CN111766899B - Interference observer-based quad-rotor unmanned aerial vehicle cluster anti-interference formation control method - Google Patents

Interference observer-based quad-rotor unmanned aerial vehicle cluster anti-interference formation control method Download PDF

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CN111766899B
CN111766899B CN202010801729.4A CN202010801729A CN111766899B CN 111766899 B CN111766899 B CN 111766899B CN 202010801729 A CN202010801729 A CN 202010801729A CN 111766899 B CN111766899 B CN 111766899B
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CN111766899A (en
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余翔
郭克信
刘偲
张霄
郭雷
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Beihang University
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Abstract

The invention relates to a quad-rotor unmanned aerial vehicle cluster anti-interference formation control method based on an interference observer, which comprises the following steps of: step one, constructing a single four-rotor coupling dynamic model containing external force disturbance; establishing a disturbance observer aiming at moment disturbance generated by external wind borne by the unmanned aerial vehicle; then, estimating a disturbance value according to the disturbance observer; estimating the direction of wind disturbance according to the disturbance values of the x axis and the y axis of the unmanned aerial vehicle leader estimated by the disturbance observer, and designing a four-rotor anti-interference control law; and step four, according to the wind disturbance direction estimated by the leader, when external disturbance is encountered, the formation of the four-rotor cluster keeps an I shape, and an anti-interference formation control law of the four-rotor cluster is designed to realize the anti-interference control of the unmanned aerial vehicle cluster formation. The method can remarkably improve the track control precision of the single unmanned aerial vehicle, reduces external wind disturbance on the unmanned aerial vehicle cluster, reduces disturbance compensation of the single unmanned aerial vehicle, and achieves the purpose of saving energy.

Description

Interference observer-based quad-rotor unmanned aerial vehicle cluster anti-interference formation control method
Technical Field
The invention relates to an interference observer-based anti-interference formation control method for a quad-rotor unmanned aerial vehicle cluster, which is suitable for a task execution scene of the unmanned aerial vehicle cluster when external wind is disturbed and time is changed, and belongs to the field of anti-interference control of the unmanned aerial vehicle cluster.
Background
Along with the continuous development of unmanned aerial vehicle technique in recent years, its task complexity is bigger and bigger, and the demand of many unmanned aerial vehicle cluster tasks is also bigger and bigger, requires that the unmanned aerial vehicle cluster can realize quick formation control. In addition, as the task scene of the unmanned aerial vehicle cluster is increasingly complex, the cluster communication conditions become more severe, and communication equipment with certain anti-interference capability is required; the task execution scene of the unmanned aerial vehicle cluster is complex, collision of unmanned aerial vehicles in the cluster is avoided, a specific formation is quickly formed, and the requirement on the control accuracy of cluster formation is high; in addition, to unmanned aerial vehicle, external disturbance mainly produces by wind-force, and wind-force acts on the rotation axis of four rotors, produces the moment of rotation, and when wind-force was less strong, the trail tracking precision of four rotors received the influence, and when wind-force was great, four rotors took place to topple, finally leads to the damage of cluster, consequently, need further consider four rotor unmanned aerial vehicle's anti-interference control problem.
Patent application No. 201911029214.0 provides an unmanned aerial vehicle cluster formation control method, device and storage medium, has solved the problem that current unmanned aerial vehicle cluster formation control method is difficult to control the unmanned aerial vehicle cluster and flies according to general closed curve route, nevertheless has two problems: (1) the patent does not analyze the influence of external disturbance on the clusters; (2) a corresponding cluster disturbance rejection algorithm is not proposed, and the practical use is limited. Patent application No. 201811244037.3 proposes a master-slave cooperative formation control method for multiple four rotors based on second-order consistency and active disturbance rejection, wherein the proposed method has the following problems: (1) the external disturbance can not be actively dealt with due to lack of analysis on the external disturbance; (2) the disturbance rejection method of the single unmanned aerial vehicle in the method belongs to passive disturbance rejection, and has no unmanned aerial vehicle cluster disturbance rejection strategy, so the method is inferior to the method provided by the invention in precision and rapidity.
Disclosure of Invention
In order to solve the technical problems, the invention provides an interference observer-based anti-interference formation control method for a quad-rotor unmanned aerial vehicle cluster, which aims at the problem that the cluster control precision of the quad-rotor unmanned aerial vehicle cluster is influenced by external moment disturbance which may be encountered by the quad-rotor unmanned aerial vehicle cluster in the task execution process, can obviously improve the track control precision of a single unmanned aerial vehicle, reduces external wind disturbance to the unmanned aerial vehicle cluster, reduces disturbance compensation of the single unmanned aerial vehicle, and achieves the purpose of saving energy.
The technical scheme of the invention is as follows: an interference observer-based anti-interference formation control method for quad-rotor unmanned aerial vehicle clusters comprises the following steps:
step one, constructing a single four-rotor coupling dynamic model containing external force disturbance;
establishing a disturbance observer aiming at moment disturbance generated by external wind borne by the unmanned aerial vehicle; then, according to the disturbance value estimated by the disturbance observer;
estimating the direction of wind disturbance according to the disturbance values of the x axis and the y axis of the unmanned aerial vehicle leader estimated by the disturbance observer, and designing a four-rotor anti-interference control law;
step four, according to the wind disturbance direction estimated by the leader, when external disturbance is encountered, the formation of the four-rotor cluster keeps an I shape, and an anti-interference formation control law of the four-rotor cluster is designed to realize the anti-interference control of the unmanned aerial vehicle cluster formation;
further, the first step is as follows:
aiming at the wind disturbance moment disturbance received in the four-rotor flying process, a decoupling dynamic model of the four-rotor is established at the same time, and the moment disturbance generated by wind power to the four-rotor in the horizontal plane is assumed, so that the attitude angle of the four-rotor is changed, and the four-rotor decoupling dynamic model is expressed as follows:
Figure BDA0002627641300000021
Figure BDA0002627641300000022
in the formula, m represents the mass of the four rotors, and J is a rotational inertia matrix of three axes of the four rotors; v is the linear speed of the four rotors,
Figure BDA0002627641300000031
is four-rotor linear acceleration, F isTotal lift force generated by the propeller, g is gravity acceleration, omegabAnd
Figure BDA0002627641300000032
the four-rotor-wing-type wind power generator is divided into a rotation angular velocity and a rotation angular acceleration of the four rotors under a body coordinate system, wherein tau is the moment borne by three rotation shafts of the four rotors, and d is the external moment disturbance borne by the four rotors;
establishing a body coordinate system and a geodetic coordinate system, wherein a conversion matrix W of the Euler angle change rate and the body angular velocity is expressed as follows:
Figure BDA0002627641300000033
in the formula, t, c, s, phi, theta and psi respectively represent a tangent function, a cosine function, a sine function, a roll angle, a pitch angle and a yaw angle; the rotation matrix from the earth-fixed coordinate system to the body coordinate system is represented as follows:
Figure BDA0002627641300000034
further, the second step of establishing a disturbance observer for moment disturbance generated by external wind on the unmanned aerial vehicle is as follows:
Figure BDA0002627641300000035
Figure BDA0002627641300000036
where ξ, ζ and p (ξ) represent the system state, the internal state of the nonlinear disturbance observer and the nonlinear function of the desired design, respectively,
Figure BDA0002627641300000037
and
Figure BDA0002627641300000038
representing the derivative of the internal state of the disturbance observer and the disturbance estimate, g, respectively1、g2And f are smooth functions of the state variables, and u represents the control input.
The gain of the disturbance observer, l (ξ), is determined by:
Figure BDA0002627641300000039
the NDOB system of the nonlinear disturbance observer can be gradually stable, reasonable l (xi) is selected, and the convergence speed and the overshoot of the observer can obtain corresponding matching requirements;
Figure BDA00026276413000000310
where d represents the actual perturbation or perturbations,
Figure BDA0002627641300000041
is the error in the estimation of the disturbance,
Figure BDA0002627641300000042
is edThe first derivative of the disturbance observer is gradually stable all the time, and is irrelevant to the state of the four rotors, and for the four-rotor aircraft, external wind disturbance mainly acts on an x axis and a y axis of an engine body to generate disturbance torque.
Further, the anti-interference control law of the four rotors is designed in the third step, and the method specifically comprises the following steps:
and (3) designing a cascade control law by combining the dynamics characteristics of the four rotors and a coupling kinematics model, wherein an inner ring controller controls the postures of the four rotors: pitch, roll, yaw, altitude, outer loop controller controls the position of the quadrotors: x-axis, y-axis; the torque generated by the propeller directly acts on the attitude of the quadrotors, and the response time of the position ring is longer compared with that of an attitude ring controller due to the second derivative relation between the displacement of the quadrotors and the attitude; the specific process is as follows:
step 3.1. position loop controller:
Figure BDA0002627641300000043
Figure BDA0002627641300000044
Figure BDA0002627641300000045
wherein xd、yd、zdAnd
Figure BDA0002627641300000046
representing desired and desired velocities, x, y, z and
Figure BDA0002627641300000047
representing three-axis position and velocity, kpx、kpy、kpzAnd kdx、kdy、kdzRepresenting proportional and differential gains, ux、uy、uzAnd (3) representing the three-axis control quantity of the position ring, and obtaining a control law of a roll angle and a pitch angle according to a rigid body kinematics model of the four rotors:
Figure BDA0002627641300000048
Figure BDA0002627641300000049
φd、θdpsi and g denote the roll angle desired, pitch angle desired, yaw angle and gravity constants of the quadrotors, respectively.
Step 3.2, the attitude ring controller:
the attitude ring controller receives the control input of the reference attitude angle, namely a pitch angle and a roll angle, and the yaw control is coupled with the pitch control and the roll control by the kinematics and dynamics model of the four rotors, and the position control of the aircraft can still be realized only through the change of the pitch control and the roll control without considering the yaw control of the four rotors:
Figure BDA0002627641300000051
Figure BDA0002627641300000052
Figure BDA0002627641300000053
wherein k ispφ,kpθ,kpψAnd k isdφ,kdθ,kdψRespectively representing the proportion and differential gain of roll angle, pitch angle and yaw angle, through a feedback linearization method,
Figure BDA0002627641300000054
uψ、uφ、uθand the control quantity of the yaw rate, the yaw angle, the roll angle and the pitch angle is represented. The throttle control amount T is expressed as follows:
Figure BDA0002627641300000055
neglecting air resistance, the simplified linear feedback control law is designed as follows:
Figure BDA0002627641300000056
Figure BDA0002627641300000057
Figure BDA0002627641300000058
Ω＝-w1+w2-w3+w4
wherein L is the arm length of the four rotors, wi(i ═ 1,2,3,4) denotes the rotational speed of the propeller, T, τφ,τθτψThe control torque of each coordinate axis of the machine body is shown,
Figure BDA0002627641300000059
omega represents the difference between the pitch angle velocity, the yaw angle velocity, the roll angle velocity and the propeller rotation speed, Jyy、Jzz、Jxx、JrThe three-axis moment of inertia and the motor moment of inertia are respectively expressed, and the relation between the rotating moment and the propeller lift force is as follows:
T＝F1+F2+F3+F4
τθ＝L(F2-F4)
τφ＝L(F3-F1)
τψ＝Kyaw(F1+F3-F2-F4)
wherein, F1，F2，F3，F4，KyawRespectively representing lift force and yaw coefficients generated by four propellers of the four rotors to obtain respective lift force control signals of the four propellers; the propeller has a rotational speed constraint so that the total lift force has a certain constraint within which the control signal needs to be.
Further, the step four designs an anti-interference formation control law of the four-rotor cluster, which is specifically as follows:
4.1. designing a formation controller:
a cluster formation is defined for any quad drone i as follows:
Figure BDA0002627641300000061
where j is the neighbor of the ith drone, able to communicate with each other in relative position, ΔijIs a desired formation, for each quad-rotor i in the cluster, a formation control u is designedi fWherein u isiIndicating position loop control input ux,uyAnd uzIntroducing a formation position controller:
Figure BDA0002627641300000062
wherein k ispf> 0 is the formation control gain, niIs the number of neighbors of the ith drone, NiIs the neighbor set of the ith unmanned aerial vehicle, and the three-axis decoupling formation position control law is designed as follows:
u′x＝ux+ux f
u′y＝uy+uy f
u′z＝uz+uz f
u′x、u′y、u′zand the unmanned plane position loop control output in the formation state is represented.
4.2. Designing a disturbance factor and an anti-interference formation:
designing a disturbance factor according to an aerodynamic model, estimating the direction of wind disturbance, directly acting the disturbance torque of external wind disturbance on the x axis and the y axis of a four-rotor body, and setting deltax,δyRepresenting the magnitude of the disturbance torque, the disturbance factor is defined as follows:
Figure BDA0002627641300000063
wherein gamma belongs to [ -pi, pi ], represents the angle between the direction of external wind disturbance and the x axis, and contains the information of wind direction; combining the attenuation characteristic of wind power in the air and a laminar flow model, the direction of the wind is considered to be unchanged after the wind acts on the cluster leader, and the attenuation value is in direct proportion to the distance of the leader; defining an initial formation in a cluster anti-interference state:
Δi＝[xdl ydl]T-[xdi ydi]T＝[0 i·ρ]T
ρ≥ρ0
wherein xdl,ydlIndicating the desired position of the leader, xdi,ydiDenotes the iththPosition of the slave, ρ representing the safety distance between adjacent drones, ρ0Minimum safe distance between unmanned aerial vehicles; further, obtaining a time-varying anti-interference formation form:
Figure BDA0002627641300000071
Δi,anti＝Rγ·Δi
wherein Δi,anti＝Rγ·ΔiIndicating an anti-interference formation, RγThe direction of the anti-interference formation is changed, and the distance between adjacent unmanned aerial vehicles is not reduced, so that the safety of unmanned aerial vehicle formation is ensured.
Has the advantages that:
the invention provides an anti-interference control method for formation of quad-rotor unmanned aerial vehicles, wherein under the environment of natural wind disturbance, the unmanned aerial vehicles form an I-shaped formation, and the I-shaped formation improves the overall active anti-interference capability of the formation and reduces the overall energy loss of the formation under the condition that the energy loss of a leader is not increased.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying 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, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
As shown in fig. 1, the invention provides a quad-rotor unmanned aerial vehicle cluster anti-interference formation control method based on an interference observer, which includes the following steps:
step one, constructing a single four-rotor coupling dynamic model containing external force disturbance;
establishing a disturbance observer aiming at moment disturbance generated by external wind borne by the unmanned aerial vehicle; then, according to the disturbance value estimated by the disturbance observer;
estimating the direction of wind disturbance according to the disturbance values of the x axis and the y axis of the unmanned aerial vehicle leader estimated by the disturbance observer, and designing a four-rotor anti-interference control law;
step four, according to the wind disturbance direction estimated by the leader, when external disturbance is encountered, the formation of the four-rotor cluster keeps an I shape, and an anti-interference formation control law of the four-rotor cluster is designed to realize the anti-interference control of the unmanned aerial vehicle cluster formation;
further, the first step is as follows:
aiming at the wind disturbance moment disturbance received in the four-rotor flying process, a decoupling dynamic model of the four-rotor is established at the same time, and the moment disturbance generated by wind power to the four-rotor in the horizontal plane is assumed, so that the attitude angle of the four-rotor is changed, and the four-rotor decoupling dynamic model is expressed as follows:
Figure BDA0002627641300000081
Figure BDA0002627641300000082
in the formula, m represents the mass of the four rotors, and J is a rotational inertia matrix of three axes of the four rotors; v is the linear speed of the four rotors,
Figure BDA0002627641300000083
linear acceleration of four rotors, F total lift force generated by propeller, g gravity acceleration, omegabAnd
Figure BDA0002627641300000084
the four-rotor-wing-type wind power generator is divided into a rotation angular velocity and a rotation angular acceleration of the four rotors under a body coordinate system, wherein tau is the moment borne by three rotation shafts of the four rotors, and d is the external moment disturbance borne by the four rotors;
establishing a body coordinate system and a geodetic coordinate system, wherein a conversion matrix W of the Euler angle change rate and the body angular velocity is expressed as follows:
Figure BDA0002627641300000091
wherein t, c, s, phi, theta and psi respectively represent tan, cos, sin, roll angle, pitch angle and yaw angle; the rotation matrix from the earth-fixed coordinate system to the body coordinate system is represented as follows:
Figure BDA0002627641300000092
further, the second step of establishing a disturbance observer for moment disturbance generated by external wind on the unmanned aerial vehicle is as follows:
Figure BDA0002627641300000093
Figure BDA0002627641300000094
where ξ, ζ and p (ξ) represent the system state, the internal state of the nonlinear disturbance observer and the nonlinear function of the desired design, respectively,
Figure BDA0002627641300000095
and
Figure BDA0002627641300000096
representing the derivative of the internal state of the disturbance observer and the disturbance estimate, g, respectively1、g2And f are smooth functions of the state variables.
The gain of the disturbance observer, l (ξ), is determined by:
Figure BDA0002627641300000097
the NDOB system of the nonlinear disturbance observer can be gradually stable, reasonable l (xi) is selected, and the convergence speed and the overshoot of the observer can obtain corresponding matching requirements;
Figure BDA0002627641300000098
wherein
Figure BDA0002627641300000099
Is the error in the estimation of the disturbance,
Figure BDA00026276413000000910
is edThe first derivative of the disturbance observer is gradually stable all the time, and is irrelevant to the state of the four rotors, and for the four-rotor aircraft, external wind disturbance mainly acts on an x axis and a y axis of an engine body to generate disturbance torque.
Further, the anti-interference control law of the four rotors is designed in the third step, and the method specifically comprises the following steps:
and (3) designing a cascade control law by combining the dynamics characteristics of the four rotors and a coupling kinematics model, wherein an inner ring controller controls the postures of the four rotors: pitch, roll, yaw, altitude, outer loop controller controls the position of the quadrotors: x-axis, y-axis; the torque generated by the propeller directly acts on the attitude of the quadrotors, and the response time of the position ring is longer compared with that of an attitude ring controller due to the second derivative relation between the displacement of the quadrotors and the attitude; the specific process is as follows:
step 3.1. position loop controller:
Figure BDA0002627641300000101
Figure BDA0002627641300000102
Figure BDA0002627641300000103
wherein xd、yd、zdAnd
Figure BDA0002627641300000104
representing desired and desired velocities, x, y, z and
Figure BDA0002627641300000105
representing three-axis position and velocity, kpx、kpy、kpzAnd kdx、kdy、kdzRepresenting proportional and differential gains, ux、uy、uzAnd (3) representing the three-axis control quantity of the position ring, and obtaining a control law of a roll angle and a pitch angle according to a rigid body kinematics model of the four rotors:
Figure BDA0002627641300000106
Figure BDA0002627641300000107
φd、θdpsi and g denote the roll angle desired, pitch angle desired, yaw angle and gravity constants of the quadrotors, respectively.
Step 3.2, the attitude ring controller:
the attitude ring controller receives the control input of the reference attitude angle, namely a pitch angle and a roll angle, and the yaw control is coupled with the pitch control and the roll control by the kinematics and dynamics model of the four rotors, and the position control of the aircraft can still be realized only through the change of the pitch control and the roll control without considering the yaw control of the four rotors:
Figure BDA0002627641300000108
Figure BDA0002627641300000109
Figure BDA00026276413000001010
wherein k ispφ,kpθ,kpψAnd k isdφ,kdθ,kdψRespectively representing the proportion and differential gain of roll angle, pitch angle and yaw angle, through a feedback linearization method,
Figure BDA00026276413000001011
uψ、uφ、uθand the control quantity of the yaw rate, the yaw angle, the roll angle and the pitch angle is represented. The throttle control amount T is expressed as follows:
Figure BDA0002627641300000111
neglecting air resistance, the simplified linear feedback control law is designed as follows:
Figure BDA0002627641300000112
Figure BDA0002627641300000113
Figure BDA0002627641300000114
Ω＝-w1+w2-w3+w4
wherein L is the arm length of the four rotors, wi(i ═ 1,2,3,4) denotes the rotational speed of the propeller, T, τφ,τθτψThe control torque of each coordinate axis of the machine body is shown,
Figure BDA0002627641300000115
omega represents the difference between the pitch angle velocity, the yaw angle velocity, the roll angle velocity and the propeller rotation speed, Jyy、Jzz、Jxx、JrThe three-axis moment of inertia and the motor moment of inertia are respectively expressed, and the relation between the rotating moment and the propeller lift force is as follows:
T＝F1+F2+F3+F4
τθ＝L(F2-F4)
τφ＝L(F3-F1)
τψ＝Kyaw(F1+F3-F2-F4)
wherein, F1，F2，F3，F4，KyawRespectively representing lift force and yaw coefficients generated by four propellers of the four rotors to obtain respective lift force control signals of the four propellers; the propeller has a rotational speed constraint so that the total lift force has a certain constraint within which the control signal needs to be.
Further, the step four designs an anti-interference formation control law of the four-rotor cluster, which is specifically as follows:
4.1. designing a formation controller:
a cluster formation is defined for any quad drone i as follows:
Figure BDA0002627641300000116
where j is the neighbor of the ith drone, able to communicate with each other in relative position, ΔijIs a desired formation, for each quad-rotor i in the cluster, a design compilationTeam control item ui fWherein u isiIndicating position loop control input ux,uyAnd uzIntroducing a formation position controller:
Figure BDA0002627641300000121
wherein k ispfIf the value is more than 0, the formation control gain is obtained, and the triaxial decoupling formation position control law is designed as follows:
u′x＝ux+ux f
u′y＝uy+uy f
u′z＝uz+uz f
u′x、u′y、u′zand under the formation state, the unmanned plane position ring is controlled and output.
4.2. Designing a disturbance factor and an anti-interference formation:
designing a disturbance factor according to an aerodynamic model, estimating the direction of wind disturbance, directly acting the disturbance torque of external wind disturbance on the x axis and the y axis of a four-rotor body, and setting deltax,δyRepresenting the magnitude of the disturbance torque, the disturbance factor is defined as follows:
Figure BDA0002627641300000122
wherein gamma belongs to [ -pi, pi ], represents the angle between the direction of external wind disturbance and the x axis, and contains the information of wind direction; combining the attenuation characteristic of wind power in the air and a laminar flow model, the direction of the wind is considered to be unchanged after the wind acts on the cluster leader, and the attenuation value is in direct proportion to the distance of the leader; defining an initial formation in a cluster anti-interference state:
Δi＝[xdl ydl]T-[xdi ydi]T＝[0 i·ρ]T
ρ≥ρ0
wherein xdl,ydlIndicating the desired position of the leader, xdi,ydiDenotes the iththPosition of the slave, ρ representing the safety distance between adjacent drones, ρ0Minimum safe distance between unmanned aerial vehicles; further, obtaining a time-varying anti-interference formation form:
Figure BDA0002627641300000131
Δi,anti＝Rγ·Δi
wherein Δi,anti＝Rγ·ΔiIndicating an anti-interference formation, RγThe direction of the anti-interference formation is changed, and the distance between adjacent unmanned aerial vehicles is not reduced, so that the safety of unmanned aerial vehicle formation is ensured.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but various changes may be apparent to those skilled in the art, and it is intended that all inventive concepts utilizing the inventive concepts set forth herein be protected without departing from the spirit and scope of the present invention as defined and limited by the appended claims.

Claims (3)

1. An interference observer-based anti-interference formation control method for quad-rotor unmanned aerial vehicles clusters is characterized by comprising the following steps:
step one, constructing a single four-rotor coupling dynamic model containing external force disturbance;
establishing a disturbance observer aiming at moment disturbance generated by external wind borne by the unmanned aerial vehicle; then, estimating a disturbance value according to the disturbance observer;
estimating the direction of wind disturbance according to the disturbance values of the x axis and the y axis of the unmanned aerial vehicle leader estimated by the disturbance observer, and designing a four-rotor anti-interference control law;
step four, according to the wind disturbance direction estimated by the leader, when external disturbance is encountered, the formation of the four-rotor cluster keeps an I shape, and an anti-interference formation control law of the four-rotor cluster is designed to realize the anti-interference control of the unmanned aerial vehicle cluster formation;
the step three is to design a four-rotor anti-interference control law, which specifically comprises the following steps:
and (3) designing a cascade control law by combining the dynamics characteristics of the four rotors and a coupling kinematics model, wherein an inner ring controller controls the postures of the four rotors: pitch, roll, yaw, altitude, outer loop controller controls the position of the quadrotors: x-axis, y-axis; the torque generated by the propeller directly acts on the attitude of the quadrotors, and the response time of the position ring is longer compared with that of an attitude ring controller due to the second derivative relation between the displacement of the quadrotors and the attitude; the specific process is as follows:
step 3.1. position loop controller:
Figure FDA0003132554220000011
Figure FDA0003132554220000012
Figure FDA0003132554220000013
wherein xd、yd、zdAnd
Figure FDA0003132554220000014
representing desired and desired velocities, x, y, z and
Figure FDA0003132554220000015
representing three-axis position and velocity, kpx、kpy、kpzAnd kdx、kdy、kdzExpressing proportional and differential gains, u, of three axesx、uy、uzAnd (3) representing the three-axis control quantity of the position ring, and obtaining a control law of a roll angle and a pitch angle according to a rigid body kinematics model of the four rotors:
Figure FDA0003132554220000021
Figure FDA0003132554220000022
φd、θdpsi and g respectively represent the roll angle expectation, pitch angle expectation, yaw angle and gravity constant of the four rotors;
step 3.2, the attitude ring controller:
the attitude ring controller receives the control input of the reference attitude angle, namely a pitch angle and a roll angle, and the yaw control is coupled with the pitch control and the roll control by the kinematics and dynamics model of the four rotors, and the position control of the aircraft can still be realized only through the change of the pitch control and the roll control without considering the yaw control of the four rotors:
Figure FDA0003132554220000023
Figure FDA0003132554220000024
Figure FDA0003132554220000025
wherein k ispφ,kpθ,kpψAnd k isdφ,kdθ,kdψRespectively representing the proportion and differential gain of roll angle, pitch angle and yaw angle, through a feedback linearization method,
Figure FDA0003132554220000026
uψ、uφ、uθrepresenting the control quantity of the yaw rate, the yaw angle, the roll angle and the pitch angle; the throttle control amount T is expressed as follows:
Figure FDA0003132554220000027
neglecting air resistance, the simplified linear feedback control law is designed as follows:
Figure FDA0003132554220000028
Figure FDA0003132554220000029
Figure FDA00031325542200000210
Ω＝-w1+w2-w3+w4
wherein L is the arm length of the four rotors, wiIndicating the speed of rotation of the propeller, where i ═ 1,2,3,4, T, τφ,τθτψThe control torque of each coordinate axis of the machine body is shown,
Figure FDA00031325542200000211
omega represents the difference between the pitch angle velocity, the yaw angle velocity, the roll angle velocity and the propeller rotation speed, Jyy、Jzz、Jxx、JrThe three-axis moment of inertia and the motor moment of inertia are respectively expressed, and the relation between the rotating moment and the propeller lift force is as follows:
T＝F1+F2+F3+F4
τθ＝L(F2-F4)
τφ＝L(F3-F1)
τψ＝Kyaw(F1+F3-F2-F4)
wherein, F1，F2，F3，F4，KyawRespectively representing lift force and yaw coefficients generated by four propellers of the four rotors to obtain respective lift force control signals of the four propellers; the propeller has a rotational speed constraint so that the total lift force has a certain constraint within which the control signal needs to be.
2. The interference observer-based clustered anti-interference formation control method for quad-rotor unmanned aerial vehicles according to claim 1, wherein the interference observer for moment disturbance generated by external wind on the unmanned aerial vehicles is established in the second step, which is as follows:
Figure FDA0003132554220000031
Figure FDA0003132554220000032
where ξ, ζ and p (ξ) represent the system state, the internal state of the nonlinear disturbance observer and the nonlinear function of the desired design, respectively,
Figure FDA0003132554220000033
and
Figure FDA0003132554220000034
representing the derivative of the internal state of the disturbance observer and the disturbance estimate, g, respectively1、g2F and f are both smooth functions of state variables, u represents the control input;
the gain of the disturbance observer, l (ξ), is determined by:
Figure FDA0003132554220000035
the NDOB system of the nonlinear disturbance observer can be gradually stable, reasonable l (xi) is selected, and the convergence speed and the overshoot of the observer can obtain corresponding matching requirements;
Figure FDA0003132554220000036
wherein
Figure FDA0003132554220000037
d is the actual disturbance value, edIs the error in the estimation of the disturbance,
Figure FDA0003132554220000038
is edThe first derivative of the disturbance observer is gradually stable all the time, and is irrelevant to the state of the four rotors, and for the four-rotor aircraft, external wind disturbance mainly acts on an x axis and a y axis of an engine body to generate disturbance torque.
3. The interference observer-based interference-free formation control method for the quad-rotor unmanned aerial vehicle cluster is characterized in that the interference-free formation control law for the quad-rotor cluster is designed according to the fourth step, and specifically comprises the following steps:
4.1. designing a formation controller:
a cluster formation is defined for any quad drone i as follows:
Figure FDA0003132554220000041
where j is the neighbor of the ith drone, able to communicate with each other in relative position, ΔijIs a desired formation, for each quad-rotor i in the cluster, a formation control u is designedi fWherein u isiRepresentation positionLoop control input ux,uyAnd uzIntroducing a formation position controller:
Figure FDA0003132554220000042
wherein k ispf> 0 is the formation control gain, niIs the number of neighbors of the ith drone, NiIs the neighbor set of the ith unmanned aerial vehicle, and the three-axis decoupling formation position control law is designed as follows:
u′x＝ux+ux f
u′y＝uy+uy f
u′z＝uz+uz f
u′x、u′y、u′zrepresenting unmanned aerial vehicle position loop control output in a formation state;
4.2. designing a disturbance factor and an anti-interference formation:
designing a disturbance factor according to an aerodynamic model, estimating the direction of wind disturbance, directly acting the disturbance torque of external wind disturbance on the x axis and the y axis of a four-rotor body, and setting deltax,δyRepresenting the magnitude of the disturbance torque, the disturbance factor is defined as follows:
Figure FDA0003132554220000051
wherein gamma belongs to [ -pi, pi ], represents the angle between the direction of external wind disturbance and the x axis, and contains the information of wind direction;
combining the attenuation characteristic of wind power in the air and a laminar flow model, the direction of the wind is considered to be unchanged after the wind acts on the cluster leader, and the attenuation value is in direct proportion to the distance of the leader; defining an initial formation in a cluster anti-interference state:
Δi＝[xdl ydl]T-[xdi ydi]T＝[0 i·ρ]T
ρ≥ρ0
wherein xdl,ydlIndicating the desired position of the leader, xdi,ydiDenotes the iththPosition of the slave, ρ representing the safety distance between adjacent drones, ρ0Represents a minimum safe distance between drones; further, obtaining a time-varying anti-interference formation form:
Figure FDA0003132554220000052
Δi,anti＝Rγ·Δi
wherein Δi,anti＝Rγ·ΔiIndicating an anti-interference formation, RγThe direction of the anti-interference formation is changed, and the distance between adjacent unmanned aerial vehicles is not reduced, so that the safety of unmanned aerial vehicle formation is ensured.
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