CN109324636A - Master-slave cooperative formation control method for multiple quadrotors based on second-order consistency and active disturbance rejection - Google Patents

Abstract

The invention discloses a multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection. Aiming at the problems of geometric formation generation, stable maintenance and cooperative anti-interference during multi-quadrotor formation flight, a multi-quadrotor master-slave cooperative formation control method is proposed, which can cope with external environmental interference and aerodynamic parameter uncertainty. First, Establish the quadrotor kinematics/dynamics model with external disturbances; secondly, design the multi-quadrotor master-slave communication topology and formation pattern as well as the position and speed information of the leader; then, construct the multi-quadrotor distributed position keeping controller, The necessary desired commands are provided for the subsequent attitude controller construction; finally, a multi-quadrotor attitude tracking controller based on ADRC is constructed. The proposed formation control method can significantly improve the anti-jamming capability of the quadrotor formation system under the premise of local agent communication, and improve the stability of the multi-quadrotor formation geometry in the interference environment.

Description

Master-slave cooperative formation control of multiple quadrotors based on second-order consistency and active disturbance rejection method

technical field

The invention relates to the navigation and guidance direction, the field of multi-quadrotor formation, in particular to a multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection, which is mainly applied to external disturbances and parameter uncertainties. Multiple quadrotor formation missions.

Background technique

The multi-rotor cooperative formation refers to the multi-rotor maintaining the predetermined spatial geometric topology, with the help of global or local information interaction and sharing, to realize the group aggregation behavior of the multi-rotor system, forming the collaborative transcendence ability of the multi-agent system, for the execution of the multi-rotor system. Provide effective solutions to complex tasks that a single unit cannot handle. For example, multi-rotors can use reasonable formation flight instead of soldiers to perform military tasks such as target reconnaissance and enemy information collection in harsh and dangerous environments. It has important military/civilian dual-use research value and urgent practical significance to solve the disadvantages of incomplete and insufficient timeliness in obtaining environmental information.

As one of the application examples of the cooperative control theory of multi-agent systems, multi-quadrotor cooperative formation control is more challenging in controller construction and synthesis than the formation of two-degree-of-freedom moving bodies such as unmanned vehicles and unmanned ships. It is manifested in: (1) The quadrotor itself is an underactuated and strongly nonlinear multi-input multi-output six-degree-of-freedom system. In order to ensure the stability of the formation geometric formation, the position and speed of each quadrotor must be made during the formation flight. The coordinating variables tend to be consistent. However, most of the current multi-agent consistency theories are developed for low-order, linear and other ideal particle kinematic models, which cannot be directly applied to the multi-quadrotor formation system model; (2) The aerodynamic parameters of the quadrotor are limited by the lack of corresponding measurements Instruments cannot be accurately obtained, which brings large parameter uncertainties to the model. In addition, the quadrotor is inevitably affected by the unknown external wind disturbance during the space flight. The above factors bring difficulties to the formation of the quadrotor to maintain the structure of the anti-jamming controller. Therefore, it is urgent to construct a multi-quadrotor cooperative formation control method with strong robustness that is suitable for the typical dynamic characteristics of quadrotors while considering the constraints of formation geometry, parameter uncertainty and external disturbances.

SUMMARY OF THE INVENTION

In order to solve the problems of geometric formation generation, stable maintenance and cooperative anti-interference in the process of multi-quadrotor formation flight, the present invention provides a second-order consistency and active anti-interference based on the pilot-follower cooperative control strategy. Multi-quadrotor master-slave cooperative formation control method.

The present invention is achieved through the following technical solutions: a multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection, comprising the following steps:

(1) Establish a quadrotor kinematics/dynamics model with external disturbances;

(2) Using the knowledge of algebraic graph theory, design the multi-quadcopter master-slave communication topology and formation style, as well as the position and speed information of the leader;

(3) According to the quadrotor kinematics model established in step (1) and the multi-quadrotor communication topology and formation pattern in step (2), as well as the position and speed information of the leader, construct a structure that is suitable for the master-slave formation task and has The multi-quadrotor distributed position-keeping controller with asymptotic convergence capability provides desired instructions for subsequent attitude controller construction;

(4) According to the quadrotor dynamics model established in step (1) and the attitude expectation command generated in step (3), construct a multi-quadrotor attitude tracking controller based on active disturbance rejection control.

The multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection provided by the present invention is specifically introduced into the quadrotor trajectory loop by introducing second-order consistency theory, combined with algebraic graph theory and communication topology, to achieve The position of the leader is used as the geometric center of the dynamic formation, and the problem of generating and maintaining the desired geometric formation of the multi-rotor is transformed into the control problem of the relative position deviation between the position consistency tracking of the slave and the leader, so as to construct a multi-quad with asymptotic convergence ability. Rotor distributed position keeping controller; for the parameter uncertainty and external disturbance of the attitude loop, the idea of ADRC is used for reference, and the parameter uncertainty and external disturbance are regarded as lumped disturbance, and the extended state observer is used to conduct online analysis on it. Observation and compensation to achieve high-precision tracking control for a given attitude.

In the above steps: the quadrotor kinematics/dynamic model in step (1) is as follows:

Define the set of quadrotor formation numbers Γ=(1,2,...,n), i∈Γ, and give the kinematics/dynamic model of the i-th quadrotor in the formation composed of n quadrotors:

Where: m _i is the mass of the i-th quadrotor, t is time, G _i =[0,0,m _i g] ^T , g is the acceleration of gravity, J _i =diag(J _i,1 ,J _i,2 ,J _i,3 )∈R ^3×3 represents a positive definite diagonal inertia matrix, J _i,1 , J _i,2 , J _i,3 are the x,y edges of the i-th quadrotor in the body coordinate system, respectively , moment of inertia of the z-axis; g _1,i =[c(ψ _i )s(θ _i )c(φ _i )+s(ψ _i )s(φ _i ),s(ψ _i )s(θ _i ) c(φ _i )-c(ψ _i )s(φ _i ),c(θ _i )c(φ _i )] ^T represents the position loop input matrix related to attitude, s( ) and c( ) represent respectively sine and cosine functions;

p _i =[x _i ,y _i ,z _i ] ^T ,Θ _i =[φ _i ,θ _i ,ψ _i ] ^T represents the position vector of the i-th quadrotor in the inertial coordinate system and the position vector in the body coordinate system, respectively _{Attitude angle of ; _ _ _ _} is the air damping matrix of the i-th quadrotor position and attitude loop, k _r,i ∈ R, is the air damping coefficient of the i-th quadrotor; τ _i =[τ _x,i τ _y,i τ _z,i ] ^T is the three control moments around the x, y, z axes of the body, and the control input u _i ∈R is the pulling force of the _i -th quadrotor; g _{2,i =} diag(li ,li , _ci )∈R ^3×3 , where li is the geometric distance from the propeller to the _quadrotor ’s center of mass, _ci is the moment coefficient, d _Θ,i (t)=[d _φ,i ,d _θ,i ,d _ψ,i ] ^T represents the bounded external disturbance in the attitude loop;

In order to facilitate the construction of the subsequent position controller and attitude controller, the following symbol definitions are introduced:

Among them, F _i =[F _i,x ,F _i,y ,F _i,z ] ^T ∈R ^3×1 represents the virtual control input, d _4,i is the lumped disturbance of the attitude loop, including external disturbance and parameters The combined effect of uncertainty, δ _1,i and δ _2,i are the parametric uncertainty matrix of the i-th quadrotor, are the nominal values of Π _2,i and g _2,i respectively;

With the help of the above intermediate variables, the quadrotor motion/dynamic model (1) is rewritten into the following strict feedback form:

In step (2), the multi-quadrotor communication topology and formation style, as well as the position and speed information of the leader are as follows: The quadrotor formation adopts a master-slave structure, and the leader is defined as a node numbered 0, and each slave is in turn. are _numbered ¹ , . ^×n is the adjacency weight matrix; if the quadrotor i and the quadrotor j are connected, then a _ij =a _ji >0, otherwise a _ij =a _ji =0, in addition, define a _ii =0; The connectivity weight between the two is represented by b _i , if the i-th slave can directly obtain the leader information, then b _i > 0, otherwise b _i =0;

Define the navigator as the geometric center of the multi-quadcopter formation style, that is, the origin of the formation style coordinates. According to the expected formation geometry, design the position vector Δ _i = [Δ _{i, x} ,Δ _i,y ,Δ _i,z ] ^T and Δ _j =[Δ _j,x ,Δ _j,y ,Δ _j,z ] ^T , the relative position deviation between the i-th and j-th slaves can be calculated by Δ _ij =Δ _i -Δ _j =[Δ _i,x ,Δ _i,y ,Δ _i,z ] ^T -[Δ _j,x ,Δ _j,y ,Δ _j,z ] ^T =[Δ _ij,x , _Δij,y , _Δij,z ] ^T description;

The trajectory motion information of the leader can be generated by the following formula:

Among them, x ^d , y ^d , and z ^d are the position components of the navigator along the x, y, and z axes in the inertial coordinate system, respectively, are the velocity components of the pilot along the x, y, and z axes in the inertial coordinate system, respectively.

The multi-quadrotor distributed position keeping controller of step (3) is as follows:

According to the multi-quadrotor master-slave formation communication topology and the expected leader trajectory information, combined with the multi-agent second-order consistency principle, the following virtual control input (Fi _,x ,Fi _,y ,Fi _,z ) ^T is constructed:

Among them, k ₁ and k ₂ represent the controller parameters to be designed, and N _i represents the set of quadrotors with direct communication connection with the i-th quad-rotor, _xi is the position component of the i-th quad-rotor along the x-axis in the inertial coordinate system, x _j is the j-th quad-rotor along the x-axis Position component, v _i,x is the velocity component of the i-th quadrotor along the x-axis in the inertial coordinate system, v _j,x is the velocity component of the j-th quadrotor along the x-axis in the inertial coordinate system;

On the basis of obtaining the above virtual control input (Fi _,x ,Fi _,y ,Fi _,z ) ^T , and combining formula (2) for inverse dynamics solution, the following desired attitude angle command can be obtained

Among them, _ui is the expected pulling force of the quadrotor UAV, are the desired roll angle, pitch angle and yaw angle in the body coordinate system, respectively.

Step (4) The details of the multi-quadrotor attitude tracking controller are as follows:

in, is the positive proportional gain of the controller, k _d =2w _c is the positive differential gain of the controller, and w _c is the controller bandwidth of the attitude loop; is an estimate of the aggregate disturbance of the attitude loop, which can be given by the following model-aided expanded state observer that only depends on the control input torque and attitude angle measurement output:

where z _1,i is an estimate of x _3,i , z _2,i is an estimate of x _4,i , and z _3,i is an estimate of , w _o is the attitude loop observer bandwidth.

Compared with the prior art, the present invention has the following beneficial effects: Unlike most current multi-agent consistency theories that only consider low-order linear models, the present invention fully considers the six-degree-of-freedom nonlinearity and strong coupling of the quadrotor. Kinematics/dynamic model; for formation geometry constraints and parameter uncertainty and external disturbances, an anti-jamming controller for the quadrotor attitude loop is constructed, and the position keeping control and attitude tracking control of multi-quadrotor formations are solved It can greatly improve the anti-jamming capability of the quadrotor formation system, and improve the stability of the multi-quadrotor formation geometry in the interference environment, which is of great significance for enriching and developing the theory of multi-agent cooperative control.

Description of drawings

FIG. 1 is a control block diagram of a multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection of the present invention.

Figure 2 shows the communication topology and formation pattern of a multi-quadrotor formation with the navigator as the coordinate origin.

Figure 3 is the projection of the multi-quadrotor formation movement trajectory on the x-y plane in the inertial coordinate system.

Figure 4 is the position response and adjacent distance change curves of each quadrotor.

Figure 5 is the attitude angle response curve of each quadrotor.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

A multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection, as shown in Figure 1, includes the following steps:

(1) Establish a quadrotor kinematics/dynamics model with external interference: the details are as follows:

Define the set of quadrotor formation numbers Γ=(1,2,...,n), i∈Γ, and give the kinematics/dynamic model of the i-th quadrotor in the formation composed of n quadrotors:

Where: m _i is the mass of the i-th quadrotor, t is time, G _i =[0,0,m _i g] ^T , g is the acceleration of gravity, J _i =diag(J _i,1 ,J _i,2 ,J _i,3 )∈R ^3×3 represents a positive definite diagonal inertia matrix, J _i,1 , J _i,2 , J _i,3 are the x,y edges of the i-th quadrotor in the body coordinate system, respectively , moment of inertia of the z-axis; g _1,i =[c(ψ _i )s(θ _i )c(φ _i )+s(ψ _i )s(φ _i ),s(ψ _i )s(θ _i ) c(φ _i )-c(ψ _i )s(φ _i ),c(θ _i )c(φ _i )] ^T represents the position loop input matrix related to attitude, s( ) and c( ) represent respectively sine and cosine functions;

p _i =[x _i ,y _i ,z _i ] ^T ,Θ _i =[φ _i ,θ _i ,ψ _i ] ^T represents the position vector of the i-th quadrotor in the inertial coordinate system and the position vector in the body coordinate system, respectively _{Attitude angle of ; _ _ _ _} is the air damping matrix of the i-th quadrotor position and attitude loop, k _r,i ∈ R, is the air damping coefficient of the i-th quadrotor; τ _i =[τ _x,i τ _y,i τ _z,i ] ^T is the three control moments around the x, y, z axes of the body, and the control input u _i ∈R is the pulling force of the _i -th quadrotor; g _{2,i =} diag(li ,li , _ci )∈R ^3×3 , where li is the geometric distance from the propeller to the _quadrotor ’s center of mass, _ci is the moment coefficient, d _Θ,i (t)=[d _φ,i ,d _θ,i ,d _ψ,i ] ^T represents the bounded external disturbance in the attitude loop;

In order to facilitate the construction of the subsequent position controller and attitude controller, the following symbol definitions are introduced:

Among them, F _i =[F _i,x ,F _i,y ,F _i,z ] ^T ∈R ^3×1 represents the virtual control input, d _4,i is the lumped disturbance of the attitude loop, including external disturbance and parameters The combined effect of uncertainty, δ _1,i and δ _2,i are the parametric uncertainty matrix of the i-th quadrotor, are the nominal values of Π _2,i and g _2,i respectively;

With the help of the above intermediate variables, the quadrotor motion/dynamic model (1) is rewritten into the following strict feedback form:

(2) Using the knowledge of algebraic graph theory, design the multi-quadcopter master-slave communication topology and formation style, as well as the position and speed information of the leader, as follows:

The quadrotor formation adopts a master-slave structure, which defines the leader as a node numbered 0, and each slave is numbered 1,...,n in turn; the communication topology between the quadrotors can be used as an undirected graph G={V, E, A} represents; V is the node set, E is the edge set, A=[a _ij ]∈R ^n×n is the adjacency weight matrix; if the quadrotor i and the quadrotor j are connected, then a _ij =a _ji >0 , otherwise a _ij = a _ji = 0, in addition, define a _ii = 0; the connection weight between the leader and the slave i is represented by b _i , if the i-th slave can directly obtain the leader information, then b _i >0, otherwise _bi = 0;

Define the navigator as the geometric center of the multi-quadcopter formation style, that is, the origin of the formation style coordinates. According to the expected formation geometry, design the position vector Δ _i = [Δ _{i, x} ,Δ _i,y ,Δ _i,z ] ^T and Δ _j =[Δ _j,x ,Δ _j,y ,Δ _j,z ] ^T , the relative position deviation between the i-th and j-th slaves can be calculated by Δ _ij =Δ _i -Δ _j =[Δ _i,x ,Δ _i,y ,Δ _i,z ] ^T -[Δ _j,x ,Δ _j,y ,Δ _j,z ] ^T =[Δ _ij,x , _Δij,y , _Δij,z ] ^T description;

The trajectory motion information of the leader can be generated by the following formula:

Among them, x ^d , y ^d , and z ^d are the position components of the navigator along the x, y, and z axes in the inertial coordinate system, respectively, are the velocity components of the pilot along the x, y, and z axes in the inertial coordinate system, respectively.

(3) According to the quadrotor kinematics model established in step (1) and the multi-quadrotor communication topology and formation pattern in step (2), as well as the position and speed information of the leader, construct a structure that is suitable for the master-slave formation task and has The multi-quadrotor distributed position-holding controller with asymptotic convergence capability provides desired instructions for the subsequent construction of the attitude controller: the multi-quadrotor distributed position-holding controller is as follows:

According to the multi-quadrotor master-slave formation communication topology and the expected leader trajectory information, combined with the multi-agent second-order consistency principle, the following virtual control input (Fi _,x ,Fi _,y ,Fi _,z ) ^T is constructed:

Among them, k ₁ and k ₂ represent the controller parameters to be designed, and N _i represents the set of quadrotors with direct communication connection with the i-th quad-rotor, _xi is the position component of the i-th quad-rotor along the x-axis in the inertial coordinate system, x _j is the j-th quad-rotor along the x-axis Position component, v _i,x is the velocity component of the i-th quadrotor along the x-axis in the inertial coordinate system, v _j,x is the velocity component of the j-th quadrotor along the x-axis in the inertial coordinate system;

On the basis of obtaining the above-mentioned virtual control input (Fi _,x ,Fi _,y ,Fi _,z ) ^T , combined with formula (2) for inverse dynamics solution, the following desired attitude angle command can be obtained

Among them, _ui is the expected pulling force of the quadrotor UAV, are the desired roll angle, pitch angle and yaw angle in the body coordinate system, respectively.

(4) According to the quadrotor dynamics model established in step (1) and the attitude expectation command generated in step (3), construct a multi-quadrotor attitude tracking controller based on active disturbance rejection control: step (4) multi-quadrotor attitude The tracking controller is as follows:

in, is the positive proportional gain of the controller, k _d =2w _c is the positive differential gain of the controller, and w _c is the controller bandwidth of the attitude loop; is an estimate of the aggregate disturbance of the attitude loop, which can be given by the following model-aided expanded state observer that only depends on the control input torque and attitude angle measurement output:

where z _1,i is an estimate of x _3,i , z _2,i is an estimate of x _4,i , and z _3,i is an estimate of , w _o is the attitude loop observer bandwidth.

Example:

In order to evaluate the performance of the constructed controller, the quadrotor kinematics/dynamics model described by equation (1) is used for simulation. The parameters of the quadrotor kinematics/dynamics model are shown in Table 1.

The model parameters used for controller construction are selected as follows: quadrotor mass m _i is 2kg, gravitational acceleration g is 9.8m/s ² , inertia matrix J _i =diag(J _i,1 ,J _i,2 ,J _i,3 )=diag(0.16,0.16,0.32)kgm ² , the air damping matrix Π _1,i =diag(k _x,i , _ky,i ,k _z,i )=diag(0.01,0.01,0.01)Nms ² , Air damping matrix Π _2,i =diag(k _φ,i ,k _θ,i ,k _{ψ,i )} =diag(0.01,0.01,0.01)Nms ² , the geometric distance li from the propeller to the quadrotor center of mass is 0.4 meters , the moment coefficient c _i is 0.05, and the parameter uncertainties δ _1,i and δ _2,i are respectively and

Table 1 Parameters of quadrotor kinematics/dynamics model

The communication topology and formation style of the multi-quadrotor formation considered by the present invention are shown in FIG. 2 . Obviously, the number of quadrotors participating in the formation is 5, that is, n=5. The adjacency weight coefficients of the undirected graph are as follows: a ₁₂ =a ₂₁ =1, a ₂₃ =a ₃₂ =1, a ₃₄ =a ₄₃ =1, b ₁ =1. In order to facilitate the analysis, the square determined in the xy plane of the inertial coordinate system is selected as the formation pattern, and the side length is 2 meters, and the leader is the geometric center of the formation pattern, so the position vector of the slave relative to the leader is: Δ ₁ = [1,1,0] ^T , Δ ₂ =[-1,1,0] ^T ,Δ ₃ =[-1,-1,0] ^T ,Δ ₄ =[1,-1,0] ^T . The trajectory of the leader is set as: (x ^d , y ^d , z ^d ) ^T = (0.5t, 5cos(0.2t), 0.5t) ^T . The initial state of attitude angle and angular velocity of each slave is zero, and the initial state of position and velocity is designed as follows:

[x ₁ (0),y ₁ (0),z ₁ (0),v _1,x (0),v _1,y (0),v _1,z (0),]=[0.8,0, 2,0,0,0]

[ _x2 (0),y2( ₀ ),z2(0),v2 _,x (0),v2 _,y (0),v2 _,z ( ₀ ),]=[0,0.8, 5,0,0,0]

[ _x3 (0),y3(0), _z3 (0), _{v3 ,x} (0),v3 _,y (0),v3 _,z (0),]=[-0.5,0.8 ,0,0,0,0]

[ _x4 (0),y4(0), _z4 (0),v4, _x (0),v4 _,y (0),v4 _,z (0),]=[- _0.5,0 ,0.8,0,0,0]

In order to adjust the performance of the controller, the controller parameters are selected. The controller parameters are shown in Table 2.

The controller parameters are selected as follows: the position holding controller parameter k ₁ is 1.7, the position holding controller parameter k ₂ is 1.7, the attitude controller proportional gain k _p is 25, and the attitude controller differential gain k _d is 10.

Table 2 Controller parameters

In order to test the anti-interference ability of the controller, the following external disturbances are set in the quadrotor attitude loop:

The projection of the multi-quadrotor formation movement trajectory on the x-y plane in the inertial coordinate system is shown in Figure 3. It can be seen that under the action of the provided control method, even if there are unknown external disturbances and parameter uncertainties, the multi-quadrotor still remains. The desired square formation configuration can be maintained.

The position response curve of each quadrotor is shown in Figure 4. It can be seen from the figure that the trajectory status of each quadrotor maintains a good consistency within a limited time; Stable convergence, and finally consistent with the desired geometric configuration edge length of 2 meters.

The attitude angle response curve of each quadrotor is shown in Figure 5. It can be seen from the figure that despite the external interference and parameter uncertainty, the four response curves tend to be stable and consistent faster, indicating that the attitude angle response of each quadrotor is It is smooth and smooth, and eventually tends to be consistent, and the control effect is as expected.

To sum up, the following conclusions can be drawn from this embodiment: the multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection involved in the present invention is not stable in external disturbance and parameter uncertainty. Under the influence of stability, the stability of the multi-quadrotor formation can be improved, and the anti-jamming capability of the multi-quadrotor formation system can be improved.

The scope of protection of the present invention is not limited to the above specific embodiments, and for those skilled in the art, the present invention may have various modifications and changes, any modifications, improvements and equivalents made within the concept and principle of the present invention All replacements should be included within the protection scope of the present invention.

Claims (5)

1. a multi-four-rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection, is characterized in that: comprise the steps: (1) Establish a quadrotor kinematics/dynamics model with external disturbances; (2) Using the knowledge of algebraic graph theory, design the multi-quadcopter master-slave communication topology and formation style, as well as the position and speed information of the leader; (3) According to the quadrotor kinematics model established in step (1) and the multi-quadrotor communication topology and formation pattern in step (2), as well as the position and speed information of the leader, construct a structure that is suitable for the master-slave formation task and has The multi-quadrotor distributed position-keeping controller with asymptotic convergence capability provides desired instructions for subsequent attitude controller construction; (4) According to the quadrotor dynamics model established in step (1) and the attitude expectation command generated in step (3), construct a multi-quadrotor attitude tracking controller based on active disturbance rejection control. 2. the multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection according to claim 1, it is characterized in that: in described step (1), quadrotor kinematics/dynamic model is concrete as follows: Define the set of quadrotor formation numbers Γ=(1,2,...,n), i∈Γ, and give the kinematics/dynamic model of the i-th quadrotor in the formation composed of n quadrotors: Where: m _i is the mass of the i-th quadrotor, t is time, G _i =[0,0,m _i g] ^T , g is the acceleration of gravity, J _i =diag(J _i,1 ,J _i,2 ,J _i,3 )∈R ^3×3 represents a positive definite diagonal inertia matrix, J _i,1 , J _i,2 , J _i,3 are the x,y edges of the i-th quadrotor in the body coordinate system, respectively , the moment of inertia of the z-axis; represents the position loop input matrix related to the attitude, s( ) and c( ) represent the sine function and cosine function respectively; p _i =[x _i ,y _i ,z _i ] ^T ,Θ _i =[φ _i ,θ _i ,ψ _i ] ^T represents the position vector of the i-th quadrotor in the inertial coordinate system and the position vector in the body coordinate system, respectively _{Attitude angle of ; _ _ _ _} is the air damping matrix of the i-th quadrotor position and attitude loop, is the air damping coefficient of the i-th quadrotor; τ _i =[τ _x,i τ _y,i τ _z,i ] ^T is the three control moments around the x, y, z axes of the body, and the control input u _i ∈R is the pulling force of the _i -th quadrotor; g _{2,i =} diag(li ,li , _ci )∈R ^3×3 , where li is the geometric distance from the propeller to the _quadrotor ’s center of mass, _ci is the moment coefficient, d _Θ,i (t)=[d _φ,i ,d _θ,i ,d _ψ,i ] ^T represents the bounded external disturbance in the attitude loop; In order to facilitate the construction of the subsequent position controller and attitude controller, the following symbol definitions are introduced: Among them, F _i =[F _i,x ,F _i,y ,F _i,z ] ^T ∈R ^3×1 represents the virtual control input, d _4,i is the lumped disturbance of the attitude loop, including external disturbance and parameters The combined effect of uncertainty, δ _1,i and δ _2,i are the parametric uncertainty matrix of the i-th quadrotor, are the nominal values of Π _2,i and g _2,i respectively; With the help of the above intermediate variables, the quadrotor motion/dynamic model (1) is rewritten into the following strict feedback form: 3. the multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection according to claim 1, is characterized in that: described step (2) multi-quadrotor communication topology and formation pattern and pilot The position and speed information of the person are as follows: The quadrotor formation adopts a master-slave structure, which defines the leader as a node numbered 0, and each slave is numbered 1,...,n in turn; the communication topology between the quadrotors can be used as an undirected graph G={V, E, A} represents; V is the node set, E is the edge set, A=[a _ij ]∈R ^n×n is the adjacency weight matrix; if the quadrotor i and the quadrotor j are connected, then a _ij =a _ji >0 , otherwise a _ij =a _ji =0, in addition, define a _ii =0; the connection weight between the leader and the slave i is represented by b _i , if the i-th slave can directly obtain the leader information, then b _i >0, otherwise _bi = 0; Define the navigator as the geometric center of the multi-quadcopter formation style, that is, the origin of the formation style coordinates. According to the expected formation geometry, design the position vector Δ _i = [Δ _{i, x} ,Δ _i,y ,Δ _i,z ] ^T and Δ _j =[Δ _j,x ,Δ _j,y ,Δ _j,z ] ^T , the relative position deviation between the i-th and j-th slaves can be calculated by Δ _ij =Δ _i -Δ _j =[Δ _i,x ,Δ _i,y ,Δ _i,z ] ^T -[Δ _j,x ,Δ _j,y ,Δ _j,z ] ^T =[Δ _ij,x , _Δij,y , _Δij,z ] ^T description; The trajectory motion information of the leader can be generated by the following formula: Among them, x ^d , y ^d , and z ^d are the position components of the navigator along the x, y, and z axes in the inertial coordinate system, respectively, are the velocity components of the pilot along the x, y, and z axes in the inertial coordinate system, respectively. 4. the multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection according to claim 1, it is characterized in that: the multi-quadrotor distributed position keeping controller of described step (3) details as follows: According to the multi-quadrotor master-slave formation communication topology and the expected leader trajectory information, combined with the multi-agent second-order consistency principle, the following virtual control input (Fi _,x ,Fi _,y ,Fi _,z ) ^T is constructed: Among them, k ₁ and k ₂ represent the controller parameters to be designed, and N _i represents the set of quadrotors with direct communication connection with the i-th quad-rotor, _xi is the position component of the i-th quad-rotor along the x-axis in the inertial coordinate system, x _j is the j-th quad-rotor along the x-axis Position component, v _i,x is the velocity component of the i-th quadrotor along the x-axis in the inertial coordinate system, v _j,x is the velocity component of the j-th quadrotor along the x-axis in the inertial coordinate system; On the basis of obtaining the above virtual control input (Fi _,x ,Fi _,y ,Fi _,z ) ^T , and combining formula (2) for inverse dynamics solution, the following desired attitude angle command can be obtained Among them, _ui is the expected pulling force of the quadrotor UAV, are the desired roll angle, pitch angle and yaw angle in the body coordinate system, respectively. 5. the multi-quadrotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection according to claim 1, is characterized in that: described step (4) multi-quadrotor attitude tracking controller is specifically as follows: in, is the positive proportional gain of the controller, k _d =2w _c is the positive differential gain of the controller, and w _c is the controller bandwidth of the attitude loop; is an estimate of the aggregate disturbance of the attitude loop, which can be given by the following model-aided expanded state observer that only depends on the control input torque and attitude angle measurement output: where z _1,i is an estimate of x _3,i , z _2,i is an estimate of x _4,i , and z _3,i is an estimate of , w _o is the attitude loop observer bandwidth.