CN109324636A - Formation control method is cooperateed with based on second order consistency and more quadrotor master-slave modes of active disturbance rejection - Google Patents

Abstract

Formation control method is cooperateed with based on second order consistency and more quadrotor master-slave modes of active disturbance rejection the invention discloses a kind of.It generated for geometry formation during more quadrotor formation flights, consolidate holding and collaboration anti-interference problem, propose a kind of more quadrotor master-slave modes collaboration formation control method that can cope with external environment interference and pneumatic parameter uncertainty: firstly, establishing, there are the quadrotor of external disturbance kinematics/kinetic models；Secondly, designing more quadrotor master-slave communication topologys and formation pattern and the position and speed information of pilotage people；Then, more quadrotor distributed locations are constructed and keep controller, provide necessary expectation instruction for subsequent attitude controller construction；Finally, more quadrotor Attitude tracking control devices of the construction based on Active Disturbance Rejection Control.Mentioned formation control method can significantly improve the anti-interference ability of quadrotor fleet system under the premise of local intelligence body communication, promote the stability of more quadrotor formation geometric configurations under interference environment.

Description

Multi-four-rotor master-slave type cooperative formation control method based on second-order consistency and active disturbance rejection

Technical Field

The invention relates to the field of navigation guidance direction and multi-four-rotor formation, in particular to a multi-four-rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection, which is mainly applied to a multi-four-rotor formation task with external disturbance and parameter uncertainty.

Background

The multi-four-rotor cooperative formation means that the multi-four rotors realize the group gathering behavior of a multi-rotor system by keeping a preset space geometric topological form and by means of global or local information interaction and sharing, so that the cooperative exceeding capability of the multi-intelligent system is formed, and an effective solution is provided for executing complex tasks which cannot be performed by a single body. For example, the four rotors can adopt reasonable formation flying to replace soldiers to execute military tasks such as target detection, enemy situation collection and the like in severe and dangerous environments, can also be used for civil occasions such as searching and rescuing of personnel in the terrain environment of complex mountainous areas, mineral exploration and the like, can greatly make up the defects that single bodies acquire incomplete environmental information and insufficient timeliness, and has important military/civil dual-purpose research value and urgent practical significance.

The multi-four-rotor cooperative formation control is one of application examples of the multi-agent system cooperative control theory, and compared with two-degree-of-freedom moving body formation such as unmanned vehicles and unmanned ships, the controller formation control is more challenging in the aspects of controller construction and synthesis, and is represented by the following steps: (1) the four rotors are an under-actuated strong nonlinear multi-input multi-output six-degree-of-freedom system, and in order to ensure the stability of the formation geometry, the coordination variables such as the position, the speed and the like of each four rotor in the formation flight process need to be consistent. However, most of the existing multi-agent consistency theory is developed aiming at ideal point kinematics models such as low order and linearity, and cannot be directly applied to multi-four-rotor formation system models; (2) aerodynamic parameters of the four rotors are limited by the fact that corresponding measuring instruments are not available accurately, and large parameter uncertainty is brought to a model. In addition, the influence of external unknown wind disturbance cannot be avoided in the four-rotor space flight process, and the factors bring difficulty to formation of the four rotors to keep the structure of the anti-interference controller. Therefore, it is highly desirable to construct a multi-quad rotor cooperative formation control method suitable for the typical dynamics of quad rotors and having strong robustness, considering formation geometry constraints and parameter uncertainty, and external disturbances.

Disclosure of Invention

The invention provides a multi-quad rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection, aiming at solving the problems of geometric formation generation, stable maintenance and cooperative disturbance rejection in the flight process of multi-quad rotor formation and based on a pilot-follower cooperative control strategy.

The invention is realized by the following technical scheme: a multi-four-rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection comprises the following steps:

(1) establishing a four-rotor kinematic/dynamic model with external interference;

(2) designing a master-slave communication topology and a formation style of a plurality of four rotors and position and speed information of a pilot by utilizing algebraic graph theory knowledge;

(3) aiming at the four-rotor kinematic model established in the step (1), the multi-four-rotor communication topology and formation style in the step (2) and the position and speed information of a pilot, constructing a multi-four-rotor distributed position maintaining controller which is suitable for a master-slave type formation task and has asymptotic convergence capacity, and providing expected instructions for subsequent attitude controller construction;

(4) and (3) constructing a multi-quad-rotor attitude tracking controller based on active disturbance rejection control aiming at the quad-rotor dynamic model established in the step (1) and the attitude expectation command generated in the step (3).

The invention provides a multi-quad rotor master-slave type cooperative formation control method based on second-order consistency and active disturbance rejection, which is characterized in that a second-order consistency theory is introduced into a quad rotor track loop, an algebraic graph theory and a communication topology are combined, the position of a pilot is used as a geometric center of dynamic formation, and the generation and maintenance problems of the multi-quad rotor expected geometric formation are converted into the relative position deviation control problems of the position consistency tracking of the slave and the pilot, so that a multi-quad rotor distributed position maintenance controller with asymptotic convergence capability is constructed; for the parameter uncertainty and the external interference of the attitude loop, the idea of active disturbance rejection control is used for reference, the parameter uncertainty and the external interference are regarded as lumped disturbance, and an extended state observer is adopted to carry out online observation and compensation on the lumped disturbance, so that the high-precision tracking control of the given attitude is realized.

The steps are as follows: the four-rotor kinematics/dynamics model in step (1) is specifically as follows:

defining a set of four-rotor formation number Γ ═ 1,2,. and n, i ∈ Γ, giving the ith four-rotor kinematic/kinetic model in the n-frame four-rotor composition formation:

wherein: m is_iMass of the ith four rotors, t time, G_i＝[0,0,m_ig]^TG is the acceleration of gravity, J_i＝diag(J_i,1,J_i,2,J_i,3)∈R^3×3Representing a positive definite diagonal inertia matrix, J_i,1、J_i,2、J_i,3Respectively, the ith four rotors are arranged along x and y in a body coordinate systemThe 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)]^TRepresenting a position loop input matrix related to the attitude, s (-) and c (-) representing a sine function and a cosine function respectively;

p_i＝[x_i,y_i,z_i]^T,Θ_i＝[φ_i,θ_i,ψ_i]^Trespectively representing the position vector of the ith four rotors under an inertial coordinate system and the attitude angle of the ith four rotors under a machine body coordinate system; II type_1,i＝diag(k_x,i,k_y,i,k_z,i),Π_2,i＝diag(k_φ,i,k_θ,i,k_ψ,i) Air damping matrix, k, for the ith four rotor position and attitude loop, respectively_r,i∈R,Is the air damping coefficient of the ith frame quad-rotor; tau is_i＝[τ_x,iτ_y,iτ_z,i]^TControl input u for three control moments about the x, y, z axes of the machine_iE, R is the pulling force of the ith frame of four rotors; g_2,i＝diag(l_i,l_i,c_i)∈R^3×3Wherein l is_iIs the geometric distance of the propeller from the center of mass of the four rotors, c_iIs the moment coefficient, d_Θ,i(t)＝[d_φ,i,d_θ,i,d_ψ,i]^TRepresenting bounded external disturbances in the attitude loop;

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

wherein, F_i＝[F_i,x,F_i,y,F_i,z]^T∈R^3×1Representing virtual control input, d_4,iFor lumped disturbances of the attitude loop, including the combined effect of external disturbances and uncertainty of the parameters, δ_1,i、δ_2,iIs a parameterized uncertainty matrix for the ith quad-rotor,are respectively pi_2,i、g_2,iA nominal value of (d);

with the above intermediate variables, the quadrotor motion/dynamics model (1) is rewritten as a strict feedback form as follows:

in the step (2), the communication topology and formation style of the multiple four rotors and the position and speed information of the pilot are as follows: the four-rotor formation adopts a master-slave structure, the pilot is defined as a node with the number of 0, and each slave is sequentially numbered as 1, … and n; the communication topology between the four rotors can be represented by an undirected graph G ═ V, E, a }; v is node set, E is edge set, A ═ a_ij]∈R^n×nIs an adjacency weight matrix; if four rotors i and j are connected, then a_ij＝a_ji> 0, otherwise a_ij＝a_ji0, and further, definition a_ii0; communication weight reuse b between pilot and slave i_iIndicating that if the ith rack slave can directly acquire the pilot information, b_i> 0, otherwise b_i＝0；

Defining a pilot as the geometric center of a multi-four-rotor formation pattern, namely a formation pattern coordinate origin, and designing a position vector delta of an ith frame slave machine and a jth frame slave machine relative to the pilot according to a desired formation geometry_i＝[Δ_i,x,Δ_i,y,Δ_i,z]^TAnd Δ_j＝[Δ_j,x,Δ_j,y,Δ_j,z]^TThe relative position deviation between the ith frame and the jth frame slave can be represented by delta_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,Δ_ij,y,Δ_ij,z]^TDescription is given;

the navigator trajectory motion information can be generated by:

wherein x is^d、y^d、z^dThe position components of the pilot along the x, y and z axes in the inertial coordinate system,the velocity components of the pilot along the x, y, and z axes, respectively, in the inertial frame.

The multi-four-rotor distributed position maintaining controller in the step (3) is specifically as follows:

constructing the following virtual control input (F) according to multi-quad rotor master-slave formation communication topology and expected navigator track information and combining a multi-agent second-order consistency principle_i,x,F_i,y,F_i,z)^T：

Wherein k is₁、k₂Represents the parameters of the controller to be designed,and isN_iRepresenting a set of quadrotors, x, with direct communication connection with the ith frame quadrotors_iFor the i-th frame with four rotors along the x-axis under the inertial framePosition component, x_jIs the component of the position of the jth quad-rotor along the x-axis, v_i,xIs the velocity component of the ith four rotors along the x-axis under the inertial coordinate system, v_j,xThe velocity component along the x axis under the inertia coordinate system of the jth frame of the four rotors;

after obtaining the virtual control input (F)_i,x,F_i,y,F_i,z)^TOn the basis, inverse dynamics calculation is carried out by combining a formula (2), and the following expected attitude angle command can be obtained

Wherein u is_iFor the desired pull of a quad-rotor drone,respectively, a desired roll angle, a pitch angle and a yaw angle in a coordinate system of the body.

The multi-four-rotor attitude tracking controller in the step (4) is specifically as follows:

wherein,proportional gain of the controller, k, being positive_d＝2w_cPositive controller differential gain, w_cA controller bandwidth for the attitude loop;for estimation of the lumped disturbance of the attitude loop, it can be given by a model-assisted extended state observer that relies only on the control input torque and the attitude angle measurement output as follows:

wherein z is_1,iIs to x_3,iEstimate of (b), z_2,iIs to x_4,iEstimate of (b), z_3,iIs toEstimate of (a), w_oIs the attitude loop observer bandwidth.

Compared with the prior art, the invention has the following beneficial effects: different from the model that only low-order linearity is considered in most multi-agent consistency theories at present, the six-degree-of-freedom nonlinear and strong coupling kinematics/dynamics model of the four rotors is fully considered; aiming at formation geometric configuration constraint, parameter uncertainty and external interference, an anti-interference controller for a four-rotor attitude loop is constructed, the problems of position keeping control and attitude tracking control of a plurality of four-rotor formations are solved, the anti-interference capability of a four-rotor formation system can be greatly improved, the stability of the geometric configuration of the plurality of four-rotor formations in an interference environment is improved, and the anti-interference controller has important significance for enriching and developing a multi-agent cooperative control theory.

Drawings

Fig. 1 is a control block diagram of a multi-quad rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection.

Fig. 2 is a communication topology and formation style for multi-quad rotor formation with a pilot as a coordinate origin.

Fig. 3 is a projection of the motion trail of the formation of the four rotors on an x-y plane under an inertial coordinate system.

Figure 4 is a graph of position response and adjacent distance change for four rotors per frame.

Figure 5 is a response curve for attitude angle for four rotors per rack.

Detailed Description

The invention is described in further detail below with reference to the figures and specific examples.

A multi-four-rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection is disclosed, as shown in FIG. 1, and comprises the following steps:

(1) establishing a four-rotor kinematic/dynamic model with external interference: the method comprises the following specific steps:

defining a set of four-rotor formation number Γ ═ 1,2,. and n, i ∈ Γ, giving the ith four-rotor kinematic/kinetic model in the n-frame four-rotor composition formation:

wherein: m is_iMass of the ith four rotors, t time, G_i＝[0,0,m_ig]^TG is the acceleration of gravity, J_i＝diag(J_i,1,J_i,2,J_i,3)∈R^3×3Representing a positive definite diagonal inertia matrix, J_i,1、J_i,2、J_i,3The rotary inertia of the ith four rotors along the x, y and z axes under the body coordinate system; 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)]^TRepresenting a position loop input matrix related to the attitude, s (-) and c (-) representing a sine function and a cosine function respectively;

p_i＝[x_i,y_i,z_i]^T,Θ_i＝[φ_i,θ_i,ψ_i]^Trespectively representing the position vector of the ith four rotors under an inertial coordinate system and the attitude angle of the ith four rotors under a machine body coordinate system; II type_1,i＝diag(k_x,i,k_y,i,k_z,i),Π_2,i＝diag(k_φ,i,k_θ,i,k_ψ,i) Air damping matrix, k, for the ith four rotor position and attitude loop, respectively_r,i∈R,Is the air damping coefficient of the ith frame quad-rotor; tau is_i＝[τ_x,iτ_y,iτ_z,i]^TControl input u for three control moments about the x, y, z axes of the machine_iE, R is the pulling force of the ith frame of four rotors; g_2,i＝diag(l_i,l_i,c_i)∈R^3×3Wherein l is_iIs the geometric distance of the propeller from the center of mass of the four rotors, c_iIs the moment coefficient, d_Θ,i(t)＝[d_φ,i,d_θ,i,d_ψ,i]^TRepresenting bounded external disturbances in the attitude loop;

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

wherein, F_i＝[F_i,x,F_i,y,F_i,z]^T∈R^3×1Representing virtual control input, d_4,iFor lumped disturbances of the attitude loop, including the combined effect of external disturbances and uncertainty of the parameters, δ_1,i、δ_2,iIs a parameterized uncertainty matrix for the ith quad-rotor,are respectively pi_2,i、g_2,iA nominal value of (d);

with the above intermediate variables, the quadrotor motion/dynamics model (1) is rewritten as a strict feedback form as follows:

(2) by utilizing algebraic graph theory knowledge, a master-slave communication topology and a formation style of a plurality of four rotors and position and speed information of a pilot are designed, and the method specifically comprises the following steps:

the four-rotor formation adopts a master-slave structure, the pilot is defined as a node with the number of 0, and each slave is sequentially numbered as 1, … and n; the communication topology between the four rotors can be represented by an undirected graph G ═ V, E, a }; v is node set, E is edge set, A ═ a_ij]∈R^n×nIs an adjacency weight matrix; if four rotors i and j are connected, then a_ij＝a_ji> 0, otherwise a_ij＝a_ji0, and further, definition a_ii0; communication weight reuse b between pilot and slave i_iIndicating that if the ith rack slave can directly acquire the pilot information, b_i> 0, otherwise b_i＝0；

Defining a pilot as the geometric center of a multi-four-rotor formation pattern, namely a formation pattern coordinate origin, and designing a position vector delta of an ith frame slave machine and a jth frame slave machine relative to the pilot according to a desired formation geometry_i＝[Δ_i,x,Δ_i,y,Δ_i,z]^TAnd Δ_j＝[Δ_j,x,Δ_j,y,Δ_j,z]^TThe relative position deviation between the ith frame and the jth frame slave can be represented by delta_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,Δ_ij,y,Δ_ij,z]^TDescription is given;

the navigator trajectory motion information can be generated by:

wherein x is^d、y^d、z^dThe position components of the pilot along the x, y and z axes in the inertial coordinate system,the velocity components of the pilot along the x, y, and z axes, respectively, in the inertial frame.

(3) Aiming at the four-rotor kinematic model established in the step (1), the multi-four-rotor communication topology and formation style in the step (2) and the position and speed information of a pilot, constructing a multi-four-rotor distributed position maintaining controller which is suitable for a master-slave formation task and has asymptotic convergence capacity, and providing expected instructions for subsequent attitude controller construction: the multi-four-rotor distributed position holding controller is concretely as follows:

constructing the following virtual control input (F) according to multi-quad rotor master-slave formation communication topology and expected navigator track information and combining a multi-agent second-order consistency principle_i,x,F_i,y,F_i,z)^T：

Wherein k is₁、k₂Represents the parameters of the controller to be designed,and isN_iRepresenting a set of quadrotors, x, with direct communication connection with the ith frame quadrotors_iIs the position component of the ith four rotors along the x axis under the inertial coordinate system, x_jIs the component of the position of the jth quad-rotor along the x-axis, v_i,xIs the velocity component of the ith four rotors along the x-axis under the inertial coordinate system, v_j,xThe velocity component along the x axis under the inertia coordinate system of the jth frame of the four rotors;

after obtaining the virtual control input (F)_i,x,F_i,y,F_i,z)^TOn the basis, inverse dynamics calculation is carried out by combining a formula (2), and the following expected attitude angle command can be obtained

Wherein u is_iFor the desired pull of a quad-rotor drone,respectively, a desired roll angle, a pitch angle and a yaw angle in a coordinate system of the body.

(4) Aiming at the four-rotor dynamic model established in the step (1) and the attitude expectation command generated in the step (3), constructing a multi-four-rotor attitude tracking controller based on active disturbance rejection control: the multi-four-rotor attitude tracking controller in the step (4) is specifically as follows:

wherein,proportional gain of the controller, k, being positive_d＝2w_cPositive controller differential gain, w_cA controller bandwidth for the attitude loop;for estimation of the lumped disturbance of the attitude loop, it can be given by a model-assisted extended state observer that relies only on the control input torque and the attitude angle measurement output as follows:

wherein z is_1,iIs to x_3,iEstimate of (b), z_2,iIs to x_4,iEstimate of (b), z_3,iIs toEstimate of (a), w_oIs the attitude loop observer bandwidth.

Example (b):

to assess the performance of the constructed controller, simulations were performed using a four-rotor kinematics/dynamics model described by equation (1). The four-rotor kinematics/dynamics model parameters are shown in table 1.

The model parameters for the controller configuration were selected as follows: mass m of four rotors_i2kg, the acceleration of gravity g is 9.8m/s²Inertia matrix J_i＝diag(J_i,1,J_i,2,J_i,3)＝diag(0.16,0.16,0.32)kgm²Air damping matrix pi_1,i＝diag(k_x,i,k_y,i,k_z,i)＝diag(0.01,0.01,0.01)Nms²Air damping matrix pi_2,i＝diag(k_φ,i,k_θ,i,k_ψ,i)＝diag(0.01,0.01,0.01)Nms²Geometrical distance l of the propeller to the center of mass of the four rotors_i0.4 m, moment coefficient c_iIs 0.05, parameter uncertainty δ_1,i、δ_2,iAre respectively asAnd

TABLE 1 quadrotor kinematics/dynamics model parameters

The communication topology and formation pattern of the formation of multiple four rotors considered by the present invention are shown in fig. 2, and it is obvious that the number of four rotors participating in the formation is 5, that is, n is 5. The neighboring weight coefficients of the undirected graph are as follows: a is₁₂＝a₂₁＝1,a₂₃＝a₃₂＝1,a₃₄＝a₄₃＝1,b₁1. For the convenience of analysis, a square determined in an x-y plane of an inertial coordinate system is selected as a formation pattern, the side length is 2 meters, a pilot is taken as the geometric center of the formation pattern, and therefore the position vector of a slave relative to the pilot is as follows: delta₁＝[1,1,0]^T,Δ₂＝[-1,1,0]^T,Δ₃＝[-1,-1,0]^T,Δ₄＝[1,-1,0]^T. The trajectory of the pilot is set as: (x)^d,y^d,z^d)^T＝(0.5t,5cos(0.2t),0.5t)^T. The attitude angle and angular speed initial state of each slave is zero, and the position and speed initial state is designed as follows:

[x₁(0),y₁(0),z₁(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),v_2,x(0),v_2,y(0),v_2,z(0),]＝[0,0.8,5,0,0,0]

[x₃(0),y₃(0),z₃(0),v_3,x(0),v_3,y(0),v_3,z(0),]＝[-0.5,0.8,0,0,0,0]

[x₄(0),y₄(0),z₄(0),v_4,x(0),v_4,y(0),v_4,z(0),]＝[-0.5,0,0.8,0,0,0]

to adjust the performance of the controller, controller parameters are selected. The controller parameters are shown in table 2.

The controller parameters were selected as follows: position hold controller parameter k₁Is 1.7, position holding controller parameter k₂Is 1.7, the attitude controller proportional gain k_pTo 25, the attitude controller differential gain k_dIs 10.

TABLE 2 controller parameters

In order to test the interference immunity of the controller, the following external disturbances are set in the four-rotor attitude loop:

the projection of the formation motion trail of the multiple quadrotors in the inertial coordinate system on the x-y plane is shown in fig. 3, and it can be seen that under the action of the provided control method, the multiple quadrotors can still maintain the expected square formation configuration even if unknown external interference and parameter uncertainty exist.

The position response curve of each four-rotor is shown in fig. 4, and it can be seen that the track states of the four rotors keep better consistency in a limited time; in addition, the adjacent distance between the slaves can be converged quickly and stably, and finally, the side length of the slave is consistent with the side length of 2 meters of the expected geometric configuration.

The attitude angle response curve of each four rotors is shown in fig. 5, and it can be seen from the graph that although external interference and parameter uncertainty exist, the four response curves tend to be stable and consistent relatively quickly, which means that the attitude angle response of each four rotors is stable and smooth and finally tends to be consistent, and the control effect reaches the expectation.

In summary, the following conclusions can be drawn from the present embodiment: the master-slave cooperative formation control method for the multiple four rotors based on the second-order consistency and the active disturbance rejection can improve the stability of formation of the multiple four rotors and improve the disturbance rejection of a multiple four rotor formation system under the influence of external disturbance and parameter uncertainty.

The scope of the invention is not limited to the above embodiments, and various modifications and changes may be made by those skilled in the art, and any modifications, improvements and equivalents within the spirit and principle of the invention should be included in the scope of the invention.

Claims (5)

1. A master-slave type cooperative formation control method for multiple four rotors based on second-order consistency and active disturbance rejection is characterized by comprising the following steps: the method comprises the following steps:

(1) establishing a four-rotor kinematic/dynamic model with external interference;

(2) designing a master-slave communication topology and a formation style of a plurality of four rotors and position and speed information of a pilot by utilizing algebraic graph theory knowledge;

(3) aiming at the four-rotor kinematic model established in the step (1), the multi-four-rotor communication topology and formation style in the step (2) and the position and speed information of a pilot, constructing a multi-four-rotor distributed position maintaining controller which is suitable for a master-slave type formation task and has asymptotic convergence capacity, and providing expected instructions for subsequent attitude controller construction;

(4) and (3) constructing a multi-quad-rotor attitude tracking controller based on active disturbance rejection control aiming at the quad-rotor dynamic model established in the step (1) and the attitude expectation command generated in the step (3).

2. The multi-quad rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection according to claim 1, wherein the control method comprises the following steps: the four-rotor kinematic/kinetic model in the step (1) is specifically as follows:

defining a set of four-rotor formation number Γ ═ 1,2,. and n, i ∈ Γ, giving the ith four-rotor kinematic/kinetic model in the n-frame four-rotor composition formation:

wherein: m is_iMass of the ith four rotors, t time, G_i＝[0,0,m_ig]^TG is the acceleration of gravity, J_i＝diag(J_i,1,J_i,2,J_i,3)∈R^3×3Representing a positive definite diagonal inertia matrix, J_i,1、J_i,2、J_i,3The rotary inertia of the ith four rotors along the x, y and z axes under the body coordinate system;representing a position loop input matrix related to the attitude, s (-) and c (-) representing a sine function and a cosine function respectively;

p_i＝[x_i,y_i,z_i]^T,Θ_i＝[φ_i,θ_i,ψ_i]^Trespectively representing the position vector of the ith four rotors under an inertial coordinate system and the attitude angle of the ith four rotors under a machine body coordinate system; II type_1,i＝diag(k_x,i,k_y,i,k_z,i),Π_2,i＝diag(k_φ,i,k_θ,i,k_ψ,i) Respectively, the air damping matrix for the ith four-rotor position and attitude loop,is the air damping coefficient of the ith frame quad-rotor; tau is_i＝[τ_x,iτ_y,iτ_z,i]^TControl input u for three control moments about the x, y, z axes of the machine_iE, R is the pulling force of the ith frame of four rotors; g_2,i＝diag(l_i,l_i,c_i)∈R^3×3Wherein l is_iIs the geometric distance of the propeller from the center of mass of the four rotors, c_iIs the moment coefficient, d_Θ,i(t)＝[d_φ,i,d_θ,i,d_ψ,i]^TRepresenting bounded external disturbances in the attitude loop;

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

wherein, F_i＝[F_i,x,F_i,y,F_i,z]^T∈R^3×1Representing virtual control input, d_4,iFor lumped disturbances of the attitude loop, including the combined effect of external disturbances and uncertainty of the parameters, δ_1,i、δ_2,iIs a parameterized uncertainty matrix for the ith quad-rotor,are respectively pi_2,i、g_2,iA nominal value of (d);

with the above intermediate variables, the quadrotor motion/dynamics model (1) is rewritten as a strict feedback form as follows:

3. the multi-quad rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection according to claim 1, wherein the control method comprises the following steps: the multi-four-rotor communication topology and formation style in the step (2) and the position and speed information of a pilot are as follows:

the four-rotor formation adopts a master-slave structure, the pilot is defined as a node with the number of 0, and each slave is sequentially numbered as 1, … and n; the communication topology between the four rotors can be represented by an undirected graph G ═ V, E, a }; v is node set, E is edge set, A ═ a_ij]∈R^n×nIs an adjacency weight matrix; if four rotors i and j are connected, then a_ij＝a_ji> 0, otherwise a_ij＝a_ji0, and further, definition a_ii0; communication weight reuse b between pilot and slave i_iIndicating that if the ith rack slave can directly acquire the pilot information, b_i> 0, otherwise b_i＝0；

Defining a pilot as the geometric center of a multi-four-rotor formation pattern, namely a formation pattern coordinate origin, and designing a position vector delta of an ith frame slave machine and a jth frame slave machine relative to the pilot according to a desired formation geometry_i＝[Δ_i,x,Δ_i,y,Δ_i,z]^TAnd Δ_j＝[Δ_j,x,Δ_j,y,Δ_j,z]^TThe relative position deviation between the ith frame and the jth frame slave can be represented by delta_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,Δ_ij,y,Δ_ij,z]^TDescription is given;

the navigator trajectory motion information can be generated by:

wherein x is^d、y^d、z^dRespectively, the navigator is along x under the inertial coordinate system,the position components of the y, z axes,the velocity components of the pilot along the x, y, and z axes, respectively, in the inertial frame.

4. The multi-quad rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection according to claim 1, wherein the control method comprises the following steps: the multi-four-rotor distributed position holding controller in the step (3) is specifically as follows:

constructing the following virtual control input (F) according to multi-quad rotor master-slave formation communication topology and expected navigator track information and combining a multi-agent second-order consistency principle_i,x,F_i,y,F_i,z)^T：

Wherein k is₁、k₂Represents the parameters of the controller to be designed,and isN_iRepresenting a set of quadrotors, x, with direct communication connection with the ith frame quadrotors_iIs the position component of the ith four rotors along the x axis under the inertial coordinate system, x_jIs the component of the position of the jth quad-rotor along the x-axis, v_i,xIs the velocity component of the ith four rotors along the x-axis under the inertial coordinate system, v_j,xThe velocity component along the x axis under the inertia coordinate system of the jth frame of the four rotors;

after obtaining the virtual control input (F)_i,x,F_i,y,F_i,z)^TOn the basis, inverse dynamics calculation is carried out by combining a formula (2), and the following expected attitude angle command can be obtained

Wherein u is_iFor the desired pull of a quad-rotor drone,respectively, a desired roll angle, a pitch angle and a yaw angle in a coordinate system of the body.

5. The multi-quad rotor master-slave cooperative formation control method based on second-order consistency and active disturbance rejection according to claim 1, wherein the control method comprises the following steps: the multi-four-rotor attitude tracking controller in the step (4) is specifically as follows:

wherein,proportional gain of the controller, k, being positive_d＝2w_cPositive controller differential gain, w_cA controller bandwidth for the attitude loop;for estimation of the lumped disturbance of the attitude loop, it can be given by a model-assisted extended state observer that relies only on the control input torque and the attitude angle measurement output as follows:

wherein z is_1,iIs to x_3,iEstimate of (b), z_2,iIs to x_4,iEstimate of (b), z_3,iIs toEstimate of (a), w_oIs the attitude loop observer bandwidth.