CN111026160A - Trajectory tracking control method for quad-rotor unmanned aerial vehicle - Google Patents

Trajectory tracking control method for quad-rotor unmanned aerial vehicle Download PDF

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CN111026160A
CN111026160A CN201911367910.2A CN201911367910A CN111026160A CN 111026160 A CN111026160 A CN 111026160A CN 201911367910 A CN201911367910 A CN 201911367910A CN 111026160 A CN111026160 A CN 111026160A
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angle
loop
aerial vehicle
unmanned aerial
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CN111026160B (en
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刘智伟
程星
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Huazhong University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft

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Abstract

The invention belongs to the field of robot control, and particularly relates to a trajectory tracking control method for a quad-rotor unmanned aerial vehicle, which comprises the following steps: estimating the disturbance of the loop in real time by adopting a position and speed control loop, and calculating the resultant force control quantity of the unmanned aerial vehicle, a first angle and the corresponding angular speed and angular acceleration of the first angle based on the disturbance estimation quantity, wherein the first angle is a roll angle and a pitch angle, and the disturbance estimation error of the loop is converged to zero within fixed time; estimating the loop disturbance in real time by adopting an attitude angle control loop, and respectively calculating moment control quantities of the unmanned aerial vehicle rotating around x, y and z axes of a coordinate system of the body based on the disturbance estimation quantity, wherein the second angle is a yaw angle, and the loop disturbance estimation error converges to zero within fixed time; and controlling the unmanned aerial vehicle trajectory tracking based on the resultant force control quantity and the moment control quantity, wherein the angle, the angular speed error, the position and the speed error of the unmanned aerial vehicle are converged to zero in fixed time. The invention realizes the high-precision track tracking control of the unmanned aerial vehicle at fixed time.

Description

Trajectory tracking control method for quad-rotor unmanned aerial vehicle
Technical Field
The invention belongs to the field of robot control, and particularly relates to a trajectory tracking control method for a quad-rotor unmanned aerial vehicle.
Background
Along with the development of modern control theory and rotor unmanned aerial vehicle technical research, rotor unmanned aerial vehicle can realize stable hovering, and good characteristics such as fixed point take-off and descending, rotor unmanned aerial vehicle has encouraged a large amount of scientific research personnel to engage in the research work of rotor unmanned aerial vehicle control system relevant topic as the mainstream development direction of realizing future air logistics transportation.
However, the system for the single-rotor unmanned aerial vehicle often has poor control difficulty and high stability in practical application, and researchers start to turn research objects to a four-rotor unmanned aerial vehicle system aiming at the stability simplicity of the application field. On the other hand, because of there are more input variables, four rotors often more nimble, easily control and stability better than single rotor unmanned aerial vehicle, can be when flying, accomplish some high-demand tasks simultaneously, like taking photo by plane. Therefore, four rotor unmanned aerial vehicle more accord with practical application demand.
In practical application, a quad-rotor unmanned aerial vehicle system may be required to complete a trajectory tracking task at a fixed time, and the current mainstream control method cannot realize fixed time trajectory tracking, so that the fixed time tracking method is particularly important for meeting the requirements of practical application. In addition, like most mechanical rigid structures, the dynamic characteristics of a quad-rotor drone can be expressed by a mathematical model represented by its mechanical parameters, but provided that the structure of the drone is known and the mechanical parameters are known. In fact, during the working process of the unmanned aerial vehicle, part of mechanical parameters of the unmanned aerial vehicle are often unable to be accurately measured under the influence of working conditions and external interference. So parameter uncertainty usually needs to be considered when mathematically modeling the drone.
Therefore, in combination with the above, the finite time trajectory tracking control of the quad-rotor unmanned aerial vehicle system considering the disturbance and the uncertainty of the model parameters in the task space has great significance.
Disclosure of Invention
The invention provides a trajectory tracking control method for a quad-rotor unmanned aerial vehicle, which is used for solving the technical problem that high-precision tracking control of the unmanned aerial vehicle on time and trajectory cannot be realized in practical application due to the fact that mechanical parameters cannot be accurately obtained and the trajectory tracking time cannot be fixed during modeling in the existing trajectory tracking control of the quad-rotor unmanned aerial vehicle.
The technical scheme for solving the technical problems is as follows: a trajectory tracking control method for a quad-rotor unmanned aerial vehicle comprises the following steps:
based on the expected position, the speed and the acceleration corresponding to the expected position, the real-time acquired actual position, the speed and the angle corresponding to the actual position, a position and speed control loop is adopted to estimate the disturbance of the loop in real time, and based on the estimation quantity of the disturbance, the resultant force control quantity of the unmanned aerial vehicle is calculated, and a first reference angle, the angular speed and the angular acceleration corresponding to the first reference angle are calculated, wherein the first angle is a roll angle and a pitch angle, and the disturbance estimation error of the loop converges to zero within a fixed time;
estimating the disturbance of the loop in real time by adopting an attitude angle control loop based on the reference first angle and the angular velocity and the angular acceleration corresponding to the reference first angle, the angular velocity and the angular acceleration corresponding to the expected second angle, and the actual angle and the angular velocity corresponding to the actual angle, and respectively calculating the moment control quantity of the unmanned aerial vehicle rotating around x, y and z axes of a body coordinate system based on the estimation quantity of the disturbance, wherein the second angle is a yaw angle, and the disturbance estimation error of the loop converges to zero within a fixed time;
and controlling the unmanned aerial vehicle to track based on the resultant force control quantity and the moment control quantity, wherein the angle, the angular speed error, the position and the speed error of the unmanned aerial vehicle are converged to zero in fixed time.
The invention has the beneficial effects that: the method is a fixed time trajectory tracking control method considering disturbance and model parameter uncertainty, and achieves the purposes that the disturbance estimation error in a position speed ring and the disturbance estimation error in an attitude angle control ring are both converged to zero within fixed time, so that the position speed control ring enables the angle and the angular speed error of the unmanned aerial vehicle to be converged to zero within fixed time, and the attitude angle control ring enables the position and the speed error of the unmanned aerial vehicle to be converged to zero within fixed time. In the concrete implementation, the uncertainty of dynamic parameters and external disturbance in a four-rotor unmanned aerial vehicle model can be considered, and appropriate control parameters are selected to meet the requirements on the working speed and the working precision of the robot, so that the related control method can realize that a four-rotor unmanned aerial vehicle system completes a track tracking task in fixed time in practical application, the timeliness is good, the practicability is higher, and the high-precision tracking control of the unmanned aerial vehicle on time and track in practical application is realized.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, the position and speed control loop comprises a controller for making the disturbance estimation error of the loop at a first fixed time T1A state estimator that internally converges to zero, represented as:
Figure BDA0002338929550000031
wherein,
Figure BDA0002338929550000032
is the actual disturbance D of the loop1At an initial time t0Actual disturbance quantity D of the loop1Is zero, L1An upper bound for the actual disturbance component rate of change of the loop; k is a radical ofiI is 1,2,3 is a control gain constant;
Figure BDA0002338929550000033
v is the actual velocity vector of the drone, vdIs the desired velocity vector of the drone, g is the acceleration of gravity, u1For the total force control quantity, ezExpressing a unit vector of a z axis under a geodetic coordinate system, wherein m is the quality of the unmanned aerial vehicle, and R belongs to R3×3Is a rotation matrix sequentially rotated in the z, y, x order of the body coordinate system, adIs the desired acceleration vector of the drone;
said first fixed time T1Expressed as:
Figure BDA0002338929550000034
further, the resultant force control amount u1Expressed as:
Figure BDA0002338929550000035
Figure BDA0002338929550000041
Figure BDA0002338929550000042
wherein, αi＞0,βi＞0,0＜ni＜mi,0＜pi＜qi,i＝1,2，mi,ni,pi,qiAre all positive odd numbers; p is the actual position of the drone, pdIs the desired position of the drone, evFor speed error of the drone, S1The slip form surface is preset for the loop.
Further, the calculation expression of the reference first angle is:
Figure BDA0002338929550000043
where ψ is a yaw angle in the geodetic coordinate system.
Further, the position and speed error of the position and speed control loop control is at a fourth fixed time T4Inner convergence is at zero, and the expression is:
Figure BDA0002338929550000044
the invention has the further beneficial effects that: the invention adopts the state estimator and the control law in the position and speed control loop to carry out the synergistic action, and the formula of the fourth fixed time can know that the position and speed errors can be effectively converged to zero in the fixed time only by effectively setting parameters according to actual needs, so that the practicability is strong.
Further, the attitude angle control element comprises a control unit for enabling the disturbance estimation error of the loop to be at a second fixed time T2The inter-state estimator that internally converges to zero is represented as:
Figure BDA0002338929550000045
wherein,
Figure BDA0002338929550000046
is WD2Estimate of (2), D2For actual disturbance of the loop, L2For an upper bound on the rate of change of the actual disturbance components of the loop, at an initial time t0Actual disturbance quantity D of the loop2Zero, W is a coordinate system transformation matrix, I is an identity matrix, omega is an actual angular velocity vector under a body coordinate system,
Figure BDA0002338929550000051
the expected angular velocity vector of the unmanned aerial vehicle under the geodetic coordinate system is shown, and tau' is a sliding mode control law of the ring; k is a radical ofiI is 4,5 and 6 are control gain constants,
Figure BDA0002338929550000052
said second fixed time T2Expressed as:
Figure BDA0002338929550000053
further, the moment control quantities of the unmanned aerial vehicle rotating around the x, y and z axes of the body coordinate system are u respectively2、u3、u4Expressed as: [ u ] of2,u3,u4]T＝τ；τ＝I-1Wτ'；
Figure BDA0002338929550000054
Figure BDA0002338929550000055
Wherein, αi＞0,βi＞0,0＜ni＜mi,0＜pi＜qi,i＝3,4，mi,ni,pi,qiAre all positive odd numbers; theta is the actual angle vector of the unmanned aerial vehicle under the geodetic coordinate system, and thetadFor the desired angular vector of the drone in the geodetic coordinate system,
Figure BDA0002338929550000056
for a desired angular acceleration vector of the drone in the geodetic coordinate system,
Figure BDA0002338929550000057
is the derivative of W and is,
Figure BDA0002338929550000058
S2the slip form surface is preset for the loop.
Further, the error of the angle and the angular speed controlled by the attitude angle control loop is in a third fixed time T3Inner convergence to zero, T3The expression of (a) is:
Figure BDA0002338929550000059
the invention has the further beneficial effects that: the state estimator and the control law in the attitude angle control loop are adopted to carry out the synergistic action, the formula of the third fixed time can know that the convergence of the angle and the angular speed error to zero in the fixed time can be effectively realized only by effectively setting parameters according to actual needs, and the practicability is strong.
Further, the total convergence time T of the track tracking is less than or equal to max (T)1,T2)+T3+T4。
The invention has the further beneficial effects that: the errors of angle and angular velocity converge first, then the errors of position and velocity converge again, and the disturbance convergence time T1、T2And the method is irrelevant to the control input quantity, and based on the control input quantity, the determined total convergence time of the trajectory tracking is high in accuracy and strong in practicability.
The invention also provides a storage medium, wherein the storage medium stores instructions, and when the instructions are read by a computer, the instructions cause the computer to execute any one of the trajectory tracking control methods of the quad-rotor unmanned aerial vehicle.
Drawings
Fig. 1 is a flow chart of a trajectory tracking control method for a quad-rotor unmanned aerial vehicle according to an embodiment of the present invention;
fig. 2 is a schematic diagram of trajectory tracking dual-loop control of a quad-rotor unmanned aerial vehicle according to an embodiment of the present invention;
fig. 3 is a diagram of a model of a quad-rotor drone provided in accordance with an embodiment of the present invention;
FIG. 4 is a block diagram of a position and velocity control loop provided by an embodiment of the present invention;
fig. 5 is a structural diagram of an attitude angle control ring according to an embodiment of the present invention;
FIG. 6 is a diagram illustrating a comparison between disturbance estimators and actual disturbances in position velocity control loops and attitude angle control loops, according to an embodiment of the present invention;
FIG. 7 is a diagram of tracking trajectories of position and attitude angles in a task space provided by an embodiment of the invention;
fig. 8 is a schematic diagram of control input of the unmanned aerial vehicle according to the embodiment of the present invention;
FIG. 9 is a diagram of position and attitude angular trajectory tracking in task space provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Example one
A method 100 of trajectory tracking control of a quad-rotor drone, as shown in fig. 1, comprising:
step 110, estimating disturbance of the loop in real time by adopting a position and speed control loop based on the expected position, the speed and the acceleration corresponding to the expected position, the actual position acquired in real time, and the speed and the angle corresponding to the actual position, and calculating a resultant force control quantity of the unmanned aerial vehicle and a reference first angle and an angular speed and an angular acceleration corresponding to the reference first angle based on the estimation quantity of the disturbance, wherein the first angle is a roll angle and a pitch angle, and the disturbance estimation error of the loop converges to zero within a fixed time;
step 120, estimating disturbance of the loop in real time by adopting an attitude angle control loop based on a reference first angle and an angular velocity and an angular acceleration corresponding to the reference first angle, an expected second angle and an angular velocity and an actual angle and an angular velocity corresponding to the expected second angle, and respectively calculating moment control quantities of the unmanned aerial vehicle rotating around x, y and z axes of a coordinate system of the body based on the estimation quantity of the disturbance, wherein the second angle is a yaw angle, and the disturbance estimation error of the loop is converged to zero within a fixed time;
and step 130, controlling the unmanned aerial vehicle to track based on the resultant force control quantity and the moment control quantity, wherein the angle, the angular speed error, the position and the speed error of the unmanned aerial vehicle are converged to zero in fixed time.
It should be noted that, the method firstly considers disturbance and carries out dynamics and kinematics modeling on the unmanned aerial vehicle; then the track tracking control of the unmanned aerial vehicle is converted into double-loop control, the outer loop is a position and speed control loop, and the inner loop is attitude angle loop control; as shown in fig. 2, the position speed control loop inputs a desired position and speed and an actual position and speed, part of control input amounts output to the motor and reference desired angles and angular speeds to the attitude angle control loop; the attitude angle control loop inputs a desired angle and angular speed and an actual angle and angular speed, and outputs the angle and angular speed to the other part of the motor to control input quantity. Next, designing an inner-outer ring controller, specifically including: the position and speed controller design comprises a fixed time state estimator and a fixed time sliding mode controller design, wherein the state estimator can accurately estimate the disturbance of a position and speed control loop after fixed time, and can track an expected position and speed track under the control of the proposed sliding mode control law after accurately compensating the disturbance of the position and speed control loop and after another fixed time; the attitude angle controller design comprises a fixed time state estimator and a fixed time sliding mode controller design, wherein the state estimator can accurately estimate the disturbance of an attitude angle control loop after fixed time, and can track an expected angle and an expected angular speed under the control of the proposed sliding mode control law after accurately compensating the disturbance of the attitude angle control loop and after another fixed time. Wherein the time at which the estimation error of the state estimator converges to 0 is uniquely determined by its parameters; after compensating for the disturbance, the sliding mode controller controls the time for the position velocity to converge to the desired position velocity value to be uniquely determined by its parameters. Based on the system design, the trajectory tracking control of the quad-rotor unmanned aerial vehicle is carried out. And the roll angle, the pitch angle and the yaw angle are all angles in a geodetic coordinate system.
The method is a fixed time trajectory tracking control method considering disturbance and model parameter uncertainty, and achieves the purposes that the disturbance estimation error in a position speed ring and the disturbance estimation error in an attitude angle control ring are both converged to zero within fixed time, so that the position speed control ring enables the angle and the angular speed error of the unmanned aerial vehicle to be converged to zero within fixed time, and the attitude angle control ring enables the position and the speed error of the unmanned aerial vehicle to be converged to zero within fixed time. In the concrete implementation, the uncertainty of dynamic parameters and external disturbance in a four-rotor unmanned aerial vehicle model can be considered, and appropriate control parameters are selected to meet the requirements on the working speed and the working precision of the robot, so that the related control method can realize that a four-rotor unmanned aerial vehicle system completes a track tracking task in fixed time in practical application, and the control method is good in timeliness and higher in practicability.
In order to ensure the correctness of the results of the method, the method is based on the following three conditions:
(1) the disturbance of the position and speed control loop satisfies the following conditions:
Figure BDA0002338929550000081
namely, the disturbance initial value of the position and speed control loop is 0, and the disturbance initial value exists once and is bounded;
(2) posture correction deviceThe disturbance of the attitude angle control loop satisfies the following conditions:
Figure BDA0002338929550000082
namely, the initial value of the disturbance of the attitude angle control loop is 0, and the disturbance exists once and is bounded;
(3) rotation angle of quad-rotor unmanned aerial vehicle satisfies
Figure BDA0002338929550000083
The dynamics and kinematics modeling model was:
Figure BDA0002338929550000091
a model diagram of a quad-rotor drone as shown in fig. 3, where E ═ Ex,ey,ezDenotes the geodetic coordinate system, B ═ Bx,by,bzDenotes the unmanned plane body coordinate system, p ═ x, y, z]T∈R3Representing the position of the drone in the world coordinate system, v ═ vx,vy,vz]T∈R3For the velocity of the drone in the world coordinate system, Θ ═ phi, θ, ψ]T∈R3For the Euler angle of the unmanned plane in the world coordinate system, omega ═ omega [ omega ]x,ωy,ωz]T∈R3For the angular velocity of the unmanned aerial vehicle in the coordinate system of the fuselage, g, m are the acceleration of gravity and the mass of the unmanned aerial vehicle, respectively, ezIs a unit vector in the z direction, D1＝[dx,dy,dz]T∈R3,D2＝[dφ,dθ,dψ]T∈R3Is a disturbance; i ═ diag (I)xx,Iyy,Izz)∈R3×3Representing an inertia matrix; τ ═ u2,u3,u4]T∈R3Representing the system input torque, u1Representing the system input unmanned plane total lift; r is formed by R3×3,W∈R3×3Representing a rotation matrix, C·＝cos(·),S·Sin (·), additionally:
Figure BDA0002338929550000092
Figure BDA0002338929550000093
the mathematical expression of the tracking target is as follows:
Figure BDA0002338929550000094
the expression is the current tracking target, pd＝[xd,yd,zd]T∈R3，vd＝[vx_d,vy_d,vz_d]T∈R3，ad＝[ax_d,ay_d,az_d]T∈R3Respectively representing the position state, velocity and acceleration of the tracking target.
The physical parameters of a quad-rotor drone are shown in table 1 below:
TABLE 1 physical parameters of quad-rotor unmanned aerial vehicle
Figure BDA0002338929550000095
Figure BDA0002338929550000101
Combining the position, the speed and the acceleration of the target, and obtaining a position and speed control equation according to Newton's second law:
Figure BDA0002338929550000102
wherein, T4Is an upper bound of convergence time, a constant determined by design parameters,
Figure BDA0002338929550000103
is an estimate of the disturbance. Thereby can obtain
Figure BDA0002338929550000104
Order to
Figure BDA0002338929550000105
Then u is1,
Figure BDA0002338929550000106
It can be determined that,
Figure BDA0002338929550000107
angle of target thetad＝[φd,θd,ψd]T∈R3It is possible to obtain:
Figure BDA0002338929550000108
ψdcan be designed by self and is generally set as 0; to thetadsObtaining the target angular velocity by calculating the derivative
Figure BDA0002338929550000109
aΩ_d＝[aωx_d,aωy_d,aωz_d]T∈R3Target angular acceleration, aΩ_dIs determined by the design parameters of the controller, theta is the roll angle, phi is the pitch angle, and psi is the yaw angle.
And (3) combining the angle, the angular velocity and the acceleration of the target to obtain a control equation of the attitude angle control loop:
Figure BDA0002338929550000111
wherein, T3Is an upper bound of convergence time, a constant determined by design parameters,
Figure BDA0002338929550000112
is an estimate of the disturbance. From this it is possible to obtain τ, then u2,u3,u4Can be determined.
Preferably, the above-mentioned bitThe speed control loop comprises a first fixed time T for making the disturbance estimation error of the loop1A state estimator that internally converges to zero, represented as:
Figure BDA0002338929550000113
wherein,
Figure BDA0002338929550000114
is the actual disturbance D of the loop1At an initial time t0Actual disturbance quantity D of the loop1Is zero, L1An upper bound for the actual disturbance component rate of change of the loop; k is a radical ofiI is 1,2,3 is a control gain constant;
Figure BDA0002338929550000115
v is the actual velocity vector of the drone, vdIs the desired velocity vector of the drone, g is the acceleration of gravity, u1For the total force control quantity, ezExpressing a unit vector of a z axis under a geodetic coordinate system, wherein m is the quality of the unmanned aerial vehicle, and R belongs to R3×3Is a rotation matrix sequentially rotated in the z, y, x order of the body coordinate system, adIs the desired acceleration vector of the drone; the first fixed time T1Expressed as:
Figure BDA0002338929550000116
preferably, the total force control amount u is set to be smaller than the total force control amount u1Expressed as:
Figure BDA0002338929550000117
Figure BDA0002338929550000121
Figure BDA0002338929550000122
wherein, αi＞0,βi＞0,0＜ni＜mi,0＜pi＜qi,i＝1,2，mi,ni,pi,qiAre all positive odd numbers; p is the actual position of the drone, pdIs the desired position of the drone, evFor speed error of the drone, S1The slip form surface is preset for the loop.
Preferably, the position and speed error controlled by the position and speed control loop is at a fourth fixed time T4Inner convergence is at zero, and the expression is:
Figure BDA0002338929550000123
as shown in fig. 4, the structure of the position and velocity control loop includes a state estimator and a control law, in which:
Figure BDA0002338929550000124
Figure BDA0002338929550000125
Figure BDA0002338929550000126
preferably, the attitude angle control unit includes a controller for controlling the disturbance estimation error of the loop at a second fixed time T2The inter-state estimator that internally converges to zero is represented as:
Figure BDA0002338929550000127
wherein,
Figure BDA0002338929550000131
is WD2Estimate of (2), D2For actual disturbance of the loop, L2Is divided into actual disturbances of the loopUpper bound of rate of change of quantity, at initial time t0Actual disturbance quantity D of the loop2Zero, W is a coordinate system transformation matrix, I is an identity matrix, omega is an actual angular velocity vector under a body coordinate system,
Figure BDA0002338929550000132
the expected angular velocity vector of the unmanned aerial vehicle under the geodetic coordinate system is shown, and tau' is a sliding mode control law of the ring; k is a radical ofiI is 4,5 and 6 are control gain constants,
Figure BDA0002338929550000133
the second fixed time T2Expressed as:
Figure BDA0002338929550000134
the parameters of each estimator are specifically selected as shown in table 2 below, and the perturbation is set as follows:
di＝0.2sin(5t),i＝x,y,z,φ,θ,ψ；
TABLE 2 parameters of the estimator
Parameter name Value of parameter Parameter name Value of parameter
k1 3 k4 3
k2 0.5 k5 0.5
k3 4 k 6 4
μ1 0.5 μ2 0.5
λ 1 2 λ 2 2
Preferably, the torque control amount of the unmanned aerial vehicle rotating around the x, y and z axes of the body coordinate system is u2、u3、u4Expressed as: [ u ] of2,u3,u4]T＝τ；τ＝I-1Wτ'；
Figure BDA0002338929550000135
Figure BDA0002338929550000136
Wherein, αi＞0,βi＞0,0＜ni＜mi,0＜pi＜qi,i＝3,4，mi,ni,pi,qiAre all positive odd numbers; theta is the coordinate of the earthActual angle vector of the unmanned aerial vehicle under tether, ΘdFor the desired angular vector of the drone in the geodetic coordinate system,
Figure BDA0002338929550000141
for a desired angular acceleration vector of the drone in the geodetic coordinate system,
Figure BDA0002338929550000142
is the derivative of W and is,
Figure BDA0002338929550000143
S2the slip form surface is preset for the loop.
Preferably, the attitude angle control loop controls the angle and the angular velocity error at a third fixed time T3Inner convergence to zero, T3The expression of (a) is:
Figure BDA0002338929550000144
preferably, the total convergence time T of the trajectory tracking is less than or equal to max (T)1,T2)+T3+T4。
As shown in fig. 5, the structure diagram of the attitude angle control loop includes a state estimator and a control law, in which:
Figure BDA0002338929550000145
Figure BDA0002338929550000146
Figure BDA0002338929550000147
Figure BDA0002338929550000148
the selection of the control parameters in each control law can be specifically seen in the following table 3, and the target trajectory is set as:
Figure BDA0002338929550000149
Figure BDA00023389295500001410
zd(t)＝0.25,ψd(t)＝0；
TABLE 3 control parameters
Figure BDA00023389295500001411
Figure BDA0002338929550000151
To better illustrate the invention, it has now been demonstrated that the state estimator is fixed time converged, as follows:
defining state observer estimation error
Figure BDA0002338929550000152
The position and speed control loop state estimator is derived to obtain:
Figure BDA0002338929550000153
analyzing the state estimator to obtain the following analysis results:
(1) when | | | Δ1When | | ≠ 0, both sides simultaneously multiply left
Figure BDA0002338929550000154
Obtaining:
Figure BDA0002338929550000155
the mathematical expression of the state estimator satisfies the following conditions:
Figure BDA0002338929550000156
let s | | | Δ1||，
Figure BDA0002338929550000157
Constructing the Lyapunov function
Figure BDA0002338929550000158
The derivation can be:
Figure BDA0002338929550000159
so it is progressively stabilized.
When the V is greater than 1, the reaction mixture is,
Figure BDA0002338929550000161
v will be at
Figure BDA0002338929550000162
Then converge to 1;
when V is less than or equal to 1,
Figure BDA0002338929550000163
v will be at
Figure BDA0002338929550000164
It converges to 0.
So elapsed time
Figure BDA0002338929550000165
Then, V, s, Δ1Will converge to 0 because
Figure BDA0002338929550000166
Passing through t1+t2After a period of time
Figure BDA0002338929550000167
(2) When | | | Δ1When the value of | is 0,
Figure BDA0002338929550000168
time to converge to 0
Figure BDA0002338929550000169
Wherein,
Figure BDA00023389295500001610
elapsed time T1，
Figure BDA00023389295500001611
Error of estimated value of state observer
Figure BDA00023389295500001612
Converging to 0.
Total elapsed time T for the same reason2Error of estimated value of state observer
Figure BDA00023389295500001613
Converging to 0.
Figure BDA00023389295500001614
As shown in fig. 6, the left plot corresponds to the position velocity control loop, the right plot corresponds to the attitude angle control loop, the position velocity control loop and the attitude angle control loop disturbance estimates and the actual disturbance values, and each component of the position and attitude angle disturbance estimates converges to its corresponding disturbance value at a fixed time under the influence of the state estimator designed.
The designed control rate is demonstrated below
Figure BDA00023389295500001615
The position velocity can be guaranteed to be fixed time converged:
to slip form surface S1Taking the derivative, we can get:
Figure BDA00023389295500001616
modeling dynamics and kinematics
Figure BDA00023389295500001617
Of (2) and designed
Figure BDA00023389295500001618
Substituting the expression of (a) into the above formula, one can obtain:
Figure BDA0002338929550000171
wherein
Figure BDA0002338929550000172
Is the estimation error.
According to the above, the time T passes1，
Figure BDA0002338929550000173
Obtaining:
Figure BDA0002338929550000174
constructing the Lyapunov function
Figure BDA0002338929550000175
The derivation can be:
Figure BDA0002338929550000176
V1when the pressure is higher than 1,
Figure BDA0002338929550000177
V1will be at
Figure BDA0002338929550000178
And then converges to 1.
V1When the content is less than or equal to 1,
Figure BDA0002338929550000179
V1will be at
Figure BDA00023389295500001710
And then converges to 0.
So elapsed time
Figure BDA00023389295500001711
Rear, V1,S1Will converge to 0.
From S 10, get
Figure BDA00023389295500001712
Let ep＝p-pd，ev＝v-vdThen, then
Figure BDA00023389295500001713
Elapsed time of the same reason
Figure BDA00023389295500001714
After, epAnd evWill converge to 0.
The position and speed control loop convergence time is as follows:
Figure BDA00023389295500001715
the convergence time of the attitude angle control loop is as follows:
Figure BDA00023389295500001716
the errors of angle and angular speed are converged firstly, then the errors of position and speed are converged, and the disturbance convergence time T1、T2Independent of the control input, the total time of trajectory tracking convergence is expressed as:
T≤max(T1,T2)+T3+T4。
as shown in fig. 7, under the action of the designed estimator-based fixed time controller, the tracking trajectory diagram of the position and attitude angle in the task space converges to its corresponding tracking target trajectory in a fixed time (within 8 seconds). Based on fig. 6 and 7, the control input of the unmanned aerial vehicle is obtained, including the resultant force control quantity and all the moment control quantities, as shown in fig. 8, and finally, a position and attitude angle trajectory tracking diagram in the task space is obtained, as shown in fig. 9, the result of the simulation of fig. 9 is very close to that of fig. 7, only because the accuracy problem of the sensor causes a slight error in the position and attitude angle tracking, and the error caused by the factor is removed, so that the position and attitude angle can be converged to the corresponding tracking target trajectory within a fixed time (within 8 seconds), and the result can support the control effect of the method of the embodiment.
Example two
A storage medium having instructions stored therein, which when read by a computer, cause the computer to execute a method for trajectory tracking control of a quad-rotor drone according to the first embodiment.
The related technical solution is the same as the first embodiment, and is not described herein again.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A trajectory tracking control method for a quad-rotor unmanned aerial vehicle is characterized by comprising the following steps:
based on the expected position, the speed and the acceleration corresponding to the expected position, the real-time acquired actual position, the speed and the angle corresponding to the actual position, a position and speed control loop is adopted to estimate the disturbance of the loop in real time, and based on the estimation quantity of the disturbance, the resultant force control quantity of the unmanned aerial vehicle is calculated, and a first reference angle, the angular speed and the angular acceleration corresponding to the first reference angle are calculated, wherein the first angle is a roll angle and a pitch angle, and the disturbance estimation error of the loop converges to zero within a fixed time;
estimating the disturbance of the loop in real time by adopting an attitude angle control loop based on the reference first angle and the angular velocity and the angular acceleration corresponding to the reference first angle, the angular velocity and the angular acceleration corresponding to the expected second angle, and the actual angle and the angular velocity corresponding to the actual angle, and respectively calculating the moment control quantity of the unmanned aerial vehicle rotating around x, y and z axes of a body coordinate system based on the estimation quantity of the disturbance, wherein the second angle is a yaw angle, and the disturbance estimation error of the loop converges to zero within a fixed time;
and controlling the unmanned aerial vehicle to track based on the resultant force control quantity and the moment control quantity, wherein the angle, the angular speed error, the position and the speed error of the unmanned aerial vehicle are converged to zero in fixed time.
2. A method according to claim 1, wherein the position and velocity control loop comprises means for causing a disturbance estimation error of the loop to be at a first fixed time T1A state estimator that internally converges to zero, represented as:
Figure FDA0002338929540000011
wherein,
Figure FDA0002338929540000012
is the actual disturbance D of the loop1At an initial time t0Actual disturbance quantity D of the loop1Is zero, L1An upper bound for the actual disturbance component rate of change of the loop; k is a radical ofiI is 1,2,3 is a control gain constant;
Figure FDA0002338929540000013
k2＞0,k3＞4L1,0＜μ1＜1,λ1is greater than 1, v is the actual velocity vector of the unmanned plane, vdIs the desired velocity vector of the drone, g is the acceleration of gravity, u1For the total force control quantity, ezExpressing a unit vector of a z axis under a geodetic coordinate system, wherein m is the quality of the unmanned aerial vehicle, and R belongs to R3×3Is a rotation matrix sequentially rotated in the z, y, x order of the body coordinate system, adIs the desired acceleration vector of the drone;
the first fixed timeT1Expressed as:
Figure FDA0002338929540000021
3. the trajectory tracking control method for quad-rotor unmanned aerial vehicle according to claim 2, wherein the resultant force control amount u is1Expressed as:
Figure FDA0002338929540000022
Figure FDA0002338929540000023
Figure FDA0002338929540000024
wherein, αi＞0,βi＞0,0＜ni＜mi,0＜pi＜qi,i＝1,2，mi,ni,pi,qiAre all positive odd numbers; p is the actual position of the drone, pdIs the desired position of the drone, evFor speed error of the drone, S1The slip form surface is preset for the loop.
4. A method according to claim 3, wherein said reference first angle is calculated as:
Figure FDA0002338929540000025
where ψ is a yaw angle in the geodetic coordinate system.
5. The trajectory tracking control method for quad-rotor unmanned aerial vehicle according to claim 4, wherein the trajectory tracking control method is characterized in thatThe position and speed error controlled by the position and speed control loop is at the fourth fixed time T4Inner convergence is at zero, and the expression is:
Figure FDA0002338929540000031
6. the method of claim 5, wherein the attitude control loop comprises a second fixed time T for the disturbance estimation error of the loop to occur2The inter-state estimator that internally converges to zero is represented as:
Figure FDA0002338929540000032
wherein,
Figure FDA0002338929540000033
is WD2Estimate of (2), D2For actual disturbance of the loop, L2For an upper bound on the rate of change of the actual disturbance components of the loop, at an initial time t0Actual disturbance quantity D of the loop2Zero, W is a coordinate system transformation matrix, I is an identity matrix, omega is an actual angular velocity vector under a body coordinate system,
Figure FDA0002338929540000034
the expected angular velocity vector of the unmanned aerial vehicle under the geodetic coordinate system is shown, and tau' is a sliding mode control law of the ring; k is a radical ofiI is 4,5 and 6 are control gain constants,
Figure FDA0002338929540000035
k5＞0,k6＞4L2,0＜μ2＜1,λ2＞1；
said second fixed time T2Expressed as:
Figure FDA0002338929540000036
7. the trajectory tracking control method for a quad-rotor unmanned aerial vehicle according to claim 6, wherein the torque control amounts of the unmanned aerial vehicle rotating around x, y and z axes of the body coordinate system are u and z respectively2、u3、u4Expressed as: [ u ] of2,u3,u4]T＝τ；τ＝I- 1Wτ'；
Figure FDA0002338929540000037
Figure FDA0002338929540000038
Wherein, αi＞0,βi＞0,0＜ni＜mi,0＜pi＜qi,i＝3,4，mi,ni,pi,qiAre all positive odd numbers; theta is the actual angle vector of the unmanned aerial vehicle under the geodetic coordinate system, and thetadFor the desired angular vector of the drone in the geodetic coordinate system,
Figure FDA0002338929540000041
for a desired angular acceleration vector of the drone in the geodetic coordinate system,
Figure FDA0002338929540000042
is the derivative of W and is,
Figure FDA0002338929540000043
S2the slip form surface is preset for the loop.
8. The trajectory tracking control method for quad-rotor unmanned aerial vehicle according to claim 7, wherein the angle and angular speed errors controlled by the attitude angle control loop are within a third fixed time T3Inner convergence to zero, T3The expression of (a) is:
Figure FDA0002338929540000044
9. the method of claim 8, wherein the total convergence time T of trajectory tracking is less than or equal to max (T ≦ max)1,T2)+T3+T4。
10. A storage medium having stored thereon instructions which, when read by a computer, cause the computer to perform a method of trajectory tracking control of a quad-rotor drone according to any one of claims 1 to 9.
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