An unmanned aerial vehicle pre-determined time fault-tolerant cooperative formation control method under full state constraints

Abstract

A kind of unmanned aerial vehicle (UAV) pre-scheduled time fault-tolerant cooperative formation control method under full state constraints is provided. A nonlinear dynamic model of UAV with external unknown disturbance is established, and the model is generalized as a general expression considering the actuator fault condition. A time-varying nonlinear conversion function is used to convert the UAV cluster system under full state constraints into an unconstrained system. Then, based on the converted unconstrained system, the UAV cluster system is divided into an attitude subsystem and a position subsystem based on the adaptive backstepping control algorithm according to the topological structure between the UAV leader and the follower, and a tracking error is defined. A virtual control law is designed to stabilize the corresponding subsystem, so that the tracking error converges, and a cooperative formation controller is designed to track the leader trajectory within a predetermined time. Under the premise that all states do not violate the specified constraints, the UAV follower can track the leader trajectory well, and the feasibility condition limitation on the first virtual control law is eliminated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned aerial vehicle formation control, in particular to a method for pre-determined time fault-tolerant cooperative formation control of unmanned aerial vehicles under full state constraints. BACKGROUND

[0002] A quadrotor unmanned aerial vehicle is a multi-rotor aircraft that can take off and land vertically and generate lift through four rotors. Due to its advantages such as hovering in the air, stable flight, flexible operation, and low cost, it has been attracting more and more attention and use in recent years. With the development of the original unmanned aerial vehicle technology, multi-rotor unmanned aerial vehicles have become smaller, more flexible, and lower in cost, and have been more widely used. Today, quadrotor unmanned aerial vehicles have been widely used in different fields such as military reconnaissance, aerial photography, environmental detection, building inspection, and emergency rescue, and have become an indispensable service in people's daily life. With the increasing maturity and rapid development of unmanned aerial vehicle technology, a single unmanned aerial vehicle sometimes cannot handle tasks in some more complex scenarios, and the efficiency and success rate are relatively low. For example, when a single machine performs exploration tasks, it is often difficult to detect the target from multiple directions due to the limited angle of the sensor. Therefore, multi-unmanned aerial vehicle cooperative control has gradually attracted people's attention. Multi-vehicle cooperation can effectively deal with conflict problems in space and task level, and formation flight can improve the combat field of view and improve the task efficiency and success rate, and has a broad prospect in the fields of agriculture, business, and military. However, the flight environment of the unmanned aerial vehicle is not constant. When the unmanned aerial vehicle flies along a fixed path in an uncertain environment, it may make a wrong decision, resulting in loss of control. Therefore, the operator can help the unmanned aerial vehicle formation to better perform the task by sending command signals to the leader to modify the required reference trajectory with the help of the human-in-the-loop control technology.

[0003] Multi-unmanned aerial vehicle formation needs to determine the communication relationship between adjacent unmanned aerial vehicles on the basis of single machine control, and design a control algorithm to form a specific formation. When the formation operates outdoors, state constraints are everywhere due to the limitation of the working space and the limitation of the physical conditions. A certain unmanned aerial vehicle may also face a fault or encounter a wind disturbance, and these unfavorable factors will affect the stability of the formation flight. The state constraints of the unmanned aerial vehicle system limit the feasibility conditions of the virtual control law in cooperative formation control. It has strong practical significance to achieve good formation effect under the conditions of actuator failure, external disturbance, and system state limitation.

[0004] Furthermore, quadcopter drones require real-time transmission and calculation of external information during missions. Current quadcopter drone formation controllers are based on time-triggered control strategies. The disadvantage of this approach is the continuous updating of system control signals, which inevitably leads to a waste of system communication resources. Frequent operations or the use of control signals beyond the actuator's capabilities can cause the actuator to overheat or even fail, resulting in drone collisions. Therefore, reducing the update frequency of control signals, minimizing data transmission problems, and ensuring accurate tracking of the leader's trajectory even in the event of actuator failure are crucial both theoretically and practically. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for fault-tolerant cooperative formation control of UAVs under all-state constraints at a predetermined time, eliminating the feasibility condition restrictions on virtual control laws.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a method for fault-tolerant cooperative formation control of UAVs under full-state constraints within a predetermined time. First, a nonlinear dynamic model of the UAVs with external unknown disturbances is established, and the actuator failure situation is considered, which is summarized into a general expression. Based on the topology between the UAV leader and followers, the UAV swarm system is divided into an attitude subsystem and a position subsystem based on an adaptive backpropagation control algorithm, and the tracking error is defined. The corresponding subsystems are stabilized by designing a virtual control law to converge the tracking error, and a cooperative formation controller is designed to track the leader's trajectory within a predetermined time. Before defining the tracking error, the UAV swarm system under full-state constraints is converted into an unconstrained system using a time-varying nonlinear transformation function based on the general expression of the dynamic model. Then, based on the converted unconstrained system, the tracking error is defined according to the topology between the UAV leader and followers.

[0007] Furthermore, define a compact set Used to constrain the state of the drone swarm, where ε i,j,h This represents a constrained state, where h = 1, 2, and t ≥ 0 represents time. delta i,j,h (t) and It is a time-varying function with a value greater than 0, and the initial conditions must satisfy... The constrained state ε of the drone i,j,h Transform into an unconstrained equivalent state Γ i,j,h ,

[0008]

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

[0010]

[0011] in, For the equivalent state Γ i,j,h The result of taking the derivative with respect to time t,

[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] Describing the fault model, d i,j G represents an unknown bounded disturbance from the outside. i,j They are respectively a i Let J be the length from the point mass of the i-th UAV to the center of the propeller. i,x J i,y and J i,z Let M represent the rotational inertia of the i-th UAV along its three coordinate axes. i Let be the total mass of the i-th drone.

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

[0016]

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

[0018] Furthermore, based on the tracking error, the first step of constructing the Lyapunov function V is performed. i,1 Design the first virtual control law α to stabilize it at a predetermined time. i,j,1 Through the first step, the Lyapunov function V i,1 The time derivative confirms the first virtual control law α of the design. i,j,1Whether the attitude and position subsystems of the i-th UAV system achieve stabilization within the predetermined time of the first step.

[0019] Furthermore, based on the stability of the predetermined time in the first step, the second step Lyapunov function V is constructed. i,2 Further design of the second virtual control law α i,j,2 Coordinate formation controller with predetermined time, and design first, second, and third adaptive laws. and The second step of stabilizing the scheduled time has been achieved.

[0020] Furthermore, a pre-time coordinated formation controller is designed in conjunction 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.

[0021] Furthermore, based on the first derivative of the first virtual control law Design the second virtual control law α i,j,2 And approximate using a finite-time differentiator

[0022] Furthermore, based on the stability of the predetermined time in the second step, the Lyapunov function V is constructed in the third step, and then the gain of the controller to be designed is determined to ensure the stability of the predetermined time of the overall closed-loop system, so that the trajectory of the UAV follower can accurately track the trajectory of the leader within the predetermined time.

[0023] The beneficial effects of this invention are:

[0024] 1. Unlike existing control algorithms based on obstacle Lyapunov functions, this invention introduces a time-varying nonlinear transformation function to convert a constrained system into an unconstrained system. Under the premise that no state violates the specified constraints, the UAV follower can effectively track the leader's trajectory, eliminating the feasibility condition restrictions on the first virtual control law, and can uniformly handle constrained and unconstrained systems.

[0025] 2. Based on this, unlike finite-time stability theory and fixed-time stability theory, this invention designs a pre-time self-triggering fault-tolerant formation controller, which enables the UAV formation tracking error to converge within a predetermined time. The formula for the convergence time is explicit, and the upper bound can be directly set by a parameter of the controller.

[0026] 3. By combining the self-triggering control mechanism, a pre-time self-triggering fault-tolerant array controller is designed, which effectively avoids the continuous updating of the system control signal and does not rely heavily on the continuous monitoring triggering protocol, thus avoiding the Zeno effect and reducing the update frequency of the control signal and the wear of the actuator.

[0027] 4. In the reverse design process, the first derivative of the first virtual control law is approximated by a finite-time differentiator, which avoids the problem of "complexity explosion" and thus obtains better tracking performance.

[0028] 5. For external disturbances and deviation faults, adaptive compensation technology is adopted so that they do not require prior knowledge and can be unknown. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the design process of the UAV swarm self-triggered fault-tolerant collaborative formation controller of the present invention.

[0030] Figure 2 This is a schematic diagram of the pre-time self-triggered fault-tolerant collaborative formation control process of the UAV swarm according to the present invention.

[0031] Figure 3 This is a schematic diagram of the communication topology of a drone swarm.

[0032] Figure 4 It is a three-dimensional formation trajectory diagram of a quadcopter drone swarm.

[0033] Figure 5 It is a trajectory diagram of the attitude and position status response of a quadcopter drone swarm.

[0034] Figure 6 It is a trajectory diagram of the linear velocity and angular velocity state response of a quadcopter drone swarm.

[0035] Figure 7 This is a graph showing the formation tracking error curves of the attitude and position subsystems of a quadcopter drone swarm.

[0036] Figure 8 It shows the control input curves and trigger intervals of the control inputs for quadcopter drone swarm follower 1.

[0037] Figure 9 These are the control input curves and control input trigger interval diagrams for Quadcopter UAV swarm follower 2.

[0038] Figure 10 It shows the control input curves and control input trigger intervals for the quadcopter drone swarm follower 3.

[0039] Figure 11 It shows the control input curves and control input trigger intervals for the quadcopter drone swarm follower 4. Detailed Implementation

[0040] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. The specific contents listed in the following embodiments are not limited to the technical features necessary to solve the technical problem described in the claims. Furthermore, the enumerations are merely a part of the present invention, and not all of the embodiments.

[0041] The present invention provides a method for pre-time fault-tolerant cooperative formation control of unmanned aerial vehicles under full-state constraints, comprising the following steps:

[0042] Step 1: First, establish a nonlinear dynamics model of the UAV with unknown external disturbances. Specifically, consider a quadcopter UAV formation system consisting of a leader and N followers. The dynamics model of the i-th quadcopter UAV with unknown external disturbances is described as follows:

[0043]

[0044] In the formula: x i y i , z i φ represents the three spatial positions of the i-th quadcopter UAV; i θ i and ψ i Let represent the three flight attitude angles of the i-th quadcopter UAV, namely roll angle, pitch angle, and yaw angle. The second time derivative of * is given. The first time derivative of *, for example a i M is the length from the point mass of the i-th quadcopter UAV to the center of the propeller; i Let g be the total mass of the i-th quadcopter UAV; g be the acceleration due to gravity; J be the total mass of the i-th quadcopter UAV. i,x J i,y and J i,z Let C represent the rotational inertia of the i-th UAV along its three coordinate axes; i,j d represents the damping coefficient. i,j Let τ represent an externally unknown bounded perturbation, where j = φ, θ, ψ, z, x, y; i,F τ represents the total lift of the i-th UAV; i,φ τ i,θ and τ i,ψ These represent the input signals 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 quadcopter UAV swarm.

[0045] To simplify subsequent reasoning, the dynamic model is generalized into a general expression considering actuator failure.

[0046] The fault model of the i-th six-DOF quadrotor UAV is represented as:

[0047]

[0048] Where, ρ i,j ∈(0,1] represents the execution efficiency coefficient of the actuator, τ i,j Indicates actuator input, Π i,j This is an unknown time-varying deviation fault.

[0049] The dynamic model of the i-th quadcopter UAV system with actuator failure in formula (1) can be summarized as the general expression:

[0050]

[0051] 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 );

[0052]

[0053] (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 );

[0054]

[0055] Furthermore, all states of the i-th quadcopter UAV are required to be restricted to a compact set. In the expression, h = 1, 2, and t ≥ 0 represents time. and It is a positive time-varying function.

[0056] The total lift τ of the i-th quadcopter UAV i,F And Leader Trajectory R l,1 R l,2 pass And the leader's yaw angle trajectory R l,3 get:

[0057]

[0058] Step 2: Considering the safety distance, based on human-in-the-loop control technology, determine the leader's task, and use a time-varying nonlinear transformation function to transform the fully state-constrained UAV swarm system into an unconstrained system.

[0059] Based on the general expression (3) above, the main control objective of cooperative formation control is to make the follower output trajectory X. i,j,1 Track the leader's trajectory as much as possible. l,j This will result in 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 This represents the desired neighbor-to-neighbor formation distance.

[0060] The leader considered in this invention is a non-autonomous system whose dynamic model satisfies the following relationship:

[0061]

[0062] In the formula: and Represents the state, R l,j and u l,j These are the output and the bounded control input, respectively, where the input u l,j It can be designed by the operator. R is a known coefficient. l,j Need to meet

[0063] The state transition of the quadcopter drone swarm is as follows:

[0064]

[0065] Define a compact set Where h = 1, 2, and t ≥ 0 represent time. delta i,j,h (t) and It is a time-varying function greater than 0, used to constrain the state of the quadrotor UAV swarm after transformation. The initial conditions must satisfy...

[0066] To eliminate the feasibility condition restrictions of the first virtual control law, a time-varying nonlinear transformation function is introduced to transform the constrained state ε i,j,h (h=1,2) is transformed into the unconstrained equivalent state Γi,j,h :

[0067]

[0068] For any If Γ i,j,h ∈L ∞ (·∈L ∞ (This indicates that the symbol · is bounded), then This can be guaranteed. Among them, Γ i,j,h Taking the derivative with respect to time t, we get:

[0069]

[0070] In the formula:

[0071]

[0072] According to formulas (6), (7) and (8), the originally constrained i-th quadcopter UAV system (3) can be converted into an unconstrained new system:

[0073]

[0074] In the formula: 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 .

[0075] Step 3: Based on the unconstrained system (9) obtained in Step 2 and the topology between the quadcopter leader and the quadcopter follower, construct the tracking error.

[0076] We use directed graphs from graph theory to describe a multi-drone system consisting of one leader and N followers. Represented as in and These are the vertex set and edge set of a directed graph, respectively. This indicates that the i-th node can obtain information from the r-th node, denoted as […]. Let be the neighborhood of the i-th node, and each drone is abstracted as a node. (Directed graph) This can represent the communication relationships between quadrotor drones. Furthermore, these communication relationships can be described using an adjacency matrix, or a directed graph. Adjacency Matrix The element is defined as follows: If Then ai,r =1, otherwise a i,r =0. a i,r The physical meaning of the degree matrix can represent the distance or communication capability between related drones. The degree matrix is ​​defined as follows: Define the Laplace matrix In directed graphs There are no self-loops in the graph. If there is a directed graph... If there exists a directed graph in which at least one node can be directed to any other node in the graph, then the directed graph is... It contains a directed spanning tree. The leader is in the directed graph. In the matrix, node 0 is marked, and a diagonal matrix is ​​defined. When the i-th follower can obtain information about the leader, b i =1, otherwise b i =0.

[0077] Based on the adaptive back-thrust control algorithm, the quadrotor UAV swarm system is divided into an attitude subsystem and a position subsystem, and a tracking error variable z is introduced. i,j,1 and z i,j,2 The tracking error is constructed as follows:

[0078]

[0079] In the formula: z i,j,1 and z i,j,2 It is tracking error. and Indicates the drone status Γ i,j,1 and Γ r,j,1 , α i,j,1 It is the first virtual control law, a i,r and b i Derived from the topology between leaders and followers.

[0080] Step 4: Based on the tracking error constructed in Step 3, construct the attitude subsystem and position subsystem for the i-th (i∈[1,2,…,N]) quadcopter UAV as follows: First step Lyapunov function V i,1 :

[0081]

[0082] Furthermore, the first step of the Lyapunov function V i,1 Taking the derivative with respect to time t, we get:

[0083]

[0084] In the formula: It is formed by the constrained leader trajectory Rl,j Convert to unconstrained trajectory The derivative of .

[0085] Regarding the function h in the above formula i,j,1 The interval type II fuzzy technique is used for approximation, which can be specifically expressed as:

[0086]

[0087] In the formula: Let q represent the ideal weight vector, and q represent the number of rules. This indicates that the input is the status of a quadcopter drone. basis functions, ω i,j,1 Represents the approximation error. Represents Ξ i,j,1 The transpose of .

[0088] The following inequality can be obtained using formula (13):

[0089]

[0090] In the formula:

[0091] By using relevant inequalities, the following first virtual control law α is constructed. i,j,1 To ensure the first step achieves the predetermined time stably:

[0092]

[0093] In the formula: β and T c Let β be the parameters of the positive controller to be designed, 0 < β ≤ 0.5. It is Θ i,j,1 The estimated value, with an estimation error of sat(z i,j,1 The design is as follows:

[0094]

[0095] Where exp(*) is the exponential function, sign(*) is the sign function, and l i,j,1 and These are the positive parameters to be designed.

[0096] The first virtual control law α designed i,j,1 And using the interval type II fuzzy approximation term h i,j,1 Substituting into formula (12), we get:

[0097]

[0098] Based on Lyapunov's predetermined time stability theory, the first virtual control law α designed is used.i,j,1 The first step of stabilizing the i-th quadcopter UAV system was achieved at the predetermined time.

[0099] Step 5: Based on the stability at the predetermined time in Step 1 (if Step 1 is unstable, then Step 2 will also be unstable), construct the attitude subsystem and position subsystem for the i-th (i∈[1,2,…,N]) quadcopter UAV as follows: Step 2 Lyapunov function V i,2 :

[0100]

[0101] Furthermore, the second step involves the Lyapunov function V. i,2 Taking the derivative with respect to time t, we get:

[0102]

[0103] Regarding the function F in the above formula i,j,2 The interval type II fuzzy technique is used for approximation, which can be specifically expressed as:

[0104]

[0105] In the formula: Let q represent the ideal weight vector, and q represent the number of rules. Indicates that the input is basis functions, ω i,j,2 Represents the approximation error. Represents Ξ i,j,2 The transpose of .

[0106] The following inequality can be obtained using formula (20):

[0107]

[0108] In the formula:

[0109] Regarding the actuator deviation fault Π in formula (19) i,j and unknown external disturbances d i,j By employing adaptive techniques, the following inequalities can be obtained:

[0110]

[0111] In the formula:

[0112] To address the complex computational problems inherent in traditional back-thrust control schemes, a finite-time differentiator is designed to obtain...

[0113]

[0114] In the formula: sig(*) 0.5 =|*| 0.5 sign(*), ξ i,j,1 and ξ i,j,2 It is the differentiator state. and ξ is the positive parameter to be designed. i,j,2 It can approximate with arbitrary precision

[0115] By using relevant inequalities, the following second virtual control law α is constructed. i,j,2 To ensure the second step achieves the scheduled time stably:

[0116]

[0117] In the formula: and They are Θ i,j,2 and Θ i,j,3 The estimated value, with an estimation error of and sat(z i,j,2 The design is as follows:

[0118]

[0119] Among them, l i,j,2 and These are the positive parameters to be designed.

[0120] Since most UAV controllers are based on a time-triggered control framework, the disadvantage of this method is that the continuous updating of the system control signal inevitably leads to a waste of onboard communication resources and causes mechanical wear on the actuators. To solve this problem, this invention introduces a self-triggered control mechanism into the design of a pre-defined time-tolerant collaborative formation controller for quadcopter UAV swarms. The control signal is only updated and transmitted to the actuators when the designed triggering conditions are met, reducing the update frequency of the control signal and the wear on the actuators. The triggering rules are expressed as follows:

[0121]

[0122] In the formula: 0 < μ i,j (0) < 1, μ i,j (t)∈(0,1), δ i,j , and κ i,j These are positive design parameters, among which γ i,j (t) represents the intermediate control law, μ i,j (t)|τ i,j(t)|+δ i,j The time interval between two consecutive triggers. and κ i,j This indicates the rate of change of the control signal interval.

[0123] To introduce a 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 formulas (26) and (27), for We can obtain:

[0124]

[0125] Combined with the designed second virtual control law α i,j,2 Scheduled time coordinated formation controller τ i,j With a finite-time differentiator, equation (19) can be simplified to:

[0126]

[0127] In fact, inequalities This is clearly true, and we can construct the first adaptive law. Second Adaptive Law and the third adaptive law To ensure stable achievement of the scheduled time:

[0128]

[0129] Substitute formulas (30)-(33) into the inequalities In the derivative with respect to time t, we can simplify using inequalities to obtain:

[0130]

[0131] Step 6: If the second step is unstable (assuming the predetermined time in the second step is stable, then the third step will also be unstable), construct the following Lyapunov function V for the quadcopter drone swarm system in the third step:

[0132]

[0133] Furthermore, by differentiating the Lyapunov function V with respect to time t in the third step, we obtain:

[0134]

[0135] Then we can obtain:

[0136]

[0137] In the formula: V0 is the initial value of V, and ln(*) is the natural logarithm function with base e. i,j,1 and z i,j,2 It can be done in t max <12T c Within N, it converges to a small neighborhood near the origin.

[0138] because (·∈L ∞ (This indicates that the symbol · is bounded), which can be obtained. It is also bounded, that is, Γ i,j,1 ∈L ∞ From formula (9), we can obtain By setting and It can be further obtained Because z i,j,2 ∈L ∞ ,so and It is bounded within a finite interval, which can be deduced. and It is also bounded, that is α can be obtained i,j,2 It is bounded, that is, Γ i,j,2 ∈L ∞ From formula (9), we can obtain By setting and It can be further obtained Furthermore, the following equation holds true:

[0139]

[0140] because and visible It is bounded, that is in and Positive numbers can be obtained from formula (6). It is bounded, therefore, the formation tracking error E i,j,1 =X i,j,1 -R l,j -Δ i,j If the system state does not violate the constraint boundary, by selecting an appropriate control gain, it can converge to a small neighborhood near the origin within a predetermined time.

[0141] Based on the above stability analysis, the input signal τ i,j (t) is bounded, thus guaranteeing If the condition is bounded, then the minimum time interval between two consecutive triggers satisfies This effectively avoids the Zeno effect.

[0142] To date, the design of a time-tolerant collaborative formation controller for quadrotor drone swarms based on full-state constraints has been completed. The selected controller gain is used for the time-tolerant collaborative formation controller to achieve time-bounded convergence of the quadrotor drone swarm formation tracking error, ensuring the time-bound stability of the overall closed-loop system and enabling the drone followers to accurately track the leader's trajectory within the time limit.

[0143] To illustrate the control effect of the present invention in detail, a simulation experiment will be conducted in MATLAB 2020a / Simulink with a fixed simulation step size of 0.001. Four quadcopter drones (N=4) will follow the trajectory of leader drone 0. The communication topology is as follows: Figure 3 As shown in the table below, the system model parameters of the i-th quadcopter UAV are as follows:

[0144]

[0145] Let the unknown external disturbance be d. i,ψ =0.1cos(πt / 10),d i,θ =0.1sin(πt / 9),d i,φ =0.1cos(πt / 10), 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).

[0146] The operator's input for the leader is as follows:

[0147]

[0148] in:

[0149] The initial positions of the four drone followers were set as follows:

[0150]

[0151] The desired neighbor-to-neighbor formation distance is set as follows:

[0152] [Δ 1,1 ,Δ 1,2 ,Δ 1,3 ,Δ 1,4 ,Δ 1,5 ,Δ 1,6 ] = [0,0,0,0,0,-1],

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

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

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

[0156] Furthermore, consider the following system state constraints for a quadcopter drone swarm:

[0157]

[0158]

[0159] The controller gain is selected as follows:

[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 =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);

[0163]

[0164] σ i,1 =σ i,2 =0.01, σ i,3 =σ i,4 =σ i,5 =σ i,6 =0.05, μ i,1 (0)=μ i,2 (0) = 0.95, μ i,3 (0) = 0.7,

[0165] μ i,4 (0) = 0.3, μ i,5 (0)=μ i,6 (0)=0.4, δ i,1 =δ i,2 =0.4, δ i,3 =δ i,5 =δ i,6 =0.02, δ i,4 =0.2,

[0166] κ i,j =10, i=1,2,3,4, j=1,2,…,6.

[0167] The following results were obtained through simulation experiments using MATLAB.Figure 4 It is the 3D trajectory of a quadcopter drone swarm; Figure 5 The attitude and position tracking curves of the quadcopter drone swarm system are displayed. Figure 6 The linear and angular velocity tracking curves of a quadcopter drone swarm system are displayed. It can be observed that four followers with different initial states are able to accurately track the leader's trajectory without violating specified constraints. Specifically, the operator sends a trajectory modification command to the leader at 30 seconds. Figure 5 The yaw ψ trajectory and x-axis trajectory show that the operator's decisions were integrated into the control scheme; the tracking error of the quadcopter drone swarm is as follows: Figure 7 As shown, despite system state constraints and actuator failures in the UAV swarm system, the tracking error can converge to the neighborhood near the origin; the control input curves of each follower and... Figures 8-11 As shown, the response curve of the self-triggering controller and the time interval of the trigger point are clearly visible, and it can be intuitively seen that the Zeno effect is effectively avoided. Through simulation experiments, it is concluded that the predetermined time self-triggering fault-tolerant cooperative formation controller designed in this invention achieves predetermined time stability of the closed-loop system and integrates the operator's decision into the control scheme. Combined with self-triggering control technology, it effectively avoids continuous updates of the system control signal, reduces the update frequency of the control signal and the wear of the actuator.

[0168] The above description of specific embodiments is only for the purpose of helping to understand the technical concept and core idea of ​​the present invention. Although specific preferred embodiments have been used to describe and illustrate the technical solutions, they should not be construed as limiting the present invention itself. Those skilled in the art can make various changes in form and detail without departing from the technical concept of the present invention. These easily conceived changes or substitutions should all be covered within the protection scope of the present invention.

Claims

1. A method for fault-tolerant cooperative formation control of unmanned aerial vehicles (UAVs) under full-state constraints within a predetermined time. First, a nonlinear dynamic model of the UAVs with external unknown disturbances is established, and the actuator failure condition is considered, which is summarized into a general expression. Based on the topology between the UAV leader and followers, the UAV swarm system is divided into an attitude subsystem and a position subsystem based on an adaptive backpropagation control algorithm, and the tracking error is defined. A virtual control law is designed to stabilize the corresponding subsystems, thereby converging the tracking error. A cooperative 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 fully constrained UAV swarm system is transformed into an unconstrained system using a time-varying nonlinear transformation function based on the general expression of the dynamic model. Then, based on the transformed unconstrained system, the tracking error is defined according to the topology between the UAV leader and followers. The method is as follows: define a compact set... Used to constrain the state of the drone swarm, where ε i,j,h This represents the constrained state, h = 1, 2, t ≥ 0 represents time, and δ i,j,h (t) and It is a time-varying function with a value greater than 0, and the initial conditions must satisfy... The constrained state ε of the drone i,j,h Transform into an unconstrained equivalent state Γ i,j,h , Transform the constrained i-th UAV system into an unconstrained system: in, For the equivalent state Γ i,j,h The result of taking the derivative with respect to time t, F i,j,1 =μ i,j,1 +v i,j,1 e i,j,2 -C i,j,2 , F i,j,2 =μ i,j,2 +v i,j,2 f i,j , Describing the fault model, d i,j G represents an unknown bounded disturbance from the outside. i,j They are respectively a i Let J be the length from the point mass of the i-th UAV to the center of the propeller. i,x J i,y and J i,z Let M represent the rotational inertia of the i-th UAV along its three coordinate axes. i Let be the total mass of the i-th drone.

2. The method for pre-time fault-tolerant cooperative formation control of UAVs under full-state constraints as described in claim 1, characterized in that: The tracking error is defined as: Among them, z i,j,1 and z i,j,2 It is the tracking error, α i,j,1 It is the first virtual control law, a i,r Indicates the distance between related drones or their communication capabilities; and Indicates the drone's status; b i = 1 or 0, indicating whether the i-th follower can obtain information about the leader; R l,j This indicates the trajectory of the drone leader.

3. The method for pre-time fault-tolerant cooperative formation control of UAVs under full-state constraints as described in claim 2, characterized in that: Based on the tracking error, the first step of constructing the Lyapunov function V is as follows: i,1 Design the first virtual control law α to stabilize it at a predetermined time. i,j,1 Through the first step, the Lyapunov function V i,1 The time derivative confirms the first virtual control law α of the design. i,j,1 Does the attitude and position subsystems of the i-th UAV system achieve stabilization within the predetermined time for the first step? Wherein, the first step involves the Lyapunov function V... i,1 for: First virtual control law α i,j,1 for: In the formula, β and T c Let β be the parameters of the positive controller to be designed, 0 < β ≤ 0.

5. It is Θ i,j,1 The estimated value, Represents the ideal weight vector. It is formed by the constrained leader trajectory R l,j Convert to unconstrained trajectory The derivative of exp(*) is the exponential function, sign(*) is the sign function, and l i,j,1 and θ i,j,1 These are the positive parameters to be designed.

4. The method for pre-time fault-tolerant cooperative formation control of UAVs under full-state constraints as described in claim 3, characterized in that: Based on the stability of the predetermined time in the first step, construct the second step Lyapunov function V. i,2 Further design of the second virtual control law α i,j,2 Coordinate formation controller with predetermined time, and design first, second, and third adaptive laws. and Achieving stability at the predetermined time in the second step; wherein, the Lyapunov function V in the second step i,2 for: Second virtual control law α i,j,2 for: In the formula: ρ i,j ∈(0,1] represents the execution efficiency coefficient of the executor. and They are Θ i,j,2 and Θ i,j,3 The estimated value, sat(z i,j,2 The design is as follows: Among them, l i,j,2 and θ i,j,2 These are the positive parameters to be designed.

5. The method for pre-time fault-tolerant cooperative formation control of UAVs under full-state constraints as described in claim 4, characterized in that: A pre-time coordinated formation controller is designed by combining a self-triggering mechanism, so that the control signal is updated and transmitted to the actuator only when the designed triggering conditions are met.

6. The method for pre-time fault-tolerant cooperative formation control of UAVs under full-state constraints as described in claim 4, characterized in that: First derivative based on the first virtual control law Design the second virtual control law α i,j,2 And approximate using a finite-time differentiator 7. The method for pre-time fault-tolerant cooperative formation control of UAVs under full-state constraints as described in claim 4, characterized in that: Based on the stability of the predetermined time in the second step, the Lyapunov function V is constructed in the third step, and then the gain of the controller to be designed is determined to ensure the stability of the predetermined time of the overall closed-loop system, so that the trajectory of the UAV follower can accurately track the trajectory of the leader within the predetermined time.

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