CN112068595A

CN112068595A - Attraction domain optimization method for unmanned aerial vehicle perching and landing maneuvering switching control

Info

Publication number: CN112068595A
Application number: CN202010983557.7A
Authority: CN
Inventors: 何真; 王无天; 岳珵
Original assignee: Nanjing University of Aeronautics and Astronautics
Current assignee: Nanjing University of Aeronautics and Astronautics
Priority date: 2020-09-18
Filing date: 2020-09-18
Publication date: 2020-12-11

Abstract

The invention provides an attraction domain optimization method for unmanned aerial vehicle perching and mobile switching control, which is characterized by comprising the following steps of: step 1: generating a nominal track according to the habitat dynamic model and the constraints of each state quantity in the habitat process; step 2: linearizing the perch dynamic model along the nominal track to obtain a piecewise linear model, and designing a piecewise linear track tracking controller; and step 3: an attraction domain area of a nominal trajectory under control of the trajectory tracking controller is calculated. The invention can enlarge the feasible domain of the initial moment by optimizing the calculation of the attraction domain. The allowable initial moment can have a larger range, and under the action of the LQR controller, the actual track successfully converges to the target perching position to complete perching flight.

Description

Attraction domain optimization method for unmanned aerial vehicle perching and landing maneuvering switching control

Technical Field

The invention belongs to the technical field of unmanned aerial vehicle perching maneuver trajectory control design, and particularly relates to an attraction domain optimization method for unmanned aerial vehicle perching maneuver switching control.

Background

In nature, large birds can land quickly and accurately by enlarging the flight attack angle. This landing pattern is referred to as a perch maneuver. If the fixed-wing drone can simulate a large bird to perch and move, namely, enlarge the flight attack angle, quickly reduce the flight speed and finally perch in a target area, the application occasion of the fixed-wing drone is greatly expanded. The perch maneuver not only can keep the advantages of the fixed-wing aircraft in the aspects of endurance time, flight range, speed and the like, but also can make up for the defect that the fixed-wing aircraft can not land in a small field to a certain extent.

Disclosure of Invention

Aiming at the defects and shortcomings of the prior art, the method adopts a generalized pseudo-spectrum optimization method to optimize the perch maneuver track and generate a nominal track, linearizes a dynamic model along the nominal track, and designs a piecewise linear track tracking controller; the attraction domain of the system is then calculated using a sum of squares algorithm, and the attraction domain algorithm is optimized to find a larger perch maneuver attraction domain.

In order to achieve the purpose, the invention adopts the following technical scheme:

an attraction domain optimization method for unmanned aerial vehicle perching and maneuvering switching control comprises the following steps:

step 1: generating a nominal track according to the habitat dynamic model and the constraints of each state quantity in the habitat process;

step 2: linearizing the perch dynamic model along the nominal track to obtain a piecewise linear model, and designing a piecewise linear track tracking controller;

and step 3: an attraction domain area of a nominal trajectory under control of the trajectory tracking controller is calculated.

Preferably, the perch kinetic model in step 1 is:

wherein V is the flying speed,

Is the reciprocal of V, mu is the track angle, alpha is the angle of attack, q_rIs pitch angle rate, x is horizontal displacement, h is altitude, M is mass of the aircraft, M is aerodynamic force and moment, L is lift, D is drag, I_yIs the pitching moment of inertia of the aircraft, C_L、C_D、C_MLift, drag and moment coefficients, S_aIs the aerodynamic surface area of the unmanned aerial vehicle, and ρ is the air density, l_eIs the distance from the aerodynamic center of gravity of the elevator to the center of mass of the unmanned aerial vehicle, S_eIs the aerodynamic surface area of the elevator.

Preferably, the constraints of the various state quantities during perching in step 1 are:

variable of state	Lower limit value	Upper limit value
			V/m·s ^-1	0	25
α/rad	-π/2	π/2
			μ/rad	-π/4	π/4
q_r/rad·s^-1	-3.5	3.5
			x/m	0	15
h/m	0	10
			δ_e/rad	-π/3	π/3

。

Preferably, in the step 1, a Rudau pseudo-spectrum method is adopted for track optimization, and the selected quadratic optimization index J is as follows:

in the formula Q_fQ, R are the weights occupied by the corresponding terms, x (t), respectively_f) Is the target state of the perch endpoint, u is the input to the overall process, and x is the state variable of the overall process.

Preferably, the piecewise linear model in step 2 is:

middle X type_q(t) A function equivalent to the transformation over time is described as:

Δ X and Δ u are the difference between the actual and nominal trajectory state quantities and the input quantity, respectively,

And

as a linear time-varying matrix, the time range of the aircraft perching maneuver is [ t ]₀,t_f]N time points { t) are selected uniformly over a time range₀,t₁,…,t_n-1And has t_n-1＝t_fAt any time t_q，A_qAnd B_qAre linear time-invariant matrices at time q after segmentation.

Preferably, the control law of the trajectory tracking controller in step 2 is as follows:

k_q＝-R^-1B_q ^TS_q (7)

in the formula S_qIs a positive definite symmetric matrix satisfying the following formula, namely the ricati equation:

Q-S_qB_qR^-1B_q ^TS_q+S_qA_q+A_q ^TS_q＝0 (8)

the closed loop state equation of the trajectory tracking controller at the time q is as follows:

preferably, in order to ensure the stability of the whole perch system, the Lyapnov function value of each subsystem needs to be greater than or equal to that of the next subsystem, that is, the following formula is satisfied:

in the formula P_qAnd Q_qThe selected positive definite symmetric matrix.

Preferably, the step 3 of calculating the attraction domain is as follows:

step 3.1: the maximum rho (t) is obtained from the equation (11)_q) And keeping that moment

Wherein

r＝[Δv,Δα,Δμ,Δq,Δx,Δh]^T，

The S matrix is represented by the formula Q-S_qB_qR^-1B_q ^TS_q+S_qA_q+A_q ^TS_qCalculating as 0;

step 3.2: the maximum rho (t) obtained_q) And

substituting the equation (12) into the equation (12), and selecting a kS matrix with a solution at the previous moment when the solution does not exist until the left side of the equation (12) does not belong to the sum of squares;

wherein

0<k<1；

Step 3.3: substituting the kS matrix

In the middle, two sides are divided by k to obtain larger rho (t)_q) The largest state quantity change range can be obtained, namely the attraction domain.

Has the advantages that: the invention can enlarge the feasible domain of the initial moment by optimizing the calculation of the attraction domain. The allowable initial moment can have a larger range, and under the action of the LQR controller, the actual track successfully converges to the target perching position to complete perching flight. The simulation result of the perch track tracking control shows that the track tracking controller adopting the LQR design can well track the reference track generated by the GPOPS.

Drawings

FIG. 1 is a diagram of longitudinal force analysis of an unmanned aerial vehicle;

FIG. 2 is a state variable nominal curve;

FIG. 3 is a thrust and rudder deflection angle nominal curve;

FIG. 4 is a trajectory tracking control block diagram;

FIG. 5 is a control input curve;

FIG. 6 is a state variable tracking control curve;

FIG. 7 is an enlarged contrast view of the attraction domain;

FIG. 8 shows the perch track and attraction domain.

DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION

The invention is further illustrated by the following examples and figures.

1 unmanned aerial vehicle perches and falls mobile dynamics model

Selecting flight speed V, track angle mu, attack angle alpha, pitch angle rate q, pitch angle theta, horizontal displacement x and height h by state variables of the dynamic model, and controlling input selection thrust T and deflection angle of the elevator_e. Assuming that the thrust passes through the center of gravity and points in the direction of the nose, fig. 1 is a longitudinal force analysis diagram of the drone.

Establishing an unmanned aerial vehicle longitudinal dynamics equation under a speed coordinate system according to the figure 1:

where M is the mass of the aircraft, M is the aerodynamic force and moment, L is the lift, D is the drag, I_yIs the aircraft pitch moment of inertia. L, D, M is as follows:

in the formula C_L、C_D、C_MLift, drag and moment coefficients, S_aIs the aerodynamic surface area of the drone, and ρ is the air density. The aerodynamic coefficient of the unmanned aerial vehicle perch maneuver is obtained by a flat model method, and can be expressed as follows:

in the formula I_eIs the distance from the aerodynamic center of gravity of the elevator to the center of mass of the unmanned aerial vehicle, S_eIs the aerodynamic surface area of the elevator. The kinetic model of a perch maneuver differs from conventional drones primarily in that the perch maneuver has a large angle of attack. Perch belongs to a complex class of maneuvers, a challenge for nonlinear domain control.

2 perch trajectory control law design

2.1 non-Linear reference trajectory

The kinetic model (1) is expressed as the following equation

Where X is the state vector of the nonlinear model and f (X, u) represents the nonlinear function. And aiming at the track optimization and the generation of the nonlinear track, a numerical nonlinear optimization program based on a pseudo-spectrum method is adopted. The current generalized pseudospectrometry has four main types, which are the Guass pseudospectrometry, the Legendra pseudospectrometry, the Rudau pseudospectrometry and the Chebyshev pseudospectrometry. The invention adopts Rudau pseudo-spectrum method to optimize the track. The main reason is that the Rudau pseudo-spectrum method has higher precision compared with other three generalized pseudo-spectrum methods, and an initial point and a focus point are added on the basis of the other three pseudo-spectrum methods.

The dynamic model contains 6 state quantities, and when optimization calculation is carried out, the deflection angle quantity of the elevator is calculated_eAs a new state quantity, the stateA vector can be expressed as X ═ V, α, μ, q, X, h,_e]^T. And the reference thrust force T is set to a constant value 3.768N. The pseudo-spectrum method is to restrict the track state quantity according to the whole process and generate a nominal track according to a state equation, so that 7 state quantities need to be restricted according to the requirements of the habitat track. And setting parameters in the process of executing the perch maneuver, namely setting the initial point position as a coordinate origin, and setting the constraint range of each state according to actual conditions. The steering angle is set to a state quantity, so its derivative is taken as an input quantity u, and the constraint condition for u is given as τ (u) — 1, 1. Setting an initial time upper limit value X_h(t₀)＝[9.984,0.25,0,0,1,0,-0.15]^TAnd a lower limit value of X_l(t₀)＝[9.984,0,0.25,0,0,-1,-0.15]^T. The range in setting the state quantity is then as shown in table 1. Finally, the upper limit value X of the end point time is set_h(t_f)＝[4,π/2,π/4,3.5,15,2,π/3]^TLower limit value X_l(t_f)＝[3,-π/2,-π/4,-3.5,14,1,-π/3]^T. The position of the perching terminal is determined according to the actual perching point, such as perching on a telegraph pole, so a certain constraint range is given to the setting of the perching terminal.

TABLE 1 State variable Process constraint Table

Table 1 process constraints of state variables

Variable of state	Lower limit value	Upper limit value
			V/m·s ^-1	0	25
α/rad	-π/2	π/2
			μ/rad	-π/4	π/4
q/rad·s^-1	-3.5	3.5
			x/m	0	15
h/m	0	10
			δ_e/rad	-π/3	π/3

The selected quadratic optimization index J is as follows:

in the formula, the first term is an integral type and is used for compensating the state error and the input error generated in the whole process; the second term is of the endpoint type and compensates for errors made by the endpoint. The secondary performance index (5) is embodied as the optimization of the comprehensive performance of the perch maneuver. In the formula Q_fQ and R are respectively the weight occupied by the corresponding items; x (t)_f) Is the target state of the perch endpoint, so pair Q_fThe larger the selection of (A), the more desirable the habitatThe closer the position of the falling end point is to the designated position; u is the input of the whole process, and the larger R is, the smaller energy is required for the integral control of the input; x is the state variable of the whole process, and the larger Q is, the more stable the whole state variable is required. The range of the state quantity change of the perch motor is large, so that the state variable is not limited, and the whole optimization can be understood as reaching the optimal final perch state with the minimum input. Wherein Q_f＝diag[10,30,0,0,10,10,0]R is 90 and Q is 0. The physical parameters of the drone are shown in table 2 below.

TABLE 2 physical parameters of unmanned aerial vehicle

Table 2 physical parameters of UAV

Parameter(s)	Numerical value
		Mass m/kg	0.8kg
Average aerodynamic chord length c/m	0.25m
		Length spread b/m	1m
Lifting area S_l/m²	0.25m²
		Moment of inertia I_y(kg/m²)	0.1kg/m²

The nominal trajectories generated for the non-linear model using pseudo-spectroscopy, i.e., the GPOPS toolkit corresponding to MATLAB, according to the above constraints are shown in fig. 2 and 3.

It can be seen from fig. 2 that the height and horizontal position of the perching track designed by the track optimization can well fall within the target range of the endpoint constraint.

Record the generated nominal track as (X)_r,u_r). The equation of state of the nominal trajectory is

Wherein X_rState variables, u, of nominal trajectories obtained for GPOPS_rThe input for the nominal trajectory. The non-linear model (4) is arranged along the nominal track (X)_r,u_r) Taylor expansion:

where Δ X and Δ u are the difference between the actual and nominal track state quantities and the input quantity, respectively,

And

is a linear time-varying matrix, and O is a high-order term of Taylor expansion. Here, the linearization ignores high-order terms, and possible wind and the like can cause interference terms of the system, which can affect the control performance of the system, and the following results are obtained:

to piecewise linearize the nonlinear model, the time horizon for an aircraft perch maneuver is defined as [ t ]₀,t_f]N time points { t) are selected uniformly over a time range₀,t₁,…,t_n-1And has t_n-1＝t_f. Linearize the nominal trajectory at each instant, soAny time point t_qIs linearized by

In the formula A_qAnd B_qAre all linear time-invariant matrices of time q, assuming that the aircraft is in two adjacent time intervals t_q,t_q+1) The model in between is represented by a linear time-invariant model. So the piecewise linear model over time is:

middle X type_q(t) A function equivalent to a transformation over time can be described as:

2.2 perch control law design

The section adopts a piecewise linear optimal trajectory controller aiming at the design of the perching mobile piecewise linear model (9). Aiming at the aerocraft perch maneuvering dynamic system, an optimal control u is found_c(t) enabling X to track over X_r. The selected quadratic performance index J is as follows:

wherein Q is not less than 0, R is more than 0, is positive definite diagonal matrix constant value matrix, and Δ X_qIs the difference between the states of the actual track and the nominal track at the point of time q, Deltau_qOptimal control for the q time point needs to be compensated for the actual input. The control law k can be obtained from a linear quadratic regulator LQR_qComprises the following steps:

Δu_q＝k_qΔX_q (12)

k_q＝-R^-1B_q ^TS_q (13)

Q-S_qB_qR^-1B_q ^TS_q+S_qA_q+A_q ^TS_q＝0 (14)

the closed loop equation for the system at time q is therefore:

equation (15) sets the optimal control law for each subsystem of the piecewise linear system, so that the subsystems can be stably converged near the nominal track.

Although each of the above piecewise linear systems can ensure stability, the stability of the entire perch system cannot be ensured. In order to ensure the stability of the whole perch system, the Lyapnov function value of each subsystem needs to be greater than or equal to that of the next subsystem, namely the following formula is satisfied:

in the formula P_qAnd Q_qEquation (16) is demonstrated below for the chosen positive definite symmetric matrix.

Introduction 1: time varying system

Wherein x (t)₀)＝x₀And t is greater than or equal to t₀C (t) is a matrix of continuous and piecewise continuous functions of element at time t. The essential condition for consistent asymptotic stabilization of the system is that there is N > 0, c > 0, such that for any t₀And t is not less than t₀The state transition matrix phi (t, t)₀) Satisfy the requirement of

And (3) proving that: and constructing a Lyapaunov function expression.

At the perch time interval (t)_q-Δt,t_q+Δt]The linear subsystem of (1). Due to P_qIs a positive definite symmetric matrix that can be decomposed into P_q＝U^Tdiag(λ₁,…,λ_n) U, wherein λ_qIs P_qU is a unitary matrix. Thus satisfying the following formula in the subsystem

λ_min(P_q)ΔX^TΔX≤V_e≤λ_max(P_q)ΔX^TΔX (19)

Derived from the closed-loop subsystem of equation (15)

Further obtained from the formula (16)

Because of the fact that

-ΔX^TQ_qΔX≤-λ_min(Q_q)ΔX^TΔX (22)

Is obtained by formula (19)

Simultaneous (21), (22) and (23) to obtain

By introducing the nonlinear system comparison principle, the time interval of habitation can be proved to be (t)_q-Δt,t_q+Δt]In the linear subsystem of_eSatisfy the requirement of

The whole process of the perch maneuver is divided into N subspaces and the elapsed time is [ t ]₀,t_f]Therefore, V can be obtained from theorem 1_eAt (t)_q-Δt,t_q+Δt]This time is exponentially convergent.

Further, the equation (16) shows that the switching time t between the two subsystems is_s＝t_q- Δ t satisfies the following formula:

V_e(t_s ^-)＝ΔX^TP_qΔX≤ΔX^TP_q-1ΔX＝V_e(t_s ⁺) (26)

so that V can be comprehensively known_eConverges exponentially and does not increase after the switching instant, so the overall system is globally stable. Therefore, the control law k is calculated from equation (13)_qAnd (4) later, checking whether the formula (16) meets the gradual stability requirement of the whole system, and if the formula (11) Q, R is not met, checking again. Thus, the control law (13) satisfying the condition (16) can ensure the stability of the whole perch piecewise linear system (9).

The structure of the entire trajectory tracking control system is shown in fig. 4.

Calculation of 3 perch trajectory tracking control attraction domain

The attraction domain refers to a region where the nonlinear system is locally stable. The attraction area of the perch track can ensure that the unmanned aerial vehicle in the attraction area can perch in a specified target area within a specified time. The perch maneuver control laws designed in section 2.2 were designed for the piecewise-linearized model. While the actual model of the perch maneuver is a nonlinear dynamical system (1). It is an important problem to calculate the local stable range under the control law (13), namely the attraction domain of the perch track aiming at the nonlinear system (1).

In the section, an SOS square sum optimization algorithm is firstly used for solving an attraction domain region omega of a nominal track of a closed-loop nonlinear perch system. On the basis of solving the attraction domain, the radius of the original attraction domain is greatly enlarged by optimizing the variable solved in the SOS algorithm, so that a larger attraction domain can be searched. Section 3.1 below will describe the solution of the attraction domain for the perch nonlinear system based on the general solution of the attraction domain method. Section 3.2 expands the attraction domain by optimizing the solution variables of the SOS algorithm based on section 3.1 of the attraction domain.

3.1 perch track attraction domain algorithm

Writing a system in a non-linear time-varying fashion

Wherein f is a polynomial function with respect to x and t

For the set of systematic solutions, a given target area is noted

The state when the end of the set time converges to g, i.e. for any x ∈ RⁿWhen (t)_fAnd x) belongs to the time x belongs to the g, namely the attraction domain of the whole motion process of the system.

2, leading: if there is a continuously differentiable function V: [ t: [ [ t ]₀,t_f]×Rⁿ→ 0, ∞). For each t e [ t ∈ [ [ t ]₀,t_f]Defining: omega_t: x | V (x, t) ≦ 1} and

if every arbitrary t e [ t ∈ ]₀,t_f]And

all satisfy

And is

Then { (x, t) | t ∈ [ t { (x, t) | t ∈₀,t_f],x∈Ω_tI.e. the attraction domain of the whole process.

Defining the allowable falling point range of the perch maneuver as a target area g and defining the nominal track x of the perch maneuver_rThe candidate attraction domain regions of (a) are:

in the formula (I), the compound is shown in the specification,

representing the delta between the actual and nominal trajectories,

is positive; ρ (t) is a scalar whose time variation is larger than zero, and Ω (ρ, t) is an attraction domain region. Selection of quadratic forms

Where S is a constant matrix found using the LQR score of 2.2.

According to the theorem 2, the formula (28) is set to the attraction region, ρ (t) ≦ 1 is satisfied, and the following formula is satisfied

Formula (29) can be obtained by the general expression 2

Can be derived by derivation. When t is t, as shown in formula (29)_q-1When it is at

Then, at the next time t ═ t_qWhen it is satisfied with

V(X，t_q)≤ρ(t_q) (30)

I.e. when t equals t_qThe state quantity is still within the attraction domain.

Selecting an appropriate ρ (t) such that Ω (ρ, t) satisfies the condition:

the process of solving the attraction domain is arranged into an optimal solution form as follows:

converting the condition represented by formula (32) into the following formula

Finally converting the conditions into

Lemma 3 given set of polynomials { f₁，…，f_s}，{g₁，…，g_t}，{h₁，…，h_u}∈R_nThe following two conditions are equivalent:

(1) collection

Is an empty set.

(2) There is a polynomial f e p f₁…f_s},g∈M{g₁…g_l},

h∈I{h₁…h_uSatisfy f + g²+ h ═ 0, where R_nRepresenting a collection of n-polynomials over all real number fields.

Then according to the theorem 3, the condition (34) is converted into:

in the formula s₁，s₂，s₃∈∑_nFor simplified calculation using SOS optimization algorithm, take s ₃1 and mixing s₁And (4) item shifting. The SOS algorithm requires a linear relationship between the unknowns, so s is calculated₂Transformation of

Increase ρ (t) by a predetermined step length, and obtain

There is a solution to find the maximum ρ (t), so equation (35) translates to the following equation:

the format is set as follows:

r＝[Δv,Δα,Δμ,Δq,Δx,Δh]^Twhere U is a 6 x 6 real symmetric matrix.

Time of will perch [ t₀,t_f]And dividing the trajectory into N sections, and calculating the attraction domain of the nominal trajectory of the perch. Giving the radius rho of the terminal attraction area according to the error range of the habitat terminal_fThe value of (c). Suppose in [ t_f-1+Δt,t_f]The suction radius during this time is p_fCalculating t_f-1Radius of attraction region at time ρ_f-1At this time, ρ_f-1Estimating time t according to a linear mode_f-1-Δt,t_f-1+Δt]The inner radius.

When calculating the whole nominal track attraction domain, t is t_qTime of sampling. Because of ρ_fIs given according to the habitat end point range constraint so from t_fThe time starts counting backwards. Since the left side of equation (36) is the sum of p (t)

So by continuously incrementing the current time p (t)_q) Up to

No solution, i.e. the largest radius of the attraction domain.

3.2 optimization algorithm for enlarging radius of attraction domain

In the above derivation

Where S is the positive constant matrix obtained by solving the ricattes equation (14) at section 2.2. The S matrix in the LQR is selected to be the coefficient matrix of the Lyapunov function because it is ensured that the system is asymptotically stable, i.e., the system is stable

The demonstration process is as follows:

substituting equation (12) into model system equation (6) yields the system closed-loop equation:

from 2.2-membered formula (14)

SA+A^TS-SBR^-1B^TS＝-Q (41)

Since Q is greater than or equal to 0, S is greater than 0, and R is greater than 0

Q+SBR^-1B^TS＞0 (43)

In the formula (36), the reaction mixture is,

s in (1) and an attraction domain radius ρ (t)_q) One must be fixed to solve. When the radius of the attraction domain is solved in section 3.1, the S matrix at the moment is fixed to find the maximum radius rho (t) of the attraction domain_q)。

In order to search for a larger radius of the attraction domain, the initial radius of the attraction domain is fixed, and the radius ρ (t) of the attraction domain at the next moment is solved according to the method of section 3.1_q) To find the maximum rho (t)_q) And keeping that moment

Then, the obtained maximum rho (t) is fixed_q) And

the S matrix is continuously changed according to a set method to enlarge the attraction domain. But must be guaranteed when changing the S matrix

The following equation was then solved using MATLAB toolkit sosoos:

until the left side of equation (45) does not belong to the sum of squares, the S matrix with the solution at the previous moment without the solution is selected.

The S matrix is changed by multiplying the S matrix by a constant k (0 < k < 1), where k decreases from 1 down by a certain step size until the kS matrix makes equation (45) false. The reason for changing the S matrix is chosen as follows:

multiplying by a constant k of 0 < k < 1 ensures that the sign of the S characteristic value is not changed

Positive definite sum

The following was demonstrated:

because only the selected S matrix has changed, but the state equation obtained by the LQR controller has not changed:

therefore 0 < k < 1

This ensures that the defined region Ω (ρ, t) is the attraction domain of the perch reference track.

The reason for choosing a certain step size to decrease from 1 is that the optimal S matrix searched out in this way can change the phase to enlarge the attraction domain radius in the process of optimizing the S matrix. The derivation process is as follows:

when the S matrix is multiplied by k

Both sides are divided by k simultaneously

Since 0 < k < 1, ρ (t)/k is larger than the original ρ (t), and the radius of the suction region can be enlarged by reducing the S matrix.

4 simulation results and analysis

4.1 perch trajectory tracking control simulation

The geometric parameters of the fixed wing drone are shown in table 2, a perch maneuver nonlinear model (1) is used for the simulation, and the nominal inputs of the nonlinear model are the thrust and elevator deflection angle of the nominal trajectory obtained by GPOPS. The pneumatic parameters are calculated by the following equations (2) and (3).

The LQR controller is designed in a piecewise linearization mode, the whole perching time is set to be 2s, and reference points are selected every 0.05s to carry out control law design. Wherein R ═ diag [9,45 ]]，Q＝diag[18,100,16,100,20,50](ii) a A joint type (16) obtains a control law. Adding the obtained control law toAnd (4) obtaining the tracking track of the LQR controller by inputting the linear model. The ideal state of the initial perch of the aircraft is X^*(t₀)＝[9.984,0,0.25,0,0,0]The initial state of the nominal trajectory of the second section is also set according to the ideal state, resulting in the ideal nominal trajectory. To verify the effectiveness of the tracking controller, a bias is added to the initial state of the design reality. The initial state of the added deviation is [11, 0.1, 0.4, 0, -1, -0.7%]. The simulation results are shown in fig. 5 and 6.

As can be seen from fig. 5 and 6, the state quantities of the closed-loop curves generated by the nonlinear model under the action of the LQR controller can keep up with the reference trajectory. The designed LQR controller is effective. Control input range is respectively in T epsilon [2.7,4.4],_e∈[-0.7,0.3]It is a reasonable input range. The final position accuracy of the perch is highly desired. In the tracking curve of the aircraft perch maneuver, the perch location of the reference trajectory generated by the GPOPS is (14.80, 1.162) and the actual perch location of the aircraft under the controller is (14.79, 1.160). Therefore, even if the initial position deviation is large, the aircraft can accurately land near the perching position of the reference track through the action of the LQR controller.

4.2 simulation of motor trajectory attraction domain and extended attraction domain of perch

Based on the nonlinear model (1), a time point joint type (36) is selected every 0.05s within the time 2s of the perch, and the attraction domain of each time period is calculated. The perch maneuver attraction domain is calculated by backward-pushing from the perch endpoint time. Because the aircraft perch maneuver requires landing near the reference trajectory terminus, the allowable error of the perch location needs to be set. The allowable position error of the perching endpoint is set to be Deltax < 0.15m and Deltah < 0.15 m. The convergence radius of the habitat at the terminal 2s was set to 0.15m in accordance with the allowable error range of the habitat terminal position. Knowing the radius of 2s, the radius of the suction area at the time of 1.95s can be derived according to equation (36), thus reversing the radius of the suction area over the course of the entire process. The entire process of the aircraft perch maneuver totaled 41 attraction domain radii.

To visualize the graphics of the attraction domain, the attraction domain radius is projected onto the xh-plane, i.e. in accordance withExpression of attraction domains

General formula

In (1)

Except that the horizontal position and the height are set to be 0, the right side is the radius of the attraction domain, and then the projection of the xh plane can be obtained.

Since the attraction domain obtained according to equation (36) is relatively small. According to the 3.2 algorithm to expand the attraction domain, the attraction domain is expanded by reducing the S matrix. Fig. 7 is a projection on an xh plane according to the calculated radii of 41 attraction domains, where green is the attraction domain before no enlargement and black is the attraction domain after enlargement. Red is a plot of reference trajectory horizontal position and height generated by GPOPS according to constraints.

As can be seen from fig. 7, by optimizing the method for calculating the attraction domain, an attraction domain with greater aircraft perch maneuver can be found. This enables the aircraft to be assured of perching within the predetermined target range under greater initial state deviation.

In order to verify the reliability of the attraction domain, 4 different initial states in the 0s attraction domain are selected, the simulation result is shown in fig. 8, the perch track is all in the attraction domain, and the terminal range converges to the target area, so that the validity of the attraction domain is verified.

5 conclusion

1) The generalized pseudospectral method may generate a perch maneuver nominal trajectory based on constraints on flight conditions.

2) The simulation result of the perch track tracking control shows that the reference track generated by the GPOPS can be well tracked by the track tracking controller adopting the LQR design, and the effectiveness of the LQR controller is verified.

3) Simulation results of the attraction domain show that the attraction domain of a larger perch maneuver trajectory can be found by optimizing the process of solving the attraction domain. The simulation of the perch maneuver control on the expanded attraction domain shows that the tracks starting from the initial attraction domain are all kept in the attraction domain, and the effectiveness of the tracks is verified.

The above examples are merely illustrative of the embodiments of the present invention, and the description thereof is more specific and detailed, but not to be construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims

1. An attraction domain optimization method for unmanned aerial vehicle perching and maneuvering switching control is characterized by comprising the following steps:

2. The method of claim 1, wherein the habitat dynamics model in step 1 is:

wherein V is the flying speed,

3. The attraction domain optimization method for unmanned aerial vehicle perch maneuver switching control according to claim 2, wherein the constraints of each state quantity in the perch process in the step 1 are as follows:

variable of state Lower limit value Upper limit value V/m·s^-1 0 25 α/rad -π/2 π/2 μ/rad -π/4 π/4 q_r/rad·s^-1 -3.5 3.5 x/m 0 15 h/m 0 10 δ_e/rad -π/3 π/3

。

4. The attraction domain optimization method for unmanned aerial vehicle perch maneuver switching control according to claim 1, wherein the trajectory optimization is performed in step 1 by Rudau pseudo-spectrum method, and the selected quadratic optimization index J is:

5. The method of claim 1, wherein the piecewise linear model in step 2 is:

middle X type_q(t) corresponds to a function that varies over time and is described as:

And

6. The attraction domain optimization method for unmanned aerial vehicle perch maneuver switching control according to claim 4, wherein the control law of the trajectory tracking controller in step 2 is as follows:

k_q＝-R^-1B_q ^TS_q (7)

in the formula S_qIs a positive definite symmetric matrix satisfying equation (8), i.e., ricati equation:

Q-S_qB_qR^-1B_q ^TS_q+S_qA_q+A_q ^TS_q＝0 (8)

the closed loop equation at time q is:

7. the method of claim 6, wherein the Lyapunov function value of each segmented subsystem is greater than or equal to that of the next subsystem, so as to ensure the stability of the whole perch system, that is, the following formula is satisfied:

in the formula P_qAnd Q_qThe selected positive definite symmetric matrix.

8. The attraction domain optimization method for unmanned aerial vehicle perch maneuver switching control according to claim 7, wherein the attraction domain calculation step of step 3 is as follows:

Wherein

r＝[Δv,Δα,Δμ,Δq,Δx,Δh]^T，

U is a 6 × 6 real symmetric matrix(ii) a The S matrix is calculated by a formula (8);

step 3.2: the maximum rho (t) obtained_q) And

substituting the equation (12) into the equation (12), solving until the left side of the equation (12) does not belong to the sum of squares, and selecting a kS matrix with a solution at the previous moment without the solution;

wherein

Step 3.3: substituting the kS matrix