CN110487280B - Unmanned aerial vehicle landing guiding method in wind disturbance environment - Google Patents

Unmanned aerial vehicle landing guiding method in wind disturbance environment Download PDF

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CN110487280B
CN110487280B CN201910833094.3A CN201910833094A CN110487280B CN 110487280 B CN110487280 B CN 110487280B CN 201910833094 A CN201910833094 A CN 201910833094A CN 110487280 B CN110487280 B CN 110487280B
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谭立国
宋审民
于志刚
霍建文
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Harbin Institute of Technology
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Abstract

Wind disturbanceAn unmanned aerial vehicle landing guiding method under the environment solves the problem that the unmanned aerial vehicle landing guiding method under the wind disturbance environment is low in guiding precision, and belongs to the field of unmanned aerial vehicle landing control. The invention comprises the following steps: s1, under the control constraint condition and the windless condition, solving an auxiliary optimal control problem of transferring the unmanned aerial vehicle from any initial position to a final position, and calculating to obtain a guiding motion track of the unmanned aerial vehicle; and gives concrete control constraint conditions; s2, solving the problem of maximum approximation of the unmanned aerial vehicle motion track and the guiding motion track under the condition of random components of given wind, and determining the unmanned aerial vehicle control law; the random component of the wind speed is a random function with given statistical characteristics, and sigma is more than or equal to 0W≤|σW|M，σWRoot mean square, | σ, a random component representing wind speedW|MIs expressed as sigmaWA maximum allowable value of; and S3, realizing unmanned aerial vehicle landing guidance by utilizing the unmanned aerial vehicle control law. The method is applied to landing of an Unmanned Aerial Vehicle (UAV) on a small mobile platform in a wind disturbance environment.

Description

Unmanned aerial vehicle landing guiding method in wind disturbance environment
Technical Field
The invention relates to an unmanned aerial vehicle landing guiding method, in particular to an unmanned aerial vehicle landing guiding method in a wind disturbance environment, and belongs to the field of unmanned aerial vehicle landing control.
Background
With the increasing number of carrier-borne unmanned aerial vehicles equipped on warships such as aircraft carriers, battle trains, destroyers, defenders and amphibians, the unmanned aerial vehicles play an important role in non-contact wars which are dominated by information weapons and intelligent weapons. Along with the development of modern sea warfare to three-dimensional and multi-level, dangerous tasks such as battlefield reconnaissance, anti-submarine anti-ship, amphibious assault, air early warning and the like are executed when ships with small water displacement are used for carrying unmanned aerial vehicles to reach certain special combat areas, and sea making rights and air making rights in future warfare are mastered, so that national defense strength is enhanced, and the unmanned aerial vehicle is an important problem which is generally concerned internationally.
When an Unmanned Aerial Vehicle (UAV) lands on a small mobile platform in a wind-disturbed environment, boundary (terminal) conditions of a given state vector need to be satisfied at the moment of docking of the UAV with a landing device. The existing unmanned aerial vehicle landing guiding method in the wind disturbance environment has the problem of low guiding precision.
Disclosure of Invention
The invention provides a method for guiding the landing of an unmanned aerial vehicle in a wind disturbance environment, aiming at the problem that the existing method for guiding the landing of the unmanned aerial vehicle in the wind disturbance environment is low in guiding precision.
The invention discloses a method for guiding an unmanned aerial vehicle to land in a wind disturbance environment, which comprises the following steps:
s1, under the control constraint condition and the windless condition, solving an auxiliary optimal control problem of transferring the unmanned aerial vehicle from any initial position to a final position, and calculating to obtain the landing motion trajectory of the unmanned aerial vehicle, namely: guiding the motion track;
the control constraint conditions are as follows:
Figure GDA0002235089890000011
0<rho is less than or equal to 1, alpha (t) represents the attack angle of the unmanned aerial vehicle, and alphaMRepresents the maximum allowable value of alpha (t), R (t) represents the electric propeller pulling force of the unmanned aerial vehicle, RMRepresents the maximum allowable value of R (t);
within the tolerance of the random component of the wind speed, p makes the mathematical expectation of the criterion J at a given constant component of the wind speed
Figure GDA0002235089890000012
Less than a set allowable value epsilon;
the criterion J is as follows:
Figure GDA0002235089890000021
v, theta, x and y respectively represent the flying speed of the unmanned aerial vehicle, the inclination angle of the flying speed vector and the ground rectangular coordinate system ox0y0The center of mass of the unmanned aerial vehicle in (1) is in x-axis coordinates and y-axis coordinates,
Figure GDA0002235089890000022
and
Figure GDA0002235089890000023
representing a given boundary value, tFIndicating the time corresponding to the terminal position;
s2, solving the problem of maximum approximation of the unmanned aerial vehicle motion track and the guiding motion track under the condition of random components of given wind, and determining the unmanned aerial vehicle control law;
the random component of the wind speed is a random function with given statistical characteristics, and sigma is more than or equal to 0W≤|σW|M，σWRoot mean square, | σ, a random component representing wind speedW|MIs expressed as sigmaWA maximum allowable value of;
and S3, realizing unmanned aerial vehicle landing guidance by utilizing the unmanned aerial vehicle control law.
Preferably, the S1 includes:
under windless conditions and constraints
Figure GDA0002235089890000024
Then, t is guaranteedFAt the moment, the drone follows a given unit vector l ═ 00 sin ξ cos ξ]The displacement of the direction from any initial position to the position of a given boundary constraint condition is maximum, and a guide track is determined; xi represents vectors l and ox0The included angle between the axes, when determining the guiding track, the direction of unit vector l is solved by using the maximum value principle, and the criterion J is further enabled2＝-lTz(t0) Is a maximum or criterion J3＝lTz(t0)＝y(t0)sinξ+x(t0) cos ξ is the minimum value;
z(t)＝[V,θ,y,x]Tv, theta, x and y respectively represent the flying speed of the unmanned aerial vehicle, the inclination angle of the flying speed vector and the ground rectangular coordinate system ox0y0Unmanned aerial vehicle in (1) centroid x-axis coordinate and y-axis coordinate, tFIndicating the time, t, at which the terminal position corresponds0A time indicating an initial position;
the phase vector of the guiding track is calculated as:
wT(t)＝[wV(t) wθ(t) wy(t) wx(t)]
wV(t)、wθ(t)、wy(t) and wx(t) represents V or thetaX and y.
Preferably, the representation form of the drone control law in S2 is:
Figure GDA0002235089890000031
wherein,
Figure GDA0002235089890000032
representing the movement of the drone in a vertical plane under wind disturbance conditions; xW(t) front drag, Y, of the droneW(t) represents the lift of the drone.
Preferably, the representation form of the drone control law in S2 is:
Figure GDA0002235089890000033
wherein,
Figure GDA0002235089890000034
representing the movement of the drone in a vertical plane under wind disturbance conditions; xW(t) front drag, Y, of the droneW(t) represents the lift of the drone;
t*according to
Figure GDA0002235089890000035
Is calculated to obtain wy(t*) Representing the point on the guiding motion track with the closest height; h denotes the search time interval for determining the height closest point.
Preferably, in S1, the method for acquiring the random component allowable range and η of the wind speed includes:
when the requirement of 0 ≦ sigmaW≤|σW|M、0<While rho is less than or equal to 1, the sigma is changed singlyWOr η, recalculating
Figure GDA0002235089890000036
To obtain
Figure GDA0002235089890000037
All sigma less than the set allowable value epsilonWAnd eta, and determining the random component allowable range of the wind speed according to the corresponding relation.
The invention has the beneficial effects that the invention researches the problem that the unmanned aerial vehicle is guided to the shipborne landing device within the specified time under the condition of wind disturbance and on the premise of meeting the given terminal constraint, and provides a method for guiding the unmanned aerial vehicle with the terminal constraint to land on a small-sized mobile platform under the wind disturbance environment, wherein the statistical characteristic of wind is unknown but limited. Considering the problem as countering the differential gaming problem, a steering control method is used to solve the problem. Simulation results prove that the method has very small error and improves the guiding precision.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive efforts based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
The motion of the drone in the vertical plane under wind turbulence conditions can be expressed in the form of the following vector differential equations:
Figure GDA0002235089890000041
wherein z ═ V, θ, y, x]T(ii) a V represents the flight speed of the drone; θ represents the inclination of the flight velocity vector; x, y denote the ground rectangular coordinate system ox0y0Unmanned aerial vehicle centroid coordinates;
Figure GDA0002235089890000042
r represents the electric propeller tension; m represents the unmanned aerial vehicle mass; α represents an angle of attack; g represents the gravitational acceleration;
Figure GDA0002235089890000043
representing frontal drag;
Figure GDA0002235089890000044
represents lift;
Figure GDA0002235089890000045
representing the airspeed of the drone; wxAnd WyRepresents the projection of the wind speed vector in the speed coordinate system; cx(α+△αW)＝Cx0+A(α+△αW)2Representing the frontal drag coefficient;
Figure GDA0002235089890000046
represents a lift coefficient; cx0，A，
Figure GDA0002235089890000047
Representing dimensionless aerodynamic coefficients; delta alphaWThe added value of the attack angle caused by wind disturbance is shown,
Figure GDA0002235089890000051
ρ represents the air density, neglecting its variation with altitude; s represents the maximum cross-sectional area.
In this embodiment, one control quantity of the drone is the angle of attack, and its constraint conditions are:
|α(t)|≤αM (2)
another control quantity of the unmanned aerial vehicle is the tension of an electric propeller, and the constraint conditions are as follows:
0≤R(t)≤RM (3)
wind velocity vector is in ground coordinate system ox0y0The projection on the respective coordinate axis can be expressed as:
Figure GDA0002235089890000052
wherein,
Figure GDA0002235089890000053
and
Figure GDA0002235089890000054
unit vectors representing respective coordinate axes;
Figure GDA0002235089890000055
Figure GDA0002235089890000056
and
Figure GDA0002235089890000057
representing the projection of the wind speed constant component on the corresponding coordinate axis; zetax(x0,y0) And ζy(x0,y0) Representing the projection of the random component of the wind speed on the corresponding coordinate axis.
The projection W of the wind speed vector on the corresponding coordinate axis of the speed coordinate systemxAnd WyBy the relation Wx＝Wx0cosθ+Wy0sin θ and Wy＝Wx0sinθ+Wy0cos theta and wind speed vector are in ground coordinate system ox0y0Are associated with the projection on the respective coordinate axis.
During the landing of the drone, the constant component of the wind speed is almost unchanged, therefore, it is assumed that the projection of the constant component of the wind speed is constant. Shaping filter equation to shape the random component of wind speed ζx＝ζx(x0,y0)，ζy＝ζy(x0,y0) Represented as a random functional form with given statistical properties.
The random component of wind speed is unknown, but bounded. During the simulation, the random component of the wind speed is set to σW(root mean square of turbulent velocity) which varies over the range:
0≤σW≤|σW|M (4)
initial moment t of unmanned aerial vehicle landing maneuver0And completion time tFAre known. Under the conditions of control constraints (2) and (3), the influence of wind disturbance is considered, the constant component is known, the random component meets the constraint condition (4)) to design the control law of the unmanned aerial vehicle, and the criterion (5) is ensured to take the minimum value:
Figure GDA0002235089890000061
wherein,
Figure GDA0002235089890000062
indicating a given boundary (terminal) condition.
The problem studied involves an uncertainty factor due to the presence of the random component of the wind. In this embodiment, the problem to be solved is considered to be a resistant differential game problem with two players participating. Wherein the first player acts in accordance with our interests, seeking the minimum value of the criterion (5), and the second player acts in opposition, seeking the maximum value of the criterion (5).
The first player's control set U, consisting of all the feasible control rates that satisfy constraints (2) and (3), is divided into two subsets U1And U2. Subset U1And the method is used for solving the auxiliary optimal control problem under the windless condition, and the landing motion trajectory obtained by calculation is called as a guiding trajectory. Subset U2For compensating for deviations between the actual motion trajectory and the guide trajectory.
Theoretically, it is difficult to separate a subset U for compensating the effects of wind turbulence from the problem under study2. Therefore, the method for guiding the landing of the unmanned aerial vehicle in the wind disturbance environment comprises the following steps:
s1, under the control constraint condition and the windless condition, solving an auxiliary optimal control problem of transferring the unmanned aerial vehicle from any initial position to a final position, and calculating to obtain the landing motion trajectory of the unmanned aerial vehicle, namely: guiding the motion track;
the present embodiment introduces a coefficient η varying from 0 to 1, i.e., 0<Eta is less than or equal to 1, and an unmanned aerial vehicle control constraint set U is adopted1Expressed as:
Figure GDA0002235089890000063
α (t) denotes the angle of attack of the drone, αMRepresents the maximum allowable value of alpha (t), R (t) represents the electric propeller pulling force of the unmanned aerial vehicle, RMRepresents the maximum allowable value of R (t);
eta is a mathematical expectation of the criterion J for a given constant component of wind speed, within a range allowed by the random component of wind speed
Figure GDA0002235089890000064
Less than a set allowable value epsilon;
the criterion J is as follows:
Figure GDA0002235089890000065
v, theta, x and y respectively represent the flying speed of the unmanned aerial vehicle, the inclination angle of the flying speed vector and the ground rectangular coordinate system ox0y0The center of mass of the unmanned aerial vehicle in (1) is in x-axis coordinates and y-axis coordinates,
Figure GDA0002235089890000071
and
Figure GDA0002235089890000072
representing a given boundary value, tFIndicating the time corresponding to the terminal position;
s2, solving the problem of maximum approximation of the unmanned aerial vehicle motion track and the guiding motion track under the condition of random components of given wind, and determining the unmanned aerial vehicle control law;
the random component of the wind speed is a random function with given statistical characteristics, and sigma is more than or equal to 0W≤|σW|M，σWRoot mean square, | σ, a random component representing wind speedW|MIs expressed as sigmaWA maximum allowable value of;
and S3, realizing unmanned aerial vehicle landing guidance by using the unmanned aerial vehicle control law.
The present embodiment has been studied with respect to the problem of guiding an unmanned aerial vehicle to a shipborne landing gear within a specified time, in the presence of wind disturbances, with the statistical properties of the wind being unknown but limited, on the premise of satisfying given terminal constraints. Considering this problem as countering the differential game problem, the introduction of η uses a guided control method to solve the problem. Simulation results prove that the method has very small error and improves the guiding precision.
The present embodiment introduces a coefficient η varying from 0 to 1, i.e., 0<Eta is less than or equal to 1, and an unmanned aerial vehicle control constraint set U is adopted1Expressed as:
Figure GDA0002235089890000073
in the present embodiment, the method solves the auxiliary optimal control problem, and determines and calculates the landing motion trajectory of the unmanned aerial vehicle, and in a preferred embodiment, S1 of the present embodiment includes:
under the condition of no wind, the guiding motion is determined according to the vector equation (1), and the controlled variable meets the constraint condition (6). Given an initial moment t of the controlled movement0And a termination time tFAnd t is equal to tFBoundary condition of time of day
Figure GDA0002235089890000074
Guarantee that t is tFThe time instant along a given unit vector l ═ 00 sin ξ cos ξ]Direction from an arbitrary initial position (t)0Time of day) to a final position (t)FTime of day) is maximized, where ξ represents the vectors l and ox0The angle between the axes, i.e. the criterion J needs to be found1＝lT[z(tF)-z(t0)]Is measured. Since in this context z (t)F) Is known, so only the criterion J needs to be found2＝-lTz(t0) Maximum or criterion J3＝lTz(t0)＝y(t0)sinξ+x(t0) The minimum value of cos ξ.
According to an initial time (t ═ t)0) The flying height of the unmanned aerial vehicle sets the direction of the vector l. Solving the direction problem of the vector l by using the necessary condition of the Pontryagin maximum value principle, and solving the boundary problem by using a Krylov-Chernousko successive approximation method.
The phase vector of the guiding track is calculated as:
wT(t)＝[wV(t) wθ(t) wy(t) wx(t)] (7)
wV(t)、wθ(t)、wy(t) and wx(t) represents phase vectors corresponding to V, theta, x, and y, respectively.
The present embodiment gives the root mean square σ of the constant component of the wind speed and the turbulent velocityW；
S2 of the present embodiment solves the random component (σ) in a given windW) And (3) solving the problem that the motion trail of the unmanned aerial vehicle and the guide motion trail are maximally approximated under the condition. The constant component of the wind is constant. The control amount of the drone satisfies the constraints (2) and (3), i.e., full control capability is used. Unmanned plane at t0The initial condition at the moment corresponds to t obtained by solving the secondary optimal control problem0The value of the phase vector of the pilot trajectory at the time instant.
In a preferred embodiment, the representation of the unmanned aerial vehicle control law in S2 of the present embodiment is as follows:
Figure GDA0002235089890000081
wherein,
Figure GDA0002235089890000082
indicating that the unmanned aerial vehicle is vertically flat under wind disturbance conditionsAn in-plane motion; xW(t) denotes the frontal drag of the drone, YW(t) represents the lift of the drone.
In the present embodiment, the method for acquiring the random component allowable range and ρ of the wind speed is as follows:
when the requirement of 0 ≦ sigmaW≤|σW|M、0<While rho is less than or equal to 1, the sigma is changed singlyWOr rho, recalculation
Figure GDA0002235089890000083
To obtain
Figure GDA0002235089890000084
All sigma less than the set allowable value epsilonWAnd p, and determining the random component allowable range of the wind speed according to the corresponding relation. The method specifically comprises the following steps:
step 1, solving random component (sigma) of given windW) The problem of maximum approximation of the motion trail of the unmanned aerial vehicle and the guide motion trail under the condition;
step 2, the problem is solved by customs, and the mathematical expectation of the criterion (5) is found
Figure GDA0002235089890000091
Step 3, if the mathematic expectation of criterion (5)
Figure GDA0002235089890000092
Less than the set allowable value epsilon, the random component (sigma) of the wind can be completely eliminated at the moment of docking the unmanned aerial vehicle with the landing gearW) The influence of (c). Will sigmaWIncrease in value of [ delta ] sigmaWThen, go to step 1;
step 4, if the mathematic expectation of criterion (5)
Figure GDA0002235089890000093
Greater than the set allowed value epsilon, the drone will not be able to compensate for the random component of the given wind (sigma) for a given value of pW) And the effect of a constant component.
Change the rho value and calculate the pairsMaximum allowable value σ of mean square error of wind speed random component for each value of ρWFinding the allowable range of the random component of the wind, within which the mathematical expectation of the criterion (5) is given a constant component of the wind speed
Figure GDA0002235089890000094
Less than the set allowable value epsilon.
Simulation verification:
the terminal constraint conditions are as follows: t is tF＝60s；
Figure GDA0002235089890000095
Figure GDA0002235089890000096
The parameters of the unmanned aerial vehicle are as follows: c. Cx0＝0.34；A＝0.01；
Figure GDA0002235089890000097
m＝20kg；S＝0.0357m2；αM＝0.4°；RM＝98N。
The problem under study was solved under the condition that the coefficient ρ was 0.8.
Under the condition of control constraint (6), the unmanned plane is solved from any initial position (t ═ t)0) Location of transfer to given terminal constraints (t ═ t)F) To determine the guiding trajectory. When determining the guide track, the direction of the unit vector l is t ═ t according to t0At a time of height y (t)0)＝y0Drone location condition determination at 250 m.
The optimum angle of attack is constant, and α (t) is 0.8 αM0.32 deg.. Turbulent velocity root mean square sigmaMThe variation range of (2) is 0.1 m/s-30 m/s.
When designing the drone control law, equation (8) is not used, but (x (t) -w (t)*) Calculate the deviation between the drone and the guidance track, i.e. using the following equation:
Figure GDA0002235089890000101
in equation (9), t*Calculated according to equation (10).
Figure GDA0002235089890000102
Wherein wy(t*) Representing the point on the guiding motion track with the closest height; h denotes the search time interval for determining the height closest point. In the simulation process, H is selected to be 5 s.
In this case, when the unmanned aerial vehicle control sampling period Δ t is selected to be 0.01s and under a windless condition, the deviation of the unmanned aerial vehicle image coordinates at the time of docking the unmanned aerial vehicle with the landing gear from the given terminal condition is minimized. Wherein deviation of flying speed
Figure GDA0002235089890000107
Figure GDA0002235089890000108
Deviation of velocity vector inclination
Figure GDA0002235089890000109
Deviation of flying height
Figure GDA0002235089890000105
Deviation of flight distance
Figure GDA0002235089890000106
Changing the value sigma of the root mean square of the turbulent velocity while studying the effect of the random component of the wind speedMThe constant component of the wind speed is zero.
The mathematical expectations of the optimization criterion (5) for the coefficients p 0.8, and p 0.6 and p 0.4 are given in table 1. Data given in Table 1
Figure GDA0002235089890000103
Is calculated according to the results of 20 times of simulation experiments.
TABLE 1 mathematical expectation of criterion (5)
Figure GDA0002235089890000104
Figure GDA0002235089890000111
As can be seen from the experimental data in table 1, if the mathematical expectation allowance of the criterion (5) is less than 2 in absolute value, the root mean square value of the wind speed random components should not exceed 1m/s under the condition of ρ ═ 0.8, should not exceed 5m/s under the condition of ρ ═ 0.6, and should not exceed 10m/s under the condition of ρ ═ 0.4.
Simulation results show that the control algorithm based on the guide track provided by the embodiment can be used for guiding the unmanned aerial vehicle to be recovered on the landing device of the small-sized motion platform, and can be used for evaluating the influence of wind disturbance on the guiding precision of the butt joint of the unmanned aerial vehicle and the landing device.

Claims (6)

1. An unmanned aerial vehicle landing guidance method in a wind disturbance environment is characterized by comprising the following steps:
s1, under the control constraint condition and the windless condition, solving an auxiliary optimal control problem of transferring the unmanned aerial vehicle from any initial position to a final position, and calculating to obtain the landing motion trajectory of the unmanned aerial vehicle, namely: guiding the motion track;
the control constraint conditions are as follows:
Figure FDA0003642374520000011
eta is more than 0 and less than or equal to 1, alpha (t) represents the attack angle of the unmanned aerial vehicle, and alphaMRepresents the maximum allowable value of alpha (t), R (t) represents the electric propeller tension of the unmanned aerial vehicle, RMRepresents the maximum allowable value of R (t);
eta is the number of the criterion J within the allowable range of the random component of the wind speed under the given constant component of the wind speedStudying expectation
Figure FDA0003642374520000012
Less than a set allowable value epsilon;
the criterion J is as follows:
Figure FDA0003642374520000013
v, theta, x and y respectively represent the flying speed of the unmanned aerial vehicle, the inclination angle of the flying speed vector and the ground rectangular coordinate system ox0y0The center of mass of the unmanned aerial vehicle in (1) is in x-axis coordinates and y-axis coordinates,
Figure FDA0003642374520000014
and
Figure FDA0003642374520000015
denotes a given boundary value of V, theta, x and y, respectively, tFIndicating the time corresponding to the terminal position;
s2, solving the problem of maximum approximation of the unmanned aerial vehicle motion track and the guiding motion track under the condition of random components of given wind, and determining the unmanned aerial vehicle control law;
the random component of the wind speed is a random function with given statistical characteristics, and sigma is more than or equal to 0W≤|σW|M，σWRoot mean square, | σ, a random component representing wind speedW|MIs expressed as sigmaWA maximum allowable value of;
s3, realizing unmanned aerial vehicle landing guidance by utilizing the unmanned aerial vehicle control law;
wherein, the representation form of the unmanned aerial vehicle control law in S2 is:
Figure FDA0003642374520000016
wherein,
Figure FDA0003642374520000021
representing the movement of the drone in a vertical plane under wind disturbance conditions; xW(t) denotes the frontal drag of the drone, YW(t) represents the lift of the drone; < ρ is a coefficient.
2. The method for guiding unmanned aerial vehicle landing in wind-disturbed environment according to claim 1, wherein the step S1 includes:
under windless conditions and constraints
Figure FDA0003642374520000022
Then, t is guaranteedFAt the moment, the drone follows a given unit vector l ═ 00 sin ξ cos ξ]The displacement of the direction from any initial position to the position of a given boundary constraint condition is maximum, and a guide track is determined; xi represents vectors l and ox0The included angle between the shafts is used for solving the direction of the unit vector l by utilizing the maximum value principle when determining the guide track, so that the criterion J is further ensured2＝-lTz(t0) Is a maximum or criterion J3＝lTz(t0)＝y(t0)sinξ+x(t0) cos ξ is the minimum value;
z(t)＝[V,θ,y,x]Tv, theta, x and y respectively represent the flying speed of the unmanned aerial vehicle, the inclination angle of the flying speed vector and the ground rectangular coordinate system ox0y0Unmanned aerial vehicle in (1) centroid x-axis coordinate and y-axis coordinate, tFIndicating the time, t, at which the terminal position corresponds0A time indicating an initial position;
the phase vector of the guiding track is calculated as:
wT(t)＝[wV(t) wθ(t) wy(t) wx(t)]
wV(t)、wθ(t)、wy(t) and wx(t) represents phase vectors corresponding to V, theta, x, and y, respectively.
3. The method for guiding unmanned aerial vehicle to land in a wind-disturbed environment according to claim 1, wherein in S1, the method for obtaining the allowable range and η of the random component of the wind speed is as follows:
when the requirement of 0 ≦ sigmaW≤|σW|MRho is more than 0 and less than or equal to 1, and simultaneously, sigma is singly changedWOr η, recalculating
Figure FDA0003642374520000023
Obtaining
Figure FDA0003642374520000024
All sigma less than the set allowable value epsilonWAnd eta, and determining the random component allowable range of the wind speed according to the corresponding relation.
4. An unmanned aerial vehicle landing guidance method in a wind disturbance environment is characterized by comprising the following steps:
s1, under the control constraint condition and the windless condition, solving an auxiliary optimal control problem of transferring the unmanned aerial vehicle from any initial position to a final position, and calculating to obtain the landing motion trajectory of the unmanned aerial vehicle, namely: guiding the motion track;
the control constraint conditions are as follows:
Figure FDA0003642374520000031
eta is more than 0 and less than or equal to 1, alpha (t) represents the attack angle of the unmanned aerial vehicle, and alphaMRepresents the maximum allowable value of alpha (t), R (t) represents the electric propeller tension of the unmanned aerial vehicle, RMRepresents the maximum allowable value of R (t);
eta is a mathematical expectation of the criterion J for a given constant component of wind speed, within a range allowed by the random component of wind speed
Figure FDA0003642374520000032
Less than a set allowable value epsilon;
the criterion J is as follows:
Figure FDA0003642374520000033
v, theta, x and y areAn inclination angle and a ground rectangular coordinate system ox respectively representing the flight speed and the flight speed vector of the unmanned aerial vehicle0y0The center of mass of the unmanned aerial vehicle in (1) is in x-axis coordinates and y-axis coordinates,
Figure FDA0003642374520000034
and
Figure FDA0003642374520000035
denotes a given boundary value of V, theta, x and y, respectively, tFIndicating the time corresponding to the terminal position;
s2, solving the problem of maximum approximation of the unmanned aerial vehicle motion trail and the guiding motion trail under the condition of random components of given wind, and determining the unmanned aerial vehicle control law;
the random component of the wind speed is a random function with given statistical characteristics, and sigma is more than or equal to 0W≤|σW|M，σWRoot mean square, | σ, a random component representing wind speedW|MIs expressed as sigmaWA maximum allowable value of;
s3, realizing unmanned aerial vehicle landing guidance by utilizing the unmanned aerial vehicle control law;
wherein, the representation form of the unmanned aerial vehicle control law in S2 is:
Figure FDA0003642374520000036
wherein,
Figure FDA0003642374520000037
representing the movement of the drone in a vertical plane under wind disturbance conditions; xW(t) denotes the frontal drag of the drone, YW(t) represents the lift of the drone;
t*according to
Figure FDA0003642374520000041
Is calculated to obtain wy(t*) Representing the point of the guiding motion track with the closest height; h denotes determinationA search time interval of the height closest point; < ρ is a coefficient.
5. The method for guiding unmanned aerial vehicle to land in the wind-disturbed environment according to claim 4, wherein in the step S1, the random component allowable range and η of the wind speed are obtained by:
when the requirement of 0 ≦ sigmaW≤|σW|MRho is more than 0 and less than or equal to 1, and simultaneously, sigma is singly changedWOr η, recalculating
Figure FDA0003642374520000042
To obtain
Figure FDA0003642374520000043
All sigma less than the set allowable value epsilonWAnd eta, and determining the random component allowable range of the wind speed according to the corresponding relation.
6. The method for guiding unmanned aerial vehicle landing in wind-disturbed environment according to claim 4, wherein the step S1 includes:
under windless conditions and constraints
Figure FDA0003642374520000044
Then, t is guaranteedFAt the moment, the drone follows a given unit vector l ═ 00 sin ξ cos ξ]The displacement of the direction from any initial position to the position of a given boundary constraint condition is maximum, and a guide track is determined; xi represents vectors l and ox0The included angle between the axes is used for solving the direction of the unit vector l by utilizing the maximum value principle when determining the guide track, so that the criterion J is further ensured2＝-lTz(t0) Is a maximum or criterion J3＝lTz(t0)＝y(t0)sinξ+x(t0) cos xi is the minimum value;
z(t)＝[V,θ,y,x]Tv, theta, x and y respectively represent the flying speed of the unmanned aerial vehicle, the inclination angle of the flying speed vector and the ground rectangular coordinate system ox0y0Unmanned aerial vehicle barycenter x axle inCoordinates and y-axis coordinates, tFIndicating the time, t, at which the terminal position corresponds0A time indicating an initial position;
the phase vector of the guiding track is calculated as:
wT(t)＝[wV(t) wθ(t) wy(t) wx(t)]
wV(t)、wθ(t)、wy(t) and wx(t) represents phase vectors corresponding to V, theta, x, and y, respectively.
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