Predefined time multi-quadrotor unmanned aerial vehicle formation control method based on observer

Abstract

The invention discloses a pre-defined time multi-quadrotor unmanned aerial vehicle formation control method based on an observer, and relates to the technical field of unmanned aerial vehicle control, and the method comprises the following steps: S1, building a position and attitude dynamic model of a multi-quadrotor unmanned aerial vehicle, and initializing a system state, sampling time and control parameters; s2, constructing a predefined time state observer for each quad-rotor unmanned aerial vehicle; s3, designing a position sliding mode surface and an attitude sliding mode surface of each quad-rotor unmanned aerial vehicle; s4, designing a predefined time position controller and an attitude controller; based on the state observer, sliding mode control and predefined time control, the multi-quad-rotor unmanned aerial vehicle formation control method based on the state observer is designed, and it is ensured that each quad-rotor unmanned aerial vehicle can accurately obtain position and speed state information of a virtual navigator within predefined time. It is guaranteed that the expected formation can be formed within the predefined time, and stable control over the system is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle control, and in particular to an observer-based predefined time multi-quad-rotor unmanned aerial vehicle formation control method. Background Art

[0002] With the development of unmanned aerial vehicle technology, multi-quadrotor drones have been widely used in military, civilian and other fields. Especially when performing formation flight missions, multiple quadrotor drones can work together to complete various tasks such as monitoring, surveying and mapping, and cargo transportation.

[0003] There are many control methods for the control problem of multi-quadrotor UAV formation system, such as PID control, adaptive control, sliding mode control, etc. Sliding mode control is considered to be one of the effective robust control methods in solving system uncertainty and external disturbances. The sliding mode control method has the advantages of simple algorithm, fast response speed, strong robustness to external noise interference and parameter perturbation. Therefore, the sliding mode control method is widely used in various fields. Compared with traditional linear sliding mode control, the superiority of terminal sliding mode control lies in its finite time convergence characteristics. However, the finite time convergence depends on the initial state of the system, which limits its application in practical systems to a certain extent.

[0004] Although sliding mode control and its variants offer many advantages, there are still some challenges in the formation control of multi-quadrotors. When the formation performs urgent tasks, traditional methods may not be able to meet the system's demand for rapid response, especially when the formation time needs to be strictly controlled. In order to solve these problems, predefined time control methods have emerged. Predefined time control allows the convergence time of the control target to be set in advance, so it performs well in dealing with the rapidity problem of nonlinear systems. In addition, in the formation control of multi-quadrotors, the drones need to obtain the position and velocity state information of the virtual navigator. However, due to sensor failures, measurement noise and the high cost of installing additional high-precision sensors, this hinders the drone's ability to effectively obtain the state information of the virtual navigator. Therefore, building an efficient state observer becomes the key to solving sensor limitations and improving system robustness. To this end, a predefined time multi-quadrotor formation control method based on an observer is proposed. Summary of the invention

[0005] The purpose of the present invention is to solve the problems in the prior art and to propose a predefined time multi-quadrotor UAV formation control method based on an observer.

[0006] A method for controlling a multi-quadrotor UAV formation at a predefined time based on an observer comprises the following steps:

[0007] S1. Establish the position and attitude dynamics model of the multi-quadrotor UAV, initialize the system state, sampling time and control parameters;

[0008] S2, build a predefined time state observer for each quadrotor drone;

[0009] S3. Design the position sliding surface and attitude sliding surface of each quadrotor drone;

[0010] S4, designing a predefined time position controller and a posture controller;

[0011] S5. Control the corresponding quadrotor drone according to the designed position controller and attitude controller to achieve the desired formation.

[0012] Preferably, in step S1, the position and attitude dynamics model of the multi-quadrotor UAV system is expressed as:

[0013]

[0014]

[0015] Where i = 1, 2, .., N, i represents the i-th drone, N represents the number of drones; x i ,y i and z i represents the position of the i-th UAV in the inertial coordinate system; and are the accelerations along the x-axis, y-axis and z-axis in the inertial coordinate system; m i represents the mass of the drone; g represents the acceleration due to gravity; T i Indicates the lift generated by the rotor; φ i ,θ i and ψ i Respectively represent the three attitude angles of the i-th UAV: ​​roll angle, pitch angle and yaw angle; and are the angular velocities of roll, pitch and yaw respectively; and are the angular accelerations of roll angle, pitch angle and yaw angle respectively; J xx , J yy and J zz is the moment of inertia; d i,x , d i,y and d i,z Respectively represent the i-th drone at x i ,y i and z i External disturbance in direction, d i,φ , d i,θ and d i,ψRespectively represent the i-th UAV in φ i ,θ i and ψ i External disturbance in direction; τ i,φ , τ i,θ and τ i,ψ Represent the control inputs of the roll angle, pitch angle and yaw angle channels respectively;

[0016] Simplify equation (1) into the following second-order nonlinear system:

[0017]

[0018] Among them, p i =[x i ,y i ,z i ] T , u i =[u i,x ,u i,y ,u i,z ] T and d i,p =[d i,x ,d i,y ,d i,z ] T ∈R 3 Respectively represent the position vector, velocity vector, position control input vector and external disturbance vector of the i-th UAV;

[0019] The dynamic model expression of the virtual navigator is:

[0020]

[0021] Among them, p 0 =[x 0 ,y 0 ,z 0 ] T , and u 0 =[u 0,x ,u 0,y ,u 0,z ] T ∈R 3 They represent the position vector, velocity vector and position control input vector of the virtual navigator respectively.

[0022] Preferably, in step S2, a predefined time state observer is constructed for each quadrotor drone, and the process is as follows:

[0023] Design the predefined time state observer as:

[0024]

[0025] Where j = 1, 2, ..., N, j represents the jth UAV, and j ≠ i; η ∈ (0, 1); and denotes the position and velocity estimates of the virtual navigator by the i-th UAV and the j-th UAV, respectively, and γ ≥ 0 is u 0 The known upper bound of ij represents the communication connection between the i-th UAV and the j-th UAV, b i Represents the communication connection between the i-th UAV and the virtual leader; defines n represents the vector dimension, λ min (H) is the minimum eigenvalue of the Laplace matrix H; the control parameter α 1 , α 2 , β 1 , β 2 It can be expressed as and T c1 and T c2 are the upper bounds of the convergence time of the pre-set observer velocity and position observation errors; the function sig 1-η (·)=[|· 1 | 1-η sign(· 1 ),..,|· n | 1-η sign(· n )] T , ·∈R, sign(·) is the sign function, sig(·) is the vector form of sign(·);

[0026] The observation error of the predefined time state observer is defined as: Then the observation error vector of position and velocity is: The observation error of the predefined time state observer is further obtained as:

[0027]

[0028] Among them, 1 N represents the N-dimensional unit column vector, represents the Kronecker product.

[0029] Preferably, in step S3, the position sliding surface and attitude sliding surface of each quadrotor drone are designed, and the process is as follows:

[0030] According to the estimated value of formula (5), the trajectory tracking error of the i-th quadrotor drone is defined as:

[0031]

[0032] Among them, e i,x and e i,v represents the tracking error of the position and velocity of the virtual navigator by the i-th UAV, h i represents the expected relative distance between the i-th UAV and the virtual navigator;

[0033] By taking the derivative of formula (7), we can get:

[0034]

[0035] in, and represents the tracking error derivative of the position and velocity of the virtual navigator of the i-th UAV;

[0036] Due to the coupling relationship between the attitude system and the position system of the quadrotor drone, the position control input u i =[u i,x ,u i,y ,u i,z ] T The desired attitude angle can be generated as follows:

[0037]

[0038] Among them, ψ i is the yaw angle of the drone, ψ i =ψ 0 , ψ 0 is the yaw angle of the known virtual navigator;

[0039] Taking the roll angle of the i-th quadrotor drone as an example, we first define the attitude angle tracking error as:

[0040] e i,φ =φ i -φ i d (10)

[0041] Among them, e i,φ represents the error between the actual roll angle and the expected roll angle of the i-th UAV;

[0042] By taking the derivative of formula (10), we can get:

[0043]

[0044] in, represents the error derivative between the actual roll angle and the expected roll angle of the i-th UAV; represents the angular velocity of the desired roll angle of the i-th UAV;

[0045] Based on e i,x , e i,v and e i,φ , Design the position and attitude sliding surface of the i-th quadrotor drone as

[0046]

[0047] Among them, T c4 It is the upper bound of the convergence time of the preset UAV trajectory tracking error and attitude tracking error.

[0048] Preferably, in step S4, a predefined time position controller and a posture controller are designed, and the process is as follows:

[0049]

[0050] Among them, T c3 is the upper bound of the convergence time of the preset position sliding surface and attitude sliding surface, σ i,p and σ i,a is the known upper bound of the external interference to the drone’s position system and attitude system. is the angular acceleration of the desired roll angle of the i-th UAV;

[0051] First, we prove that the velocity observation error vector v e At the predefined time T c1 The inner convergence is zero, and the Lyapunov function is designed as:

[0052]

[0053] Taking the derivative of equation (14) and substituting the second equation of equation (6) into it, we can obtain:

[0054]

[0055] Formula (15) complies with , then determine v e At a predefined time T c1 Inner convergence;

[0056] Then it is proved that the position observation error vector x e At the predefined time T c2 The inner convergence is zero, and the Lyapunov function is designed as:

[0057]

[0058] From formula (15), we know that at the predefined time T c1 Inner e converges to zero, then when t ≥ T c1When , the first equation of formula (6) can be simplified to: Taking the derivative of equation (16) and substituting the first equation of equation (6) into it, we can obtain:

[0059]

[0060] Formula (17) complies with , then determine x e At a predefined time T c2 Inner convergence; Based on the above analysis, when t≥T c1 +T c2 When the virtual navigator is in flight, each quadrotor drone can accurately obtain the position and speed information of the virtual navigator;

[0061] It is proved below that the position sliding surface and the attitude sliding surface are in the predefined time T c3 Inner convergence, the Lyapunov function is designed as:

[0062]

[0063] Deriving equation (18) and substituting equation (13) into it, we can obtain:

[0064]

[0065] Formula (19) complies with , then determine s i,p and i,φ At a predefined time T c3 Inner convergence; when t ≥ T c1 +T c2 +T c3 When i,p ≡0,s i,φ ≡0, (12) can be rewritten as:

[0066]

[0067] Then we prove that the position tracking error e i,x and attitude tracking error e i,φ At a predefined time T c4 Inner convergence, the Lyapunov function is designed as:

[0068]

[0069] Deriving equation (21) and substituting equation (20) into it, we can obtain:

[0070]

[0071] Formula (22) complies with , then determine e i,x and ei,φ At a predefined time T c4 Inner convergence;

[0072] Based on the above analysis, we can see that when t≥T c1 +T c2 +T c3 +T c4 When the sliding surface and tracking error converge within the predefined time, each quadrotor UAV can accurately track the desired trajectory and desired attitude within the predefined time.

[0073] Compared with the prior art, the present invention has the following advantages:

[0074] Based on state observer, sliding mode control and predefined time control, the present invention designs a multi-quadrotor UAV formation control method based on state observer, ensuring that each quadrotor UAV can accurately obtain the position and speed state information of the virtual navigator within the predefined time, ensuring that the expected formation can be formed within the predefined time, and realizing stable control of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a control flow diagram of the present invention.

[0076] Figure 2 For the present invention c1 =1s, T c2 Schematic diagram of the position observation error of the virtual navigator by the state observer designed for two quadrotor drones at =1s.

[0077] Figure 3 For the present invention c1 =1s, T c2 Schematic diagram of the speed observation error of the virtual navigator by the state observer designed for two quadrotor drones at =1s.

[0078] Figure 4 For the present invention c3 =2s, T c4 Schematic diagram of the tracking error of two quadrotor drones to the desired position when =5s.

[0079] Figure 5 For the present invention c3 =2s, T c4 Schematic diagram of the tracking error of two quadrotor drones to the desired attitude when =5s.

[0080] Figure 6 For the present invention c1 =1s, T c2 =1s, T c3 =2s, T c4 Schematic diagram of position control input of two quadrotor drones at =5s.

[0081] Figure 7 For the present invention c1 =1s, T c2 =1s, T c3 =2s, T c4 Schematic diagram of attitude control input of two quadrotor drones at =5s.

[0082] Figure 8 For the present invention c1 =0.4s, T c2 Schematic diagram of the information observation error of the virtual navigator's position by the state observer designed for two quadrotor drones at =0.6s.

[0083] Fig. 9 For the present invention c1 =0.4s, T c2 Schematic diagram of the information observation error of the state observer designed for two quadrotor drones on the speed of the virtual navigator when =0.6s.

[0084] Fig.10 For the present invention c3 =1s, T c4 Schematic diagram of the tracking error of two quadrotor drones to the desired position when =4s.

[0085] Fig.11 For the present invention c3 =1s, T c4 Schematic diagram of the tracking error of two quadrotor drones to the desired posture when =4s.

[0086] Fig.12 For the present invention c1 =0.4s, T c2 =0.6s, T c3 =1s, T c4 Schematic diagram of position control input of two quadrotor drones at =4s.

[0087] Fig.13 For the present invention c1 =0.4s, T c2 =0.6s, T c3 =1s, T c4 Schematic diagram of attitude control input of two quadrotor drones at =4s. DETAILED DESCRIPTION

[0088] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0089] Reference Figure 1As shown, a predefined time multi-quadrotor UAV formation control method based on an observer comprises the following steps:

[0090] S1. Establish the position and attitude dynamics model of the multi-quadrotor UAV, initialize the system state, sampling time and control parameters;

[0091] S2, build a predefined time state observer for each quadrotor drone;

[0092] S3. Design the position sliding surface and attitude sliding surface of each quadrotor drone;

[0093] S4, designing a predefined time position controller and a posture controller;

[0094] S5. Control the corresponding quadrotor drone according to the designed position controller and attitude controller to achieve the desired formation.

[0095] In step S1, the position and attitude dynamics model of the multi-quadrotor UAV system is expressed as:

[0096]

[0097]

[0098] Where i = 1, 2, .., N, i represents the i-th drone, N represents the number of drones; x i ,y i and z i represents the position of the i-th UAV in the inertial coordinate system; and are the accelerations along the x-axis, y-axis and z-axis in the inertial coordinate system; m i represents the mass of the drone; g represents the acceleration due to gravity; T i Indicates the lift generated by the rotor; φ i ,θ i and ψ i Respectively represent the three attitude angles of the i-th UAV: ​​roll angle, pitch angle and yaw angle; and are the angular velocities of roll, pitch and yaw respectively; and are the angular accelerations of roll angle, pitch angle and yaw angle respectively; J xx , J yy and J zz is the moment of inertia; d i,x , d i,y and d i,z Respectively represent the i-th drone at x i ,y i and zi External disturbance in direction, d i,φ , d i,θ and d i,ψ Respectively represent the i-th UAV in φ i ,θ i and ψ i External disturbance in direction; τ i,φ , τ i,θ and τ i,ψ Represent the control inputs of the roll angle, pitch angle and yaw angle channels respectively;

[0099] Simplify equation (1) into the following second-order nonlinear system:

[0100]

[0101] Among them, p i =[x i ,y i ,z i ] T , u i =[u i,x ,u i,y ,u i,z ] T and d i,p =[d i,x ,d i,y ,d i,z ] T ∈R 3 Respectively represent the position vector, velocity vector, position control input vector and external disturbance vector of the i-th UAV;

[0102] The dynamic model expression of the virtual navigator is:

[0103]

[0104] Among them, p 0 =[x 0 ,y 0 ,z 0 ] T , and u 0 =[u 0,x ,u 0,y ,u 0,z ] T ∈R 3 They represent the position vector, velocity vector and position control input vector of the virtual navigator respectively.

[0105] In step S2, a predefined time state observer is constructed for each quadrotor drone so that each drone in the formation system can obtain the position and speed state information of the virtual navigator within a predefined time. The process is as follows:

[0106] Design the predefined time state observer as:

[0107]

[0108] Where j = 1, 2, ..., N, j represents the jth UAV, and j ≠ i; η ∈ (0, 1); and denotes the position and velocity estimates of the virtual navigator by the i-th UAV and the j-th UAV, respectively, and γ ≥ 0 is u 0 The known upper bound of ij represents the communication connection between the i-th UAV and the j-th UAV, b i Represents the communication connection between the i-th UAV and the virtual leader; defines n represents the vector dimension, λ min (H) is the minimum eigenvalue of the Laplace matrix H; the control parameter α 1 , α 2 , β 1 , β 2 It can be expressed as and T c1 and T c2 are the upper bounds of the convergence time of the pre-set observer velocity and position observation errors; the function sig 1-η (·)=[|· 1 | 1-η sign(· 1 ),..,|· n | 1-η sign(· n )] T , ·∈R, sign(·) is the sign function, sig(·) is the vector form of sign(·);

[0109] The observation error of the predefined time state observer is defined as: Then the observation error vector of position and velocity is: The observation error of the predefined time state observer is further obtained as:

[0110]

[0111] Among them, 1 N represents the N-dimensional unit column vector, represents the Kronecker product.

[0112] In step S3, the position sliding surface and attitude sliding surface of each quadrotor drone are designed, and the process is as follows:

[0113] According to the estimated value of formula (5), the trajectory tracking error of the i-th quadrotor drone is defined as:

[0114]

[0115] Among them, e i,x and e i,v represents the tracking error of the position and velocity of the virtual navigator by the i-th UAV, h i represents the expected relative distance between the i-th UAV and the virtual navigator;

[0116] By taking the derivative of formula (7), we can get:

[0117]

[0118] in, and represents the tracking error derivative of the position and velocity of the virtual navigator of the i-th UAV;

[0119] Due to the coupling relationship between the attitude system and the position system of the quadrotor drone, the position control input u i =[u i,x ,u i,y ,u i,z ] T The desired attitude angle can be generated as follows:

[0120]

[0121] Among them, ψ i is the yaw angle of the drone, ψ i =ψ 0 , ψ 0 is the yaw angle of the known virtual navigator;

[0122] Taking the roll angle of the i-th quadrotor drone as an example, we first define the attitude angle tracking error as:

[0123]

[0124] Among them, e i,φ represents the error between the actual roll angle and the expected roll angle of the i-th UAV;

[0125] By taking the derivative of formula (10), we can get:

[0126]

[0127] in, represents the error derivative between the actual roll angle and the expected roll angle of the i-th UAV; represents the angular velocity of the desired roll angle of the i-th UAV;

[0128] Based on e i,x , e i,v and e i,φ , Design the position and attitude sliding surface of the i-th quadrotor drone as

[0129]

[0130] Among them, T c4 It is the upper bound of the convergence time of the preset UAV trajectory tracking error and attitude tracking error.

[0131] In step S4, the predefined time position controller and attitude controller are designed to ensure that each quadrotor drone in the formation system can accurately track the desired trajectory and desired attitude within the predefined time, that is, form the desired formation formation, and the process is as follows:

[0132]

[0133] Among them, T c3 is the upper bound of the convergence time of the preset position sliding surface and attitude sliding surface, σ i,p and σ i,a is the known upper bound of the external interference to the drone’s position system and attitude system. is the angular acceleration of the desired roll angle of the i-th UAV;

[0134] First, we prove that the velocity observation error vector v e At the predefined time T c1 The inner convergence is zero, and the Lyapunov function is designed as:

[0135]

[0136] Taking the derivative of equation (14) and substituting the second equation of equation (6) into it, we can obtain:

[0137]

[0138] Formula (15) complies with , then determine v e At a predefined time T c1 Inner convergence;

[0139] Then it is proved that the position observation error vector x e At the predefined time T c2The inner convergence is zero, and the Lyapunov function is designed as:

[0140]

[0141] From formula (15), we know that at the predefined time T c1 Inner e converges to zero, then when t ≥ T c1 When , the first equation of formula (6) can be simplified to: Taking the derivative of equation (16) and substituting the first equation of equation (6) into it, we can obtain:

[0142]

[0143] Formula (17) complies with , then determine x e At a predefined time T c2 Inner convergence; Based on the above analysis, when t≥T c1 +T c2 When the virtual navigator is in flight, each quadrotor drone can accurately obtain the position and speed information of the virtual navigator;

[0144] It is proved below that the position sliding surface and the attitude sliding surface are in the predefined time T c3 Inner convergence, the Lyapunov function is designed as:

[0145]

[0146] Deriving equation (18) and substituting equation (13) into it, we can obtain:

[0147]

[0148] Formula (19) complies with , then determine s i,p and i,φ At a predefined time T c3 Inner convergence; when t ≥ T c1 +T c2 +T c3 When i,p ≡0,s i,φ ≡0, (12) can be rewritten as:

[0149]

[0150] Then we prove that the position tracking error e i,x and attitude tracking error e i,φ At a predefined time T c4 Inner convergence, the Lyapunov function is designed as:

[0151]

[0152] Deriving equation (21) and substituting equation (20) into it, we can obtain:

[0153]

[0154] Formula (22) complies with , then determine e i,x and e i,φ At a predefined time T c4 Inner convergence;

[0155] Based on the above analysis, we can see that when t≥T c1 +T c2 +T c3 +T c4 When the sliding surface and tracking error converge within the predefined time, each quadrotor UAV can accurately track the desired trajectory and desired attitude within the predefined time.

[0156] In order to verify the effectiveness of the proposed control method, numerical simulation is performed through MATLAB. We assume that the multi-quadrotor UAV formation system contains two quadrotor UAVs and a virtual navigator. The initial state and control parameters of the relevant system are designed as follows:

[0157] The initial values ​​of the position, speed, and attitude angle of the two quadrotor drones are: 1 =[5,2,0] T , p 2 =[1,2,0] T , v 1 =[0,0,0] T , v 2 =[0,0,0] T ,φ 1 =0.1,θ 1 =0.1,ψ 1 =0.1,φ 2 =-0.1,θ 2 =0.1,ψ 2 =0.1; the motion trajectory and yaw angle of the virtual navigator are: p 0 =[4sin(0.1t),4cos(0.1t),1+0.6t] T , ψ 0 =0; the relevant model parameters are designed as: m 1 =0.5, m 2 =0.5, g=9.8, J xx =1.5×10 -2 , J yy =2.5×10 -2 , J zz =2.8×10 -2; The relevant control parameters are designed as: η = 0.2, γ = 0.1; In addition, we select different pre-set convergence times T c1 , T c2 , T c3 , T c4 Used to verify whether the state observation error and the time to form the expected formation can be achieved as expected.

[0158] Case 1: T c1 =1s, T c2 =1s, T c3 =2s, T c4 =5s.

[0159] from Figure 2 and Figure 3 We can see that the information estimation errors of the state observer designed for the two quadrotor drones for the position and velocity of the virtual navigator converge at about 0.06 seconds and 0.1 seconds, respectively, which are less than the preset convergence time. This shows that the drone can obtain the state information of the virtual navigator within the preset time; Figure 4 and Figure 5 Schematic diagram of the tracking error of two UAVs for the desired position and desired attitude. Figure 6 and Figure 7 Schematic diagram of the position control input and attitude control input of the two UAVs. The position tracking error and attitude tracking error converge in about 2 seconds and 3 seconds respectively, which shows that the designed position controller and attitude controller can ensure that the multi-quadrotor UAV can achieve the desired performance within the preset time t = T c1 +T c2 +T c3 +T c4 =The desired formation is formed within 9s.

[0160] Case 2: T c1 =0.4s, T c2 =0.6s, T c3 =1s, T c4 =3s.

[0161] from Figure 8 and Fig. 9 We can see that the information estimation errors of the state observer on the virtual navigator's position and velocity converge at about 0.02 seconds and 0.04 seconds, respectively, which are less than the preset convergence time; Fig.10 and Fig.11 Schematic diagram of the tracking error of two UAVs for the desired position and desired attitude. Fig.12 and Fig.13The schematic diagram of the position control input and attitude control input of the two UAVs shows that the position tracking error and attitude tracking error converge in about 1 second and 1.5 seconds respectively, which is less than the preset upper limit of the convergence time t = T c1 +T c2 +T c3 +T c4 =5s.

[0162] In summary, by setting different convergence time parameters, it can be seen that the control method designed this time can solve the problems of difficulty for UAVs in obtaining virtual navigator information in the formation system and inability to pre-set the formation time in advance.

[0163] It is known from common technical knowledge that the present invention can be implemented by other embodiments that do not deviate from its spirit or essential features. Therefore, the above disclosed embodiments are only illustrative in all respects and are not exclusive. All changes within the scope of the present invention or within the scope equivalent to the present invention are included in the present invention.

Claims

1. A predefined time multi-quadrotor UAV formation control method based on an observer, characterized in that: The following steps are involved: S1. Establish the position and attitude dynamics model of the multi-quadrotor UAV, initialize the system state, sampling time and control parameters; S2, build a predefined time state observer for each quadrotor drone; S3. Design the position sliding surface and attitude sliding surface of each quadrotor drone; S4, designing a predefined time position controller and a posture controller; S5. Control the corresponding quadrotor drone according to the designed position controller and attitude controller to achieve the desired formation.

2. The observer-based predefined time multi-quadrotor UAV formation control method according to claim 1, characterized in that: In step S1, the position and attitude dynamics model of the multi-quadrotor UAV system is expressed as: Where i = 1, 2, .., N, i represents the i-th drone, N represents the number of drones; x i ,y i and z i represents the position of the i-th UAV in the inertial coordinate system; and are the accelerations along the x-axis, y-axis and z-axis in the inertial coordinate system; m i represents the mass of the drone; g represents the acceleration due to gravity; T i Indicates the lift generated by the rotor; φ i ,θ i and ψ i Respectively represent the three attitude angles of the i-th UAV: ​​roll angle, pitch angle and yaw angle; and are the angular velocities of roll, pitch and yaw respectively; and are the angular accelerations of roll angle, pitch angle and yaw angle respectively; J xx , J yy and J zz is the moment of inertia; d i,x , d i,y and d i,z Respectively represent the i-th drone at x i ,y i and z i External disturbance in direction, d i,φ , d i,θ and d i,ψ Respectively represent the i-th UAV in φ i ,θ i and ψ i External disturbance in direction; τ i,φ , τ i,θ and τ i,ψ Represent the control inputs of the roll angle, pitch angle and yaw angle channels respectively; Simplify equation (1) into the following second-order nonlinear system: Among them, p i =[x i ,y i ,z i ] T , u i =[u i,x ,u i,y ,u i,z ] T and d i,p =[d i,x ,d i,y ,d i,z ] T ∈R 3 Respectively represent the position vector, velocity vector, position control input vector and external disturbance vector of the i-th UAV; The dynamic model expression of the virtual navigator is: Where p0 = [x0, y0, z0] T , and u0=[u 0,x ,u 0,y ,u 0,z ] T ∈R 3 They represent the position vector, velocity vector and position control input vector of the virtual navigator respectively.

3. The method for controlling a multi-quadrotor UAV formation at a predefined time based on an observer according to claim 2, characterized in that: In step S2, a predefined time state observer is constructed for each quadrotor drone, and the process is as follows: Design the predefined time state observer as: Where j = 1, 2, ..., N, j represents the jth UAV, and j ≠ i; η ∈ (0, 1); and denote the estimates of the position and velocity of the virtual navigator by the i-th UAV and the j-th UAV respectively, and γ ≥ 0 is the known upper bound of u0; a ij represents the communication connection between the i-th UAV and the j-th UAV, b i Represents the communication connection between the i-th UAV and the virtual leader; defines n represents the vector dimension, λ min (H) is the minimum eigenvalue of the Laplace matrix H; the control parameters α1, α2, β1, β2 can be expressed as and T c1 and T c2 are the upper bounds of the convergence time of the pre-set observer velocity and position observation errors; the function sig 1-η (·)=[|·1| 1-η sign(·1),..,|· n | 1-η sign(· n )] T , ·∈R, sign(·) is the sign function, sig(·) is the vector form of sign(·); The observation error of the predefined time state observer is defined as: Then the observation error vector of position and velocity is: The observation error of the predefined time state observer is further obtained as: Among them, 1 N represents the N-dimensional unit column vector, represents the Kronecker product.

4. The method for controlling a multi-quadrotor UAV formation at a predefined time based on an observer according to claim 3, characterized in that: In step S3, the position sliding surface and attitude sliding surface of each quadrotor drone are designed, and the process is as follows: According to the estimated value of formula (5), the trajectory tracking error of the i-th quadrotor drone is defined as: Among them, e i,x and e i,v represents the tracking error of the position and velocity of the virtual navigator by the i-th UAV, h i represents the expected relative distance between the i-th UAV and the virtual navigator; By taking the derivative of formula (7), we can get: in, and represents the tracking error derivative of the position and velocity of the virtual navigator of the i-th UAV; Due to the coupling relationship between the attitude system and the position system of the quadrotor drone, the position control input u i =[u i,x ,u i,y ,u i,z ] T The desired attitude angle can be generated as follows: Among them, ψ i is the yaw angle of the drone, ψ i =ψ0, ψ0 is the known yaw angle of the virtual navigator; Taking the roll angle of the i-th quadrotor drone as an example, we first define the attitude angle tracking error as: Among them, e i,φ represents the error between the actual roll angle and the expected roll angle of the i-th UAV; By taking the derivative of formula (10), we can get: in, represents the error derivative between the actual roll angle and the expected roll angle of the i-th UAV; represents the angular velocity of the desired roll angle of the i-th UAV; Based on e i,x , e i,v and e i,φ , Design the position and attitude sliding surface of the i-th quadrotor drone as Among them, T c4 It is the upper bound of the convergence time of the preset UAV trajectory tracking error and attitude tracking error.

5. The observer-based predefined time multi-quadrotor UAV formation control method according to claim 4, characterized in that: In step S4, a predefined time position controller and a posture controller are designed, and the process is as follows: Among them, T c3 is the upper bound of the convergence time of the preset position sliding surface and attitude sliding surface, σ i,p and σ i,a is the known upper bound of the external interference to the drone’s position system and attitude system. is the angular acceleration of the desired roll angle of the i-th UAV; First, we prove that the velocity observation error vector v e At the predefined time T c1 The inner convergence is zero, and the Lyapunov function is designed as: Taking the derivative of equation (14) and substituting the second equation of equation (6) into it, we can obtain: Formula (15) complies with , then determine v e At a predefined time T c1 Inner convergence; Then it is proved that the position observation error vector x e At the predefined time T c2 The inner convergence is zero, and the Lyapunov function is designed as: From formula (15), we know that at the predefined time T c1 Inner e converges to zero, then when t ≥ T c1 When , the first equation of formula (6) can be simplified to: Taking the derivative of equation (16) and substituting the first equation of equation (6) into it, we can obtain: Formula (17) complies with , then determine x e At a predefined time T c2 Inner convergence; Based on the above analysis, when t≥T c1 +T c2 When the virtual navigator is in flight, each quadrotor drone can accurately obtain the position and speed information of the virtual navigator; It is proved below that the position sliding surface and the attitude sliding surface are in the predefined time T c3 Inner convergence, the Lyapunov function is designed as: Deriving equation (18) and substituting equation (13) into it, we can obtain: Formula (19) complies with , then determine s i,p and i,φ At a predefined time T c3 Inner convergence; when t ≥ T c1 +T c2 +T c3 When i,p ≡0,s i,φ ≡0, (12) can be rewritten as: Then we prove that the position tracking error e i,x and attitude tracking error e i,φ At a predefined time T c4 Inner convergence, the Lyapunov function is designed as: Deriving equation (21) and substituting equation (20) into it, we can obtain: Formula (22) complies with , then determine e i,x and e i,φ At a predefined time T c4 Inner convergence; Based on the above analysis, we can see that when t≥T c1 +T c2 +T c3 +T c4 When the sliding surface and tracking error converge within the predefined time, each quadrotor UAV can accurately track the desired trajectory and desired attitude within the predefined time.

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