CN107608367B - Multivariable interference compensation quadrotor unmanned aerial vehicle trajectory and attitude cooperative control method - Google Patents

Multivariable interference compensation quadrotor unmanned aerial vehicle trajectory and attitude cooperative control method Download PDF

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CN107608367B
CN107608367B CN201710794252.XA CN201710794252A CN107608367B CN 107608367 B CN107608367 B CN 107608367B CN 201710794252 A CN201710794252 A CN 201710794252A CN 107608367 B CN107608367 B CN 107608367B
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田栢苓
刘丽红
鲁瀚辰
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Tianjin University
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Abstract

本发明涉及无人飞行器控制技术领域，为提出一种基于多变量干扰补偿的有限时间轨迹姿态协同控制算法，突破传统四旋翼无人机控制方法在控制精度、响应速度及抗干扰方面的不足，解决四旋翼无人机在综合干扰影响下轨迹与姿态的高精度快速稳定跟踪控制问题，达到提高四旋翼无人机控制性能，增强系统安全性和可靠性的目的。多变量干扰补偿四旋翼无人机轨迹与姿态协同控制方法，具体步骤如下：第一部分，轨迹控制器‑干扰补偿器设计；第二部分，姿态解算；第三部分，姿态控制器‑干扰补偿器设计。本发明主要应用于无人飞行器控制场合。

Figure 201710794252

The invention relates to the technical field of unmanned aerial vehicle control. In order to propose a limited-time trajectory and attitude cooperative control algorithm based on multi-variable interference compensation, and to break through the deficiencies of the traditional four-rotor unmanned aerial vehicle control method in terms of control accuracy, response speed and anti-interference, It solves the problem of high-precision, fast and stable tracking control of the trajectory and attitude of the quad-rotor UAV under the influence of comprehensive interference, and achieves the purpose of improving the control performance of the quad-rotor UAV and enhancing the safety and reliability of the system. Multivariable interference compensation quadrotor UAV trajectory and attitude collaborative control method, the specific steps are as follows: the first part, the design of the trajectory controller-disturbance compensator; the second part, the attitude calculation; the third part, the attitude controller-disturbance compensation device design. The invention is mainly applied to the unmanned aerial vehicle control occasion.

Figure 201710794252

Description

Multivariable interference compensation quadrotor unmanned aerial vehicle trajectory and attitude cooperative control method
Technical Field
The invention relates to the technical field of unmanned aerial vehicle control, in particular to the field of high-precision rapid trajectory and attitude cooperative control of a quad-rotor unmanned aerial vehicle. In particular to a multivariable interference compensation quadrotor unmanned aerial vehicle track and attitude cooperative control method.
Background
Four rotor unmanned aerial vehicle have the axial symmetry on mechanical structure, and four even distributions of rotor are on four endpoints of cross structure, and this type unmanned aerial vehicle's power is provided by the lift that each rotor produced, only needs to change the rotation rate of four rotors, can realize actions such as rolling, every single move, driftage of unmanned aerial vehicle. The quad-rotor unmanned aerial vehicle has the advantages of small volume, light weight, good concealment, suitability for multi-platform and multi-space use, capability of flexibly and vertically taking off and landing on the ground and warships, and the like. The aircraft has a simple structure, ultra-strong maneuverability and a unique flight mode, shows great application value in the military and civil fields, and is widely applied to the fields of military reconnaissance, dangerous area detection, target capture, battlefield management, firepower support, electronic interference, communication relay and the like.
However, the quad-rotor unmanned aerial vehicle is a complex controlled object integrating multivariable, uncertain, nonlinear, fast time-varying, strong coupling, static instability and under-actuation, and the flight control technology of the quad-rotor unmanned aerial vehicle is always the key point and the difficulty point of the research in the field of aviation. At present, a traditional control method based on a classical theory, such as a PID control algorithm, is widely used in the field of flight control due to simple structure, easy realization and independence of a system mathematical model. However, when the control method based on the traditional theory is used for designing the four-rotor unmanned aerial vehicle, the defects are mainly reflected in the following aspects: (1) when a flight control system is designed based on a traditional control strategy, a multi-input multi-output unmanned aerial vehicle model is generally simplified into a plurality of single-input single-output models, then controller design is carried out on each channel, and the design strategy of artificial forced decoupling is easy to cause instability when the unmanned aerial vehicle carries out rapid maneuvering flight; (2) the conventional flight control system designed based on the Lyapunov theory can only realize asymptotic stable tracking control on a given reference instruction, and limits the ultimate flight capability of the unmanned aerial vehicle, and the conventional theory shows that the flight control system based on limited time can comprehensively improve the tracking precision, the convergence speed and the robustness of the system while ensuring the stability of the system; (3) the parameter adjustment of the controller designed based on the traditional control method depends heavily on the uncertainty of a system model and external interference, during actual flight control, due to the existence of unknown interference, the flight control performance is often difficult to obtain an expected control effect, and the parameter adjustment of the controller designed based on the strategy is time-consuming and labor-consuming.
Aiming at the limitations, the invention firstly provides a multivariable interference compensation finite time trajectory attitude cooperative control method for the quad-rotor unmanned aerial vehicle in a multivariable control framework, and a flight control system designed based on the method can carry out online estimation and compensation on comprehensive interferences such as uncertain system model parameters, unmodeled dynamic conditions, external wind interference and the like, thereby obviously improving the capability of the quad-rotor unmanned aerial vehicle for coping with complex flight environments; in addition, the controller designed based on the method can realize the finite time cooperation of the track and the attitude of the quad-rotor unmanned aerial vehicle, ensure that a flight control system has higher control precision, faster convergence speed and stronger robustness, and effectively enhance the control performance of the system; more importantly, the selection of the controller parameters based on the method only depends on the nominal model of the system, and is irrelevant to the uncertainty of the system model and the external comprehensive interference, so that the parameter debugging of the control system is greatly simplified.
The invention relates to the technical field of flight control of quad-rotor unmanned aerial vehicles. Specifically, a multivariable interference compensation-based four-rotor unmanned aerial vehicle trajectory attitude cooperative control algorithm different from the traditional control mode is provided, and then the validity of the algorithm provided by the invention is verified through the comparative analysis of Simulink simulation and the traditional PID method.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a high-precision and quick track attitude cooperative control algorithm applied to a quad-rotor unmanned aerial vehicle. Particularly, the urgent need of safe, stable and reliable flight under the complex flight environment of the unmanned aerial vehicle is considered, under the condition that the model parameters of the unmanned aerial vehicle are uncertain, the dynamic state without modeling and the external interference influence are comprehensively considered, a finite time track attitude cooperative control algorithm based on multivariable interference compensation is provided, the defects of the traditional control method of the quad-rotor unmanned aerial vehicle in the aspects of control precision, response speed and interference resistance are overcome, the problem of high-precision, rapid and stable tracking control of tracks and attitudes of the quad-rotor unmanned aerial vehicle under the comprehensive interference influence is solved, and the purposes of improving the control performance of the quad-rotor unmanned aerial vehicle and enhancing the safety and reliability of the. The technical scheme adopted by the invention is that the multivariable interference compensation quadrotor unmanned aerial vehicle track and attitude cooperative control method comprises the following specific steps:
first part, trajectory controller-disturbance compensator design: designing a multivariable track controller and an interference compensator with a finite time convergence characteristic aiming at an outer ring position subsystem based on a homogeneous theory, wherein the interference compensator is used for completing online observation of external interference of the position subsystem and transmitting an interference estimation value to the track controller in real time, and the track controller ensures that high-precision rapid tracking of a reference track is realized within finite time and provides a feasible virtual control instruction for an attitude calculation module;
and in the second part, attitude calculation: based on the flight characteristics of the quad-rotor unmanned aerial vehicle, an analytic relation between a virtual control instruction and an expected attitude angle instruction is established, and the purpose of indirectly tracking a given reference trajectory is achieved while the follow-up inner-loop trajectory controller tracks the expected attitude;
third, attitude controller-disturbance compensator design: a multivariable attitude controller and an interference compensator with a finite time convergence characteristic are designed for an inner ring attitude subsystem based on a homogeneous theory, wherein the interference compensator is used for completing online observation of external interference of the attitude subsystem and transmitting an interference estimation value to the attitude controller in real time, and the attitude controller ensures that high-precision rapid tracking of an expected attitude is realized within finite time.
The specific implementation process is as follows:
the method comprises the following steps of firstly, analyzing a four-rotor unmanned aerial vehicle model based on multiple time scales: according to the multi-time scale characteristic of the unmanned aerial vehicle, dividing the unmanned aerial vehicle model with six degrees of freedom into a position subsystem and an attitude subsystem:
location subsystem
Figure BDA0001399949930000021
Attitude subsystem
Figure BDA0001399949930000022
Wherein xi is [ x, y, z ═ z]T∈R3Indicating the location of the drone; v ═ vx,vy,vz]TRepresenting the speed of the unmanned aerial vehicle in the directions of coordinate axes x, y and z; g represents the gravitational acceleration; e.g. of the typez＝[0,0,1]T；τfRepresenting the total lift of the unmanned aerial vehicle; m represents the mass of the drone; theta is phi, theta, psi]Representing an attitude angle vector of the unmanned aerial vehicle, wherein phi represents a pitch angle, theta represents a roll angle, and psi represents a yaw angle; w ═ ωx,ωy,ωz]TRepresenting an attitude angular velocity vector; i ═ diag [ I ═ Ix,Iy,Iz]Representing an aircraft inertia matrix; τ ═ τ [ τ ]1,τ2,τ3]TRepresents a control torque; delta1And Δ2Separate representation of position subsystems andexternal interference suffered by the attitude subsystem; the matrix W is defined as follows
Figure BDA0001399949930000031
The orthogonal rotation matrix R is defined as follows
Figure BDA0001399949930000032
The second step, four rotor unmanned aerial vehicle trajectory control ware-interference compensator design: introducing virtual control variables for a position subsystem (1)
Figure BDA0001399949930000033
To ensure control signals taufContinuously, the location subsystem (1) is extended, defining the following augmentation variables:
Figure BDA0001399949930000034
defining quad-rotor unmanned aerial vehicle trajectory tracking error
Figure BDA0001399949930000035
Wherein x1ref＝[xref,yref,zref]A reference trajectory of the drone is represented,
Figure BDA0001399949930000036
denotes x1refI times the differential signal. The augmented dynamic system based on the tracking error is expressed as
Figure BDA0001399949930000037
Aiming at a four-rotor unmanned aerial vehicle trajectory error augmentation system (6), the design control law is as shown in (7)
Figure BDA0001399949930000038
Wherein
Figure BDA0001399949930000039
In formula (7)
Figure BDA00013999499300000310
Equivalent to an interference compensator for realizing the comprehensive interference in the pair formula (6)
Figure BDA00013999499300000311
Real-time online estimation. In the formula (7), the parameter λ is selectedi(i ═ 1,2,3,4) so that polynomial s4+λ4s3+λ3s2+λ2s+λ1Is a Hurwitz polynomial, the gain k of the interference compensator1And k2Satisfy the requirement of
Figure BDA00013999499300000312
Wherein L isoComprehensive interference heald for position representative subsystem
Figure BDA00013999499300000313
Upper bound of (d), controller parameter ρi(i ═ 1.., 4.) is calculated by equation (9)
Figure BDA00013999499300000314
Thirdly, resolving the four-rotor unmanned aerial vehicle attitude: resolving through the attitude to obtain the analytic relation between the flight trajectory and the flight attitude of the quad-rotor unmanned aerial vehicle, and obtaining the total lift of the quad-rotor unmanned aerial vehicle at the same time, wherein the specific calculation process is as follows:
Figure BDA00013999499300000315
Figure BDA0001399949930000041
Figure BDA0001399949930000042
wherein τ'fi(i-1, 2,3) represents a virtual control vector τ'fThe ith element of (1), sφ＝sinφ,sθ＝sinθ,
Figure BDA0001399949930000043
cφ＝cosφ,cosθ＝cosθ,
Figure BDA0001399949930000044
φrefAnd thetarefAn expected attitude angle command obtained through attitude calculation;
fourthly, designing a four-rotor unmanned aerial vehicle attitude controller-interference compensator: introducing intermediate variables for the attitude subsystem (2)
x5＝Θ,x6＝WΩ (13)
Defining attitude tracking errors
Figure BDA0001399949930000045
Wherein Θ isref＝[φref,θref,ψref]Representing the expected attitude of the unmanned aerial vehicle, the dynamic system based on the attitude tracking error is expressed as:
Figure BDA0001399949930000046
attitude error dynamic system (15) for quad-rotor unmanned aerial vehicle, control torque is designed as shown in (16)
Figure BDA0001399949930000047
Wherein
Figure BDA0001399949930000048
The system is an interference compensator of the attitude subsystem and is used for realizing real-time online estimation of comprehensive interference of the attitude subsystem. In formula (16), λ5And λ6At an arbitrary normal value, the interference compensator gain k3And k4Satisfy the requirement of
Figure BDA0001399949930000049
Wherein L isiRepresenting the upper bound of the attitude subsystem synthetic disturbance Δ', the controller parameter ρ5＝ρ/(2-ρ),ρ6ρ, where ρ ∈ (0, 1). The actual control torque of the quad-rotor unmanned aerial vehicle can be calculated through (15) as follows: tau is IW-1τ'。
Verifying effectiveness, namely performing integrated design on a track attitude cooperative control system of the quad-rotor unmanned aerial vehicle in Matlab/Simulink, and performing a simulation experiment, wherein the simulation implementation process is as follows:
(1) parameter setting
1) Reference trajectory of quad-rotor unmanned aerial vehicle: p is a radical ofref(t)＝pr0+a3pt3+a4pt4+a5pt5Wherein p isref(t) denotes a given reference trajectory in p ∈ { x, y, z } direction, pr0Representing the initial position, coefficient a3p,a4p,a5pBy the formula
Figure BDA00013999499300000410
Is calculated to obtain wherein
Figure BDA00013999499300000411
pfAnd tfRespectively representing the position of the terminal and the time of response, and taking t in simulation f20, x, y, z direction terminal position xf＝20,yf＝5,z f10, heading reference trajectory ψref＝0。
2) Physical parameters of the quad-rotor unmanned aerial vehicle: mass m of aircraft is 0.625kg, inertia parameter Ix＝2.3×10-3kgm2，Iy＝2.4×10-3kgm2，Iz＝2.6×10-3kgm2；
3) Setting parameters of the cooperative controller: trajectory controller-disturbance compensator parameter lambda1＝6,λ2＝15,λ3＝15,λ4＝6ρ＝0.75,L o10; attitude controller-disturbance compensator parameter lambda5＝15,λ6＝20ρ＝0.7,Li＝10；
In the simulation test verification process, the sampling time is set to be a fixed step length of 1 millisecond, and the position ring external interference uses a time-varying function delta1＝50(1+cos(t)+sin(t))diag(Ix,Iy,Iz) Simulation is carried out, and the external interference delta of the attitude ring20.5(1+ cos (t) + sin (t)), and furthermore, the model was assumed in the simulation to have an inertial parameter uncertainty of 20%.
The invention has the characteristics and beneficial effects that:
comparing the algorithm provided by the invention with the traditional PID control algorithm, the simulation results obtained by the two control methods are shown in FIGS. 2-8. Wherein, fig. 2-5 are the result of the trajectory attitude cooperative control of the quad-rotor unmanned aerial vehicle based on multivariate interference compensation proposed by the invention, fig. 6-7 are the result obtained based on the conventional PID, and fig. 8 is the comparison curve of the two control algorithms on the accuracy and convergence speed of the trajectory attitude cooperative control.
When the algorithm provided by the invention is used for tracking the expected attitude command, the maximum tracking error is about 10-6Radian and tracking precision are obviously superior to those of a PID control algorithm.
Description of the drawings:
figure 1 is a diagram of a trajectory and attitude coordinated control system of a quad-rotor unmanned aerial vehicle based on multivariate disturbance compensation.
FIG. 2 illustrates a disturbance compensation-trajectory attitude co-tracking curve.
Fig. 3 shows a disturbance compensation-control input profile.
Fig. 4 interference compensation-position loop (outer loop) interference estimation curve.
Fig. 5 interference compensation-attitude loop (inner loop) interference estimation curve.
FIG. 6 is a conventional PID-trajectory pose co-tracking curve.
FIG. 7 is a conventional PID-control input profile.
FIG. 8 interference compensation-conventional PID trajectory attitude coordinated tracking error comparison.
Detailed Description
The general technical scheme of the trajectory and attitude cooperative control algorithm of the four-rotor unmanned aerial vehicle based on multivariate interference compensation is shown in figure 1, and the whole system mainly comprises three parts: the method comprises the following specific technical scheme that the method comprises the following steps of track controller-interference compensator design, attitude calculation and attitude controller-interference compensator design:
first part, trajectory controller-disturbance compensator design: a multivariable track controller and an interference compensator with a finite time convergence characteristic are designed for an outer ring position subsystem based on a homogeneous theory, wherein the interference compensator is used for achieving online observation of external interference of the position subsystem and transmitting an interference estimation value to the track controller in real time, and the track controller ensures that high-precision rapid tracking of a reference track is achieved within finite time and provides a feasible virtual control instruction for an attitude calculation module.
And in the second part, attitude calculation: based on the flight characteristics of the quad-rotor unmanned aerial vehicle, an analytic relation between an outer ring virtual control instruction and an inner ring expected attitude angle instruction is established, and the purpose of indirectly tracking a given reference trajectory is achieved while a subsequent inner ring trajectory controller tracks an expected attitude.
Third, attitude controller-disturbance compensator design: a multivariable attitude controller and an interference compensator with a finite time convergence characteristic are designed for an inner ring attitude subsystem based on a homogeneous theory, wherein the interference compensator is used for completing online observation of external interference of the attitude subsystem and transmitting an interference estimation value to the attitude controller in real time, and the attitude controller ensures that high-precision rapid tracking of an expected attitude is realized within finite time.
And finally, in order to verify the effectiveness of the algorithm provided by the invention, an MATLAB/Simulink simulation system for the trajectory attitude cooperative control of the quad-rotor unmanned aerial vehicle is set up, and the simulation result is compared with the traditional PID control method, so that the advantages of the algorithm provided by the invention on the tracking precision and the convergence speed are verified.
The invention provides a trajectory and attitude cooperative control algorithm of a four-rotor unmanned aerial vehicle based on multivariate interference compensation by taking a finite time control theory based on homogeneity as a main research means, and the specific implementation process is as follows.
In a first step, a quad-rotor drone model analysis based on multiple time scales. According to the multi-time scale characteristic of the unmanned aerial vehicle, dividing the unmanned aerial vehicle model with six degrees of freedom into a position subsystem and an attitude subsystem:
location subsystem
Figure BDA0001399949930000061
Attitude subsystem
Figure BDA0001399949930000062
Wherein xi is [ x, y, z ═ z]T∈R3Indicating the location of the drone; v ═ vx,vy,vz]TRepresenting the speed of the unmanned aerial vehicle in the directions of coordinate axes x, y and z; g represents the gravitational acceleration; e.g. of the typez＝[0,0,1]T；τfRepresenting the total lift of the unmanned aerial vehicle; m represents the mass of the drone; theta is phi, theta, psi]Representing the attitude of the unmanned aerial vehicle, wherein phi represents a pitch angle, theta represents a roll angle, and psi represents a yaw angle; w ═ ωx,ωy,ωz]TRepresenting an attitude angular velocity; i ═ diag [ I ═ Ix,Iy,Iz]Representing an aircraft inertia matrix; τ ═ τ [ τ ]1,τ2,τ3]TPresentation controlTorque is produced; delta1And Δ2Respectively representing external interference suffered by the position subsystem and the attitude subsystem; the matrix W is defined as follows
Figure BDA0001399949930000063
The orthogonal rotation matrix R is defined as follows
Figure BDA0001399949930000064
And step two, designing a four-rotor unmanned aerial vehicle trajectory controller-interference compensator. Introducing virtual control variables for the position subsystem (17)
Figure BDA0001399949930000065
To ensure control signals taufContinuously, the position subsystem (17) is extended, defining the following augmentation variables:
Figure BDA0001399949930000066
defining quad-rotor unmanned aerial vehicle trajectory tracking error
Figure BDA0001399949930000067
Wherein x1ref＝[xref,yref,zref]A reference trajectory of the drone is represented,
Figure BDA0001399949930000068
denotes x1refThe i-th order differential signal is expressed as the augmented dynamic system based on the track tracking error
Figure BDA0001399949930000071
Aiming at a four-rotor unmanned aerial vehicle trajectory error augmentation system (22), the design control law is shown as (23)
Figure BDA0001399949930000072
Wherein
Figure BDA0001399949930000073
In formula (23)
Figure BDA0001399949930000074
Corresponding to an interference compensator for realizing the comprehensive interference in the pair formula (22)
Figure BDA0001399949930000075
Is estimated in real time on-line, in equation (23), the parameter λ is selectedi(i is 1,2,3,4) such that the polynomial s4+λ4s3+λ3s2+λ2s+λ1Is a Hurwitz polynomial, the gain k of the interference compensator1And k2Satisfy the requirement of
Figure BDA0001399949930000076
Wherein L isoRepresenting location subsystem synthetic interference
Figure BDA0001399949930000077
Upper bound of (d), controller parameter ρi(i ═ 1.., 4.) is calculated by equation (25)
Figure BDA0001399949930000078
Thirdly, resolving the four-rotor unmanned aerial vehicle attitude: resolving through the attitude to obtain an analytic relation between the flight trajectory and the flight attitude of the quad-rotor unmanned aerial vehicle, and simultaneously obtaining the total lift of the quad-rotor unmanned aerial vehicle, wherein the specific calculation process is as follows.
Figure BDA0001399949930000079
Figure BDA00013999499300000710
Figure BDA00013999499300000711
Wherein τ'fi(i-1, 2,3) represents a virtual control vector τ'fThe ith element of (1), sφ＝sinφ,sθ＝sinθ,
Figure BDA00013999499300000712
cφ＝cosφ,cosθ＝cosθ,
Figure BDA00013999499300000713
φrefAnd thetarefIs a desired attitude angle command obtained by attitude calculation.
And fourthly, designing a four-rotor unmanned aerial vehicle attitude controller-interference compensator. Introducing intermediate variables for the pose subsystem (18)
x5＝Θ,x6＝WΩ (29)
Defining attitude tracking errors
Figure BDA00013999499300000714
Wherein Θ isref＝[φref,θref,ψref]Representing the desired pose of the drone, a dynamic system based on pose tracking errors can be expressed as
Figure BDA00013999499300000715
For attitude error dynamic system (31) of quad-rotor unmanned aerial vehicle, design control torque is as shown in (32)
Figure BDA00013999499300000716
Wherein
Figure BDA0001399949930000081
The system is an interference compensator of the attitude subsystem and is used for realizing real-time online estimation of comprehensive interference of the attitude subsystem. In formula (32), λ5And λ6At an arbitrary normal value, the interference compensator gain k3And k4Satisfy the requirement of
Figure BDA0001399949930000082
Wherein L isiRepresenting the upper bound of the attitude subsystem synthetic disturbance Δ', the controller parameter ρ5＝ρ/(2-ρ),ρ6ρ, where ρ ∈ (0, 1). The actual control torque of the quadrotor unmanned aerial vehicle can be calculated through the method (31) as follows: tau is IW-1τ'。
In order to verify the effectiveness of the trajectory attitude cooperative control algorithm of the quad-rotor unmanned aerial vehicle based on multivariate interference compensation, the trajectory attitude cooperative control system of the quad-rotor unmanned aerial vehicle is integrated and designed in Matlab/Simulink, and a simulation experiment is carried out, wherein the main simulation process comprises the following steps:
(1) parameter setting
1) Reference trajectory of quad-rotor unmanned aerial vehicle: p is a radical ofref(t)＝pr0+a3pt3+a4pt4+a5pt5Wherein p isref(t) denotes a given reference trajectory in p ∈ { x, y, z } direction, pr0Representing the initial position, coefficient a3p,a4p,a5pBy the formula
Figure BDA0001399949930000083
Is calculated to obtain wherein
Figure BDA0001399949930000084
pfAnd tfRespectively representing the position of the terminal and the time of response, and taking t in simulation f20, x, y, z direction terminal position xf＝20,yf＝5,z f10, heading reference trajectory ψref＝0。
2) Physical parameters of the quad-rotor unmanned aerial vehicle: mass m of aircraft is 0.625kg, inertia parameter Ix＝2.3×10-3kgm2，Iy＝2.4×10-3kgm2，Iz＝2.6×10-3kgm2。
3) Setting parameters of the cooperative controller: trajectory controller-disturbance compensator parameter lambda1＝6,λ2＝15,λ3＝15,λ4＝6ρ＝0.75,L o10; attitude controller-disturbance compensator parameter lambda5＝15,λ6＝20ρ＝0.7,Li＝10。
In the simulation test verification process, the sampling time is set to be a fixed step length of 1 millisecond, and the position ring external interference uses a time-varying function delta1＝50(1+cos(t)+sin(t))diag(Ix,Iy,Iz) Simulation is carried out, and the external interference delta of the attitude ring20.5(1+ cos (t) + sin (t)), and furthermore, the model was assumed in the simulation to have an inertial parameter uncertainty of 20%.
(2) Analysis of results
Under the given conditions, the algorithm provided by the invention is compared with the traditional PID control algorithm, and the simulation results obtained by the two control methods are shown in FIGS. 2-8. Wherein, fig. 2-5 are the result of the trajectory attitude cooperative control of the quad-rotor unmanned aerial vehicle based on multivariate interference compensation proposed by the invention, fig. 6-7 are the result obtained based on the conventional PID, and fig. 8 is the comparison curve of the two control algorithms on the accuracy and convergence speed of the trajectory attitude cooperative control.
And (3) analyzing the result of multivariate disturbance compensation trajectory attitude cooperative control: fig. 2 shows that in the proposed trajectory-attitude cooperative control framework (as in fig. 1) of a quad-rotor unmanned aerial vehicle, cooperative tracking control over a given reference trajectory and a desired attitude can be well achieved by using the trajectory-attitude cooperative control algorithm based on multivariate interference compensation proposed by the present invention. Fig. 3 shows the corresponding control torque and total control lift force required for realizing the cooperative control of flight trajectory attitude, from which it can be found that the control curve obtained based on the algorithm of the present invention has smooth change and is easy to realize in engineering. In addition, the algorithm can realize the track and attitude cooperative control of the quad-rotor unmanned aerial vehicle in a limited time, and can perform online observation on the comprehensive interference of the unmanned aerial vehicle, such as external interference, model uncertainty and the like, and the change curves of the position ring and attitude ring interference compensators on the comprehensive interference estimation of the position subsystem and the attitude subsystem of the quad-rotor unmanned aerial vehicle are respectively shown in fig. 4 and 5.
Analyzing the result of the multivariate interference compensation orbit and the traditional PID orbit attitude cooperative control: fig. 6 and 7 respectively show a trajectory-attitude cooperative tracking curve and a response control curve under conventional PID control, and it can be seen that, although the control strategy based on PID can better realize tracking a given trajectory, the tracking effect on an expected attitude command is not good. Further, fig. 8 shows a comparison curve of the two algorithms on the precision of the trajectory collaborative tracking control of the quad-rotor unmanned aerial vehicle, and it can be seen from the curve that the collaborative control strategy based on PID is applied to a given reference trajectory x in the x, y, z directionsref,yrefAnd zrefThe maximum steady-state tracking errors of the tracking error are respectively 0.02m,0.027m and 0.021 m; from the enlarged view of fig. 8, it can be seen that the cooperative control algorithm based on multivariate disturbance compensation proposed by the present subject has maximum steady-state tracking error of the order of 10 for a given reference trajectory in the x, y, z directions-5And m is about better than the tracking precision of a given reference track by a PID cooperative control algorithm. In addition, a comparison of the attitude tracking error curves of the two cooperative control algorithms is given in fig. 8, and a simulation result shows that the maximum attitude tracking errors of the PID in the three directions of the roll, the pitch and the yaw are respectively 1.7 × 10-3Radian 8 x 10-3 Radian sum 10-4Radian, and the maximum tracking error is about 10 when the algorithm proposed based on the invention tracks the expected attitude command-6Radian and tracking precision are obviously superior to those of a PID control algorithm.

Claims (3)

1.一种多变量干扰补偿四旋翼无人机轨迹与姿态协同控制方法，其特征是，具体步骤如下：1. a multivariable interference compensation quadrotor unmanned aerial vehicle trajectory and attitude collaborative control method, is characterized in that, concrete steps are as follows: 第一部分，轨迹控制器-干扰补偿器设计：基于齐次性理论针对外环位置子系统设计具有有限时间收敛特性的多变量轨迹控制器和干扰补偿器，其中干扰补偿器用于完成对位置子系统外界干扰的在线观测，并将干扰估计值实时传送给轨迹控制器，轨迹控制器确保在有限时间内实现对参考轨迹的高精度快速跟踪，并提供给姿态解算模块可行的虚拟控制指令；The first part, Trajectory Controller-Disturbance Compensator Design: Based on the homogeneity theory, a multivariable trajectory controller and disturbance compensator with finite-time convergence characteristics are designed for the outer loop position subsystem. The disturbance compensator is used to complete the control of the position subsystem. Online observation of external interference, and real-time transmission of the estimated interference value to the trajectory controller, the trajectory controller ensures high-precision and fast tracking of the reference trajectory within a limited time, and provides feasible virtual control instructions to the attitude calculation module; 第二部分，姿态解算：基于四旋翼无人机自身的飞行特性，构建虚拟控制指令与期望姿态角指令的解析关系，确保后续的内环轨迹控制器在通过实现对期望姿态跟踪的同时，达到间接跟踪给定参考轨迹的目的；The second part, attitude calculation: Based on the flight characteristics of the quadrotor UAV itself, the analytical relationship between the virtual control command and the desired attitude angle command is constructed to ensure that the subsequent inner loop trajectory controller can track the desired attitude while tracking the desired attitude. To achieve the purpose of indirectly tracking a given reference trajectory; 第三部分，姿态控制器-干扰补偿器设计：基于齐次性理论针对内环姿态子系统设计具有有限时间收敛特性的多变量姿态控制器和干扰补偿器，其中干扰补偿器用于完成对姿态子系统外界干扰的在线观测，并将干扰估计值实时传送给姿态控制器，姿态控制器确保在有限时间内实现对期望姿态的高精度快速跟踪。The third part, attitude controller-disturbance compensator design: based on the homogeneity theory, a multivariable attitude controller and disturbance compensator with finite time convergence characteristics are designed for the inner loop attitude subsystem. The online observation of the external disturbance of the system, and the real-time transmission of the estimated value of the disturbance to the attitude controller, the attitude controller ensures high-precision and fast tracking of the desired attitude within a limited time. 2.如权利要求1所述的多变量干扰补偿四旋翼无人机轨迹与姿态协同控制方法，其特征是，具体实现过程如下：2. multivariable interference compensation quadrotor unmanned aerial vehicle trajectory and attitude coordinated control method as claimed in claim 1, is characterized in that, concrete realization process is as follows: 第一步，基于多时间尺度的四旋翼无人机模型分析：依据无人机的多时间尺度特性，将六自由度的无人机模型划分为位置子系统和姿态子系统：The first step is to analyze the quadrotor UAV model based on multiple time scales: According to the multi-time scale characteristics of UAV, the UAV model with six degrees of freedom is divided into position subsystem and attitude subsystem: 位置子系统location subsystem
Figure FDA0002721860440000011
Figure FDA0002721860440000011
 姿态子系统attitude subsystem
Figure FDA0002721860440000012
Figure FDA0002721860440000012
 其中，ξ＝[x，y，z]T∈R3表示无人机的位置；v＝[vx,vy,vz]T表示无人机在坐标轴x，y，z方向的速度；g表示重力加速度；ez＝[0，0，1]T；τf表示无人机总升力；m表示无人机的质量；Θ＝[φ，θ，ψ]表示无人机的姿态角向量，其中φ表示俯仰角，θ表示滚转角，ψ表示偏航角；Among them, ξ=[x, y, z] T ∈ R 3 represents the position of the drone; v=[v x , v y , v z ] T represents the speed of the drone in the x, y, z directions of the coordinate axes ; g represents the acceleration of gravity; ez = [0, 0, 1] T ; τ f represents the total lift of the drone; m represents the mass of the drone; Θ=[φ, θ, ψ] represents the attitude of the drone Angle vector, where φ represents the pitch angle, θ represents the roll angle, and ψ represents the yaw angle; Ω＝[ωx,ωy,ωz]T表示姿态角速度向量；I＝diag[Ix,Iy,Iz]表示飞行器惯性矩阵；τ＝[τ1,τ2，τ3]T表示控制转矩；△1和△2分别表示位置子系统和姿态子系统所受到的外界干扰；矩阵W定义如下Ω=[ω x , ω y , ω z ] T represents the attitude angular velocity vector; I=diag[I x , I y , I z ] represents the inertial matrix of the aircraft; τ=[τ 1 , τ 2 , τ 3 ] T represents control torque; △ 1 and △ 2 represent the external disturbances to the position subsystem and attitude subsystem, respectively; the matrix W is defined as follows
Figure FDA0002721860440000013
Figure FDA0002721860440000013
 正交转动矩阵R定义如下The orthogonal rotation matrix R is defined as follows
Figure FDA0002721860440000014
Figure FDA0002721860440000014
 第二步，四旋翼无人机轨迹控制器-干扰补偿器设计：针对位置子系统(1)，引入虚拟控制变量The second step, quadrotor UAV trajectory controller-interference compensator design: for the position subsystem (1), introduce virtual control variables
Figure FDA0002721860440000021
Figure FDA0002721860440000021
 为保证控制信号τf连续，对位置子系统(1)进行扩展，定义如下的增广变量：In order to ensure the continuity of the control signal τ f , the position subsystem (1) is extended, and the following augmented variables are defined:
Figure FDA0002721860440000022
Figure FDA0002721860440000022
 定义四旋翼无人机轨迹跟踪误差Defining the Trajectory Tracking Error of a Quadrotor UAV
Figure FDA0002721860440000023
Figure FDA0002721860440000023
 其中x1ref＝[xref，yref，zref]表示无人机的参考轨迹，
Figure FDA0002721860440000024
表示x1ref的i次微分信号，则基于轨迹跟踪误差的增广动态系统表述为：where x 1ref = [x ref , y ref , z ref ] represents the reference trajectory of the UAV,
Figure FDA0002721860440000024
Representing the i-th differential signal of x 1ref , the augmented dynamic system based on the trajectory tracking error is expressed as:
Figure FDA0002721860440000025
Figure FDA0002721860440000025
 针对四旋翼无人机轨迹误差增广系统(6)，设计控制律如(7)所示For the quadrotor UAV trajectory error augmentation system (6), the design control law is shown in (7)
Figure FDA0002721860440000026
Figure FDA0002721860440000026
 其中
Figure FDA0002721860440000027
式(7)中的
Figure FDA0002721860440000028
相当于干扰补偿器，用于实现对式(6)中的综合干扰
Figure FDA0002721860440000029
的实时在线估计，式(7)中，选择参数λi，使得多项式s4+λ4s3+λ3s2+λ2s+λ1为Hurwitz多项式，干扰补偿器的增益k1和k2满足：in
Figure FDA0002721860440000027
In formula (7)
Figure FDA0002721860440000028
Equivalent to an interference compensator, it is used to realize the comprehensive interference in equation (6)
Figure FDA0002721860440000029
The real - time online estimation of _ _ 2 Satisfy:
Figure FDA00027218604400000210
Figure FDA00027218604400000210
 其中Lo代表位置子系统综合干扰
Figure FDA00027218604400000211
的上界，控制器参数ρi，通过式(9)计算：where L o represents the integrated interference of the position subsystem
Figure FDA00027218604400000211
The upper bound of , the controller parameter ρ i , is calculated by formula (9):
Figure FDA00027218604400000212
Figure FDA00027218604400000212
 第三步，四旋翼无人机姿态解算：通过姿态解算获得四旋翼无人机飞行轨迹与飞行姿态之间的解析关系，同时得到四旋翼无人机的总升力，具体计算过程如下：The third step, the attitude calculation of the quadrotor UAV: the analytical relationship between the flight trajectory and the flight attitude of the quadrotor UAV is obtained through the attitude calculation, and the total lift of the quadrotor UAV is obtained at the same time. The specific calculation process is as follows:
Figure FDA00027218604400000213
Figure FDA00027218604400000213
Figure FDA00027218604400000214
Figure FDA00027218604400000214
Figure FDA00027218604400000215
Figure FDA00027218604400000215
 其中τ'fi，i＝1，2，3表示虚拟控制向量τ'f的第i个元素，sφ＝sinφ，sθ＝sinθ，
Figure FDA00027218604400000216
cφ＝cosφ，cθ＝cosθ，
Figure FDA00027218604400000217
φref和θref为通过姿态解算获得的期望姿态角指令；where τ' fi , i=1, 2, 3 represents the i-th element of the virtual control vector τ' f , s φ =sinφ, s θ =sinθ,
Figure FDA00027218604400000216
c φ = cos φ, c θ = cos θ,
Figure FDA00027218604400000217
φ ref and θ ref are the desired attitude angle commands obtained through attitude calculation; 第四步，四旋翼无人机姿态控制器-干扰补偿器设计：针对姿态子系统(2)，引入中间变量The fourth step, quadrotor UAV attitude controller-interference compensator design: for attitude subsystem (2), introduce intermediate variables x5＝Θ，x6＝WΩ (13)x 5 =Θ, x 6 = WΩ (13) 定义姿态跟踪误差Define Attitude Tracking Error
Figure FDA0002721860440000031
Figure FDA0002721860440000031
 其中Θref＝[φref，θref，ψref]表示无人机的期望姿态，则基于姿态跟踪误差的动态系统表述为：where Θ ref = [φ ref , θ ref , ψ ref ] represents the desired attitude of the UAV, then the dynamic system based on attitude tracking error is expressed as:
Figure FDA0002721860440000032
Figure FDA0002721860440000032
 针对四旋翼无人机的姿态误差动态系统(15)，设计控制转矩如(16)所示For the attitude error dynamic system (15) of the quadrotor UAV, the design control torque is shown in (16)
Figure FDA0002721860440000033
Figure FDA0002721860440000033
 其中
Figure FDA0002721860440000034
Figure FDA0002721860440000035
为姿态子系统的干扰补偿器，用以实现对姿态子系统综合干扰的实时在线估计，式(16)中，λ5和λ6为任意的正常值，干扰补偿器增益k3和k4满足
Figure FDA0002721860440000036
k4>2Li，其中Li表示姿态子系统综合干扰△'的上界，控制器参数ρ5＝ρ/(2-ρ)，ρ6＝ρ，其中ρ∈(0，1)，四旋翼无人机实际控制转矩可通过(15)计算为：τ＝IW-1τ'。in
Figure FDA0002721860440000034
Figure FDA0002721860440000035
is the interference compensator of the attitude subsystem, which is used to realize the real-time online estimation of the comprehensive interference of the attitude subsystem. In formula (16), λ 5 and λ 6 are arbitrary normal values, and the gains k 3 and k 4 of the interference compensator satisfy
Figure FDA0002721860440000036
k 4 >2L i , where Li represents the upper bound of the comprehensive disturbance Δ' of the attitude subsystem, the controller parameters ρ 5 =ρ/(2-ρ), ρ 6 =ρ, where ρ∈(0,1), four The actual control torque of the rotor UAV can be calculated by (15) as: τ=IW -1 τ'. 3.如权利要求1所述的多变量干扰补偿四旋翼无人机轨迹与姿态协同控制方法，其特征是，验证有效性具体步骤，将四旋翼无人机的轨迹姿态协同控制系统在Matlab/Simulink中进行集成设计，并进行仿真实验，仿真实现过程如下：3. multi-variable interference compensation quadrotor unmanned aerial vehicle trajectory and attitude coordination control method as claimed in claim 1, it is characterized in that, verifying the effectiveness concrete steps, the trajectory attitude coordination control system of quadrotor unmanned aerial vehicle is in Matlab/ The integrated design is carried out in Simulink, and the simulation experiment is carried out. The simulation implementation process is as follows: 1)四旋翼无人机参考轨迹：pref(t)＝pr0+a3pt3+a4pt4+a5pt5，其中pref(t)表示p∈{x，y,z}方向上给定的参考轨迹，pr0代表初始位置，系数a3p，a4p，a5p由公式1) Quadrotor UAV reference trajectory: pref (t)=p r0 +a 3p t 3 +a 4p t 4 +a 5p t 5 , where pref (t) represents p∈{x,y,z} The given reference trajectory in the direction, p r0 represents the initial position, the coefficients a 3p , a 4p , a 5p are given by the formula
Figure FDA0002721860440000037
Figure FDA0002721860440000037
 计算得到，其中
Figure FDA0002721860440000038
pf和tf分别表示终端位置及响应的时刻，仿真中取tf＝20，x，y，z方向的终端位置xf＝20,yf＝5,zf＝10，航向参考轨迹ψref＝0；calculated, where
Figure FDA0002721860440000038
p f and t f represent the terminal position and the time of response, respectively. In the simulation, t f =20, the terminal position in the x, y, and z directions is x f =20, y f =5, z f =10, and the heading reference trajectory ψ ref = 0; 2)四旋翼无人机物理参数：飞行器质量m＝0.625kg，惯性参数Ix＝2.3×10-3kgm2，Iy＝2.4×10-3kgm2，Iz＝2.6×10-3kgm2；2) Four-rotor UAV physical parameters: aircraft mass m=0.625kg, inertial parameters Ix =2.3× 10-3 kgm 2 , I y =2.4× 10-3 kgm 2 , I z =2.6× 10-3 kgm 2 ; 3)协同控制器参数设置：轨迹控制器-干扰补偿器参数λ1＝6，λ2＝15，λ3＝15，λ4＝6ρ＝0.75，Lo＝10；姿态控制器-干扰补偿器参数λ5＝15，λ6＝20ρ＝0.7，Li＝10；3) Co-controller parameter setting: trajectory controller-disturbance compensator parameters λ 1 =6, λ 2 =15, λ 3 =15, λ 4 =6ρ=0.75, L o =10; attitude controller-disturbance compensator Parameters λ 5 =15, λ 6 = 20ρ =0.7, Li =10; 仿真测试验证过程中，采样时间设置为定步长1毫秒，位置环外界干扰用时变函数△1＝50(1+cos(t)+sin(t))diag(Ix,Iy，Iz)进行模拟，姿态环外界干扰△2＝0.5(1+cos(t)+sin(t))，此外，仿真中假定模型存在20％的惯性参数不确定。In the simulation test and verification process, the sampling time is set to a fixed step size of 1 millisecond, and the time-varying function △ 1 =50(1+cos(t)+sin(t))diag(I x ,I y ,I z is used for the external interference of the position loop ) to simulate, the external disturbance of the attitude loop is Δ 2 =0.5(1+cos(t)+sin(t)). In addition, it is assumed that the model has 20% uncertainty of inertial parameters in the simulation.
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