)] T The status of the position is indicated,
Figure FDA0003712282480000021
Figure FDA0003712282480000022
M ai indicating the quality of the ith drone,
Figure FDA0003712282480000023
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.
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 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:
Figure FDA0003712282480000024
wherein x is i (t)∈R 2 ,v i (t)∈R 2 ,u i (t)∈R 2 Respectively representing position information, speed information and control input, 0 < rho i ≤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:
Figure FDA0003712282480000025
wherein x is i (t)∈R,v i (t)∈R,u i (t) E R represents position information, speed information and control input respectively; rho is more than 0 i ≤1；
Desired time-varying formation of
Figure FDA0003712282480000026
Wherein h is i (t)＝[h xi (t),h vi (t)] T (ii) a A multi-agent system can be considered to achieve formation control if the following two equations can hold:
Figure FDA0003712282480000027
3. the adaptive compensation method for actuator faults in formation control of heterogeneous multi-agent system composed of unmanned aerial vehicles and unmanned vehicles according to claim 1, characterized in that in step 3, the multi-agent communication topology is considered as a strong communication diagram 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
Figure FDA0003712282480000028
Satisfy the requirement of
Figure FDA0003712282480000029
Wherein
Figure FDA00037122824800000210
4. 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 assumed i (t),v i (t),u i (t) is one-dimensional, and the two-dimensional model result can be obtained by popularizing the kronecker product;
suppose that
Figure FDA0003712282480000031
While making z i (t)＝x i (t)-h xi (t)，m i (t)＝v i (t)-h vi (t), herein defined
Figure FDA0003712282480000032
If it is used
Figure FDA0003712282480000033
Can obtain
Figure FDA0003712282480000034
Namely, the multi-agent system realizes formation control;
definition of
Figure FDA0003712282480000035
ξ(t)＝[ξ 1 (t),ξ 2 (t),...,ξ N (t)] T Error variables can be obtained
Figure FDA0003712282480000036
And ξ (t) as:
Figure FDA0003712282480000037
Figure FDA0003712282480000038
wherein P = diag { ρ } 1 ,ρ 2 ,...,ρ N }；
ξ (t) can be considered as a virtual control signal in the first expression; first, a virtual control signal α is designed to ensure when ξ (t) = α
Figure FDA0003712282480000039
Then designing a control signal u (t) to ensure the required system performance; design α is:
Figure FDA00037122824800000310
wherein k is 1 If the value is more than 0, the validity of the virtual control signal alpha can be verified;
in addition, G = P is defined -1 At the same time define
Figure FDA00037122824800000311
Is an estimate of G; the design of the reference nominal control signal, the design control signal u (t) is:
Figure FDA00037122824800000312
in order to realize the control signal shown in the above formula, the following adaptive law pair is designed
Figure FDA00037122824800000313
Updating:
Figure FDA00037122824800000314
thus, the effectiveness of the control law u (t) under the adaptive law updating can be proved.
5. The adaptive compensation method for actuator faults in formation control of heterogeneous multi-agent system consisting of unmanned aerial vehicles and unmanned vehicles according to claim 1, wherein in step 5, reference position signal x is given d (t) and a reference velocity signal v d (t) definition of
Figure FDA0003712282480000041
The following error dynamics equations are obtained for the position tracking error and the velocity tracking error, respectively:
Figure FDA0003712282480000042
Figure FDA0003712282480000043
consider that
Figure FDA0003712282480000044
Can be regarded as a virtual control signal in the first formula; firstly, a virtual control signal beta is designed i To ensure when
Figure FDA0003712282480000045
When the utility model is used, the water is discharged,
Figure FDA0003712282480000046
then the control input signal u is designed i (t) to ensure
Figure FDA0003712282480000047
Designing a virtual control signal beta i Comprises the following steps:
Figure FDA0003712282480000048
wherein k is 1i > 0 is a given normal number, the dummy control signal beta can be verified i The effectiveness of (a);
definition of
Figure FDA0003712282480000049
Definition of
Figure FDA00037122824800000410
Is λ i Estimation of (2), estimation error
Figure FDA00037122824800000411
Is defined as
Figure FDA00037122824800000412
Designed control signal u i (t) and for updating
Figure FDA00037122824800000413
The adaptation law of (1) is as follows:
Figure FDA00037122824800000414
Figure FDA00037122824800000415
wherein k is 2i ＞0，γ i > 0 is two given normal numbers; thereby proving that the control law u is updated under the self-adaptive law i (t) effectiveness.
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