CN112230670A - Formation control method for multi-four-rotor aircraft with predictor - Google Patents

Abstract

The invention provides a formation control method of a multi-four-rotor aircraft with a predictor, which comprises the following steps: step 1, setting a four-rotor aircraft as a leader, setting N four-rotor aircraft with unknown dynamics as followers, and using a networked system formed by connecting the followers and the leader through a one-way topological graph as a controlled object; step 2, the ith follower in the N followers is provided with a position controller and an attitude controller, the input ends of the position controller and the attitude controller of the ith follower are connected with the output end of the directed graph G, the output end of the position controller of the ith follower is connected with the input end of the position controller of the ith follower, and the output end of the attitude controller of the ith follower is connected with the input end of the attitude controller of the ith follower; the control method realizes collision avoidance, connection maintenance and completion of the expected formation among the multi-four-rotor aircraft, avoids obstacles and completes the formation control target within a preset performance range.

Description

Formation control method for multi-four-rotor aircraft with predictor

Technical Field

The invention relates to a design of a multi-four-rotor aircraft formation collision avoidance controller with an estimator, and belongs to the technical field of industrial process control.

Background

In recent years, the four-rotor aircraft is very suitable for tasks such as near-field reconnaissance, monitoring, aerial photography, agricultural scattering and the like due to the advantages of small volume, light weight and the like, and is widely applied to military and civil fields. However, quad-rotor aircraft have had a centurie history of development, and the first quad-rotor helicopter in the world was first manufactured by the Breguet brother Louis france in 1907. The french engineer, etianne oemhen, by the mark automobile company, designed the oldest hover-capable quad-rotor aircraft in 1924. In 1956, the american designer Convertawing built a quad-rotor aircraft using two engines, the attitude of which was controlled by varying the speed of each propeller. However, due to limitations in generator size, etc., until the nineties of the twentieth century, there has been no significant progress in the development of quad-rotor aircraft. In recent decades, with the development of microsystem technology, sensor technology, control theory, etc., research on quad-rotor aircrafts has begun to break through.

The modern four-rotor aircraft has light weight and weak anti-interference capability, and has high requirement on the attitude control precision of the aircraft, so that the establishment of an aircraft mathematical model and the design of a control system become complicated, great challenges exist, and important research significance is realized in theory and practical application. In addition, the system control research of the multi-aircraft has stronger superiority than the system control research of a single aircraft, and can efficiently complete tasks and realize complex tasks which are difficult to complete by the single aircraft through mutual cooperation. By using the formation control technology of the unmanned aerial vehicle, the purposes of high efficiency and rapidness can be achieved in the aspects of agricultural seeding, pesticide spraying and the like, and the potential safety hazard is reduced; in the military aspect, the unmanned aerial vehicle group has the characteristics of penetration reconnaissance, decoy interference, cooperative operation and the like, and can meet the effective implementation of the modern military attack strategy. Therefore, the formation control technology of the unmanned aerial vehicle has wide application prospect in the fields of agriculture and military.

In the practical application of the four-rotor aircraft, a single aircraft is difficult to complete complex tasks, and due to the fact that the aircraft has unknown dynamics, the aircraft can be subjected to external unknown disturbances such as strong wind and airflow, and the aircraft can encounter obstacles in the flight process, and other complex conditions, the controller design has important practical significance for the anti-disturbance formation of the multiple four-rotor aircraft including the conditions of obstacle avoidance, collision avoidance and the like.

Disclosure of Invention

The invention aims to provide a formation control method of a multi-four-rotor aircraft with an estimator, which is used for realizing collision avoidance, connection maintenance and completion of expected formation among the multi-four-rotor aircraft, avoiding obstacles and completing a formation control target within a preset performance range.

In order to achieve the above purpose, the invention provides a formation control method of a multi-four-rotor aircraft with an estimator, which comprises the following steps:

step 1, setting a four-rotor aircraft as a leader, setting N four-rotor aircraft with unknown dynamics as followers, and using a networked system formed by connecting the followers and the leader through a one-way topological graph as a controlled object; step 2, the ith follower in the N followers is provided with a position controller and an attitude controller, and the input ends of the position controller and the attitude controller of the ith follower are connected with the directed graph

The output end of the position controller of the ith follower is connected with the input end of the position controller of the ith follower, and the output end of the posture controller of the ith follower is connected with the input end of the posture controller of the ith follower; and 3, providing a leader expectation signal by the leader, outputting position information by the position controller of the follower, outputting posture information by the posture controller of the follower, and forming an expected formation form by the output of the follower and the leader by utilizing the position information and the posture information of the follower.

As a further technical solution of the present invention, the position controller in the step 2The specific definition is as follows: the system comprises a potential energy function operation unit, an error conversion operation unit, a first nonlinear operation unit, a first comparator unit, a first tracking differentiator unit, a position system neural network weight updating unit, a position system neural network activation function unit, a second nonlinear operation unit, a position system predictor operation unit, a second comparator unit, a position system disturbance observer unit, a third nonlinear operation unit, a first filtering unit and a position input nonlinear operation unit; two input ends of the potential energy function operation unit are respectively the output χ of the ith follower_i,1And the position of the obstacle ×_c(ii) a The input ends of the error conversion operation units are directed graphs respectively

Output information χ of jth follower in (1)_j,1Hexix-_j,2Adjacent communication a_ijAnd b_iLeader information χ_dAnd

output χ of ith follower_i,1(ii) a The input ends of the first nonlinear operation units are directed graphs respectively

State χ of jth follower in (1)_j,2Adjacent communication a_ijAnd b_iLeader derivative information

Output of potential energy function arithmetic unit

Output e of error conversion arithmetic unit_i,1、Π_i,jAnd pi_i,0(ii) a The first comparator unit is an error surface e_i,2,χThe input end of the system is in a position system state x_i,2And the output alpha of the first non-linear operation unit_i,2,χ(ii) a The input end of the first tracking differentiator unit is a first nonlinear operationOutput of the computing unit alpha_i,2,χ(ii) a The input end of the position system neural network activation function unit is a position system state x_i,2And the output u of the first filtering unit_i,χ,f(ii) a The input end of the position system neural network weight updating unit is the output phi of the position system neural network activation function unit_i,χAnd the output of the second comparator unit

The input ends of the second nonlinear operation units are respectively the output phi of the position system neural network activation function unit_i,χOutput of the weight updating unit

And the output of the second comparator unit

The input ends of the position system predictor operation unit are respectively the output of the second comparator unit

Output of the second non-linear operation unit

Output of a position system disturbance observer unit

And the output u of the third non-linear operation unit_i,χ(ii) a The input end of the second comparator unit is the output of the position system predictor operation unit

And position system state χ_i,2(ii) a The input end of the position system disturbance observer unit is the output of the second comparator unit

Position system state ×_i,2The first stepOutput of two non-linear arithmetic units

And the output u of the third non-linear operation unit_i,χ(ii) a The input end of the third nonlinear operation unit is the output e of the error conversion operation unit_i,1,χAnd pi_i,jThe output r of the first tracking differentiator unit_i,2,χThe output e of the first comparator unit_i,2,χOutput of a position system disturbance observer unit

Output of the second non-linear operation unit

The input end of the first filtering unit is the output u of the third nonlinear operation unit_i,χ(ii) a The input end of the position input nonlinear operation unit is the output u of the third nonlinear operation unit_i,χ。

As a further technical solution of the present invention, the attitude controller in step 2 is specifically defined as follows: the system comprises an expected attitude angle linear operation unit, a third comparator unit, a second differential tracker unit, a fourth nonlinear operation unit, a second filtering unit, a fourth comparator unit, an attitude system neural network activation function unit, an attitude system neural network weight updating unit, a fifth nonlinear operation unit, an attitude system predictor operation unit, a fifth comparator unit, an attitude system disturbance observer unit, a sixth nonlinear operation unit and a third filtering unit; the input of the expected attitude angle linear operation unit is the output u of the position input nonlinear operation unit_i,1And the desired yaw angle ψ of the leader_d(ii) a The input ends of the third comparator units are respectively the attitude angle p of the ith follower_iDesired attitude angle nonlinear operation unit output p_d(ii) a The input end of the second differential tracker unit is the output p of the expected attitude angle nonlinear operation unit_d(ii) a The input of the fourth nonlinear operation unit is a second differential tracker unitOutput r_i,2,pAnd the output e of the third comparator unit_i,1,p(ii) a The input end of the second filtering unit outputs alpha to the fourth nonlinear operation unit_i,2,p(ii) a The fourth comparator unit is an error surface e_i,2,pWith input terminal in attitude system state p_i,2And the output of the second filtering unit

The input end of the attitude system neural network activation function unit is an attitude system state p_i,2And the output u of the third filtering unit_i,p,f(ii) a The input end of the attitude system neural network weight updating unit is the output phi of the attitude system neural network activation function unit_i,pAnd the output of the fifth comparator unit

The input ends of the fifth nonlinear operation units are respectively the output phi of the attitude system neural network activation function unit_i,pOutput of the weight updating unit

And the output of the fifth comparator unit

The input ends of the attitude system predictor operation units are respectively the output of a fifth comparator unit

Output of the fifth nonlinear operation unit

Output of the attitude system disturbance observer unit

And the output u of the sixth nonlinear operation unit_i,p(ii) a The input end of the fifth comparator unit is the output of the attitude system predictor operation unit

And attitude System State p_i,2(ii) a The input end of the attitude system disturbance observer unit is the output of a fifth comparator unit

Output of the fifth nonlinear operation unit

And the output u of the sixth nonlinear operation unit_i,p(ii) a The input end of the sixth nonlinear operation unit is the output e of the third comparator unit_i,1,pThe output of the second filtering unit

Fourth comparator unit output e_i,2,pOutput of a disturbance observer unit of an attitude system

Output of the fifth nonlinear operation unit

The input end of the third filtering unit is the output u of the sixth nonlinear operation unit_i,p。

As a further technical scheme of the invention, the directed graph in the step 2 is defined as

Wherein

Representing a set of N nodes, v₁,…,ν_NRepresenting follower 1 through follower N,

representing sets of edges, topological graphs

Is represented by (v)_i,ν_j)，ν_i,ν_jRespectively representing the ith follower and the jth follower; if it is

V is then_jV is_iAdjacent node of (2) representing v_iIs a neighboring node of

The adjacency matrix of followers in the directed graph is defined as

If it is not

Then a_ij1, otherwise a_ij0; the degree matrix of the follower in the directed graph is defined as D ═ diag [ D ═ D₁,…,d_N]Wherein

The Laplace matrix of followers in the directed graph is defined as

Wherein

The adjacency matrix between the leader and the follower in the directed graph is defined as B ═ diag [ B ═ B₁,…,b_N]If the ith follower can access the information of the leader, b _i1, otherwise b_i＝0。

As a further technical solution of the present invention, the mathematical model of the ith four-rotor aircraft in the follower in step 2 is:

wherein

Indicating the positional acceleration of the ith follower,

respectively represents three attitude angular accelerations of the i-th follower, namely roll, pitch and yaw, m_iIs the quality of the ith follower, I_x,i、I_y,i、I_z,iIs the moment of inertia, ξ, of the ith follower_x,i、ξ_y,i、ξ_z,i、ξ_φ,i、ξ_θ,i、ξ_ψ,iRepresenting the aerodynamic damping coefficient of the i-th follower, g is the gravitational acceleration, d_i,1、d_i,2、d_i,3、d_i,4、d_i,5、d_i,6Is the disturbance, u, to the ith follower_i,1、u_i,2、u_i,3、u_i,4Is the control force of the ith follower;

let the position system status of the follower be X_i，1＝[χ_i，1,x,χ_i，1,y,χ_i，1,z]^T＝[x_i,y_i,z_i]^TAnd

let the state of the follower's posture system be p_i,1＝[p_i,1,φ,p_i,1,θ,p_i,1,ψ]^T＝[φ_i,θ_i,ψ_i]^TAnd

wherein the virtual control input in the x, y, z directions is Q_i,x、Q_i,y、Q_i,z，

The mathematical model of a quad-rotor aircraft may be transformed into fourRotorcraft position system

And four-rotor aircraft attitude system

Wherein u is_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TAnd u_i,p＝[u_i,2,u_i,3,u_i,4]^TRespectively inputting a position system and an attitude system;

F_i,χ,f＝f_i,χ+g_i,χu_i,χ,f-u_i,χ,ffor the system dynamics of the converted position,

F_i,p,f＝f_i,p+g_i,pu_i,p,f-u_i,p,fis a transformed pose system dynamic, wherein

g_i,χ＝diag[1/m_i,1/m_i,1/m_i]，

u_i,χ,fAnd u_i,p,fRespectively as position system input u_i,χAnd gesture System input u_i,pOutput through a first order filter; the error generated by the conversion of the position system and the error generated by the conversion of the attitude system are respectively Δ F_i,χ＝(g_i,χ-1)(u_i,χ-u_i,χ,f) And Δ F_i,p＝(g_i,p-1)(u_i,p-u_i,p,f) (ii) a The unknown disturbance on the position system and the attitude system is d_i,χ＝[d_i,1,d_i,2,d_i,3]^TAnd d_i,p＝[d_i,4,d_i,5,d_i,6]^T。

As a further technical solution of the present invention, the specific operation content of the position controller in step 3 is as follows, a1, and a potential energy function operation unit: two input ends of the potential energy function operation unit are respectively the output χ of the ith follower_i,1And the position of the obstacle ×_c(ii) a Is a potential energy function of the energy calculation unit of

Wherein s is_i,c＝χ_i-χ_cDifference between position coordinates of i-th follower and c-th obstacle, χ_c＝[x_c,y_c,z_c]^TFor the coordinates of the c-th obstacle,

the distance between the ith follower and the c-th obstacle is defined as r, the obstacle detection distance is defined as r, and d is the minimum obstacle avoidance distance; potential energy function pair chi_iThe partial derivatives of (a) are obtained by calculation of the following formula:

a2, error conversion arithmetic unit: the input ends of the error conversion arithmetic units are respectively directed graphs

Output information χ of jth follower in (1)_j,1Hexix-_j,2Adjacent communication a_ijAnd b_iLeader information χ_dAnd

output χ of ith follower_i,1(ii) a Calculating the error position conversion function by the following formula

And calculate

Wherein

L_i,jAnd L_i,0Indicates the connection holding distance, D_i,jAnd D_i,0Indicating the desired formation distance, R_i,jAnd R_i,0Represents the minimum safe distance, s_i,j＝χ_i-χ_jDistance error, s, for follower i and follower j_i,0＝χ_i-χ_dThe distance error between the follower i and the leader is obtained;

a3, first nonlinear operation means: the input ends of the first nonlinear operation units are directed graphs respectively

State χ of jth follower in (1)_j,2Adjacent communication a_ijAnd b_iLeader derivative information

Output of potential energy function arithmetic unit

Output e of error conversion arithmetic unit_i,1、Π_i,jAnd pi_i,0(ii) a The output alpha of the first nonlinear operation unit is obtained through calculation of the following formula_i,2.χ：

Wherein k is_i,1,χ>0 is a parameter to be designed,

a4, first comparator cell error surface e_i,2,χ: first comparator sheetElement is error surface e_i,2,χThe input end of the system is in a position system state x_i,2And the output alpha of the first non-linear operation unit_i,2,χ(ii) a E is obtained by calculation of the following formula_i,2,χ：e_i,2,χ＝χ_i,2-α_i,2,χ；

A5, first tracking differentiator unit: the input end of the first tracking differentiator unit is the output alpha of the first nonlinear operation unit_i,2,χ(ii) a The first tracking differentiator output r is obtained by calculation of the following formula_i,2,χDerivative of (2)

Wherein r is_i,2,χIs the output alpha of the first non-linear operation unit_i,2,χEstimation of the derivative, λ_TD>0 is the tracking differentiator velocity factor, α_TDE (0,1) is a filtering factor of a tracking differentiator;

a6, a position system neural network activation function unit: the input end of the position system neural network activation function unit is the position system state x_i,2And the output u of the first filtering unit_i,χ,f(ii) a Position system neural network activation function unit output phi_i,χThe following formula is used for calculation:

wherein gamma is_i,χ>0 is a parameter to be designed,

as a function of activation,%_i,2,x、χ_i,2,yHexix-_i,2,zIs a position system state χ_i,2Element of (5), Q_i,x,f、Q_i,y,fAnd Q_i,z,fIs the output u of the first filtering unit_i,χ,fThe element in (1) is the central value of the activation function, mu and xi are the widths of the activation function; finally obtaining the output

A6, a location system neural network weight updating unit: the input end of the position system neural network weight value updating unit is the output phi of the position system neural network activation function unit_i,χAnd the output of the second comparator unit

The weight value updating unit output of the neural network of the position system is obtained through the calculation of the following formula

Wherein phi_i,x、Φ_i,yAnd phi_i,zActivating the output phi of the functional unit for the neural network of the position system_i,χThe elements (A) and (B) in (B),

and

is the output of the second comparator unit

Of (b), gamma_i,χ>0 and σ_i,χ>0 is a parameter to be designed; finally obtaining the output

A7, second nonlinear operation means: the input ends of the second nonlinear operation units are respectively the output phi of the position system neural network activation function unit_i,χOutput of the weight updating unit

And the output of the second comparator unit

Performing product calculation on all input ends to obtain the output of the second nonlinear operation unit

A8, position system predictor operation unit: the input ends of the position system predictor operation units are respectively the output ends of the second comparator units

Output of the second non-linear operation unit

Output of a position system disturbance observer unit

And the output u of the third non-linear operation unit_i,χ(ii) a The output of the computing unit of the position system predictor is obtained through the calculation of the following formula

Wherein h is_i,χ>0 is a parameter to be designed;

A9、a second comparator unit: the input end of the second comparator unit is the output of the position system predictor operation unit

And position system state χ_i,2；

The output estimated error of the second comparator is obtained through the calculation of the following formula

A10, position system disturbance observer unit: the input end of the position system disturbance observer unit is the output of the second comparator unit

Position system state ×_i,2The output of the second non-linear operation unit

And the output u of the third non-linear operation unit_i,χ(ii) a The output of the position system disturbance observer is obtained by the calculation of the following formula

Wherein c is_d,i,χ>0 is a parameter to be designed;

a11, third nonlinear operation means: the input end of the third nonlinear operation unit is the output e of the error conversion operation unit_i,1,χAnd pi_i,j，0The output r of the first tracking differentiator unit_i,2,χThe output e of the first comparator unit_i,2,χOutput of a position system disturbance observer unit

Output of the second non-linear operation unit

Obtaining the virtual control input u of the position system by the calculation of the following formula_i,χ：

Wherein k is_i,2,χ>0 is a parameter to be designed;

a12, first filtering unit: the input end of the first filtering unit is the output u of the third nonlinear operation unit_i,χ(ii) a The output u of the first filtering unit is obtained through the calculation of the following formula_i,χ,f：

Wherein eta is_i,χIs the filter time constant;

a13, position input nonlinear operation means: the input end of the position input nonlinear operation unit is the output u of the third nonlinear operation unit_i,χ(ii) a The output u of the position input nonlinear operation unit is obtained by the calculation of the following formula_i,1：

Wherein Q_i,x、Q_i,yAnd Q_i,zIs the output u of the third non-linear operation unit_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TThe elements of (1); to this end, a position system input u is obtained_i,1。

As a further technical solution of the present invention, the specific calculation content of the attitude controller in step 3 is as follows, B1, desired attitude angle nonlinear calculation means: the input of the desired attitude angle linear operation unit is the output u of the third nonlinear operation unit_i,χAnd the desired yaw angle ψ of the leader_d(ii) a Phi is obtained by the calculation of the following formula_dAnd theta_dThen obtaining the expected attitude angleNon-linear arithmetic unit output

Wherein Q_i,x、Q_i,y、Q_i,zIs the output u of the third non-linear operation unit_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TThe elements of (1);

b2, design of third comparator cell: the input ends of the third comparator units are respectively the attitude angle p of the ith follower_i,1Desired attitude angle nonlinear operation unit output p_d(ii) a The output e of the third comparator unit is obtained by calculation of the following formula_i,1,p：e_i,1,p＝p_i,1-p_d(ii) a B3, second differential tracker unit: the input end of the second differential tracker unit is the output p of the expected attitude angle nonlinear operation unit_d(ii) a The output r of the second differential tracker is obtained by calculation of the following formula_i,2,p：

Wherein r is_i,2,pIs the output p of the desired attitude angle nonlinear arithmetic unit_dEstimation of the derivative, λ_TD>0 is the tracking differentiator velocity factor, α_TDE (0,1) is a filtering factor of a tracking differentiator;

b4, fourth nonlinear operation means: the input of the fourth nonlinear operation unit is the output r of the second differential tracker unit_i,2,pAnd the output e of the third comparator unit_i,1,p(ii) a The output alpha of the fourth nonlinear operation unit is obtained through the calculation of the following formula_i,2,p：

α_i,2,p＝-k_i,1,pe_i,1,p+r_i,2,pWherein k is_i,1,p>0 is a parameter to be designed;

b5, second filtering unit: of the second filtering unitThe input end is the output alpha of the fourth nonlinear operation unit_i,2,p(ii) a The output of the second filtering unit is obtained through the calculation of the following formula

And

wherein eta_i,pIs the filter time constant.

B6, fourth comparator unit: the fourth comparator unit is an error surface e_i,2,pWith input terminal in attitude system state p_i,2And the output of the second filtering unit

The output e of the fourth comparator unit is obtained by calculation of the following formula_i,2,p：

B7, a neural network activation function unit of the attitude system: the input end of the neural network activation function unit of the attitude system is an attitude system state p_i,2And the output u of the third filtering unit_i,p,f(ii) a The output phi of the neural network activation function unit of the attitude system is obtained by calculation of the following formula_i,p：

Wherein gamma is_i,p>0 is a parameter to be designed,

for activating functions, p_i,2,φ、p_i,2,θAnd p_i,2,ψIs an attitude system state p_i,2Element (ii) u_i,2,f、u_i,3,fAnd u_i,4,fIs the output u of the third filtering unit_i,p,fThe element in (1) is the central value of the activation function, mu and xi are the widths of the activation function; finally obtaining the output

B8, a posture system neural network weight updating unit: the input end of the attitude system neural network weight updating unit is the output phi of the attitude system neural network activation function unit_i,pAnd the output of the fifth comparator unit

The weight value updating unit output of the neural network of the attitude system is obtained through the calculation of the following formula

Wherein phi_i,φ、Φ_i,θAnd phi_i,ψActivating the output phi of the functional unit for the neural network of the attitude system_i,pThe elements (A) and (B) in (B),

and

is the output of the second comparator unit

Wherein, Γ_i,p>0 and σ_i,p>0 is a parameter to be designed; finally obtain the outputGo out

B9, fifth nonlinear operation means: the input ends of the fifth nonlinear operation units are respectively the output phi of the attitude system neural network activation function unit_i,pOutput of the weight updating unit

And the output of the fifth comparator unit

Performing product calculation on all input ends to obtain the output of a fifth nonlinear operation unit

B10, attitude system predictor operation unit: the input ends of the attitude system predictor operation units are respectively the output of the fifth comparator unit

Output of the fifth nonlinear operation unit

Output of the attitude system disturbance observer unit

And the output u of the sixth nonlinear operation unit_i,p(ii) a The output of the attitude system predictor operation unit is obtained through the calculation of the following formula

Wherein the content of the first and second substances,

is a parameter to be designed;

b11, fifth comparator unit: the input end of the fifth comparator unit is the output of the attitude system predictor operation unit

And attitude System State p_i,2(ii) a The estimated error of the output attitude system of the fifth comparator is obtained through the calculation of the following formula

B12, attitude system disturbance observer unit: the input end of the attitude system disturbance observer unit is the output of the fifth comparator unit

Output of the fifth nonlinear operation unit

And the output u of the sixth nonlinear operation unit_i,p(ii) a The output of the attitude system disturbance observer is obtained through the calculation of the following formula

Wherein

Is a parameter to be designed;

b13, sixth nonlinear operation means: the input end of the sixth nonlinear operation unit is the output e of the third comparator unit_i,1,pThe output of the second filtering unit

Fourth comparator unit output e_i,2,pOutput of a disturbance observer unit of an attitude system

Output of the fifth nonlinear operation unit

Obtaining the control input u of the attitude system by the calculation of the following formula_i,p：

Wherein

Is a parameter to be designed;

b14, third filtering unit: the input end of the third filtering unit is the output u of the sixth nonlinear operation unit_i,p(ii) a The output u of the third filtering unit is obtained through the calculation of the following formula_i,p,f：

Wherein eta is_i,pIs the filter time constant.

Compared with the prior art, the invention has the following technical effects: 1) the invention designs a novel potential energy function, which has the advantages that after an obstacle enters the detection range of an aircraft, the designed potential energy function is smoothly increased from zero along with the approach of the distance between the aircraft and the obstacle, so that the potential energy function is prevented from being suddenly changed when the aircraft meets the obstacle, and the abrasion of an actuator mechanism is prevented from occurring for a long time.

2) The invention designs a neural network based on a predictor, estimates the norm of the ideal weight of the neural network, reduces the number of learning parameters required by a controller, overcomes the problem of excessive learning parameters in the traditional neural network method, updates the weight by using a prediction error, improves the approximation performance of the neural network and enlarges the selection range of the parameters of the controller.

3) The invention designs a disturbance observer which is used for observing generalized disturbance including external unknown disturbance, system transformation error and neural network approximation error, the disturbance observer and the neural network based on estimation error update have combined action, the approximation precision of the system dynamic is greatly improved, and the disturbance observer avoids the occurrence of high-frequency oscillation phenomenon caused by overlarge self-adaptive control parameters or improper proportion by means of the neural network based on the predictor.

Drawings

Fig. 1 is a schematic structural diagram of a formation collision avoidance controller for a multi-quad rotor aircraft including an estimator according to the present invention.

Figure 2 is a topology of two quad-rotor aircraft and a leader.

Fig. 3 is a diagram of the obstacle avoidance formation motion trajectories of two quad-rotor aircraft and a leader.

Figure 4 shows the collision avoidance and communication maintenance performance effects of two quad-rotor aircraft.

Fig. 5 is a control input curve for two quad-rotor aircraft.

Figure 6 is a dynamic approximation of the effect of the first quad-rotor aircraft.

Fig. 7 shows the potential energy function and its partial derivative when the first aircraft encounters an obstacle.

Detailed Description

The technical scheme of the invention is further explained in detail by combining the attached drawings 1-2:

the invention provides a formation control method of a multi-four-rotor aircraft with a predictor, which comprises the following steps:

step 1, setting a four-rotor aircraft as a leader, setting N four-rotor aircraft with unknown dynamics as followers, and using a networked system formed by connecting the followers and the leader through a one-way topological graph as a controlled object;

step 2, N follow-upThe ith follower is provided with a position controller and an attitude controller, and the input ends of the position controller and the attitude controller of the ith follower are connected with a directed graph

The output end of the position controller of the ith follower is connected with the input end of the position controller of the ith follower, and the output end of the posture controller of the ith follower is connected with the input end of the posture controller of the ith follower;

the position controller is specifically defined as follows:

the system comprises a potential energy function operation unit, an error conversion operation unit, a first nonlinear operation unit, a first comparator unit, a first tracking differentiator unit, a position system neural network weight updating unit, a position system neural network activation function unit, a second nonlinear operation unit, a position system predictor operation unit, a second comparator unit, a position system disturbance observer unit, a third nonlinear operation unit, a first filtering unit and a position input nonlinear operation unit; two input ends of the potential energy function operation unit are respectively the output χ of the ith follower_i,1And the position of the obstacle ×_c(ii) a The input ends of the error conversion arithmetic units are respectively directed graphs

Output information χ of jth follower in (1)_j,1Hexix-_j,2Adjacent communication a_ijAnd b_iLeader information χ_dAnd

output χ of ith follower_i,1(ii) a The input ends of the first nonlinear operation units are directed graphs respectively

State χ of jth follower in (1)_j,2Adjacent communication a_ijAnd b_iLeader derivative information

Output of potential energy function arithmetic unit

Output e of error conversion arithmetic unit_i,1、Π_i,jAnd pi_i,0(ii) a The first comparator unit being an error surface e_i,2,χThe input end of the system is in a position system state x_i,2And the output alpha of the first non-linear operation unit_i,2,χ(ii) a The input end of the first tracking differentiator unit is the output alpha of the first nonlinear operation unit_i,2,χ(ii) a The input end of the position system neural network activation function unit is the position system state x_i,2And the output u of the first filtering unit_i,χ,f(ii) a The input end of the position system neural network weight value updating unit is the output phi of the position system neural network activation function unit_iχAnd the output of the second comparator unit

The input ends of the second nonlinear operation units are respectively the output phi of the position system neural network activation function unit_i,χOutput of the weight updating unit

And the output of the second comparator unit

The input ends of the position system predictor operation units are respectively the output ends of the second comparator units

Output of the second non-linear operation unit

Output of a position system disturbance observer unit

And a third non-linear operation unitOutput u_i,χ(ii) a The input end of the second comparator unit is the output of the position system predictor operation unit

And position system state χ_i,2(ii) a The input end of the position system disturbance observer unit is the output of the second comparator unit

Position system state ×_i,2The output of the second non-linear operation unit

And the output u of the third non-linear operation unit_i,χ(ii) a The input end of the third nonlinear operation unit is the output e of the error conversion operation unit_i,1,χAnd pi_i,jThe output r of the first tracking differentiator unit_i,2,χThe output e of the first comparator unit_i,2,χOutput of a position system disturbance observer unit

Output of the second non-linear operation unit

The input end of the first filtering unit is the output u of the third nonlinear operation unit_i,χ(ii) a The input end of the position input nonlinear operation unit is the output u of the third nonlinear operation unit_i,χ。

The attitude controller is specifically defined as follows: the system comprises an expected attitude angle linear operation unit, a third comparator unit, a second differential tracker unit, a fourth nonlinear operation unit, a second filtering unit, a fourth comparator unit, an attitude system neural network activation function unit, an attitude system neural network weight updating unit, a fifth nonlinear operation unit, an attitude system predictor operation unit, a fifth comparator unit, an attitude system disturbance observer unit, a sixth nonlinear operation unit and a third filtering unit; the input of the desired attitude angle linear operation unit isOutput u of position input nonlinear operation unit_i,1And the desired yaw angle ψ of the leader_d(ii) a The input ends of the third comparator units are respectively the attitude angle p of the ith follower_iDesired attitude angle nonlinear operation unit output p_d(ii) a The input end of the second differential tracker unit is the output p of the expected attitude angle nonlinear operation unit_d(ii) a The input of the fourth nonlinear operation unit is the output r of the second differential tracker unit_i,2,pAnd the output e of the third comparator unit_i,1,p(ii) a The input end of the second filter unit outputs alpha for the fourth nonlinear operation unit_i,2,p(ii) a The fourth comparator unit is an error surface e_i,2,pWith input terminal in attitude system state p_i,2And the output of the second filtering unit

The input end of the neural network activation function unit of the attitude system is an attitude system state p_i,2And the output u of the third filtering unit_i,p,f(ii) a The input end of the attitude system neural network weight updating unit is the output phi of the attitude system neural network activation function unit_i,pAnd the output of the fifth comparator unit

The input ends of the fifth nonlinear operation units are respectively the output phi of the attitude system neural network activation function unit_i,pOutput of the weight updating unit

And the output of the fifth comparator unit

The input ends of the attitude system predictor operation units are respectively the output of the fifth comparator unit

Output of the fifth nonlinear operation unit

Output of the attitude system disturbance observer unit

And the output u of the sixth nonlinear operation unit_i,p(ii) a The input end of the fifth comparator unit is the output of the attitude system predictor operation unit

And attitude System State p_i,2(ii) a The input end of the attitude system disturbance observer unit is the output of the fifth comparator unit

Output of the fifth nonlinear operation unit

And the output u of the sixth nonlinear operation unit_i,p(ii) a The input end of the sixth nonlinear operation unit is the output e of the third comparator unit_i,1,pThe output of the second filtering unit

Fourth comparator unit output e_i,2,pOutput of a disturbance observer unit of an attitude system

Output of the fifth nonlinear operation unit

The input end of the third filtering unit is the output u of the sixth nonlinear operation unit_i,p。

The directed graph in step 2 is defined as

Wherein

Representing a set of N nodes, v₁,…,ν_NRepresenting follower 1 through follower N,

representing sets of edges, topological graphs

Is represented by (v)_i,ν_j)，ν_i,ν_jRespectively representing the ith follower and the jth follower; if it is

V is then_jV is_iAdjacent node of (2) representing v_iIs a neighboring node of

The adjacency matrix of followers in the directed graph is defined as

If it is not

Then a_ij1, otherwise a_ij0; the degree matrix of the follower in the directed graph is defined as D ═ diag [ D ═ D₁,…,d_N]Wherein

The Laplace matrix of followers in the directed graph is defined as

Wherein

The adjacency matrix between the leader and the follower in the directed graph is defined as B ═ diag [ B ═ B₁,…,b_N]If the ith follower can access the information of the leader, b _i1, otherwise b_i＝0。

The mathematical model for the ith four-rotor aircraft in the follower was:

wherein

Indicating the positional acceleration of the ith follower,

respectively represents three attitude angular accelerations of the i-th follower, namely roll, pitch and yaw, m_iIs the quality of the ith follower, I_x,i、I_y,i、I_z,iIs the moment of inertia, ξ, of the ith follower_x,i、ξ_y,i、ξ_z,i、ξ_φ,i、ξ_θ,i、ξ_ψ,iRepresenting the aerodynamic damping coefficient of the i-th follower, g is the gravitational acceleration, d_i,1、d_i,2、d_i,3、d_i,4、d_i,5、d_i,6Is the disturbance, u, to the ith follower_i,1、u_i,2、u_i,3、u_i,4Is the control force of the ith follower;

let the position system status of the follower be X_i，1＝[χ_i，1,x,χ_i，1,y,χ_i，1,z]^T＝[x_i,y_i,z_i]^TAnd

let the state of the follower's posture system be p_i,1＝[p_i,1,φ,p_i,1,θ,p_i,1,ψ]^T＝[φ_i,θ_i,ψ_i]^TAnd

wherein the virtual control input in the x, y, z directions is Q_i,x、Q_i,y、Q_i,z，

The mathematical model of the quad-rotor aircraft can be converted into a quad-rotor aircraft position system

And four-rotor aircraft attitude system

Wherein u is_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TAnd u_i,p＝[u_i,2,u_i,3,u_i,4]^TRespectively inputting a position system and an attitude system;

F_i,χ,f＝f_i,χ+g_i,χu_i,χ,f-u_i,χ,ffor the system dynamics of the converted position,

F_i,p,f＝f_i,p+g_i,pu_i,p,f-u_i,p,fis a transformed pose system dynamic, wherein

g_i,χ＝diag[1/m_i,1/m_i,1/m_i]，g_i,p＝diag[1/I_x,i,1/I_y,i,1/I_z,i]；

u_i,χ,fAnd u_i,p,fRespectively as position system input u_i,χAnd gesture System input u_i,pOutput through a first order filter; the error generated by the conversion of the position system and the error generated by the conversion of the attitude system are respectively Δ F_i,χ＝(g_i,χ-1)(u_i,χ-u_i,χ,f) And Δ F_i,p＝(g_i,p-1)(u_i,p-u_i,p,f) (ii) a The unknown disturbance on the position system and the attitude system is d_i,χ＝[d_i,1,d_i,2,d_i,3]^TAnd d_i,p＝[d_i,4,d_i,5,d_i,6]^T。

And 3, providing a leader expectation signal by the leader, outputting position information by the position controller of the follower, outputting posture information by the posture controller of the follower, and forming an expected formation form by the output of the follower and the leader by utilizing the position information and the posture information of the follower.

The specific operation of the position controller is as follows,

a1, potential energy function arithmetic unit:

two input ends of the potential energy function operation unit are respectively the output χ of the ith follower_i,1And the position of the obstacle ×_c；

Is a potential energy function of the energy calculation unit of

Wherein s is_i,c＝χ_i-χ_cDifference between position coordinates of i-th follower and c-th obstacle, χ_c＝[x_c,y_c,z_c]^TFor the coordinates of the c-th obstacle,

the distance between the ith follower and the c-th obstacle is defined as r, the obstacle detection distance is defined as r, and d is the minimum obstacle avoidance distance;

potential energy function pair chi_iThe partial derivatives of (a) are obtained by calculation of the following formula:

a2, error conversion arithmetic unit:

the input ends of the error conversion arithmetic units are respectively directed graphs

Output information χ of jth follower in (1)_j,1Hexix-_j,2Adjacent throughLetter a_ijAnd b_iLeader information χ_dAnd

output χ of ith follower_i,1；

Calculating the error position conversion function by the following formula

And calculate

Wherein

L_i,jAnd L_i,0Indicates the connection holding distance, D_i,jAnd D_i,0Indicating the desired formation distance, R_i,jAnd R_i,0Represents the minimum safe distance, s_i,j＝χ_i-χ_jDistance error, s, for follower i and follower j_i,0＝χ_i-χ_dThe distance error between the follower i and the leader is obtained;

a3, first nonlinear operation means:

the input ends of the first nonlinear operation units are directed graphs respectively

State χ of jth follower in (1)_j,2Adjacent communication a_ijAnd b_iLeader derivative information

Output of potential energy function arithmetic unit

Output e of error conversion arithmetic unit_i,1、Π_i,jAnd pi_i,0(ii) a The output alpha of the first nonlinear operation unit is obtained through calculation of the following formula_i,2.χ：

Wherein k is_i,1,χ>0 is a parameter to be designed,

a4, first comparator cell error surface e_i,2,χ：

The first comparator unit being an error surface e_i,2,χThe input end of the system is in a position system state x_i,2And the output alpha of the first non-linear operation unit_i,2,χ(ii) a E is obtained by calculation of the following formula_i,2,χ：

e_i,2,χ＝χ_i,2-α_i,2,χ；

A5, first tracking differentiator unit:

the input end of the first tracking differentiator unit is the output alpha of the first nonlinear operation unit_i,2,χ(ii) a The first tracking differentiator output r is obtained by calculation of the following formula_i,2,χDerivative of (2)

Wherein r is_i,2,χIs the output alpha of the first non-linear operation unit_i,2,χEstimation of the derivative, λ_TD>0 is the tracking differentiator velocity factor, α_TDE (0,1) is a filtering factor of a tracking differentiator;

a6, a position system neural network activation function unit:

the input end of the position system neural network activation function unit is the position system state x_i,2And the output u of the first filtering unit_i,χ,f(ii) a Position system neural network activation function unit output phi_i,χThe following formula is used for calculation:

wherein gamma is_i,χ>0 is a parameter to be designed,

as a function of activation,%_i,2,x、χ_i,2,yHexix-_i,2,zIs a position system state χ_i,2Element of (5), Q_i,x,f、Q_i,y,fAnd Q_i,z,fIs the output u of the first filtering unit_i,χ,fThe element in (1) is the central value of the activation function, mu and xi are the widths of the activation function; finally obtaining the output

A6, a location system neural network weight updating unit:

the input end of the position system neural network weight value updating unit is the output phi of the position system neural network activation function unit_i,χAnd the output of the second comparator unit

The weight value updating unit output of the neural network of the position system is obtained through the calculation of the following formula

Wherein phi_i,x、Φ_i,yAnd phi_i,zActivating the output phi of the functional unit for the neural network of the position system_i,χThe elements (A) and (B) in (B),

and

is the output of the second comparator unit

Of (b), gamma_i,χ>0 and σ_i,χ>0 is a parameter to be designed; finally obtaining the output

A7, second nonlinear operation means:

the input ends of the second nonlinear operation units are respectively the output phi of the position system neural network activation function unit_i,χOutput of the weight updating unit

And the output of the second comparator unit

Performing product calculation on all input ends to obtain the output of the second nonlinear operation unit

A8, position system predictor operation unit:

the input ends of the position system predictor operation units are respectively the output ends of the second comparator units

Output of the second non-linear operation unit

Output of a position system disturbance observer unit

And the output u of the third non-linear operation unit_i,χ(ii) a The output of the computing unit of the position system predictor is obtained through the calculation of the following formula

Wherein h is_i,χ>0 is a parameter to be designed;

a9, second comparator unit:

the input end of the second comparator unit is the output of the position system predictor operation unit

And position system state χ_i,2(ii) a The output estimated error of the second comparator is obtained through the calculation of the following formula

A10, position system disturbance observer unit:

the input end of the position system disturbance observer unit is the output of the second comparator unit

Position system state ×_i,2The output of the second non-linear operation unit

And the output u of the third non-linear operation unit_i,χ(ii) a The output of the position system disturbance observer is obtained by the calculation of the following formula

Wherein c is_d,i,χ>0 is a parameter to be designed;

a11, third nonlinear operation means:

the input end of the third nonlinear operation unit is the output e of the error conversion operation unit_i,1,χAnd pi_i,j，0The output r of the first tracking differentiator unit_i,2,χThe output e of the first comparator unit_i,2,χOutput of a position system disturbance observer unit

Output of the second non-linear operation unit

Obtaining the virtual control input u of the position system by the calculation of the following formula_i,χ：

Wherein k is_i,2,χ>0 is a parameter to be designed;

a12, first filtering unit:

the input end of the first filtering unit is the output u of the third nonlinear operation unit_i,χ(ii) a The output u of the first filtering unit is obtained through the calculation of the following formula_i,χ,f：

Wherein eta is_i,χIs the filter time constant;

a13, position input nonlinear operation means:

the input end of the position input nonlinear operation unit is the output u of the third nonlinear operation unit_i,χ(ii) a The output u of the position input nonlinear operation unit is obtained by the calculation of the following formula_i,1：

Wherein Q_i,x、Q_i,yAnd Q_i,zIs the output u of the third non-linear operation unit_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TThe elements of (1); to this end, a position system input u is obtained_i,1。

The specific operation of the attitude controller is as follows,

b1, desired attitude angle nonlinear operation unit:

the input of the desired attitude angle linear operation unit is the output u of the third nonlinear operation unit_i,χAnd the desired yaw angle ψ of the leader_d(ii) a Phi is obtained by the calculation of the following formula_dAnd theta_dThen obtaining the output p of the desired attitude angle nonlinear operation unit_d＝[φ_d,θ_d,ψ_d]^T：

Wherein Q_i,x、Q_i,y、Q_i,zIs the output u of the third non-linear operation unit_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TThe elements of (1);

b2, design of third comparator cell:

the input ends of the third comparator units are respectively the attitude angle p of the ith follower_i,1Desired attitude angle nonlinearityOutput p of arithmetic unit_d(ii) a The output e of the third comparator unit is obtained by calculation of the following formula_i,1,p：e_i,1,p＝p_i,1-p_d；

B3, second differential tracker unit:

the input end of the second differential tracker unit is the output p of the expected attitude angle nonlinear operation unit_d(ii) a The output r of the second differential tracker is obtained by calculation of the following formula_i,2,p：

Wherein r is_i,2,pIs the output p of the desired attitude angle nonlinear arithmetic unit_dEstimation of the derivative, λ_TD>0 is the tracking differentiator velocity factor, α_TDE (0,1) is a filtering factor of a tracking differentiator;

b4, fourth nonlinear operation means:

the input of the fourth nonlinear operation unit is the output r of the second differential tracker unit_i,2,pAnd the output e of the third comparator unit_i,1,p(ii) a The output alpha of the fourth nonlinear operation unit is obtained through the calculation of the following formula_i,2,p：

α_i,2,p＝-k_i,1,pe_i,1,p+r_i,2,pWherein k is_i,1,p>0 is a parameter to be designed;

b5, second filtering unit:

the input end of the second filter unit outputs alpha for the fourth nonlinear operation unit_i,2,p(ii) a The output of the second filtering unit is obtained through the calculation of the following formula

And

wherein eta_i,pIs the filter time constant.

B6, fourth comparator unit:

the fourth comparator unit is an error surface e_i,2,pWith input terminal in attitude system state p_i,2And the output of the second filtering unit

The output e of the fourth comparator unit is obtained by calculation of the following formula_i,2,p：

B7, a neural network activation function unit of the attitude system:

the input end of the neural network activation function unit of the attitude system is an attitude system state p_i,2And the output u of the third filtering unit_i,p,f(ii) a The output phi of the neural network activation function unit of the attitude system is obtained by calculation of the following formula_i,p：

Wherein gamma is_i,p>0 is a parameter to be designed,

for activating functions, p_i,2,φ、p_i,2,θAnd p_i,2,ψIs an attitude system state p_i,2Element (ii) u_i,2,f、u_i,3,fAnd u_i,4,fIs the output u of the third filtering unit_i,p,fThe element in (1) is the central value of the activation function, mu and xi are the widths of the activation function; finally obtaining the output

B8, a posture system neural network weight updating unit:

the input end of the attitude system neural network weight updating unit is the output phi of the attitude system neural network activation function unit_i,pAnd the output of the fifth comparator unit

The weight value updating unit output of the neural network of the attitude system is obtained through the calculation of the following formula

Wherein phi_i,φ、Φ_i,θAnd phi_i,ψActivating the output phi of the functional unit for the neural network of the attitude system_i,pThe elements (A) and (B) in (B),

and

is the output of the second comparator unit

Wherein, Γ_i,p>0 and σ_i,p>0 is a parameter to be designed; finally obtaining the output

B9, fifth nonlinear operation means:

the input ends of the fifth nonlinear operation units are respectively the output phi of the attitude system neural network activation function unit_i,pRight of chargeOutput of the value update unit

And the output of the fifth comparator unit

Performing product calculation on all input ends to obtain the output of a fifth nonlinear operation unit

B10, attitude system predictor operation unit:

the input ends of the attitude system predictor operation units are respectively the output of the fifth comparator unit

Output of the fifth nonlinear operation unit

Output of the attitude system disturbance observer unit

And the output u of the sixth nonlinear operation unit_i,p(ii) a The output of the attitude system predictor operation unit is obtained through the calculation of the following formula

Wherein the content of the first and second substances,

is a parameter to be designed;

b11, fifth comparator unit:

the input end of the fifth comparator unit is the output of the attitude system predictor operation unit

And attitude System State p_i,2(ii) a The estimated error of the output attitude system of the fifth comparator is obtained through the calculation of the following formula

B12, attitude system disturbance observer unit:

the input end of the attitude system disturbance observer unit is the output of the fifth comparator unit

Output of the fifth nonlinear operation unit

And the output u of the sixth nonlinear operation unit_i,p(ii) a The output of the attitude system disturbance observer is obtained through the calculation of the following formula

Wherein

Is a parameter to be designed;

b13, sixth nonlinear operation means:

the input end of the sixth nonlinear operation unit is the output e of the third comparator unit_i,1,pThe output of the second filtering unit

Fourth comparator unit output e_i,2,pOutput of a disturbance observer unit of an attitude system

Output of the fifth nonlinear operation unit

Obtaining the control input u of the attitude system by the calculation of the following formula_i,p：

Wherein

Is a parameter to be designed;

b14, third filtering unit:

the input end of the third filtering unit is the output u of the sixth nonlinear operation unit_i,p(ii) a The output u of the third filtering unit is obtained through the calculation of the following formula_i,p,f：

In the present invention, a multi-quad rotor aircraft system with two followers and one leader is taken as an example, and the communication topology is shown in fig. 2, where 0 is the number of the leader and 1 and 2 are the numbers of the two followers. Further obtaining a Laplace matrix

Leader adjacency matrix B ═ diag [ 11]. The mathematical models for two four-rotor aircraft are:

wherein

Indicating the positional acceleration of the ith follower,

respectively represents three attitude angular accelerations of the i-th follower, namely roll, pitch and yaw, m_iIs the mass of the ith four-rotor aircraft, I_x,i、I_y,i、I_z,iIs the moment of inertia, ξ, of the ith four-rotor aircraft_x,i、ξ_y,i、ξ_z,i、ξ_φ,i、ξ_θ,i、ξ_ψ,iExpressing the aerodynamic damping coefficient of the ith four-rotor aircraft, g is the gravitational acceleration, d_i,1、d_i,2、d_i,3、d_i,4、d_i,5、d_i,6Is the disturbance to the ith four-rotor aircraft, u_i,1、u_i,2、u_i,3、u_i,4Is the control force of the ith quad-rotor aircraft;

let's Chi_i，1＝[χ_i，1,x,χ_i，1,y,χ_i，1,z]^T＝[x_i,y_i,z_i]^TAnd

is the position system state, p_i,1＝[p_i,1,φ,p_i,1,θ,p_i,1,ψ]^T＝[φ_i,θ_i,ψ_i]^TAnd

is an attitude system state, and

Q_i,x、Q_i,y、Q_i,zvirtual control inputs in the x, y, and z directions, respectively;

the quad-rotor model may be converted into a quad-rotor position system

And four-rotor aircraft attitude system

Wherein

u_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TAnd u_i,p＝[u_i,2,u_i,3,u_i,4]^TRespectively inputting a position system and an attitude system;

F_i,χ,f＝f_i,χ+g_i,χu_i,χ,f-u_i,χ,fand F_i,p,f＝f_i,p+g_i,pu_i,p,f-u_i,p,fDynamic for the transformed position system and attitude system, respectively, wherein

g_i,χ＝diag[1/m_i,1/m_i,1/m_i]，

u_i,χ,fAnd u_i,p,fRespectively as position system input u_i,χAnd gesture System input u_i,pOutput through a first order filter; Δ F_i,χ＝(g_i,χ-1)(u_i,χ-u_i,χ,f) And Δ F_i,p＝(g_i,p-1)(u_i,p-u_i,p,f) Errors generated for systematic transformations; d_i,χ＝[d_i,1,d_i,2,d_i,3]^TAnd d_i,p＝[d_i,4,d_i,5,d_i,6]^TUnknown disturbance to the position system and the attitude system;

two four-rotor aircraft model parameter selections: acceleration of gravity g-9.8 m/s²Mass m 2kg, moment of inertia I_x＝1.25N·s²/rad、I_y＝1.25N·s²/rad、I_z＝2.5N·s²Rad, aerodynamic damping coefficient ξ_x＝0.012N·s²/rad、ξ_y＝0.012N·s²/rad、ξ_z＝0.012N·s²/rad、ξ_φ＝0.012N·s²/rad、ξ_θ＝0.012N·s²/rad、ξ_ψ＝0.012N·s²(ii)/rad. The system is disturbed by d_i,1＝0.2sin(t)、d_i,2＝0.5cos(t)+sin(χ_i,1,y)、d_i,3＝1.5、d_i,1＝0.2+sin(10t)、d_i,1＝0.5、d_i,1＝2+cos(5p_i,1,θ)。

Aircraft control parameter selection: r_1,0＝[3，-3,-1]^T、R_2,0＝[-2，2,-1]^T，D_1,0＝[4,-4,0]^T、D_2,0＝[-4,4,0]^T，L_1,0＝[5,-5,1]^T、L_2,0＝[-5,5,1]^T；r＝2、d＝1；k_i,1,χ＝2、k_i,1,χ＝5、k_i,1,p＝2、k_i,2,p＝2、Γ_i,χ＝10、Γ_i,p＝10、σ_i,χ＝0.01、σ_i,p＝0.01、h_i,χ＝2、h_i,p＝2、c_d,i,χ＝5、c_d,i,p＝10、λ_TD＝10、α_TD＝0.8、η_i,χ＝0.5、η_i,p＝0.1、γ_i,χ＝1、γ_i,p1, i is 1,2 in all parameters; leader signal χ_d(t)＝[t,t,3-3e^-2t]^T(m), desired yaw angle ψ_d(t) 0 (rad); number 1 machine initial position chi₁(0) X, 2 # machine starting position ═ 3.5, -3.5,0) (m)₂(0) (-3.5,3.5,0) (m), obstacle position χ_1,c＝(8.5，1.5,3)(m)、χ_2,c＝(1.8，10.2,3)(m)。

As shown in FIGS. 3-5, system input u is entered at a location_i,1I ═ 1,2 and attitude system control input u_i,p＝[u_i,2,u_i,3,u_i,4]^TUnder the action of 1 and 2, the followers and the leader of the two four-rotor aircraft keep flying in a parallel formation. At coordinates (7.6, -0.3,3) when the system is running for 3.8s, the obstacle enters the detection range of follower # 1, and the potential energy function unit in the control input starts to function, as shown in fig. 7. At this time, the No. 1 follower begins to avoid the obstacle and has potential energyFunction(s)

Peak 1.6 was reached at 5 s. In the process, the error conversion function unit limits the distance between the follower No. 1 and the leader to the minimum safe distance R_1,0＝[3，-3,-1]^TTo a connection holding distance L_1,0＝[5,-5,1]^TAs shown in fig. 4. When the system runs for 6s, at the coordinates (10.5,2 and 3), the obstacle leaves the detection range of the follower No. 1, the follower No. 1 finishes obstacle avoidance and continues to form a formation with the leader.

When the system runs for 4.6s, the obstacle enters the detection range of the follower No. 2 at the coordinates (0.6,8.6 and 3), and the follower No. 2 starts to avoid the obstacle. In the process, the error conversion function unit limits the distance between the No. 2 follower and the leader to the minimum safe distance R_2,0＝[-2，2,-1]^TTo a connection holding distance L_2,0＝[-5,5,1]^TAs shown in fig. 4. When the system runs for 7.2s, the barrier leaves the detection range of the follower No. 2, the follower No. 2 finishes obstacle avoidance and continues to form a formation with the leader. Fig. 5 is a control input curve for two quad-rotor aircraft, where it can be seen that after an obstacle enters the detection range of flight, the change is smooth and no jump occurs. Fig. 6 shows the system dynamics approximation effect of the first quad-rotor aircraft, and it can be found that under the combined action of the neural network based on the predictor and the disturbance observer, the system dynamics can still keep good approximation effect when changing. Fig. 7 is a numerical curve of the potential energy function and the partial derivative value thereof when the follower No. 1 encounters an obstacle, and it can be found that, during the obstacle avoidance period of the follower No. 1 from 3.8s to 6s, the change of the potential energy function is smooth, and no sudden jump occurs, which has an important effect on protecting the actuator mechanism.

The above embodiments are only specific examples of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the claims.

Claims (7)

1. A formation control method of a multi-four-rotor aircraft with an estimator is characterized by comprising the following steps:

step 1, setting a four-rotor aircraft as a leader, setting N four-rotor aircraft with unknown dynamics as followers, and using a networked system formed by connecting the followers and the leader through a one-way topological graph as a controlled object;

step 2, the ith follower in the N followers is provided with a position controller and an attitude controller, and the input ends of the position controller and the attitude controller of the ith follower are connected with the directed graph

The output end of the position controller of the ith follower is connected with the input end of the position controller of the ith follower, and the output end of the posture controller of the ith follower is connected with the input end of the posture controller of the ith follower;

and 3, providing a leader expectation signal by the leader, outputting position information by the position controller of the follower, outputting posture information by the posture controller of the follower, and forming an expected formation form by the output of the follower and the leader by utilizing the position information and the posture information of the follower.

2. A method of controlling formation of a plurality of quad-rotor aircraft including forecaster according to claim 1, wherein: the position controller in step 2 is specifically defined as follows:

the system comprises a potential energy function operation unit, an error conversion operation unit, a first nonlinear operation unit, a first comparator unit, a first tracking differentiator unit, a position system neural network weight updating unit, a position system neural network activation function unit, a second nonlinear operation unit, a position system predictor operation unit, a second comparator unit, a position system disturbance observer unit, a third nonlinear operation unit, a first filtering unit and a position input nonlinear operation unit;

two input ends of the potential energy function operation unit are respectively the output χ of the ith follower_i,1And the position of the obstacle ×_c；

The input ends of the error conversion operation units are directed graphs respectively

Output information χ of jth follower in (1)_j,1Hexix-_j,2Adjacent communication a_ijAnd b_iLeader information χ_dAnd

output χ of ith follower_i,1；

The input ends of the first nonlinear operation units are directed graphs respectively

State χ of jth follower in (1)_j,2Adjacent communication a_ijAnd b_iLeader derivative information

Output of potential energy function arithmetic unit

Output e of error conversion arithmetic unit_i,1、Π_i,jAnd pi_i,0；

The first comparator unit is an error surface e_i,2,χThe input end of the system is in a position system state x_i,2And the output alpha of the first non-linear operation unit_i,2,χ；

The input end of the first tracking differentiator unit is the output alpha of the first nonlinear operation unit_i,2,χ；

The input end of the position system neural network activation function unit is a position system state x_i,2And a firstOutput u of the filter unit_i,χ,f；

The input end of the position system neural network weight updating unit is the output phi of the position system neural network activation function unit_i,χAnd the output of the second comparator unit

The input ends of the second nonlinear operation units are respectively the output phi of the position system neural network activation function unit_i,χOutput of the weight updating unit

And the output of the second comparator unit

The input ends of the position system predictor operation unit are respectively the output of the second comparator unit

Output of the second non-linear operation unit

Output of a position system disturbance observer unit

And the output u of the third non-linear operation unit_i,χ；

The input end of the second comparator unit is the output of the position system predictor operation unit

And position system state χ_i,2；

The input end of the position system disturbance observer unit is the output of the second comparator unit

Position system state ×_i，2The output of the second non-linear operation unit

And the output u of the third non-linear operation unit_i,χ；

The input end of the third nonlinear operation unit is the output e of the error conversion operation unit_i,1,χAnd pi_i,jThe output r of the first tracking differentiator unit_i,2,χThe output e of the first comparator unit_i,2,χOutput of a position system disturbance observer unit

Output of the second non-linear operation unit

The input end of the first filtering unit is the output u of the third nonlinear operation unit_i,χ(ii) a The input end of the position input nonlinear operation unit is the output u of the third nonlinear operation unit_i,χ。

3. A method of controlling formation of a plurality of quad-rotor aircraft including forecaster according to claim 2, wherein: the attitude controller in step 2 is specifically defined as follows:

the system comprises an expected attitude angle linear operation unit, a third comparator unit, a second differential tracker unit, a fourth nonlinear operation unit, a second filtering unit, a fourth comparator unit, an attitude system neural network activation function unit, an attitude system neural network weight updating unit, a fifth nonlinear operation unit, an attitude system predictor operation unit, a fifth comparator unit, an attitude system disturbance observer unit, a sixth nonlinear operation unit and a third filtering unit;

the input of the desired attitude angle linear operation unit is position inputOutput u of non-linear arithmetic unit_i,1And the desired yaw angle ψ of the leader_d；

The input ends of the third comparator units are respectively the attitude angle p of the ith follower_iDesired attitude angle nonlinear operation unit output p_d；

The input end of the second differential tracker unit is the output p of the expected attitude angle nonlinear operation unit_d；

The input of the fourth nonlinear operation unit is the output r of the second differential tracker unit_i,2,pAnd the output e of the third comparator unit_i,1,p；

The input end of the second filtering unit outputs alpha to the fourth nonlinear operation unit_i,2,p；

The fourth comparator unit is an error surface e_i,2,pWith input terminal in attitude system state p_i,2And the output of the second filtering unit

The input end of the attitude system neural network activation function unit is an attitude system state p_i,2And the output u of the third filtering unit_i,p,f；

The input end of the attitude system neural network weight updating unit is the output phi of the attitude system neural network activation function unit_i,pAnd the output of the fifth comparator unit

The input ends of the fifth nonlinear operation units are respectively the output phi of the attitude system neural network activation function unit_i,pOutput of the weight updating unit

And the output of the fifth comparator unit

The input ends of the attitude system predictor operation units are respectively the output of a fifth comparator unit

Output of the fifth nonlinear operation unit

Output of the attitude system disturbance observer unit

And the output u of the sixth nonlinear operation unit_i,p；

The input end of the fifth comparator unit is the output of the attitude system predictor operation unit

And attitude System State p_i,2；

The input end of the attitude system disturbance observer unit is the output of a fifth comparator unit

Output of the fifth nonlinear operation unit

And the output u of the sixth nonlinear operation unit_i,p；

The input end of the sixth nonlinear operation unit is the output e of the third comparator unit_i,1,pThe output of the second filtering unit

Fourth comparator unit output e_i,2,pOutput of a disturbance observer unit of an attitude system

Output of the fifth nonlinear operation unit

The input end of the third filtering unit is the output u of the sixth nonlinear operation unit_i,p。

4. A method of fleet control for a multi-quad rotor aircraft with forecaster, according to claim 3, wherein: the directed graph in the step 2 is defined as

Wherein

Representing a set of N nodes, v₁,…,ν_NRepresenting follower 1 through follower N,

representing sets of edges, topological graphs

Is represented by (v)_i,ν_j)，ν_i,ν_jRespectively representing the ith follower and the jth follower; if it is

V is then_jV is_iAdjacent node of (2) representing v_iIs a neighboring node of

The adjacency matrix of followers in the directed graph is defined as

If it is not

Then a_ij1, otherwise a_ij0; the degree matrix of the follower in the directed graph is defined as D ═ diag [ D ═ D₁,...,d_N]Wherein

The Laplace matrix of followers in the directed graph is defined as

Wherein

The adjacency matrix between the leader and the follower in the directed graph is defined as B ═ diag [ B ═ B₁,…,b_N]If the ith follower can access the information of the leader, b_i1, otherwise b_i＝0。

5. The method of claim 4 for fleet control of a multi-quad rotor aircraft with forecaster, wherein: the mathematical model of the ith four-rotor aircraft in the follower in step 2 is:

wherein

Indicating the positional acceleration of the ith follower,

respectively represents three attitude angular accelerations of the i-th follower, namely roll, pitch and yaw, m_iIs the quality of the ith follower, I_x,i、I_y,i、I_z,iIs the moment of inertia, ξ, of the ith follower_x,i、ξ_y,i、ξ_z,i、ξ_φ,i、ξ_θ,i、ξ_ψ,iRepresenting the aerodynamic damping coefficient of the i-th follower, g is the gravitational acceleration, d_i,1、d_i,2、d_i,3、d_i,4、d_i,5、d_i,6Is the disturbance, u, to the ith follower_i,1、u_i,2、u_i,3、u_i,4Is the control force of the ith follower; let the position system status of the follower be X_i，1＝[χ_i，1,x,χ_i，1,y,χ_i，1,z]^T＝[x_i,y_i,z_i]^TAnd

let the state of the follower's posture system be p_i,1＝[p_i,1,φ,p_i,1,θ,p_i,1,ψ]^T＝[φ_i,θ_i,ψ_i]^TAnd

wherein the virtual control input in the x, y, z directions is Q_i,x、Q_i,y、Q_i,z，

The mathematical model of the quad-rotor aircraft can be converted into a quad-rotor aircraft position system

And four-rotor aircraft attitude system

Wherein u is_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TAnd u_i,p＝[u_i,2,u_i,3,u_i,4]^TRespectively inputting a position system and an attitude system;

F_i,χ,f＝f_i,χ+g_i,χu_i,χ,f-u_i,χ,ffor the system dynamics of the converted position,

F_i,p,f＝f_i,p+g_i,pu_i,p,f-u_i,p,fis a transformed pose system dynamic, wherein

g_i,χ＝diag[1/m_i,1/m_i,1/m_i]，

u_i,χ,fAnd u_i,p,fRespectively as position system input u_i,χAnd gesture System input u_i,pOutput through a first order filter; the error due to the conversion of the position system and the error due to the conversion of the attitude system are respectively Δ F_i,χ＝(g_i,χ-1)(u_i,χ-u_i,χ,f) And Δ F_i,p＝(g_i,p-1)(u_i,p-u_i,p,f) (ii) a The unknown disturbance on the position system and the attitude system is d_i,χ＝[d_i,1,d_i,2,d_i,3]^TAnd d_i,p＝[d_i,4,d_i,5,d_i,6]^T。

6. The method of claim 5, wherein the method comprises: the specific operation content of the position controller in the step 3 is as follows,

a1, potential energy function arithmetic unit:

two potential energy function arithmetic unitsThe input ends are respectively the output χ of the ith follower_i,1And the position of the obstacle ×_c；

Is a potential energy function of the energy calculation unit of

Wherein s is_i,c＝χ_i-χ_cDifference between position coordinates of i-th follower and c-th obstacle, χ_c＝[x_c,y_c,z_c]^TFor the coordinates of the c-th obstacle,

the distance between the ith follower and the c-th obstacle is defined as r, the obstacle detection distance is defined as r, and d is the minimum obstacle avoidance distance;

potential energy function pair chi_iThe partial derivatives of (a) are obtained by calculation of the following formula:

a2, error conversion arithmetic unit:

the input ends of the error conversion arithmetic units are respectively directed graphs

Output information χ of jth follower in (1)_j,1Hexix-_j,2Adjacent communication a_ijAnd b_iLeader information χ_dAnd

output χ of ith follower_i,1(ii) a Calculating the error position conversion function by the following formula

And calculate

Wherein

L_i,jAnd L_i,0Indicates the connection holding distance, D_i,jAnd D_i,0Indicating the desired formation distance, R_i,jAnd R_i,0Represents the minimum safe distance, s_i,j＝χ_i-χ_jDistance error, s, for follower i and follower j_i,0＝χ_i-χ_dThe distance error between the follower i and the leader is obtained;

a3, first nonlinear operation means:

the input ends of the first nonlinear operation units are directed graphs respectively

State χ of jth follower in (1)_j,2Adjacent communication a_ijAnd b_iLeader derivative information

Output of potential energy function arithmetic unit

Output e of error conversion arithmetic unit_i,1、Π_i,jAnd pi_i,0(ii) a The output alpha of the first nonlinear operation unit is obtained through calculation of the following formula_i,2.χ：

Wherein k is_i，1，χ>0 is a parameter to be designed,

a4, first comparator cell error surface e_i,2,χ：

The first comparator unit being an error surface e_i,2,χThe input end of the system is in a position system state x_i,2And the output alpha of the first non-linear operation unit_i,2,χ(ii) a E is obtained by calculation of the following formula_i,2,χ：

e_i,2,χ＝χ_i,2-α_i,2,χ；

A5, first tracking differentiator unit:

the input end of the first tracking differentiator unit is the output alpha of the first nonlinear operation unit_i,2,χ(ii) a The first tracking differentiator output r is obtained by calculation of the following formula_i,2,χDerivative of (2)

Wherein r is_i,2,χIs the output alpha of the first non-linear operation unit_i,2,χEstimation of the derivative, λ_TD>0 is the tracking differentiator velocity factor, α_TDE (0,1) is a filtering factor of a tracking differentiator;

a6, a position system neural network activation function unit:

the input end of the position system neural network activation function unit is the position system state x_i,2And the output u of the first filtering unit_i,χ,f(ii) a Position system neural network activation function unit output phi_i,χThe following formula is used for calculation:

wherein gamma is_i,χ>0 is a parameter to be designed,

as a function of activation,%_i,2,x、χ_i,2,yHexix-_i,2,zIs a position system state χ_i,2Element of (5), Q_i,x,f、Q_i,y,fAnd Q_i,z,fIs the output u of the first filtering unit_i,χ,fThe element in (1) is the central value of the activation function, mu and xi are the widths of the activation function; finally obtaining the output

A6, a location system neural network weight updating unit:

the input end of the position system neural network weight value updating unit is the output phi of the position system neural network activation function unit_i,χAnd the output of the second comparator unit

The weight value updating unit output of the neural network of the position system is obtained through the calculation of the following formula

Wherein phi_i,x、Φ_i,yAnd phi_i,zActivating functions for location system neural networksOutput of cell phi_i,χThe elements (A) and (B) in (B),

and

is the output of the second comparator unit

Of (b), gamma_i,χ>0 and σ_i,χ>0 is a parameter to be designed; finally obtaining the output

A7, second nonlinear operation means:

the input ends of the second nonlinear operation units are respectively the output phi of the position system neural network activation function unit_i,χOutput of the weight updating unit

And the output of the second comparator unit

Performing product calculation on all input ends to obtain the output of the second nonlinear operation unit

A8, position system predictor operation unit:

the input ends of the position system predictor operation units are respectively the output ends of the second comparator units

Output of the second non-linear operation unit

Output of a position system disturbance observer unit

And the output u of the third non-linear operation unit_i,χ(ii) a The output of the computing unit of the position system predictor is obtained through the calculation of the following formula

Wherein h is_i,χ>0 is a parameter to be designed;

a9, second comparator unit:

the input end of the second comparator unit is the output of the position system predictor operation unit

And position system state χ_i,2(ii) a The output estimated error of the second comparator is obtained through the calculation of the following formula

A10, position system disturbance observer unit:

the input end of the position system disturbance observer unit is the output of the second comparator unit

Position system state ×_i,2The output of the second non-linear operation unit

And the output u of the third non-linear operation unit_i,χ(ii) a The output of the position system disturbance observer is obtained by the calculation of the following formula

Wherein c is_d,i,χ>0 is a parameter to be designed;

a11, third nonlinear operation means:

the input end of the third nonlinear operation unit is the output e of the error conversion operation unit_i,1,χAnd pi_i,j，0The output r of the first tracking differentiator unit_i,2,χThe output e of the first comparator unit_i,2,χOutput of a position system disturbance observer unit

Output of the second non-linear operation unit

Obtaining the virtual control input u of the position system by the calculation of the following formula_i,χ：

Wherein k is_i,2,χ>0 is a parameter to be designed;

a12, first filtering unit:

the input end of the first filtering unit is the output u of the third nonlinear operation unit_i,χ(ii) a The output u of the first filtering unit is obtained through the calculation of the following formula_i,χ,f：

Wherein eta is_i,χIs the filter time constant;

a13, position input nonlinear operation means:

the input end of the position input nonlinear operation unit is the output u of the third nonlinear operation unit_i,χ(ii) a The output u of the position input nonlinear operation unit is obtained by the calculation of the following formula_i,1：

Wherein Q_i,x、Q_i,yAnd Q_i,zIs the output u of the third non-linear operation unit_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TThe elements of (1); to this end, a position system input u is obtained_i,1。

7. The method of claim 6, wherein the method comprises: the specific operation content of the attitude controller in the step 3 is as follows,

b1, desired attitude angle nonlinear operation unit:

the input of the desired attitude angle linear operation unit is the output u of the third nonlinear operation unit_i,χAnd the desired yaw angle ψ of the leader_d(ii) a Phi is obtained by the calculation of the following formula_dAnd theta_dThen obtaining the output p of the desired attitude angle nonlinear operation unit_d＝[φ_d,θ_d,ψ_d]^T：

Wherein Q_i,x、Q_i,y、Q_i,zIs the output u of the third non-linear operation unit_i,χ＝[Q_i,x,Q_i,y,Q_i,z]^TThe elements of (1);

b2, design of third comparator cell:

the input ends of the third comparator units are respectively the attitude angle p of the ith follower_i,1Desired attitude angle nonlinear operation unit output p_d(ii) a The output e of the third comparator unit is obtained by calculation of the following formula_i,1,p：e_i,1,p＝p_i,1-p_d；

B3, second differential tracker unit:

the input end of the second differential tracker unit is the output p of the expected attitude angle nonlinear operation unit_d(ii) a The output r of the second differential tracker is obtained by calculation of the following formula_i,2,p：

Wherein r is_i,2,pIs the output p of the desired attitude angle nonlinear arithmetic unit_dEstimation of the derivative, λ_TD>0 is the tracking differentiator velocity factor, α_TDE (0,1) is a filtering factor of a tracking differentiator;

b4, fourth nonlinear operation means:

the input of the fourth nonlinear operation unit is the output r of the second differential tracker unit_i,2,pAnd the output e of the third comparator unit_i,1,p(ii) a The output alpha of the fourth nonlinear operation unit is obtained through the calculation of the following formula_i,2,p：α_i,2,p＝-k_i,1,pe_i,1,p+r_i,2,p，

Wherein k is_i,1,p>0 is a parameter to be designed;

b5, second filtering unit:

second oneThe input end of the filter unit is the output alpha of the fourth nonlinear operation unit_i,2,p(ii) a The output of the second filtering unit is obtained through the calculation of the following formula

And

wherein eta_i,pIs the filter time constant.

B6, fourth comparator unit:

the fourth comparator unit is an error surface e_i,2,pWith input terminal in attitude system state p_i,2And the output of the second filtering unit

The output e of the fourth comparator unit is obtained by calculation of the following formula_i,2,p：

B7, a neural network activation function unit of the attitude system:

the input end of the neural network activation function unit of the attitude system is an attitude system state p_i,2And the output u of the third filtering unit_i,p,f(ii) a The output of the neural network activation function unit of the attitude system is obtained through the calculation of the following formula

Φ_i,p：

Wherein gamma is_i,p>0 is to be setThe parameters are measured, and the parameters are calculated,

for activating functions, p_i,2,φ、p_i,2,θAnd p_i,2,ψIs an attitude system state p_i,2Element (ii) u_i,2,f、u_i,3,fAnd u_i,4,fIs the output u of the third filtering unit_i,p,fThe element in (1) is the central value of the activation function, mu and xi are the widths of the activation function; finally obtaining the output

B8, a posture system neural network weight updating unit:

the input end of the attitude system neural network weight updating unit is the output phi of the attitude system neural network activation function unit_i,pAnd the output of the fifth comparator unit

The weight value updating unit output of the neural network of the attitude system is obtained through the calculation of the following formula

Wherein phi_i,φ、Φ_i,θAnd phi_i,ψActivating the output phi of the functional unit for the neural network of the attitude system_i,pThe elements (A) and (B) in (B),

and

is the output of the second comparator unit

Wherein, Γ_i,p>0 and σ_i，p>0 is a parameter to be designed; finally obtaining the output

B9, fifth nonlinear operation means:

the input ends of the fifth nonlinear operation units are respectively the output phi of the attitude system neural network activation function unit_i,pOutput of the weight updating unit

And the output of the fifth comparator unit

Performing product calculation on all input ends to obtain the output of a fifth nonlinear operation unit

B10, attitude system predictor operation unit:

the input ends of the attitude system predictor operation units are respectively the output of the fifth comparator unit

Output of the fifth nonlinear operation unit

Output of the attitude system disturbance observer unit

And the output u of the sixth nonlinear operation unit_i,p(ii) a The output of the attitude system predictor operation unit is obtained through the calculation of the following formula

Wherein the content of the first and second substances,

is a parameter to be designed;

b11, fifth comparator unit:

the input end of the fifth comparator unit is the output of the attitude system predictor operation unit

And attitude System State p_i,2(ii) a The estimated error of the output attitude system of the fifth comparator is obtained through the calculation of the following formula

B12, attitude system disturbance observer unit:

the input end of the attitude system disturbance observer unit is the output of the fifth comparator unit

Fifth nonlinear operation unitOutput of (2)

And the output u of the sixth nonlinear operation unit_i,p(ii) a The output of the attitude system disturbance observer is obtained through the calculation of the following formula

Wherein

Is a parameter to be designed;

b13, sixth nonlinear operation means:

the input end of the sixth nonlinear operation unit is the output e of the third comparator unit_i,1,pThe output of the second filtering unit

Fourth comparator unit output e_i,2,pOutput of a disturbance observer unit of an attitude system

Output of the fifth nonlinear operation unit

Obtaining the control input u of the attitude system by the calculation of the following formula_i,p：

Wherein

Is a parameter to be designed;

b14, third filtering unit:

the input end of the third filtering unit is the output u of the sixth nonlinear operation unit_i,p(ii) a The output u of the third filtering unit is obtained through the calculation of the following formula_i,p,f：

Wherein eta is_i,pIs the filter time constant.

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