CN114115335A - Multi-quad-rotor unmanned aerial vehicle safety formation control method based on tracking differentiator - Google Patents

Abstract

The invention relates to a multi-quad rotor unmanned aerial vehicle safe formation control method based on a tracking differentiator, which comprises the following steps of firstly, constructing an asymmetric boundary preset performance controller independent of an initial value of formation errors so as to obtain smooth and rapid formation transient performance; secondly, the hyperbolic tangent tracking differentiator obtains a quick and accurate differential control signal, and meanwhile, the problem of differential explosion of a traditional backstepping controller design method is avoided; finally, a self-adaptive neural network interference estimator is adopted to realize accurate and efficient real-time estimation and compensation of lumped disturbance; the design method solves the problems of parameter uncertainty, external interference and transient performance deterioration in the existing multi-quad rotor unmanned aerial vehicle safety formation control, can form a continuous and stable formation configuration under the condition that the unmanned aerial vehicle suffers from parameter uncertainty and external environment interference, and greatly enhances the robustness, the high efficiency and the safety of the multi-quad rotor cooperative formation task.

Description

Multi-quad-rotor unmanned aerial vehicle safety formation control method based on tracking differentiator

Technical Field

The invention relates to a multi-quad rotor unmanned aerial vehicle safety formation control method based on a tracking differentiator, and belongs to the technical field of unmanned aerial vehicle collaborative formation flight.

Background

The multi-four-rotor cooperative formation means that the multi-four rotors form the cooperative exceeding capability of a multi-four-rotor system by maintaining a preset space geometric topological form and by means of global or local information interaction and sharing, and an effective solution is provided for executing complex tasks which cannot be performed by a single body. The multi-four rotors can adopt reasonable formation flying to replace soldiers to efficiently execute dangerous military tasks such as target detection, enemy situation collection and the like, 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 overcome the defects of incomplete single body acquired environment information, low task execution efficiency and limited load capacity, and has important military/civil dual-purpose research value and urgent practical significance.

In the collaborative formation process of many four rotor unmanned aerial vehicles of prior art, there are three key problems: (1) parameter uncertainty and unknown environmental interference exist in a quad-rotor unmanned aerial vehicle formation system, certain trouble is caused to safe formation flight of the unmanned aerial vehicle system, and the formation system even fails in severe cases; (2) in the formation control problem of the quad-rotor unmanned aerial vehicles, the avoidance of mutual collision among the unmanned aerial vehicles is a basic requirement for safe formation flight of the unmanned aerial vehicles, and the existing preset performance control method can avoid an effective method for mutual collision among the unmanned aerial vehicles, however, the existing preset performance control method needs the accurate known initial position information of each quad-rotor unmanned aerial vehicle in the design process of a controller, and meanwhile, the formation synchronous error overshoot is inevitably caused in the formation control process, so that certain limitation is brought to the design of the controller; (3) in the design process of the backstepping control law of the four-rotor cooperative formation, repeated derivation needs to be carried out on the virtual control quantity, the complexity of controller design and parameter calculation is inevitably increased, and the timeliness requirement of high-speed dynamic cooperative formation on data processing is not facilitated.

Disclosure of Invention

The invention aims to solve the technical problem of providing a safe formation control method of multi-quad rotor unmanned aerial vehicles based on tracking differentiators, adopting a brand-new design, being capable of overcoming the problems of parameter uncertainty, external interference, transient performance deterioration and the like, and solving the problem of high-efficiency anti-interference control of multi-quad rotor unmanned aerial vehicles.

The invention adopts the following technical scheme for solving the technical problems: the invention designs a multi-quad rotor unmanned aerial vehicle safety formation control method based on a tracking differentiator, which executes the following steps in real time according to time sequence:

step A, aiming at a preset number of quadrotor unmanned aerial vehicles, mutually communicating the quadrotor unmanned aerial vehicles, and aiming at obtaining virtual pilot information by at least one quadrotor unmanned aerial vehicle, constructing formation styles and communication topological structures corresponding to all quadrotor unmanned aerial vehicles, obtaining constraint models corresponding to the quadrotor unmanned aerial vehicles respectively, further obtaining constrained collaborative formation synchronous errors corresponding to the quadrotor unmanned aerial vehicles respectively, and entering step B;

b, obtaining unconstrained cooperative formation synchronous errors corresponding to the four-rotor unmanned aerial vehicles respectively by applying an error transformation method according to the constrained cooperative formation synchronous errors corresponding to the four-rotor unmanned aerial vehicles respectively, and then entering the step C;

step C, obtaining a speed dynamic virtual control law, an attitude angle dynamic virtual control law and an angular speed dynamic virtual control law of each four-rotor unmanned aerial vehicle according to the unconstrained cooperative formation synchronous errors respectively corresponding to each four-rotor unmanned aerial vehicle, applying a hyperbolic tangent tracking differentiator to obtain a speed differential control signal, an attitude angle differential control signal and an angular speed differential control signal of each four-rotor unmanned aerial vehicle, and then entering step D;

and D, establishing adaptive neural network interference estimators corresponding to the four-rotor unmanned aerial vehicles respectively, estimating uncertainty and environmental interference in a four-rotor unmanned aerial vehicle system in real time, and constructing a speed ring controller and an attitude ring controller corresponding to each four-rotor unmanned aerial vehicle respectively by combining a speed differential control signal, an attitude angle differential control signal and an angular speed differential control signal of each four-rotor unmanned aerial vehicle.

As a preferred technical scheme of the invention: in the step a, based on the formation styles and the communication topological structures corresponding to all the constructed quad-rotor unmanned aerial vehicles, the constraint models corresponding to the quad-rotor unmanned aerial vehicles are obtained as follows:

wherein I is more than or equal to 1 and less than or equal to I, I represents the number of the four-rotor unmanned aerial vehicles, X_i,p＝[X_i,p1,X_i,p2,X_i,p3]^TAnd X_i,v＝[X_i,v1,X_i,v2,X_i,v3]^TRespectively represents the ith four-rotor unmanned plane in an inertial coordinate system O_eX_eY_eZ_ePosition vector and velocity vector, X_i,Θ＝[X_i,Θ1,X_i,Θ2,X_i,Θ3]^TAnd X_i,ω＝[X_i,ω1,X_i,ω2,X_i,ω3]^TRespectively represent the i-th frame quad-rotor unmanned plane in a body coordinate system o_Bx_By_Bz_BThe lower attitude angle vector and the angular velocity vector,

the first derivative of the representation;

virtual control input, m, representing the i-th quad-rotor drone position dynamics_iMass, G, of the ith quad-rotor drone_i＝[0,0,mig]^TRepresenting a gravity matrix of the ith quad-rotor unmanned aerial vehicle, and g represents gravity acceleration; g_i,1Representing the i-th quad-rotor drone position input matrix, g, associated with attitude motion_i,1＝[cos(X_i,Θ3)sin(X_i,Θ2)cos(X_i,Θ1)+sin(X_i,Θ3)sin(X_i,Θ1),sin(X_i,Θ3)sin(X_i,Θ2)cos(X_i,Θ1)-cos(X_i,Θ3)sin(X_i,Θ1),cos(X_i,Θ2)cos(X_i,Θ1)]^T；u_i,1Represents the sum of the total thrust or lift of the propellers of the ith quad-rotor unmanned aerial vehicle, U_i,ω＝[u_i,2,u_i,3,u_i,4]^TRepresents the moment of the ith quad-rotor drone, u_i,1＝F_i,1+F_i,2+F_i,3+F_i,4,

u_i,3＝J_i,θ(l_iF_i,2-l_iF_i,4)，u_i,4＝J_i,ψ(-c_iF_i,1+c_iF_i,2-c_iF_i,3+c_iF_i,4)，l_iAnd c_iRespectively representing the distance from the mass center of the ith four-rotor unmanned aerial vehicle to the propeller motor and the moment coefficient, F_i,1、F_i,1、F_i,1、F_i,4Respectively representing the lift force, f, of the four propellers of the ith quad-rotor unmanned aerial vehicle_i,v(X_i,v)＝-Π_i,1X_i,v/m_iAnd

respectively representing parameterized uncertainty items pi in pneumatic coefficients of the ith frame of quad-rotor unmanned aerial vehicle_i,1Show the i-th frame quad-rotor unmanned aerial vehicle's trajectory loop damping matrix, pi_i,2Representing an attitude loop damping matrix for the ith quad-rotor drone,

represents the positive definite diagonal inertia matrix, delta, of the ith quad-rotor unmanned plane_i,v＝[Δ_i,v1,Δ_i,v2,Δ_i,v3]^TAnd Δ_i,ω＝[Δ_i,ω1,Δ_i,ω2,Δ_i,ω3]^TThe system and the method respectively represent bounded environmental interference borne by the ith quad-rotor unmanned aerial vehicle position ring and bounded environmental interference borne by the attitude ring.

As a preferred technical scheme of the invention: in the step A, constrained collaborative formation synchronization errors corresponding to each set of quad-rotor unmanned aerial vehicle are obtained as follows:

wherein, I represents that the four rotors do not haveTotal number of man-machines, e_i,pkRepresent the constrained collaborative formation synchronization error of the kth element in the corresponding position vector of the ith quad-rotor drone, k being 1, 2, 3, N_iRepresent the neighborhood set, a, that each adjacent four rotor unmanned aerial vehicle of the ith frame of four rotor unmanned aerial vehicles constitutes_ijRepresent the information weight between the ith four-rotor unmanned aerial vehicle and the jth four-rotor unmanned aerial vehicle in the neighborhood set corresponding to the ith four-rotor unmanned aerial vehicle, and if the ith four-rotor unmanned aerial vehicle keeps communication with the jth four-rotor unmanned aerial vehicle in the neighborhood set corresponding to the ith four-rotor unmanned aerial vehicle, then a_ij＝a_ji> 0, otherwise, a_ij＝a_ji＝0；b_iRepresent the information weight between the fourth rotor unmanned aerial vehicle of ith frame and virtual navigator, and if the fourth rotor unmanned aerial vehicle of ith frame can acquire virtual navigator's positional information, then b_i> 0, otherwise b_i＝0；q_ij,kRepresenting the expected relative position deviation, X, of the kth element in the corresponding position vector between the ith four-rotor unmanned aerial vehicle and the jth four-rotor unmanned aerial vehicle in the neighbor set corresponding to the ith four-rotor unmanned aerial vehicle_i,pkRepresenting the kth element, X, in the ith quad-rotor drone position vector_j,pkRepresents the kth element, B, in the position vector of the jth quad-rotor unmanned aerial vehicle in the neighborhood set corresponding to the ith quad-rotor unmanned aerial vehicle_i,pkAnd

respectively representing the lower limit and the upper limit of a preset performance function of a kth element in a corresponding position vector of the ith four-rotor unmanned aerial vehicle,

representing the virtual pilot in an inertial frame O_eX_eY_eZ_eA position vector of (1); q. q.s_i,kRepresenting the expected relative positional deviation of the kth element in the corresponding position vector between the ith quad-rotor drone and the virtual pilot.

As a preferred technical scheme of the invention: in the step B, according to the restrained cooperative formation synchronous error e corresponding to each four-rotor unmanned aerial vehicle_i,pkApplying an error transformation method, according to

Combining the following equations:

obtaining the unconstrained cooperative formation synchronous error Z corresponding to each four-rotor unmanned aerial vehicle_i,pkWherein, in the step (A),B _i,pkand

the following were used:

wherein the content of the first and second substances,δ _i,pkfor determining a preset performance function lower limit, anδ _i,pkIs a constant number greater than or equal to 1,

for determining a preset performance function lower limit, an

Is a constant number greater than or equal to 1,

for a design parameter greater than 0 a and,

for adjusting the error e_i,pkThe convergence speed of the light source is increased,

and

are each a design parameter greater than 0,

and

for determining performance boundaries for synchronization errors.

As a preferred technical scheme of the invention: the step C comprises the following steps C1 to C2:

step C1, according to the unconstrained cooperative formation synchronous errors corresponding to each four-rotor unmanned aerial vehicle, according to the following formula:

obtaining a speed dynamic virtual control law of each four-rotor unmanned aerial vehicle, and using the speed dynamic virtual control law to stabilize the unconstrained cooperative formation synchronous error of a position loop; wherein alpha is_i,vkThe speed dynamic virtual control law of the kth element in the corresponding position vector of the ith four-rotor unmanned aerial vehicle is expressed, and k is 1, 2 and 3_i,pkThe position ring of the ith four-rotor unmanned aerial vehicle is respectively corresponding to the adjustable gain of the controller under the three components of the position vector,

representing the total information weight between the ith four-rotor unmanned aerial vehicle and all the four-rotor unmanned aerial vehicles in the corresponding neighborhood set, and then entering step C2;

step C2. uses hyperbolic tangent tracking differentiator according to the following formula:

obtaining speed differential control signals and angular speed differential control signals of all the four-rotor unmanned aerial vehicles, wherein eta_1i,vkSpeed differential control signal representing kth element in corresponding position vector of ith frame quad-rotor unmanned aerial vehicleNumber r_i,vk、τ_1i,vk、τ_2i,vk、ζ_1i,vk、ζ_2i,vkAnd D, positive design parameters of the corresponding speed of the hyperbolic tangent tracking differentiator are obtained, and then the step D is carried out.

As a preferred technical scheme of the invention: the step D comprises the following steps D1 to D5;

step D1, establishing the self-adaptive neural network interference estimator corresponding to each four-rotor unmanned aerial vehicle as follows:

wherein the content of the first and second substances,

γ_i,v＝diag(γ_i,v1,γ_i,v2,γ_i,v3) Representing the adaptive gain matrix, gamma, of the i-th quad-rotor drone velocity ring_i,v1、γ_i,v2、γ_i,v3Respectively represents the adaptive gain, sigma, corresponding to three components of the speed ring of the ith four-rotor unmanned aerial vehicle_i,v＝diag(σ_i,v1,σ_i,v2,σ_i,v3) Representing the self-adaptive update law correction factor matrix, sigma, of the ith quad-rotor unmanned plane speed loop_i,v1、σ_i,v2、σ_i,v3Respectively representing correction factors corresponding to the self-adaptive update law of three components of the speed ring of the ith four-rotor unmanned aerial vehicle,

representing the ideal weight vector of the ith quad-rotor drone speed ring,

respectively representing the ideal weight of three components of the speed ring of the ith four-rotor unmanned plane, and simultaneously,

_hi,va gaussian basis function vector representing the ith quad-rotor drone velocity ring,

representing the input quantity of the corresponding Gaussian base function of the ith quad-rotor unmanned plane,

respectively represents the ith four-rotor unmanned plane in an inertial coordinate system O_eX_eY_eZ_eThen to step D2;

step D2., constructing adaptive neural network cooperative formation controllers corresponding to the four-rotor unmanned aerial vehicles respectively as follows to form speed loop controllers corresponding to the four-rotor unmanned aerial vehicles respectively;

wherein k is_i,v＝diag(k_i,v1,k_i,v2,k_i,v3) Represents the i-th quad-rotor unmanned plane speed loop controller gain matrix, k_i,v1、k_i,v2、k_i,v3Represents the adjustable gain of the controller corresponding to three components of the ith four-rotor unmanned plane speed loop, e_i,vFor the i-th frame quad-rotor unmanned aerial vehicle speed tracking error vector, e_i,v＝X_i,v-η_1i,v，η_2i,vIs alpha_i,vFirst order differential signal, eta, filtered by a tracking differentiator_2i,v＝{η_2i,v1,η_2i,v2,η_2i,v3}，α_i,v＝{α_i,v1,α_i,v2,α_i,v3}；F_i,vA virtual control input representing a corresponding speed of an ith quad-rotor drone;

wherein, for four rotor unmanned aerial vehicle speed control, then F_i,vIs in relation to the desired tension u_i,1The following relationship is satisfied:

wherein u is_i,1Representing the total thrust of the i-th quad-rotor drone propeller,

respectively representing the expected roll angle, the expected pitch angle and the expected yaw angle of the ith quad-rotor unmanned plane generated by the speed loop control signal, and then u_i,1And the desired roll and pitch angles are as follows:

and based on anticipated attitude angle of ith frame quad-rotor unmanned aerial vehicle

According to the following formula:

obtaining attitude angle differential control signal eta of each frame of quadrotor unmanned aerial vehicle_1i,ΘkWherein r is_i,Θk、τ_1i,Θk、τ_2i,Θk、ζ_1i,Θk、ζ_2i,ΘkIs a positive design parameter of the hyperbolic tangent tracking differentiator corresponding to the attitude angle,

is composed of

The kth component of (a);

wherein the yaw angle

Set by the operator; then step D3 is entered; wherein, F_i,v1、F_i,v2、F_i,v3Respectively representing the virtual control input, u, of each element in the corresponding position vector of the ith quad-rotor unmanned aerial vehicle with respect to speed_i,1Is the ith frameThe total thrust of the four propellers of the rotor unmanned aerial vehicle,

θ_i ^drespectively representing an expected roll angle and an expected pitch angle of the ith quad-rotor unmanned aerial vehicle;

d3, constructing attitude angle control laws corresponding to the four-rotor unmanned aerial vehicles respectively as follows:

α_i,ω＝-k_i,Θe_i,Θ+η_2i,Θ (10)

further obtaining angular velocity differential control signals eta of each four-rotor unmanned aerial vehicle_1i,ωkThe following were used:

wherein r is_i,ωk、τ_1i,ωk、τ_2i,ωk、ζ_1i,ωk、ζ_2i,ωkIs a positive design parameter, k, of the hyperbolic tangent tracking differentiator corresponding to the angular velocity_i,Θ＝diag(k_i,Θ1,k_i,Θ2,k_i,Θ3)，k_i,Θ1,k_i,Θ2,k_i,Θ3Positive controller gain, e_i,Θ＝X_i,Θ-η_1i,Θ，η_1i,Θ＝{η_1i,Θ1,η_1i,Θ2,η_1i,Θ3Is the expected attitude angle of the ith frame of quad-rotor unmanned aerial vehicle

Signal k filtered by hyperbolic tangent tracking differentiator_i,Θ＝{k_i,Θ1,k_i,Θ2,k_i,Θ3Denotes the ith four-rotor unmanned plane attitude angle controller gain matrix, k_i,Θ1、k_i,Θ2、k_i,Θ3Respectively representing the adjustable gain of the controller corresponding to three components of the attitude angle of the ith four-rotor unmanned aerial vehicle, e_i,ΘRepresenting the attitude angle tracking error vector, eta, of the ith quad-rotor unmanned plane_2i,Θ＝{η_2i,Θ1,η_2i,Θ2,η_2i,Θ3Means for

A first order differential signal filtered by a tracking differentiator; then step D4 is entered;

step D4. is according to e_i,ω＝X_i,ω-η_1i,ω，η_1i,ω＝{η_1i,ωkAnd designing the angular speed control laws corresponding to the four-rotor unmanned aerial vehicles respectively as follows:

wherein, U_i,ωRepresents the angular velocity loop control vector, k, corresponding to the ith quad-rotor drone_i,ω＝{k_i,ω1,k_i,ω2,k_i,ω3Denotes the i-th frame quad-rotor unmanned aerial vehicle angular velocity controller gain matrix, k_i,ω1、k_i,ω2、k_i,ω3Respectively representing the adjustable gain of the controller for three components of angular velocity, e_i,ωRepresenting the corresponding angular velocity tracking error vector, gamma, of the ith quad-rotor unmanned aerial vehicle_i,ω＝{γ_i,ω1,γ_i,ω2,γ_i,ω3Denotes the i-th frame quad-rotor unmanned aerial vehicle angular velocity loop adaptive gain matrix, gamma_i,ω1、γ_i,ω2、γ_i,ω3Respectively shows the adaptive gains corresponding to three components of the angular velocity ring of the ith frame of the quad-rotor unmanned aerial vehicle,

represents an ideal weight vector of the i-th quad-rotor drone angular velocity ring,

respectively representing ideal weights h of three components of an i-th frame quad-rotor unmanned aerial vehicle angular velocity ring_i,ωA gaussian basis function vector representing the i-th quad-rotor drone angular velocity ring,

indicate the corresponding reason of the ith frame of quad-rotor unmanned aerial vehicleVector of thought weight

Estimate of, σ_i,ω＝{σ_i,ω1,σ_i,ω2,σ_i,ω3Indicates the i-th frame of the quadrotor unmanned aerial vehicle angular velocity ring self-adaptive update law correction factor matrix, sigma_i,ω1、σ_i,ω2、σ_i,ω3Respectively representing correction factors, eta, corresponding to the adaptive update law of three components of the angular velocity ring of the ith four-rotor unmanned aerial vehicle_2i,ωDenotes alpha_i,ω＝{α_i,ω1,α_i,ω2,α_i,ω3The first order differential signal after being filtered by the tracking differentiator,

is the input quantity of the gaussian basis function,

respectively represent the i-th frame quad-rotor unmanned plane in a body coordinate system o_Bx_By_Bz_BA lower attitude angle vector and an angular velocity vector; then step D5 is entered;

and D5., forming attitude ring controllers corresponding to the four-rotor unmanned aerial vehicles respectively by the attitude angle control law and the angular speed control law corresponding to the four-rotor unmanned aerial vehicles respectively.

Compared with the prior art, the multi-quad-rotor unmanned aerial vehicle safe formation control method based on the tracking differentiator has the following technical effects:

(1) according to the multi-quad rotor unmanned aerial vehicle safe formation control method based on the tracking differentiator, firstly, an asymmetric boundary preset performance controller independent of an initial value of a formation error is constructed to obtain smooth and rapid formation transient performance; secondly, the hyperbolic tangent tracking differentiator obtains a quick and accurate differential control signal, and meanwhile, the problem of differential explosion of a traditional backstepping controller design method is avoided; finally, a self-adaptive neural network interference estimator is adopted to realize accurate and efficient real-time estimation and compensation of lumped disturbance; the design method solves the problems of parameter uncertainty, external interference and transient performance deterioration in the existing multi-quad rotor unmanned aerial vehicle safety formation control, can form a continuous and stable formation configuration under the condition that the unmanned aerial vehicle suffers from parameter uncertainty and external environment interference, and greatly enhances the robustness, the high efficiency and the safety of the multi-quad rotor cooperative formation task.

Drawings

FIG. 1 is a control structure block diagram of a tracking differentiator-based multi-quad rotor unmanned aerial vehicle safety formation control method designed by the invention;

fig. 2 is a schematic view of a communication topology for a formation of multiple quad-rotor drones;

FIG. 3 is a schematic diagram of a 3-dimensional trajectory of formation flight of multiple quad-rotor unmanned aerial vehicles in an inertial coordinate system;

FIG. 4 is a schematic diagram of X-Y plane trajectories for formation flight of multiple quad-rotor unmanned aerial vehicles in an inertial coordinate system;

figure 5 is a schematic diagram of a multi-quad rotor drone position response curve;

figure 6 is a schematic view of a multi-quad rotor drone attitude response curve;

FIG. 7 is a schematic of a filtered signal versus time derivative estimate of a tracking differentiator;

fig. 8 is the formation synchronization error of the quad-rotor drone 1.

Detailed Description

The following description will explain embodiments of the present invention in further detail with reference to the accompanying drawings.

The invention designs a tracking differentiator-based multi-quad-rotor unmanned aerial vehicle safety formation control method, as shown in fig. 1, and in practical application, the following steps are executed in real time according to time sequence.

Step A, aiming at a preset number of quad-rotor unmanned aerial vehicles, communicating among the quad-rotor unmanned aerial vehicles, and aiming at obtaining virtual pilot information by at least one quad-rotor unmanned aerial vehicle, constructing formation styles and communication topological structures corresponding to all the quad-rotor unmanned aerial vehicles, obtaining constraint models corresponding to the quad-rotor unmanned aerial vehicles respectively, further obtaining constrained collaborative formation synchronous errors corresponding to the quad-rotor unmanned aerial vehicles respectively, and then entering step B.

In the practical application of the step a, based on the formation styles and the communication topological structures corresponding to all the constructed quad-rotor unmanned aerial vehicles, the constraint models respectively corresponding to the quad-rotor unmanned aerial vehicles are obtained as follows:

wherein I is more than or equal to 1 and less than or equal to I, I represents the number of the four-rotor unmanned aerial vehicles, X_i,p＝[X_i,p1,X_i,p2,X_i,p3]^TAnd X_i,v＝[X_i,v1,X_i,v2,X_i,v3]^TRespectively represents the ith four-rotor unmanned plane in an inertial coordinate system O_eX_eY_eZ_ePosition vector and velocity vector, X_i,Θ＝[X_i,Θ1,X_i,Θ2,X_i,Θ3]^TAnd X_i,ω＝[X_i,ω1,X_i,ω2,X_i,ω3]^TRespectively represent the i-th frame quad-rotor unmanned plane in a body coordinate system o_Bx_By_Bz_BThe lower attitude angle vector and the angular velocity vector,

the first derivative of the representation;

virtual control input, m, representing the i-th quad-rotor drone position dynamics_iMass, G, of the ith quad-rotor drone_i＝[0,0,mig]^TRepresenting a gravity matrix of the ith quad-rotor unmanned aerial vehicle, and g represents gravity acceleration; g_i,1Representing the i-th quad-rotor drone position input matrix, g, associated with attitude motion_i,1＝[cos(X_i,Θ3)sin(X_i,Θ2)cos(X_i,Θ1)+sin(X_i,Θ3)sin(X_i,Θ1),sin(X_i,Θ3)sin(X_i,Θ2)cos(X_i,Θ1)-cos(X_i,Θ3)sin(X_i,Θ1),cos(X_i,Θ2)cos(X_i,Θ1)]^T；u_i,1Represents the sum of the total thrust or lift of the propellers of the ith quad-rotor unmanned aerial vehicle, U_i,ω＝[u_i,2,u_i,3,u_i,4]^TRepresents the moment of the ith quad-rotor drone, u_i,1＝F_i,1+F_i,2+F_i,3+F_i,4,

u_i,3＝J_i,θ(l_iF_i,2-l_iF_i,4)，u_i,4＝J_i,ψ(-c_iF_i,1+c_iF_i,2-c_iF_i,3+c_iF_i,4)，l_iAnd c_iRespectively representing the distance from the mass center of the ith four-rotor unmanned aerial vehicle to the propeller motor and the moment coefficient, F_i,1、F_i,1、F_i,1、F_i,4Respectively representing the lift force, f, of the four propellers of the ith quad-rotor unmanned aerial vehicle_i,v(X_i,v)＝-Π_i,1X_i,v/m_iAnd

respectively representing parameterized uncertainty items pi in pneumatic coefficients of the ith frame of quad-rotor unmanned aerial vehicle_i,1Show the i-th frame quad-rotor unmanned aerial vehicle's trajectory loop damping matrix, pi_i,2Representing an attitude loop damping matrix for the ith quad-rotor drone,

represents the positive definite diagonal inertia matrix, delta, of the ith quad-rotor unmanned plane_i,v＝[Δ_i,v1,Δ_i,v2,Δ_i,v3]^TAnd Δ_i,ω＝[Δ_i,ω1,Δ_i,ω2,Δ_i,ω3]^TThe system and the method respectively represent bounded environmental interference borne by the ith quad-rotor unmanned aerial vehicle position ring and bounded environmental interference borne by the attitude ring.

Further obtaining the restrained cooperative formation synchronous errors corresponding to each four-rotor unmanned aerial vehicle respectively as follows:

wherein I denotes the total number of quad-rotor drones, e_i,pkRepresent the constrained collaborative formation synchronization error of the kth element in the corresponding position vector of the ith quad-rotor drone, k being 1, 2, 3, N_iRepresent the neighborhood set, a, that each adjacent four rotor unmanned aerial vehicle of the ith frame of four rotor unmanned aerial vehicles constitutes_ijRepresent the information weight between the ith four-rotor unmanned aerial vehicle and the jth four-rotor unmanned aerial vehicle in the neighborhood set corresponding to the ith four-rotor unmanned aerial vehicle, and if the ith four-rotor unmanned aerial vehicle keeps communication with the jth four-rotor unmanned aerial vehicle in the neighborhood set corresponding to the ith four-rotor unmanned aerial vehicle, then a_ij＝a_ji> 0, otherwise, a_ij＝a_ji＝0；b_iRepresent the information weight between the fourth rotor unmanned aerial vehicle of ith frame and virtual navigator, and if the fourth rotor unmanned aerial vehicle of ith frame can acquire virtual navigator's positional information, then b_i> 0, otherwise b_i＝0；q_ij,kRepresenting the expected relative position deviation, X, of the kth element in the corresponding position vector between the ith four-rotor unmanned aerial vehicle and the jth four-rotor unmanned aerial vehicle in the neighbor set corresponding to the ith four-rotor unmanned aerial vehicle_i,pkRepresenting the kth element, X, in the ith quad-rotor drone position vector_j,pkRepresents the kth element in the position vector of the jth quad-rotor drone in the neighborhood set corresponding to the ith quad-rotor drone,B _i,pkand

respectively representing the lower limit and the upper limit of a preset performance function of a kth element in a corresponding position vector of the ith four-rotor unmanned aerial vehicle,

representing the virtual pilot in an inertial frame O_eX_eY_eZ_eA position vector of (1); q. q.s_i,kRepresenting an expected relative of a kth element in a corresponding position vector between an ith quad-rotor drone and a virtual pilotAnd (4) position deviation.

Step B, according to the restrained cooperative formation synchronous error e corresponding to each four-rotor unmanned aerial vehicle_i,pkApplying an error transformation method, according to

Combining the following equations:

obtaining the unconstrained cooperative formation synchronous error Z corresponding to each four-rotor unmanned aerial vehicle_i,pkAnd then proceed to step C, wherein,B _i,pkand

the following were used:

wherein the content of the first and second substances,δ _i,pkfor determining a preset performance function lower limit, anδ _i,pkIs a constant number greater than or equal to 1,

for determining a preset performance function lower limit, an

Is a constant number greater than or equal to 1,

for a design parameter greater than 0 a and,

for adjusting the error e_i,pkThe convergence speed of the light source is increased,

and

are each a design parameter greater than 0,

and

for determining performance boundaries for synchronization errors.

And step C, obtaining a speed dynamic virtual control law, an attitude angle dynamic virtual control law and an angular speed dynamic virtual control law of each four-rotor unmanned aerial vehicle according to the unconstrained cooperative formation synchronous errors corresponding to each four-rotor unmanned aerial vehicle respectively, applying a hyperbolic tangent tracking differentiator to obtain a speed differential control signal, an attitude angle differential control signal and an angular speed differential control signal of each four-rotor unmanned aerial vehicle, and then entering the step D.

In practical applications, the step C is performed as the following steps C1 to C2.

Step C1, according to the unconstrained cooperative formation synchronous errors corresponding to each four-rotor unmanned aerial vehicle, according to the following formula:

obtaining a speed dynamic virtual control law of each four-rotor unmanned aerial vehicle, and using the speed dynamic virtual control law to stabilize the unconstrained cooperative formation synchronous error of a position loop; wherein alpha is_i,vkThe speed dynamic virtual control law of the kth element in the corresponding position vector of the ith four-rotor unmanned aerial vehicle is expressed, and k is 1, 2 and 3_i,pkThe position ring of the ith four-rotor unmanned aerial vehicle is respectively corresponding to the adjustable gain of the controller under the three components of the position vector,

representing the total information weight between the ith quad-rotor drone and all quad-rotor drones in its corresponding neighborhood set, and then proceed to step C2.

Step C2. uses hyperbolic tangent tracking differentiator according to the following formula:

obtaining speed differential control signals and angular speed differential control signals of all the four-rotor unmanned aerial vehicles, wherein eta_1i,vkA speed differential control signal r representing the kth element in the corresponding position vector of the ith quad-rotor drone_i,vk、τ_1i,vk、τ_2i,vk、ζ_1i,vk、ζ_2i,vkAnd D, positive design parameters of the corresponding speed of the hyperbolic tangent tracking differentiator are obtained, and then the step D is carried out.

And D, establishing adaptive neural network interference estimators corresponding to the four-rotor unmanned aerial vehicles respectively, estimating uncertainty and environmental interference in a four-rotor unmanned aerial vehicle system in real time, and constructing a speed ring controller and an attitude ring controller corresponding to each four-rotor unmanned aerial vehicle respectively by combining a speed differential control signal, an attitude angle differential control signal and an angular speed differential control signal of each four-rotor unmanned aerial vehicle.

In practical applications, the step D specifically performs the following steps D1 to D5.

Step D1, establishing the self-adaptive neural network interference estimator corresponding to each four-rotor unmanned aerial vehicle as follows:

wherein the content of the first and second substances,

γ_i,v＝diag(γ_i,v1,γ_i,v2,γ_i,v3) Representing the self-adaptive gain matrix of the speed ring of the ith quad-rotor unmanned plane,γ_i,v1、γ_i,v2、γ_i,v3respectively represents the adaptive gain, sigma, corresponding to three components of the speed ring of the ith four-rotor unmanned aerial vehicle_i,v＝diag(σ_i,v1,σ_i,v2,σ_i,v3) Representing the self-adaptive update law correction factor matrix, sigma, of the ith quad-rotor unmanned plane speed loop_i,v1、σ_i,v2、σ_i,v3Respectively representing correction factors corresponding to the self-adaptive update law of three components of the speed ring of the ith four-rotor unmanned aerial vehicle,

representing the ideal weight vector of the ith quad-rotor drone speed ring,

respectively representing the ideal weight of three components of the speed ring of the ith four-rotor unmanned plane, and simultaneously,

_hi,va gaussian basis function vector representing the ith quad-rotor drone velocity ring,

representing the input quantity of the corresponding Gaussian base function of the ith quad-rotor unmanned plane,

respectively represents the ith four-rotor unmanned plane in an inertial coordinate system O_eX_eY_eZ_eAnd then to step D2.

Step D2. is to construct adaptive neural network cooperative formation controllers corresponding to the four-rotor unmanned aerial vehicles, respectively, as follows, to construct speed loop controllers corresponding to the four-rotor unmanned aerial vehicles, respectively.

Wherein k is_i,v＝diag(k_i,v1,k_i,v2,k_i,v3) Represents the i-th quad-rotor unmanned plane speed loop controller gain matrix, k_i,v1、k_i,v2、k_i,v3Represents the adjustable gain of the controller corresponding to three components of the ith four-rotor unmanned plane speed loop, e_i,vFor the i-th frame quad-rotor unmanned aerial vehicle speed tracking error vector, e_i,v＝X_i,v-η_1i,v，η_2i,vIs alpha_i,vFirst order differential signal, eta, filtered by a tracking differentiator_2i,v＝{η_2i,v1,η_2i,v2,η_2i,v3}，α_i,v＝{α_i,v1,α_i,v2,α_i,v3}；F_i,vAnd (4) representing the virtual control input of the corresponding speed of the ith quad-rotor unmanned aerial vehicle.

Wherein, for four rotor unmanned aerial vehicle speed control, then F_i,vIs in relation to the desired tension u_i,1The following relationship is satisfied:

wherein u is_i,1Representing the total thrust of the i-th quad-rotor drone propeller,

θ_i ^d、ψ_i ^drespectively representing the expected roll angle, the expected pitch angle and the expected yaw angle of the ith quad-rotor unmanned plane generated by the speed loop control signal, and then u_i,1And the desired roll and pitch angles are as follows:

and based on anticipated attitude angle of ith frame quad-rotor unmanned aerial vehicle

According to the following formula:

obtaining attitude angle differential control signal eta of each frame of quadrotor unmanned aerial vehicle_1i,ΘkWherein r is_i,Θk、τ_1i,Θk、τ_2i,Θk、ζ_1i,Θk、ζ_2i,ΘkIs a positive design parameter of the hyperbolic tangent tracking differentiator corresponding to the attitude angle,

is composed of

The k component of (a).

Wherein the yaw angle psi_i ^dSet by the operator; then step D3 is entered; wherein, F_i,v1、F_i,v2、F_i,v3Respectively representing the virtual control input, u, of each element in the corresponding position vector of the ith quad-rotor unmanned aerial vehicle with respect to speed_i,1For the total thrust of the four propellers of the ith quad-rotor drone,

the expected roll angle and the expected pitch angle of the ith quad-rotor unmanned aerial vehicle are respectively shown.

D3, constructing attitude angle control laws corresponding to the four-rotor unmanned aerial vehicles respectively as follows:

α_i,ω＝-k_i,Θe_i,Θ+η_2i,Θ (10)

further obtaining angular velocity differential control signals eta of each four-rotor unmanned aerial vehicle_1i,ωkThe following were used:

wherein r is_i,ωk、τ_1i,ωk、τ_2i,ωk、ζ_1i,ωk、ζ_2i,ωkIs positive design parameter of hyperbolic tangent tracking differentiator corresponding to angular velocityNumber, k_i,Θ＝diag(k_i,Θ1,k_i,Θ2,k_i,Θ3)，k_i,Θ1,k_i,Θ2,k_i,Θ3Positive controller gain, e_i,Θ＝X_i,Θ-η_1i,Θ，η_1i,Θ＝{η_1i,Θ1,η_1i,Θ2,η_1i,Θ3Is the expected attitude angle of the ith frame of quad-rotor unmanned aerial vehicle

Signal k filtered by hyperbolic tangent tracking differentiator_i,Θ＝{k_i,Θ1,k_i,Θ2,k_i,Θ3Denotes the ith four-rotor unmanned plane attitude angle controller gain matrix, k_i,Θ1、k_i,Θ2、k_i,Θ3Respectively representing the adjustable gain of the controller corresponding to three components of the attitude angle of the ith four-rotor unmanned aerial vehicle, e_i,ΘRepresenting the attitude angle tracking error vector, eta, of the ith quad-rotor unmanned plane_2i,Θ＝{η_2i,Θ1,η_2i,Θ2,η_2i,Θ3Means for

A first order differential signal filtered by a tracking differentiator; then proceed to step D4.

Step D4. is according to e_i,ω＝X_i,ω-η_1i,ω，η_1i,ω＝{η_1i,ωkAnd designing the angular speed control laws corresponding to the four-rotor unmanned aerial vehicles respectively as follows:

wherein, U_i,ωRepresents the angular velocity loop control vector, k, corresponding to the ith quad-rotor drone_i,ω＝{k_i,ω1,k_i,ω2,k_i,ω3Denotes the i-th frame quad-rotor unmanned aerial vehicle angular velocity controller gain matrix, k_i,ω1、k_i,ω2、k_i,ω3Respectively representing the adjustable gain of the controller for three components of angular velocity, e_i,ωMeans that the ith frame is four-rotor unmannedMachine-to-machine angular velocity tracking error vector, gamma_i,ω＝{γ_i,ω1,γ_i,ω2,γ_i,ω3Denotes the i-th frame quad-rotor unmanned aerial vehicle angular velocity loop adaptive gain matrix, gamma_i,ω1、γ_i,ω2、γ_i,ω3Respectively shows the adaptive gains corresponding to three components of the angular velocity ring of the ith frame of the quad-rotor unmanned aerial vehicle,

represents an ideal weight vector of the i-th quad-rotor drone angular velocity ring,

respectively representing ideal weights h of three components of an i-th frame quad-rotor unmanned aerial vehicle angular velocity ring_i,ωA gaussian basis function vector representing the i-th quad-rotor drone angular velocity ring,

represent the ideal weight vector corresponding to the ith frame of quad-rotor unmanned aerial vehicle

Estimate of, σ_i,ω＝{σ_i,ω1,σ_i,ω2,σ_i,ω3Indicates the i-th frame of the quadrotor unmanned aerial vehicle angular velocity ring self-adaptive update law correction factor matrix, sigma_i,ω1、σ_i,ω2、σ_i,ω3Respectively representing correction factors, eta, corresponding to the adaptive update law of three components of the angular velocity ring of the ith four-rotor unmanned aerial vehicle_2i,ωDenotes alpha_i,ω＝{α_i,ω1,α_i,ω2,α_i,ω3The first order differential signal after being filtered by the tracking differentiator,

is the input quantity of the gaussian basis function,

respectively represent the i-th frame quad-rotor unmanned plane in a body coordinate system o_Bx_By_Bz_BA lower attitude angle vector and an angular velocity vector; then proceed to step D5.

And D5., forming attitude ring controllers corresponding to the four-rotor unmanned aerial vehicles respectively by the attitude angle control law and the angular speed control law corresponding to the four-rotor unmanned aerial vehicles respectively.

The multi-quadrotor unmanned aerial vehicle safe formation control method based on the tracking differentiator is applied to practice, the multi-quadrotor unmanned aerial vehicle formation communication topology and the expected formation configuration are shown in figure 2, and an undirected graph adjacent matrix weight coefficient is selected as a₁₂＝a₂₁＝1,a₂₃＝a₃₂＝1,b ₁1, wherein, the initial position and the speed state of each four-rotor drone are as follows:

[X_1,p1,X_1,p2,X_1,p3,X_1,v1,X_1,v2,X_1,v3]＝[-5.5,0,5.5,0,0，0]

[X_2,p1,X_2,p2,X_2,p3,X_2,v1,X_2,v2,X_2,v3]＝[-4.5,0,3.3,0,0,0]

[X_3,p1,X_3,p2,X_3,p3,X_3,v1,X_3,v2,X_3,v3]＝[-4,0,-5.5,0,0,0]

here, four-rotor drone formation is made to track the following desired trajectory:

setting external disturbance:

to obtain better controller performance, the controller parameter γ is selected_i,v＝diag(10,10,5),γ_i,ω＝diag(10,10,20),κ_i,v＝diag(6.5,6.5,6.5),κ_i,ω＝diag(16,16,16),σ_i,v＝diag(0.6,0.6,0.6),σ_i,ω＝diag(0.1,0.1,0.1),τ_1i,v＝τ_1i,Θ＝τ_1i,ω＝diag(35,35,35),τ_2i,v＝τ_2i,Θ＝τ_2i,ω＝diag(10,10,10).。

The 3-dimensional track of formation flight of the multi-quad-rotor unmanned aerial vehicle under the inertial coordinate system is shown in fig. 3, and the X-Y plane track of formation flight of the multi-quad-rotor unmanned aerial vehicle is shown in fig. 4, so that the multi-quad-rotor unmanned aerial vehicle can form a stable formation configuration and track an expected track under the action of a designed control algorithm.

The position and attitude response curves of each quad-rotor unmanned aerial vehicle are shown in fig. 5 and fig. 6, and it can be seen that the position state of each quad-rotor unmanned aerial vehicle can still maintain good consistency under the influence of interference; each quad-rotor unmanned aerial vehicle attitude ring response has kept better stability.

The filtering signal and the time differential estimation of the virtual control quantity of the position ring of the quad-rotor unmanned aerial vehicle 1 through the tracking differentiator are shown in fig. 7, obviously, the filtering signal and the time differential estimation signal obtained by the designed hyperbolic tangent tracking differentiator are smoother and more stable, and the peak phenomenon of the original signal is avoided to a certain extent.

Fig. 8 shows the formation synchronization error of quad-rotor unmanned aerial vehicle 1 under the effect of the asymmetric boundary preset performance controller, and it can be seen that the response curve of the formation synchronization error of quad-rotor unmanned aerial vehicle is smooth and stable, and can be well limited within the range of the preset performance boundary.

According to the safe formation control method of the multi-quad rotor unmanned aerial vehicle based on the tracking differentiator, firstly, an asymmetric boundary preset performance controller independent of an initial value of a formation error is constructed to obtain smooth and rapid formation transient performance; secondly, the hyperbolic tangent tracking differentiator obtains a quick and accurate differential control signal, and meanwhile, the problem of differential explosion of a traditional backstepping controller design method is avoided; finally, a self-adaptive neural network interference estimator is adopted to realize accurate and efficient real-time estimation and compensation of lumped disturbance; the design method solves the problems of parameter uncertainty, external interference and transient performance deterioration in the existing multi-quad rotor unmanned aerial vehicle safety formation control, can form a continuous and stable formation configuration under the condition that the unmanned aerial vehicle suffers from parameter uncertainty and external environment interference, and greatly enhances the robustness, the high efficiency and the safety of the multi-quad rotor cooperative formation task.

The embodiments of the present invention have been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (6)

1. A multi-quad rotor unmanned aerial vehicle safety formation control method based on a tracking differentiator is characterized in that the following steps are executed in real time according to time sequence:

step A, aiming at a preset number of quadrotor unmanned aerial vehicles, mutually communicating the quadrotor unmanned aerial vehicles, and aiming at obtaining virtual pilot information by at least one quadrotor unmanned aerial vehicle, constructing formation styles and communication topological structures corresponding to all quadrotor unmanned aerial vehicles, obtaining constraint models corresponding to the quadrotor unmanned aerial vehicles respectively, further obtaining constrained collaborative formation synchronous errors corresponding to the quadrotor unmanned aerial vehicles respectively, and entering step B;

b, obtaining unconstrained cooperative formation synchronous errors corresponding to the four-rotor unmanned aerial vehicles respectively by applying an error transformation method according to the constrained cooperative formation synchronous errors corresponding to the four-rotor unmanned aerial vehicles respectively, and then entering the step C;

step C, obtaining a speed dynamic virtual control law, an attitude angle dynamic virtual control law and an angular speed dynamic virtual control law of each four-rotor unmanned aerial vehicle according to the unconstrained cooperative formation synchronous errors respectively corresponding to each four-rotor unmanned aerial vehicle, applying a hyperbolic tangent tracking differentiator to obtain a speed differential control signal, an attitude angle differential control signal and an angular speed differential control signal of each four-rotor unmanned aerial vehicle, and then entering step D;

and D, establishing adaptive neural network interference estimators corresponding to the four-rotor unmanned aerial vehicles respectively, estimating uncertainty and environmental interference in a four-rotor unmanned aerial vehicle system in real time, and constructing a speed ring controller and an attitude ring controller corresponding to each four-rotor unmanned aerial vehicle respectively by combining a speed differential control signal, an attitude angle differential control signal and an angular speed differential control signal of each four-rotor unmanned aerial vehicle.

2. The safe formation control method for the multi-quad rotor unmanned aerial vehicle based on the tracking differentiator according to claim 1, characterized in that: in the step a, based on the formation styles and the communication topological structures corresponding to all the constructed quad-rotor unmanned aerial vehicles, the constraint models corresponding to the quad-rotor unmanned aerial vehicles are obtained as follows:

wherein I is more than or equal to 1 and less than or equal to I, I represents the number of the four-rotor unmanned aerial vehicles, X_i,p＝[X_i,p1,X_i,p2,X_i,p3]^TAnd X_i,v＝[X_i,v1,X_i,v2,X_i,v3]^TRespectively represents the ith four-rotor unmanned plane in an inertial coordinate system O_eX_eY_eZ_ePosition vector and velocity vector, X_i,Θ＝[X_i,Θ1,X_i,Θ2,X_i,Θ3]^TAnd X_i,ω＝[X_i,ω1,X_i,ω2,X_i,ω3]^TRespectively represent the i-th frame quad-rotor unmanned plane in a body coordinate system o_Bx_By_Bz_BThe lower attitude angle vector and the angular velocity vector,

the first derivative of the representation;

is shown asi-frame quad-rotor unmanned aerial vehicle position dynamic virtual control input, m_iMass, G, of the ith quad-rotor drone_i＝[0,0,m_ig]^TRepresenting a gravity matrix of the ith quad-rotor unmanned aerial vehicle, and g represents gravity acceleration; g_i,1Representing the i-th quad-rotor drone position input matrix, g, associated with attitude motion_i,1＝[cos(X_i,Θ3)sin(X_i,Θ2)cos(X_i,Θ1)+sin(X_i,Θ3)sin(X_i,Θ1),sin(X_i,Θ3)sin(X_i,Θ2)cos(X_i,Θ1)-cos(X_i,Θ3)sin(X_i,Θ1),cos(X_i,Θ2)cos(X_i,Θ1)]^T；u_i,1Represents the sum of the total thrust or lift of the propellers of the ith quad-rotor unmanned aerial vehicle, U_i,ω＝[u_i,2,u_i,3,u_i,4]^TRepresents the moment of the ith quad-rotor drone, u_i,1＝F_i,1+F_i,2+F_i,3+F_i,4,

u_i,3＝J_i,θ(l_iF_i,2-l_iF_i,4)，u_i,4＝J_i,ψ(-c_iF_i,1+c_iF_i,2-c_iF_i,3+c_iF_i,4)，l_iAnd c_iRespectively representing the distance from the mass center of the ith four-rotor unmanned aerial vehicle to the propeller motor and the moment coefficient, F_i,1、F_i,1、F_i,1、F_i,4Respectively representing the lift force, f, of the four propellers of the ith quad-rotor unmanned aerial vehicle_i,v(X_i,v)＝-Π_i,1X_i,v/m_iAnd

respectively representing parameterized uncertainty items pi in pneumatic coefficients of the ith frame of quad-rotor unmanned aerial vehicle_i,1Show the i-th frame quad-rotor unmanned aerial vehicle's trajectory loop damping matrix, pi_i,2Representing an attitude loop damping matrix for the ith quad-rotor drone,

represents the positive definite diagonal inertia matrix, delta, of the ith quad-rotor unmanned plane_i,v＝[Δ_i,v1,Δ_i,v2,Δ_i,v3]^TAnd Δ_i,ω＝[Δ_i,ω1,Δ_i,ω2,Δ_i,ω3]^TThe system and the method respectively represent bounded environmental interference borne by the ith quad-rotor unmanned aerial vehicle position ring and bounded environmental interference borne by the attitude ring.

3. The safe formation control method for the multi-quad rotor unmanned aerial vehicle based on the tracking differentiator according to claim 2, characterized in that: in the step A, constrained collaborative formation synchronization errors corresponding to each set of quad-rotor unmanned aerial vehicle are obtained as follows:

wherein I denotes the total number of quad-rotor drones, e_i,pkRepresent the constrained collaborative formation synchronization error of the kth element in the corresponding position vector of the ith quad-rotor drone, k being 1, 2, 3, N_iRepresent the neighborhood set, a, that each adjacent four rotor unmanned aerial vehicle of the ith frame of four rotor unmanned aerial vehicles constitutes_ijRepresent the information weight between the ith four-rotor unmanned aerial vehicle and the jth four-rotor unmanned aerial vehicle in the neighborhood set corresponding to the ith four-rotor unmanned aerial vehicle, and if the ith four-rotor unmanned aerial vehicle keeps communication with the jth four-rotor unmanned aerial vehicle in the neighborhood set corresponding to the ith four-rotor unmanned aerial vehicle, then a_ij＝a_ji> 0, otherwise, a_ij＝a_ji＝0；b_iRepresent the information weight between the fourth rotor unmanned aerial vehicle of ith frame and virtual navigator, and if the fourth rotor unmanned aerial vehicle of ith frame can acquire virtual navigator's positional information, then b_i> 0, otherwise b_i＝0；q_ij,kRepresenting the expected relative position deviation, X, of the kth element in the corresponding position vector between the ith four-rotor unmanned aerial vehicle and the jth four-rotor unmanned aerial vehicle in the neighbor set corresponding to the ith four-rotor unmanned aerial vehicle_i,pkExpress four rotor unmanned aerial vehicle of ith frameThe kth element, X, in the position vector_j,pkRepresents the kth element in the position vector of the jth quad-rotor drone in the neighborhood set corresponding to the ith quad-rotor drone,B _i,pkand

respectively representing the lower limit and the upper limit of a preset performance function of a kth element in a corresponding position vector of the ith four-rotor unmanned aerial vehicle,

representing the virtual pilot in an inertial frame O_eX_eY_eZ_eA position vector of (1); q. q.s_i,kRepresenting the expected relative positional deviation of the kth element in the corresponding position vector between the ith quad-rotor drone and the virtual pilot.

4. The safe formation control method for the multi-quad rotor unmanned aerial vehicle based on the tracking differentiator according to claim 3, characterized in that: in the step B, according to the restrained cooperative formation synchronous error e corresponding to each four-rotor unmanned aerial vehicle_i,pkApplying an error transformation method, according to

Combining the following equations:

obtaining the unconstrained cooperative formation synchronous error Z corresponding to each four-rotor unmanned aerial vehicle_i,pkWherein, in the step (A),B _i,pkand

the following were used:

wherein the content of the first and second substances,δ _i,pkfor determining a preset performance function lower limit, anδ _i,pkIs a constant number greater than or equal to 1,

for determining a preset performance function lower limit, an

Is a constant number greater than or equal to 1,

for a design parameter greater than 0 a and,

for adjusting the error e_i,pkThe convergence speed of the light source is increased,

and

are each a design parameter greater than 0,

and

for determining performance boundaries for synchronization errors.

5. The safe formation control method for the multi-quad rotor unmanned aerial vehicle based on the tracking differentiator according to claim 4, characterized in that: the step C comprises the following steps C1 to C2:

step C1, according to the unconstrained cooperative formation synchronous errors corresponding to each four-rotor unmanned aerial vehicle, according to the following formula:

obtaining a speed dynamic virtual control law of each four-rotor unmanned aerial vehicle, and using the speed dynamic virtual control law to stabilize the unconstrained cooperative formation synchronous error of a position loop; wherein alpha is_i,vkThe speed dynamic virtual control law of the kth element in the corresponding position vector of the ith four-rotor unmanned aerial vehicle is expressed, and k is 1, 2 and 3_i,pkThe position ring of the ith four-rotor unmanned aerial vehicle is respectively corresponding to the adjustable gain of the controller under the three components of the position vector,

representing the total information weight between the ith four-rotor unmanned aerial vehicle and all the four-rotor unmanned aerial vehicles in the corresponding neighborhood set, and then entering step C2;

step C2. uses hyperbolic tangent tracking differentiator according to the following formula:

obtaining speed differential control signals and angular speed differential control signals of all the four-rotor unmanned aerial vehicles, wherein eta_1i,vkA speed differential control signal r representing the kth element in the corresponding position vector of the ith quad-rotor drone_i,vk、τ_1i,vk、τ_2i,vk、ζ_1i,vk、ζ_2i,vkAnd D, positive design parameters of the corresponding speed of the hyperbolic tangent tracking differentiator are obtained, and then the step D is carried out.

6. The safe formation control method for the multi-quad rotor unmanned aerial vehicle based on the tracking differentiator according to claim 5, characterized in that: the step D comprises the following steps D1 to D5;

step D1, establishing the self-adaptive neural network interference estimator corresponding to each four-rotor unmanned aerial vehicle as follows:

wherein the content of the first and second substances,

γ_i,v＝diag(γ_i,v1,γ_i,v2,γ_i,v3) Representing the adaptive gain matrix, gamma, of the i-th quad-rotor drone velocity ring_i,v1、γ_i,v2、γ_i,v3Respectively represents the adaptive gain, sigma, corresponding to three components of the speed ring of the ith four-rotor unmanned aerial vehicle_i,v＝diag(σ_i,v1,σ_i,v2,σ_i,v3) Representing the self-adaptive update law correction factor matrix, sigma, of the ith quad-rotor unmanned plane speed loop_i,v1、σ_i,v2、σ_i,v3Respectively representing correction factors corresponding to the self-adaptive update law of three components of the speed ring of the ith four-rotor unmanned aerial vehicle,

representing the ideal weight vector of the ith quad-rotor drone speed ring,

respectively representing the ideal weight of three components of the speed ring of the ith four-rotor unmanned plane, and simultaneously,

_hi,va gaussian basis function vector representing the ith quad-rotor drone velocity ring,

representing the input quantity of the corresponding Gaussian base function of the ith quad-rotor unmanned plane,

respectively represents the ith four-rotor unmanned plane in an inertial coordinate system O_eX_eY_eZ_eThen to step D2;

step D2., constructing adaptive neural network cooperative formation controllers corresponding to the four-rotor unmanned aerial vehicles respectively as follows to form speed loop controllers corresponding to the four-rotor unmanned aerial vehicles respectively;

wherein k is_i,v＝diag(k_i,v1,k_i,v2,k_i,v3) Represents the i-th quad-rotor unmanned plane speed loop controller gain matrix, k_i,v1、k_i,v2、k_i,v3Represents the adjustable gain of the controller corresponding to three components of the ith four-rotor unmanned plane speed loop, e_i,vFor the i-th frame quad-rotor unmanned aerial vehicle speed tracking error vector, e_i,v＝X_i,v-η_1i,v，η_2i,vIs alpha_i,vFirst order differential signal, eta, filtered by a tracking differentiator_2i,v＝{η_2i,v1,η_2i,v2,η_2i,v3}，α_i,v＝{α_i,v1,α_i,v2,α_i,v3}；F_i,vA virtual control input representing a corresponding speed of an ith quad-rotor drone; wherein, for four rotor unmanned aerial vehicle speed control, then F_i,vIs in relation to the desired tension u_i,1The following relationship is satisfied:

wherein u is_i,1Representing the total thrust of the i-th quad-rotor drone propeller,

respectively representDesired roll angle, desired pitch angle, desired yaw angle, then u, of the ith quad-rotor drone produced by the speed loop control signal_i,1And the desired roll and pitch angles are as follows:

and based on anticipated attitude angle of ith frame quad-rotor unmanned aerial vehicle

According to the following formula:

obtaining attitude angle differential control signal eta of each frame of quadrotor unmanned aerial vehicle_1i,ΘkWherein r is_i,Θk、τ_1i,Θk、τ_2i,Θk、ζ_1i,Θk、ζ_2i,ΘkIs a positive design parameter of the hyperbolic tangent tracking differentiator corresponding to the attitude angle,

is composed of

The kth component of (a);

wherein the yaw angle

Set by the operator; then step D3 is entered; wherein, F_i,v1、F_i,v2、F_i,v3Respectively representing the virtual control input, u, of each element in the corresponding position vector of the ith quad-rotor unmanned aerial vehicle with respect to speed_i,1For the total thrust of the four propellers of the ith quad-rotor drone,

respectively representing an expected roll angle and an expected pitch angle of the ith quad-rotor unmanned aerial vehicle;

d3, constructing attitude angle control laws corresponding to the four-rotor unmanned aerial vehicles respectively as follows:

α_i,ω＝-k_i,Θe_i,Θ+η_2i,Θ (10)

further obtaining angular velocity differential control signals eta of each four-rotor unmanned aerial vehicle_1i,ωkThe following were used:

wherein r is_i,ωk、τ_1i,ωk、τ_2i,ωk、ζ_1i,ωk、ζ_2i,ωkIs a positive design parameter, k, of the hyperbolic tangent tracking differentiator corresponding to the angular velocity_i,Θ＝diag(k_i,Θ1,k_i,Θ2,k_i,Θ3)，k_i,Θ1,k_i,Θ2,k_i,Θ3Positive controller gain, e_i,Θ＝X_i,Θ-η_1i,Θ，η_1i,Θ＝{η_1i,Θ1,η_1i,Θ2,η_1i,Θ3Is the expected attitude angle of the ith frame of quad-rotor unmanned aerial vehicle

Signal k filtered by hyperbolic tangent tracking differentiator_i,Θ＝{k_i,Θ1,k_i,Θ2,k_i,Θ3Denotes the ith four-rotor unmanned plane attitude angle controller gain matrix, k_i,Θ1、k_i,Θ2、k_i,Θ3Respectively representing the adjustable gain of the controller corresponding to three components of the attitude angle of the ith four-rotor unmanned aerial vehicle, e_i,ΘRepresenting the attitude angle tracking error vector, eta, of the ith quad-rotor unmanned plane_2i,Θ＝{η_2i,Θ1,η_2i,Θ2,η_2i,Θ3Means for

Passing through tracking differentiatorA filtered first order differential signal; then step D4 is entered;

step D4. is according to e_i,ω＝X_i,ω-η_1i,ω，η_1i,ω＝{η_1i,ωkAnd designing the angular speed control laws corresponding to the four-rotor unmanned aerial vehicles respectively as follows:

wherein, U_i,ωRepresents the angular velocity loop control vector, k, corresponding to the ith quad-rotor drone_i,ω＝{k_i,ω1,k_i,ω2,k_i,ω3Denotes the i-th frame quad-rotor unmanned aerial vehicle angular velocity controller gain matrix, k_i,ω1、k_i,ω2、k_i,ω3Respectively representing the adjustable gain of the controller for three components of angular velocity, e_i,ωRepresenting the corresponding angular velocity tracking error vector, gamma, of the ith quad-rotor unmanned aerial vehicle_i,ω＝{γ_i,ω1,γ_i,ω2,γ_i,ω3Denotes the i-th frame quad-rotor unmanned aerial vehicle angular velocity loop adaptive gain matrix, gamma_i,ω1、γ_i,ω2、γ_i,ω3Respectively shows the adaptive gains corresponding to three components of the angular velocity ring of the ith frame of the quad-rotor unmanned aerial vehicle,

represents an ideal weight vector of the i-th quad-rotor drone angular velocity ring,

respectively representing ideal weights h of three components of an i-th frame quad-rotor unmanned aerial vehicle angular velocity ring_i,ωA gaussian basis function vector representing the i-th quad-rotor drone angular velocity ring,

represent the ideal weight vector corresponding to the ith frame of quad-rotor unmanned aerial vehicle

Estimate of, σ_i,ω＝{σ_i,ω1,σ_i,ω2,σ_i,ω3Indicates the i-th frame of the quadrotor unmanned aerial vehicle angular velocity ring self-adaptive update law correction factor matrix, sigma_i,ω1、σ_i,ω2、σ_i,ω3Respectively representing correction factors, eta, corresponding to the adaptive update law of three components of the angular velocity ring of the ith four-rotor unmanned aerial vehicle_2i,ωDenotes alpha_i,ω＝{α_i,ω1,α_i,ω2,α_i,ω3The first order differential signal after being filtered by the tracking differentiator,

is the input quantity of the gaussian basis function,

respectively represent the i-th frame quad-rotor unmanned plane in a body coordinate system o_Bx_By_Bz_BA lower attitude angle vector and an angular velocity vector; then step D5 is entered;

and D5., forming attitude ring controllers corresponding to the four-rotor unmanned aerial vehicles respectively by the attitude angle control law and the angular speed control law corresponding to the four-rotor unmanned aerial vehicles respectively.

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