Unmanned aerial vehicle predetermined time fault-tolerant cooperative formation control method under full-state constraint

Abstract

The invention discloses an unmanned aerial vehicle predetermined time fault-tolerant cooperative formation control method under full-state constraint, and the method comprises the steps: building an unmanned aerial vehicle nonlinear dynamic model with external unknown disturbance, considering the fault condition of an actuator, and carrying out the general expression of the fault condition; according to the method, a time-varying nonlinear conversion function is utilized to convert an unmanned aerial vehicle cluster system constrained by a full state into an unconstrained system, and then, based on the converted unconstrained system, according to a topological structure between a leader and a follower of an unmanned aerial vehicle, the unmanned aerial vehicle cluster system is optimized. Dividing the unmanned aerial vehicle cluster system into an attitude subsystem and a position subsystem based on an adaptive backstepping control algorithm, and defining a tracking error; a corresponding subsystem is stabilized by designing a virtual control law, so that a tracking error is converged, and a cooperative formation controller is designed, so that tracking of a leader trajectory within preset time is realized. On the premise that all states do not violate specified constraints, an unmanned aerial vehicle follower can well track the trajectory of a leader, and the feasibility condition limitation on the first virtual control law is eliminated.

Description

Technical Field

[0001] The invention relates to a UAV formation control technology, in particular to a UAV predetermined time fault-tolerant collaborative formation control method under full-state constraints. Background Art

[0002] A quadcopter drone is a multi-rotor aircraft that can take off and land vertically and generate lift through four rotors. Due to its advantages such as being able to hover in the air, stable flight, flexible operation, and low cost, it has attracted more and more attention and use in recent years. With the development of the initial drone technology, multi-rotor drones have become smaller and more flexible, with lower costs and wider popularity. Today, quadcopter drones have been widely used in different fields such as military reconnaissance, aerial photography, environmental testing, building inspection, emergency rescue, etc., and have become an indispensable service in people's daily lives. With the increasing maturity and rapid development of drone technology, a single drone sometimes cannot handle tasks in some more complex scenarios, and its efficiency and success rate are relatively low. For example, when a single drone performs an exploration mission, it is often difficult to perform multi-directional detection of the target due to the limited sensor angle. Therefore, the coordinated control of multiple drones has gradually attracted people's attention. Multi-drone collaboration can effectively deal with conflicts at the spatial and mission levels. Formation flight can not only improve the combat vision, but also improve the efficiency and success rate of tasks. It has broad prospects in agriculture, commerce, military and other fields. However, the flight environment of drones is not static. When drones fly along a fixed path in an uncertain environment, they may make wrong decisions, resulting in loss of control. Therefore, the operator can use human-in-the-loop control technology to send command signals to the leader to modify the required reference trajectory, which can help the drone formation perform its mission better.

[0003] Multi-UAV formations need to determine the communication relationship between adjacent UAVs based on the control of a single UAV and design a control algorithm to form a specific formation. When the formation is operating outdoors, due to the limitations of the workspace and physical conditions, state constraints are everywhere. One of the UAVs may also face failures or encounter wind disturbances. These unfavorable factors will affect the stability of the formation flight. The state constraints of the UAV system lead to feasibility condition restrictions on the virtual control law in collaborative formation control. How to achieve a good formation effect in the event of actuator failure, external disturbances, and system state restrictions is of great practical significance.

[0004] In addition, when performing tasks, quadcopters need to transmit and calculate external information in real time. The currently designed quadcopter formation controller is based on a time-triggered control strategy. The disadvantage of this method is that the system control signal is continuously updated, which will undoubtedly lead to a waste of system communication resources. If the operation is frequently sent or the control signal is used beyond the actuator's capability range, the actuator will overheat or even be damaged, causing the drone to collide. Therefore, how to reduce the update frequency of the control signal, reduce data transmission problems, and accurately track the leader's trajectory in the event of an actuator failure is very important both in theory and in practice. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for controlling a predetermined time fault-tolerant cooperative formation of unmanned aerial vehicles under full-state constraints, thereby eliminating the feasibility condition restrictions on the virtual control law.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a method for controlling a UAV with a predetermined time fault-tolerant collaborative formation under full-state constraints, firstly, a nonlinear dynamic model of a UAV with external unknown disturbance is established, and the model is summarized as a general expression considering the actuator failure; according to the topological structure between the UAV leader and the follower, the UAV cluster system is divided into an attitude subsystem and a position subsystem based on an adaptive backstepping control algorithm, and a tracking error is defined; the corresponding subsystems are stabilized by designing a virtual control law to converge the tracking error, and a collaborative formation controller is designed to achieve tracking of the leader's trajectory within a predetermined time; before defining the tracking error, the UAV cluster system subject to full-state constraints is first converted into an unconstrained system according to the general expression of the dynamic model using a time-varying nonlinear conversion function, and then the tracking error is defined according to the topological structure between the UAV leader and the follower based on the converted unconstrained system.

[0007] Furthermore, we define a compact set Used to constrain the state of the drone group, where ε i,j,h represents the constrained state, h=1,2, t≥0 represents the time, δ i,j,h (t) and It is a time-varying function greater than 0, and the initial conditions must satisfy The constrained state ε of the drone i,j,h Transformed to the unconstrained equivalent state Γ i,j,h ,

[0008]

[0009] Furthermore, the constrained i-th UAV system is converted into an unconstrained system:

[0010]

[0011] in, is the equivalent state Γ i,j,h The derivative of time t is:

[0012] F i,j,1 =μ i,j,1 +v i,j,1 ε i,j,2 -Γ i,j,2 ,

[0013] F i,j,2 =μ i,j,2 +v i,j,2 f i,j ,

[0014] represents the fault model, d i,j represents an external unknown bounded disturbance, g i,j They are a i is the length from the mass point of the i-th UAV to the center of the rotor, J i,x , J i,y and J i,z Respectively represent the rotational inertia of the three coordinate axes of the i-th UAV, M i is the total mass of the i-th UAV.

[0015] Furthermore, the tracking error is defined as:

[0016]

[0017] Among them, z i,j,1 and z i,j,2 is the tracking error, α i,j,1 is the first virtual control law, a i,r Indicates the distance between related drones or their communication capabilities; and Indicates the drone status; b i =1 or 0, indicating whether the i-th follower can obtain the leader information;

[0018] R l,j Represents the UAV leader trajectory.

[0019] Furthermore, based on the tracking error, the first step Lyapunov function V is constructed i,1 , design the first virtual control law α to make it stable at the predetermined time i,j,1 , through the first step Lyapunov function V i,1 The time derivative confirms the designed first virtual control law α i,j,1Whether to make the attitude subsystem and position subsystem of the i-th UAV system stable within the first step of the predetermined time.

[0020] Furthermore, based on the stability of the first step predetermined time, the second step Lyapunov function V is constructed i,2 , further design the second virtual control law α i,j,2 and the scheduled time coordination formation controller, and design the first, second, and third adaptive laws and Achieve stability in the second step scheduled time.

[0021] Furthermore, a predetermined time collaborative formation controller is designed in combination with a self-triggering mechanism, so that the control signal is updated and transmitted to the actuator only when the designed triggering condition is met.

[0022] Furthermore, based on the first-order derivative of the first virtual control law Design the second virtual control law α i,j,2 , and use a finite-time differentiator to approximate

[0023] Furthermore, on the basis of the second step scheduled time stability, the third step Lyapunov function V is constructed to determine the controller gain to be designed, so as to ensure the scheduled time stability of the overall closed-loop system and realize that the trajectory of the UAV follower can accurately track the leader trajectory within the scheduled time.

[0024] The beneficial effects of the present invention are:

[0025] 1. Different from the existing control algorithm based on obstacle Lyapunov function, the present invention converts the constrained system into an unconstrained system by introducing a time-varying nonlinear conversion function. Under the premise that all states do not violate the prescribed constraints, the UAV follower can track the leader's trajectory well, eliminating the feasibility condition restrictions on the first virtual control law, and can uniformly handle constrained and unconstrained systems.

[0026] 2. On this basis, different from the finite time stability theory and the fixed time stability theory, the present invention designs a predetermined time self-triggered fault-tolerant formation controller so that the UAV formation tracking error can converge within the predetermined time. The formula for the convergence time is explicit, and the upper bound can be directly set in a parameter of the controller.

[0027] 3. Combined with the self-triggering control mechanism, a scheduled time self-triggering fault-tolerant formation controller is designed, which effectively avoids the continuous updating of the system control signal without relying heavily on the continuous monitoring trigger protocol, avoids the Zeno effect, and reduces the update frequency of the control signal and the wear of the actuator.

[0028] 4. In the process of back-stepping design, the finite-time differentiator is used to approximate the first-order derivative of the first virtual control law, avoiding the problem of "complexity explosion" and thus obtaining better tracking effect.

[0029] 5. For external interference and deviation faults, adaptive compensation technology is used so that it does not require prior knowledge and can be unknown. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a schematic diagram of the design process of the preset time self-triggering fault-tolerant collaborative formation controller of the drone cluster of the present invention.

[0031] Figure 2 It is a schematic diagram of the predetermined time self-triggering fault-tolerant collaborative formation control process of the UAV cluster of the present invention.

[0032] Figure 3 This is a schematic diagram of the communication topology structure of the UAV cluster formation.

[0033] Figure 4 It is the actual formation trajectory diagram of the four-rotor drone cluster in three-dimensional space.

[0034] Figure 5 It is the trajectory diagram of the attitude and position state response of the quadrotor drone cluster.

[0035] Figure 6 It is the linear velocity and angular velocity state response trajectory diagram of the quadrotor drone cluster.

[0036] Figure 7 It is the formation tracking error curve of the attitude subsystem and position subsystem of the quadrotor drone cluster.

[0037] Figure 8 It is the control input curve diagram of the quadrotor drone cluster follower 1 and the trigger interval diagram of the control input.

[0038] Fig. 9 It is the control input curve diagram of the quadrotor drone cluster follower 2 and the trigger interval diagram of the control input.

[0039] Fig.10 It is a control input curve diagram of the quadrotor drone cluster follower 3 and a trigger interval diagram of the control input.

[0040] Fig.11 It is a control input curve diagram of the quadrotor drone cluster follower 4 and a trigger interval diagram of the control input. DETAILED DESCRIPTION

[0041] The technical solution of the present invention is described clearly and completely below in conjunction with the accompanying drawings and specific implementation methods. The specific contents listed in the following embodiments are not limited to the technical features necessary for the technical problems to be solved by the technical solutions recorded in the claims. At the same time, the enumerated embodiments are only part of the present invention, not all embodiments.

[0042] The method for controlling a predetermined time fault-tolerant coordinated formation of unmanned aerial vehicles under full-state constraints of the present invention comprises the following steps:

[0043] Step 1: First, establish a nonlinear dynamic model of a UAV with external unknown disturbances. The specific method is as follows: consider a four-rotor UAV formation system consisting of a leader and N followers, where the dynamic model of the i-th four-rotor UAV with external unknown disturbances is described as follows:

[0044]

[0045] Where: x i ,y i , z i represents the three spatial positions of the i-th quadrotor drone; φ i ,θ i and ψ i Represents the three flight attitude angles of the i-th quadrotor drone, namely the roll angle, pitch angle and yaw angle. represents the second-order time derivative of *, represents the first time derivative of *, such as a i is the length from the mass point to the center of the rotor of the i-th quadrotor drone; M i is the total mass of the i-th quadrotor drone; g is the gravitational acceleration; J i,x , J i,y and J i,z Respectively represent the rotational inertia of the three coordinate axes of the i-th UAV; C i,j represents the damping coefficient, d i,j represents an external unknown bounded disturbance, where j = φ, θ, ψ, z, x, y; τ i,F represents the total lift of the i-th UAV; τ i,φ , τ i,θ and τ i,ψ They represent the input signals for controlling the roll, pitch and yaw moments of the i-th UAV respectively; i = 1, 2, …, N, where N is an even number, representing the number of followers in the quadrotor UAV cluster.

[0046] In order to simplify the subsequent reasoning, the dynamic model is summarized into a general expression considering the actuator failure case.

[0047] The fault model of the i-th six-degree-of-freedom quadrotor drone is expressed as:

[0048]

[0049] Among them, ρ i,j ∈(0,1] represents the execution efficiency coefficient of the actuator, τ i,j represents the actuator input, Π i,j It is an unknown time-varying deviation fault.

[0050] The dynamic model of the i-th quadrotor UAV system with actuator failure in formula (1) can be summarized as a general expression:

[0051]

[0052] In the formula, (X i,1,1 ,X i,2,1 ,X i,3,1 ,X i,4,1 ,X i,5,1 ,X i,6,1 )=(φ i ,θ i ,ψ i ,z i ,x i ,y i );

[0053]

[0054] (d i,1 ,d i,2 ,d i,3 ,d i,4 ,d i,5 ,d i,6 )=(d i,φ ,d i,θ ,d i,ψ ,d i,z ,d i,x ,d i,y );

[0055]

[0056] In addition, all states of the i-th quadrotor are required to be restricted to a tight set In which h=1,2, t≥0 represents time, and is a positive time-varying function.

[0057] The total lift τ of the i-th quadrotor drone i,F and leader track R l,1 , R l,2 pass and the leader yaw angle trajectory R l,3 get:

[0058]

[0059] Step 2: Considering the safety distance, based on the human-in-the-loop control technology, determine the leader task, and use the time-varying nonlinear transfer function to convert the drone cluster system subject to full-state constraints into an unconstrained system.

[0060] Based on the above general expression (3), the main control goal of the cooperative formation control is to make the follower output trajectory X i,j,1 Follow the leader's trajectory R as much as possible l,j , which will generate a formation tracking error E i,j,1 =X i,j,1 -R l,j -Δ i,j (i=1,2,…,N,j=1,2,…,6), Δ i,j represents the expected inter-neighbor formation distance.

[0061] The leader considered in the present invention is a non-autonomous system, and its dynamic model satisfies the following relationship:

[0062]

[0063] Where: and Indicates the state, R l,j and u l,j are the output and bounded control input respectively, where the input u l,j Can be designed by the operator. is a known coefficient, R l,j Needs to be satisfied

[0064] The state transformation of the quadrotor drone cluster is:

[0065]

[0066] Define a compact set Where h=1,2, t≥0 represents time, δ i,j,h (t) and It is a time-varying function greater than 0, which is used to constrain the state of the quadcopter swarm after the transformation. The initial condition must satisfy

[0067] In order to eliminate the feasibility condition restriction of the first virtual control law, a time-varying nonlinear transfer function is introduced to convert the constrained state ε i,j,h (h=1,2) is converted to the unconstrained equivalent state Γ i,j,h :

[0068]

[0069] For any ε i,j,h (0)∈Υ i,j,h , if Γ i,j,h ∈L ∞ (·∈L ∞ means · is bounded), then ε i,j,h ∈Υ i,j,h It can be guaranteed. i,j,h Taking the derivative with respect to time t, we get:

[0070]

[0071] Where:

[0072]

[0073] According to formulas (6), (7) and (8), the originally constrained i-th quadrotor drone system (3) can be converted into a new unconstrained system:

[0074]

[0075] Where: F i,j,1 =μ i,j,1 +v i,j,1 ε i,j,2 -Γ i,j,2 , F i,j,2 =μ i,j,2 +v i,j,2 f i,j .

[0076] Step 3: Construct a tracking error based on the unconstrained system (9) obtained in step 2 and the topological structure between the quadrotor leader and the quadrotor follower.

[0077] The directed graph in graph theory is used to describe a multi-UAV system consisting of a leader and N followers. Expressed as in and are the vertex set and edge set of a directed graph respectively. Indicates that the i-th node can obtain the information of the r-th node, record is the neighborhood of the ith node, and each drone is abstracted as a node. It can represent the communication relationship between quadrotor drones. In addition, these communication relationships can be described by adjacency matrix, directed graph Adjacency Matrix The element is defined as follows: If Then a i,r =1, otherwise a i,r =0. i,r The physical meaning of can represent the distance between related UAVs or their communication capabilities. The degree matrix is ​​defined as Define the Laplacian matrix In a directed graph There is no self-loop in the directed graph. There is at least one node in the graph that has a directed path to any other node in the graph, then the directed graph It contains a directed spanning tree. The leader in the directed graph is marked as node 0, defining the diagonal matrix When the i-th follower can obtain the leader information, b i =1, otherwise b i =0.

[0078] Based on the adaptive backstepping control algorithm, the quadrotor UAV cluster system is divided into attitude subsystem and position subsystem, and the tracking error variable z is introduced. i,j,1 and z i,j,2 , construct the tracking error as follows:

[0079]

[0080] Where: z i,j, and z i,j,2 is the tracking error, and Represents the drone state Γ i,j, and Γ r,j,1 , α i,j,1 is the first virtual control law, a i,r and b i Obtained from the topological structure between leaders and followers.

[0081] Step 4: Based on the tracking error constructed in step 3, the attitude subsystem and position subsystem of the i-th (i∈[1,2,…,N]) quadrotor drone are constructed as follows: i,1 :

[0082]

[0083] Furthermore, the first step Lyapunov function V i,1 Taking the derivative with respect to time t, we can obtain:

[0084]

[0085] Where: is the constrained leader trajectory R l,j Convert to Unconstrained Track The derivative of .

[0086] For the function h in the above formula i,j,1 , using interval type-2 fuzzy technology to approximate, which can be specifically expressed as:

[0087]

[0088] Where: represents the ideal weight vector, q represents the number of rules, Indicates that the input is a quadrotor drone state The basis function, ω i,j,1 represents the approximation error, Representative i,j,1 The transpose of .

[0089] The following inequality can be obtained through formula (13):

[0090]

[0091] Where:

[0092] By using the relevant inequalities and constructing the following first virtual control law α i,j,1 Ensure that the first step achieves stability in scheduled time:

[0093]

[0094] Where: β and T c is the positive controller parameter to be designed, 0<β≤0.5, is Θ i,j,1 The estimated value of is, and the estimated error is sat(z i,j,1 ) is designed as follows:

[0095]

[0096] Among them, exp(*) is the exponential function, sign(*) is the sign function, l i,j,1 and is the positive parameter to be designed.

[0097] The designed first virtual control law α i,j,1 and the interval type-2 fuzzy approximation term h i,j,1 Substituting into formula (12), we can get:

[0098]

[0099] Based on Lyapunov's predetermined time stability theory, the first virtual control law α is designed. i,j,1 , achieving the first step of the scheduled time stabilization of the i-th quadrotor UAV system.

[0100] Step 5. On the basis that the first step is stable within the predetermined time (if the first step is unstable, the second step will not be stable either), the attitude subsystem and position subsystem of the i-th (i∈[1,2,…,N]) quadrotor drone are constructed as follows: i,2 :

[0101]

[0102] Furthermore, the second step Lyapunov function V i,2 Taking the derivative with respect to time t, we can obtain:

[0103]

[0104] For the function F in the above formula i,j,2 , using interval type-2 fuzzy technology to approximate, which can be specifically expressed as:

[0105]

[0106] Where: represents the ideal weight vector, q represents the number of rules, Indicates that the input is The basis function of ω i,j,2 represents the approximation error, Representative i,j,2 The transpose of .

[0107] The following inequality can be obtained through formula (20):

[0108]

[0109] Where:

[0110] For the actuator deviation fault Π in formula (19), i,j and the unknown external disturbance d i,j , which will be solved by adaptive technology, can obtain the following inequality:

[0111]

[0112] Where:

[0113] In order to solve the complex calculation problem existing in the traditional backstepping control scheme, the following finite time differentiator is designed to obtain

[0114]

[0115] Where: sig(*) 0.5 =|*| 0.5 sign(*),ξ i,j,1 and i,j,2 is the differentiator state, and is the positive parameter to be designed, ξ i,j,2 Can be approximated with arbitrary precision

[0116] By using the relevant inequalities and constructing the following second virtual control law α i,j,2 Ensure that the second step achieves scheduled time stability:

[0117]

[0118] Where: and They are Θ i,j,2 and θ i,j,3 The estimated value of is, and the estimated error is and sat(z i,j,2 ) is designed as follows:

[0119]

[0120] Among them, l i,j,2 and is the positive parameter to be designed.

[0121] Since most drone controllers are based on a time-triggered control framework, the disadvantage of this control method is that the system control signal is continuously updated, which will undoubtedly lead to a waste of airborne communication resources and cause mechanical wear of the actuator. In order to solve this problem, the present invention introduces a self-triggering control mechanism into the design of a predetermined time-tolerant collaborative formation controller for a quad-rotor drone cluster. When the designed trigger conditions are met, the control signal will be updated and transmitted to the actuator, reducing the update frequency of the control signal and the wear of the actuator. The triggering rules are expressed as follows:

[0122]

[0123] Where: 0<μ i,j (0)<1,μ i,j (t)∈(0,1),δ i,j , and κ i,j is a positive design parameter, where γ i,j(t) represents the intermediate control law, μ i,j (t)|τ i,j (t)|+δ i,j is the time interval between two consecutive triggers, and κ i,j Indicates the rate of change of the control signal interval.

[0124] In order to introduce the self-triggering control mechanism, a time-varying function Φ is constructed. i,j,1 (t) and Φ i,j,2 (t), and satisfy |Φ i,j,1 (t)|≤1 and |Φ i,j,2 (t)|≤1, based on formula (26) and formula (27), for We can get:

[0125]

[0126] Combined with the designed second virtual control law α i,j,2 , scheduled time cooperative formation controller τ i,j and finite-time differentiator, formula (19) can be simplified to:

[0127]

[0128] In fact, the inequality Obviously, it holds true and constructs the first adaptive law The second adaptive law and the third adaptive law Ensure the scheduled time is stable:

[0129]

[0130] Substituting formulas (30)-(33) into the inequality In the derivation of time t, by simplifying the inequality, we can get:

[0131]

[0132] Step 6: If the second step is unstable, the third step will not be stable if the second step is stable at the scheduled time in the second step. The following third step Lyapunov function V is constructed for the quadrotor drone cluster system:

[0133]

[0134] Furthermore, by taking the derivative of the third step Lyapunov function V with respect to time t, we can obtain:

[0135]

[0136] Then we can get:

[0137]

[0138] Where: V 0 is the initial value of V, and ln(*) is the natural logarithm function with e as the base. i,j,1 and z i,j,2 Can be in t max <12T c N converges to a small neighborhood near the origin.

[0139] because (·∈L ∞ indicates that · is bounded), we can get is also bounded, that is, Γ i,j,1 ∈L ∞ , from formula (9) we can get ε i,j,1 ∈Υ i,j,1 , by setting and Can further obtain Because z i,j,2 ∈L ∞ ,so and It is bounded in a finite interval, and we can deduce and is also bounded, that is We can get α i,j,2 is bounded, that is, Γ i,j,2 ∈L ∞ , from formula (9) we can get ε i,j,2 ∈Υ i,j,2 , by setting and Can further obtain In addition, the following equation holds:

[0140]

[0141] because and R l,j ∈Υ i,j,1 ,visible is bounded, that is in and A positive constant, according to formula (6) we can get is bounded, therefore, the formation tracking error E i,j,1 =X i,j,1 -R l,j -Δ i,j Under the condition that the system state does not violate the constraint boundary, by selecting appropriate control gains, it can converge to a small neighborhood near the origin within a predetermined time.

[0142] According to the above stability analysis, the input signal τ i,j (t) is bounded, thus ensuring If the boundedness of , then the minimum time interval between two consecutive triggers satisfies Effectively avoid the Zeno effect.

[0143] So far, the design of the scheduled time fault-tolerant collaborative formation controller for a cluster of quadrotor UAVs under full-state constraints has been completed. The selected controller gain is used in the scheduled time fault-tolerant collaborative formation controller to perform bounded convergence on the tracking error of the quadrotor UAV swarm formation, ensuring the scheduled time stability of the overall closed-loop system and enabling the trajectory of the UAV follower to accurately track the trajectory of the leader within the scheduled time.

[0144] To illustrate the control effect of the scheme of the present invention in detail, a simulation experiment will be carried out in MATLAB 2020a / Simulink, and the simulation step size is a fixed step size of 0.001. The experiment selects 4 (N=4) quadrotor drones to follow the trajectory of leader 0, and the communication topology is as follows Figure 3 As shown, the model parameters of the i-th quadrotor drone system are shown in the following table:

[0145]

[0146] Set the unknown external disturbance to d i,x =0.1sin(πt / 8),d i,y =0.1cos(πt / 10),d i,z =0.1cos(πt / 9), i=1,2,…,4. The actuator fault parameters are selected as (i=1,2,…,4, j=1,2,…,6): When 0s<t<5s, ρ i,j =1, when t≥5s, ρ i,j =0.8; when t≥8s, Π i,1 =5sin(0.5t),Π i,2 =3cos(2t),Π i,3 =4sint; when t≥10s, Π i,4 =5cos(2t),Π i,5 =4sint,Π i,6 =3cos(0.5t).

[0147] The operator input to the leader looks like this:

[0148]

[0149] in:

[0150] The initial positions of the 4 drone followers are set to:

[0151]

[0152] The desired inter-neighbor formation distance is set as:

[0153] [Δ 1,1 ,Δ 1,2 ,Δ 1,3 ,Δ 1,4 ,Δ 1,5 ,Δ 1,6 ]=[0,0,0,0,0,-1],

[0154] [Δ 2,1 ,Δ 2,2 ,Δ 2,3 ,Δ 2,4 ,Δ 2,5 ,Δ 2,6 ]=[0,0,0,0,0,1],

[0155] [Δ 3,1 ,Δ 3,2 ,Δ 3,3 ,Δ 3,4 ,Δ 3,5 ,Δ 3,6 ]=[0,0,0,0,0,-2],

[0156] [Δ 4,1 ,Δ 4,2 ,Δ 4,3 ,Δ 4,4 ,Δ 4,5 ,Δ 4,6 ]=[0,0,0,0,0,2].

[0157] In addition, the system state constraints for the quadrotor drone cluster are considered as follows:

[0158]

[0159] The controller gain is selected as:

[0160] β=0.15,T c =5,q=9;

[0161]

[0162] l 1,1,1 = l 1,2,1 = l 2,1,1 = l 2,2,1 =1.5, l 1,1,2 = l 1,2,2 = l 2,1,2=l 2,2,2 =l 3,4,1 =l 4,4,1 =5, l 3,4,2 =l 3,6,2 =l 4,4,2 =

[0163] l 4,6,2 =1, l 1,4,2 =l 2,4,2 =2, l 3,5,2 =l 4,5,2 =3, l 3,6,1 =l 4,6,1 =0.5, l i,3,1 =l i,4,1 =l i,5,1 =l i,6,1 =l i,3,2 =l i,5,2 =l i,6,2 =0.8(i=1,2), l i,1,1 =l i,1,1 =l i,3,1 =l i,5,1 =l i,1,2 =l i,2,2 =l i,3,2 =0.8(i=3,4);

[0164]

[0165]

[0166] s i,1 =s i,2 =0.01,σ i,3 =s i,4 =s i,5 =s i,6 =0.05, μm i,1 (0)=μ i,2 (0)=0.95, μ i,3 (0)=0.7,μ i,4 (0)=0.3,μ i,5 (0)=μ i,6 (0)=0.4,δ i,1 =d i,2 =0.4,δ i,3 =d i,5 =d i,6 =0.02,δ i,4 =0.2, k i,j =10,i=1,2,3,4,j=1,2,…,6。

[0167] A simulation experiment was carried out by MATLAB and the following results were obtained, Figure 4 is the 3D trajectory of the quadrotor drone swarm; Figure 5 The attitude and position tracking curves of the quadrotor drone cluster system are shown. Figure 6 The linear velocity and angular velocity tracking curves of the quadrotor UAV cluster system are shown. It can be observed that the four followers with different initial states can accurately track the leader trajectory without violating the prescribed constraints. In particular, the operator sends a trajectory modification command to the leader at the 30th second. Figure 5 It can be seen from the yaw ψ trajectory and x-axis trajectory in that the operator’s decision is integrated into the control scheme; the tracking error of the quadrotor UAV cluster formation is as follows Figure 7 As shown in Figure 2, despite the existence of system state constraints and actuator failures in the UAV cluster system, the tracking error can converge to a neighborhood near the origin; the control input curves of each follower and Figure 8-11 As shown, the response curve of the self-triggering controller and the time interval of the triggering point are clearly visible, and it can be intuitively seen that the Zeno effect is effectively avoided; through the simulation experimental results, it is concluded that the predetermined time self-triggering fault-tolerant collaborative formation controller designed by the present invention realizes the predetermined time stability of the closed-loop system, and the operator's decision is integrated into the control scheme; combined with the self-triggering control technology, it effectively avoids the continuous updating of the system control signal, reduces the update frequency of the control signal and the wear of the actuator.

[0168] The above description of the specific implementation mode is only used to help understand the technical concept and core idea of ​​the present invention. Although the technical solution is described and illustrated using a specific preferred embodiment, it should not be understood as a limitation of the present invention itself. Those skilled in the art may make various changes in form and details without departing from the technical concept of the present invention. These easily conceived changes or substitutions should all be included in the protection scope of the present invention.

Claims

1. A method for fault-tolerant coordinated formation control of unmanned aerial vehicles (UAVs) with scheduled time under full-state constraints. First, a nonlinear dynamic model of UAVs with external unknown disturbances is established, and the model is summarized as a general expression considering the actuator failure. According to the topological structure between the leader and follower of the UAV, the UAV cluster system is divided into an attitude subsystem and a position subsystem based on an adaptive backstepping control algorithm, and the tracking error is defined. The corresponding subsystems are stabilized by designing a virtual control law to make the tracking error converge, and a coordinated formation controller is designed to achieve tracking of the leader's trajectory within a predetermined time. The method is characterized by: Before defining the tracking error, the UAV cluster system subject to full-state constraints is converted into an unconstrained system using a time-varying nonlinear conversion function according to the general expression of the dynamic model. Then, based on the converted unconstrained system, the tracking error is defined according to the topological structure between the UAV leader and follower.

2. A method for controlling a UAV predetermined time fault-tolerant coordinated formation under full-state constraints as claimed in claim 1, characterized in that: Define a compact set Used to constrain the state of the drone group, where ε i,j,h represents the constrained state, h=1,2, t≥0 represents the time, δ i,j,h (t) and It is a time-varying function greater than 0, and the initial conditions must satisfy The constrained state ε of the drone i,j,h Transformed to the unconstrained equivalent state Γ i,j,h , 3. A method for controlling a UAV predetermined time fault-tolerant coordinated formation under full-state constraints as claimed in claim 2, characterized in that: Convert the constrained i-th UAV system to an unconstrained system: in, is the equivalent state Γ i,j,h The derivative of time t is: F i,j,1 =μ i,j,1 +v i,j,1 e i,j,2 -C i,j,2 , represents the fault model, d i,j represents an external unknown bounded disturbance, g i,j They are a i is the length from the mass point of the i-th UAV to the center of the rotor, J i,x , J i,y and J i,z Respectively represent the rotational inertia of the three coordinate axes of the i-th UAV, M i is the total mass of the i-th UAV.

4. A method for controlling a UAV predetermined time fault-tolerant coordinated formation under full-state constraints as claimed in claim 3, characterized in that: The tracking error is defined as: Among them, z i,j,1 and z i,j,2 is the tracking error, α i,j,1 is the first virtual control law, a i,r Indicates the distance between related drones or their communication capabilities; and Indicates the drone status; b i =1 or 0, indicating whether the i-th follower can obtain the leader information; R l,j Represents the UAV leader trajectory.

5. The method for controlling a UAV predetermined time fault-tolerant coordinated formation under full-state constraints as claimed in claim 1, characterized in that: Based on the tracking error, construct the first step Lyapunov function V i,1 , design the first virtual control law α to make it stable at the predetermined time i,j,1 , through the first step Lyapunov function V i,1 The time derivative confirms the designed first virtual control law α i,j,1 Whether to make the attitude subsystem and position subsystem of the i-th UAV system stable within the first step of the predetermined time.

6. A method for controlling a UAV predetermined time fault-tolerant coordinated formation under full-state constraints as claimed in claim 5, characterized in that: On the basis of the first step of pre-determined time stability, construct the second step Lyapunov function V i,2 , further design the second virtual control law α i,j,2 and the scheduled time coordination formation controller, and design the first, second, and third adaptive laws and Achieve stability in the second step scheduled time.

7. A method for controlling a UAV predetermined time fault-tolerant coordinated formation under full-state constraints as claimed in claim 6, characterized in that: A scheduled time collaborative formation controller is designed in combination with a self-triggering mechanism, so that the control signal is updated and transmitted to the actuator only when the designed triggering conditions are met.

8. The method for controlling a pre-set time fault-tolerant coordinated formation of unmanned aerial vehicles under full-state constraints as claimed in claim 6, characterized in that: First-order derivative based on the first virtual control law Design the second virtual control law α i,j,2 , and use a finite-time differentiator to approximate 9. The method for controlling a UAV predetermined time fault-tolerant coordinated formation under full-state constraints as claimed in claim 6, characterized in that: On the basis of the second step of scheduled time stability, the third step Lyapunov function V is constructed to determine the controller gain to be designed, so as to ensure the scheduled time stability of the overall closed-loop system and realize that the trajectory of the UAV follower can accurately track the leader trajectory within the scheduled time.

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