CN114840027B - Heterogeneous four-rotor aircraft formation attitude fault-tolerant control method - Google Patents

Heterogeneous four-rotor aircraft formation attitude fault-tolerant control method Download PDF

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CN114840027B
CN114840027B CN202210766349.0A CN202210766349A CN114840027B CN 114840027 B CN114840027 B CN 114840027B CN 202210766349 A CN202210766349 A CN 202210766349A CN 114840027 B CN114840027 B CN 114840027B
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rotor
rotor aircraft
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CN114840027A (en
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严兵
程鹏
蔡晨晓
杨哲
孟高举
张勇
姚娟
邹云
王鹤翔
杨轶
赵丽媛
邱俊评
马冲
宋连港
梁巧云
曾雪雪
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Nanjing University of Science and Technology
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    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
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Abstract

The invention provides a heterogeneous four-rotor aircraft formation attitude fault-tolerant control method, which comprises the following steps of: constructing a heterogeneous quad-rotor aircraft formation attitude dynamics model under the influence of time-varying faults and uncertain functions, wherein the model comprises a dynamic equation of an attitude angle and an attitude angle rate; determining a communication topological relation between the four-rotor aircrafts in the heterogeneous formation of the four-rotor aircrafts by using an undirected graph theory; constructing a formation attitude tracking error system of a follower according to the attitude information of the pilot; designing a virtual controller for the attitude angle ring of each follower based on inversion control and a time-varying barrier Lyapunov function; and developing an actual controller according to the attitude angle rate loop of the virtual controller to the follower. The invention can still realize the fast and high-precision tracking of the attitude of the quad-rotor aircraft of the pilot under the condition of time-varying execution faults.

Description

Heterogeneous four-rotor aircraft formation attitude fault-tolerant control method
Technical Field
The invention relates to the technical field of aircraft control, in particular to a heterogeneous four-rotor aircraft formation attitude fault-tolerant control method.
Background
Because many unmanned aerial vehicles are more advantageous than single unmanned aerial vehicle under multiple scenes such as modern agriculture, disaster relief, consequently the distributed control to many unmanned aerial vehicles has aroused the extensive attention of scientific community in recent years.
Multiple drones and other distributed systems are often subject to various types of constraints. The barrier lyapunov function has better performance in dealing with constraint problems by driving the parameter values to infinity as their parameters approach prescribed boundaries. At present, the problem of processing the constraint control of multiple unmanned aerial vehicles by using the barrier Lyapunov function becomes a hot topic and gradually arouses the research interest of a plurality of scholars.
However, the existing results are mostly only applicable to homogeneous quad drone formations, i.e. all drones in the formation have the same system dynamics. In practical situations, heterogeneous drones are widely used to accomplish some complex tasks where the system dynamics of each agent may be unique. On the other hand, a failure due to aging, temperature variation, unknown disturbance, or the like is inevitably encountered. For this reason, some fault-tolerant control strategies for heterogeneous formations such as heterogeneous drones and drone-drone vehicles are already available.
In the related technology, the problem that heterogeneous quad-rotor unmanned aerial vehicles are affected by actuator faults, system uncertainty functions and time-varying full-state constraints and form distributed attitude fault-tolerant control cannot be solved at the same time.
Disclosure of Invention
The invention aims to solve the technical problems and provides a heterogeneous four-rotor aircraft formation attitude fault-tolerant control method which can realize that all state signals of heterogeneous follower four-rotor aircraft are semi-global consistent and finally bounded, and can still realize quick and high-precision tracking on the attitude of a pilot four-rotor aircraft under the condition of time-varying execution faults.
The technical scheme adopted by the invention is as follows:
a heterogeneous four-rotor aircraft formation attitude fault-tolerant control method comprises the following steps: constructing a heterogeneous four-rotor aircraft formation attitude dynamics model under the influence of time-varying faults and uncertain functions, wherein the heterogeneous four-rotor aircraft formation comprises n +1 four-rotor aircraft, the n +1 four-rotor aircraft comprises a pilot and n followers, the model comprises a dynamic equation of an attitude angle and an attitude angle rate, and n is a positive integer; determining a communication topological relation between the four-rotor aircrafts in the heterogeneous formation of the four-rotor aircrafts by using an undirected graph theory; constructing a formation attitude tracking error system of a follower according to the attitude information of the pilot; designing a virtual controller for the attitude angle ring of each follower based on inversion control and a time-varying barrier Lyapunov function; and developing an actual controller according to the attitude angle rate loop of the virtual controller to the follower.
Wherein, the model of ith four rotor crafts does:
Figure 324409DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 206914DEST_PATH_IMAGE002
and is made of
Figure 746349DEST_PATH_IMAGE003
And
Figure 688897DEST_PATH_IMAGE004
respectively roll angle, pitch angle and yaw angle,
Figure 126832DEST_PATH_IMAGE005
wherein
Figure 485132DEST_PATH_IMAGE006
And
Figure 957702DEST_PATH_IMAGE007
roll, pitch and yaw rates respectively,
Figure 71151DEST_PATH_IMAGE008
is a matrix of the inertia, and the inertia matrix,
Figure 681868DEST_PATH_IMAGE009
which represents a control input that is to be controlled,
Figure 906176DEST_PATH_IMAGE010
is the friction force of the air, and the air is the air friction force,
Figure 967673DEST_PATH_IMAGE011
the moment of the gyroscope is taken as the moment,
Figure 189706DEST_PATH_IMAGE012
in order to be able to disturb the flow,
Figure 602233DEST_PATH_IMAGE013
is composed of
Figure 630232DEST_PATH_IMAGE014
The anti-symmetric matrix of (a) is,
Figure 998765DEST_PATH_IMAGE015
is composed of
Figure 188438DEST_PATH_IMAGE016
By using a small attitude angle approximation, the model of the ith four-rotor aircraft is reconstructed as:
Figure 88261DEST_PATH_IMAGE017
wherein the content of the first and second substances,
Figure 654372DEST_PATH_IMAGE018
denotes the first
Figure 893723DEST_PATH_IMAGE019
The speed of rotation of the individual rotors is,
Figure 254297DEST_PATH_IMAGE020
which represents the coefficient of air resistance,
Figure 641416DEST_PATH_IMAGE021
indicating the distance of the motor from the center of the quadrotors,
Figure 699633DEST_PATH_IMAGE022
representing the moment of inertia of the rotor, time-varying actuator faults are modeled as
Figure 590229DEST_PATH_IMAGE023
Wherein, in the process,
Figure 387284DEST_PATH_IMAGE024
the input torque to be designed is represented,
Figure 933803DEST_PATH_IMAGE025
wherein, in the process,
Figure 107295DEST_PATH_IMAGE026
which is representative of a time-varying efficiency factor,
Figure 117976DEST_PATH_IMAGE027
indicating a time-varying bias fault when
Figure 272883DEST_PATH_IMAGE028
，
Figure 369015DEST_PATH_IMAGE029
Is a first time
Figure 80619DEST_PATH_IMAGE030
The fourth rotor craft is fault-free, and the model of the ith four rotor craft is reconstructed as follows by considering the uncertainty of unmodeled model and the fault of the time-varying actuator:
Figure 945807DEST_PATH_IMAGE031
wherein the content of the first and second substances,
Figure 22347DEST_PATH_IMAGE033
and
Figure 605775DEST_PATH_IMAGE035
is a variable of the state of the vehicle,
Figure 855491DEST_PATH_IMAGE036
，
Figure 532110DEST_PATH_IMAGE037
，
Figure 841869DEST_PATH_IMAGE038
，
Figure 912593DEST_PATH_IMAGE039
the uncertainty is represented by a representation of the time,
Figure 903682DEST_PATH_IMAGE040
；
Figure 743463DEST_PATH_IMAGE041
and is and
Figure 224122DEST_PATH_IMAGE042
。
the communication topological relation is as follows: the follower is marked as
Figure 703514DEST_PATH_IMAGE043
The pilot is marked as 0 and, if any,
Figure 560612DEST_PATH_IMAGE044
undirected graph for topology between followers
Figure 254898DEST_PATH_IMAGE045
By node assembly
Figure 844143DEST_PATH_IMAGE046
Edge collector
Figure 889459DEST_PATH_IMAGE047
And adjacency matrix
Figure 284668DEST_PATH_IMAGE048
Wherein, in the process,a ij is the connection weight; for the
Figure 521877DEST_PATH_IMAGE049
If, if
Figure 609918DEST_PATH_IMAGE050
Then, then
Figure 876952DEST_PATH_IMAGE051
Otherwise
Figure 75852DEST_PATH_IMAGE052
；
Figure 416835DEST_PATH_IMAGE053
Four-rotor aircraft
Figure 675778DEST_PATH_IMAGE054
And four-rotor aircraft
Figure 617058DEST_PATH_IMAGE030
Can exchange information with each other; four-rotor aircraft
Figure 354069DEST_PATH_IMAGE030
Is described as a neighbor set
Figure 877455DEST_PATH_IMAGE055
(ii) a Let the degree matrix be
Figure 244982DEST_PATH_IMAGE056
Wherein, in the process,
Figure 221028DEST_PATH_IMAGE057
defining a Laplace matrix as
Figure 761731DEST_PATH_IMAGE058
(ii) a By using
Figure 90688DEST_PATH_IMAGE059
Representing a pilot adjacency matrix for
Figure 425854DEST_PATH_IMAGE060
If four rotors
Figure 154776DEST_PATH_IMAGE030
Can receive the information of the four rotors of the pilot,
Figure 233590DEST_PATH_IMAGE061
otherwise
Figure 669251DEST_PATH_IMAGE062
。
The formation attitude tracking error system is defined as follows:
Figure 175319DEST_PATH_IMAGE063
wherein, the first and the second end of the pipe are connected with each other,
Figure 578487DEST_PATH_IMAGE064
and
Figure 460992DEST_PATH_IMAGE065
in order to track the error in the track,
Figure 813476DEST_PATH_IMAGE066
for a virtual controller, based on equation (3), the derivative of the system (4) is expressed as:
Figure 693708DEST_PATH_IMAGE067
wherein the content of the first and second substances,
Figure 131642DEST_PATH_IMAGE068
and
Figure 552259DEST_PATH_IMAGE069
for the purpose of the overall uncertainty term,
Figure 24829DEST_PATH_IMAGE070
and is and
Figure 561115DEST_PATH_IMAGE071
。
the virtual controller is constructed by the following process:
to ensure that the states satisfy the time-varying all-state constraint, the time-varying barrier Lyapunov function is constructed as
Figure 486345DEST_PATH_IMAGE072
Wherein, the first and the second end of the pipe are connected with each other,
Figure 710653DEST_PATH_IMAGE073
and
Figure 975413DEST_PATH_IMAGE074
is a normal number for all
Figure 259763DEST_PATH_IMAGE075
Definition of
Figure 672290DEST_PATH_IMAGE076
And
Figure 621660DEST_PATH_IMAGE077
in order to estimate the error, the error is estimated,
Figure 803243DEST_PATH_IMAGE078
and
Figure 258495DEST_PATH_IMAGE079
are respectively
Figure 158318DEST_PATH_IMAGE080
And
Figure 662112DEST_PATH_IMAGE081
the estimated value of (c), and in addition,
Figure 698201DEST_PATH_IMAGE081
is that
Figure 324354DEST_PATH_IMAGE082
The upper bound of (a) is,
Figure 391100DEST_PATH_IMAGE083
is a smooth, bounded function and is simply represented as
Figure 495322DEST_PATH_IMAGE084
，
Figure 651497DEST_PATH_IMAGE085
In the collection
Figure 448552DEST_PATH_IMAGE086
Is continuously differentiable, so that
Figure 995071DEST_PATH_IMAGE087
To obtain
Figure 168563DEST_PATH_IMAGE088
Derived from the principle of neural network
Figure 366195DEST_PATH_IMAGE089
Wherein, in the step (A),
Figure 334151DEST_PATH_IMAGE090
as a weight matrix, the weight matrix is,
Figure 430283DEST_PATH_IMAGE091
in order to activate the function(s),
Figure 813991DEST_PATH_IMAGE092
is an error, and
Figure 944758DEST_PATH_IMAGE093
in addition, in the case of a single-layer,
Figure 83615DEST_PATH_IMAGE094
，
wherein, the first and the second end of the pipe are connected with each other,
Figure 355459DEST_PATH_IMAGE095
is a constant and, in addition,
Figure 605175DEST_PATH_IMAGE096
is a bounded continuous function;
then, the virtual controller is developed
Figure 590448DEST_PATH_IMAGE097
Wherein, the first and the second end of the pipe are connected with each other,
Figure 837890DEST_PATH_IMAGE098
is constant, and
Figure 908614DEST_PATH_IMAGE099
wherein, in the step (A),
Figure 962021DEST_PATH_IMAGE100
is a small constant, and furthermore, the adaptation law is given as
Figure 801801DEST_PATH_IMAGE101
Wherein the content of the first and second substances,
Figure 469411DEST_PATH_IMAGE102
and is and
Figure 761852DEST_PATH_IMAGE103
is a normal number;
substituting the formulas (8) to (11) into the formula (7) to obtain
Figure 618950DEST_PATH_IMAGE104
By applying the Young inequality and selecting
Figure 250920DEST_PATH_IMAGE105
Then the formula (12) is changed to
Figure 902481DEST_PATH_IMAGE106
Wherein the content of the first and second substances,
Figure 947797DEST_PATH_IMAGE107
and is and
Figure 28492DEST_PATH_IMAGE108
first order differentiators are used for the estimation
Figure 577285DEST_PATH_IMAGE109
Which is determined by the following formula
Figure 665327DEST_PATH_IMAGE110
Wherein the content of the first and second substances,
Figure 870043DEST_PATH_IMAGE111
in the state of the mobile communication terminal, the state,
Figure 803364DEST_PATH_IMAGE112
is a normal number, and is,
Figure 472243DEST_PATH_IMAGE066
is to
Figure 731186DEST_PATH_IMAGE113
Is estimated by the estimation of (a) a,
Figure 406887DEST_PATH_IMAGE114
is the estimation error.
The actual controller design process is as follows:
the Lyapunov function is constructed as follows
Figure 409478DEST_PATH_IMAGE115
Wherein the content of the first and second substances,
Figure 932863DEST_PATH_IMAGE116
is a normal number of the blood vessel which is,
Figure 34811DEST_PATH_IMAGE117
in order to estimate the error, the error is estimated,
Figure 276437DEST_PATH_IMAGE118
is composed of
Figure 817140DEST_PATH_IMAGE119
The estimated value of (c), and in addition,
Figure 195031DEST_PATH_IMAGE120
is that
Figure 484192DEST_PATH_IMAGE121
An upper bound of (c);
definition of
Figure 947535DEST_PATH_IMAGE122
Is obviously provided with
Figure 291929DEST_PATH_IMAGE123
Using neural network techniques, there are
Figure 727589DEST_PATH_IMAGE124
In which
Figure 233657DEST_PATH_IMAGE125
In addition, in the case of a single-layer,
Figure 449874DEST_PATH_IMAGE126
wherein, in the step (A),
Figure 519331DEST_PATH_IMAGE127
is a constant;
the actual controller is then designed to
Figure 871814DEST_PATH_IMAGE128
Wherein the content of the first and second substances,
Figure 548783DEST_PATH_IMAGE129
is constant, and
Figure 924401DEST_PATH_IMAGE099
in which
Figure 610597DEST_PATH_IMAGE130
For a small constant, the adaptation law is given as
Figure 817588DEST_PATH_IMAGE131
Wherein the content of the first and second substances,
Figure 622383DEST_PATH_IMAGE132
and is made of
Figure 547613DEST_PATH_IMAGE133
Is a normal number;
order to
Figure 771921DEST_PATH_IMAGE134
And the formulae (16) to (20) are substituted for the formula (15) to obtain
Figure 36680DEST_PATH_IMAGE135
（21）
Wherein the content of the first and second substances,
Figure 321031DEST_PATH_IMAGE136
and is
Figure 467979DEST_PATH_IMAGE137
Satisfy the requirements of
Figure 682928DEST_PATH_IMAGE138
According to formula (21), yields
Figure 864511DEST_PATH_IMAGE139
And four rotor attitude systems are all semi-global and ultimately bounded.
The invention has the beneficial effects that:
according to the heterogeneous four-rotor aircraft formation attitude fault-tolerant control method, the influence of various adverse factors on the dynamics of the four-rotor aircraft is considered, wherein the adverse factors comprise system uncertainty, actuator faults and time-varying full-state constraint, and the method is more practical than a traditional constant full-state constraint controller and can expand the actual application range; a time-varying Lyapunov function is introduced to ensure that the attitude variables of the aircraft always obey time-varying full-state constraints; a distributed fault-tolerant control algorithm is designed for the heterogeneous four-rotor aircraft, so that the attitude of the four-rotor aircraft of a pilot can be tracked quickly and accurately under the condition that time-varying execution faults exist.
Drawings
Fig. 1 is a flowchart of a heterogeneous four-rotor aircraft formation attitude fault-tolerant control method according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a heterogeneous quad-rotor aircraft formation attitude fault-tolerant control algorithm according to an embodiment of the invention;
FIG. 3 is a schematic diagram of the communication topology between quad-rotor aircraft in a heterogeneous quad-rotor aircraft formation according to one embodiment of the present disclosure;
FIG. 4 is a graph of the roll angle output of a heterogeneous quad-rotor formation;
FIG. 5 is a pitch angle output curve for a heterogeneous quad-rotor fleet;
FIG. 6 is a plot of yaw angle output for a heterogeneous quad-rotor formation;
FIG. 7 is a plot of the roll rate output for a heterogeneous quad-rotor formation;
FIG. 8 is a pitch rate output curve for a heterogeneous quad-rotor fleet;
fig. 9 is a plot of yaw rate output for a heterogeneous quad-rotor formation.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the method for fault-tolerant control of formation attitude of heterogeneous four-rotor aircraft according to the embodiment of the present invention includes the following steps:
s1, constructing a heterogeneous four-rotor aircraft formation attitude dynamics model under the influence of time-varying faults and uncertain functions. The heterogeneous quad-rotor aircraft formation comprises n +1 quad-rotor aircraft, the n +1 quad-rotor aircraft comprises a pilot and n followers, the model comprises a dynamic equation of an attitude angle and an attitude angle rate, and n is a positive integer.
And S2, determining a communication topological relation between the four-rotor aircrafts in the heterogeneous four-rotor aircraft formation by using an undirected graph theory.
And S3, constructing a formation attitude tracking error system of the follower according to the attitude information of the pilot.
And S4, designing a virtual controller for the attitude angle ring of each follower based on inversion control and a time-varying barrier Lyapunov function.
And S5, developing an actual controller according to the attitude angle rate loop of the virtual controller to the follower.
Wherein, the model of the ith four-rotor aircraft is:
Figure 319763DEST_PATH_IMAGE001
wherein, the first and the second end of the pipe are connected with each other,
Figure 157269DEST_PATH_IMAGE002
and is and
Figure 723380DEST_PATH_IMAGE003
and
Figure 759469DEST_PATH_IMAGE004
respectively roll angle, pitch angle and yaw angle,
Figure 385622DEST_PATH_IMAGE005
wherein
Figure 195577DEST_PATH_IMAGE006
And
Figure 565379DEST_PATH_IMAGE007
respectively roll, pitch and yaw rates,
Figure 721554DEST_PATH_IMAGE008
is a matrix of the inertia, and the inertia matrix,
Figure 456292DEST_PATH_IMAGE009
which represents a control input, is provided,
Figure 65127DEST_PATH_IMAGE010
is the friction force of the air, and the air is the air friction force,
Figure 973041DEST_PATH_IMAGE011
in order to realize the moment of the gyro,
Figure 170673DEST_PATH_IMAGE012
in order to be able to disturb the flow,
Figure 138629DEST_PATH_IMAGE013
is composed of
Figure 234761DEST_PATH_IMAGE014
The anti-symmetric matrix of (a) is,
Figure 884048DEST_PATH_IMAGE015
is composed of
Figure 14815DEST_PATH_IMAGE016
By using a small attitude angle approximation, the model of the ith four-rotor aircraft is reconstructed as:
Figure 963792DEST_PATH_IMAGE140
wherein, the first and the second end of the pipe are connected with each other,
Figure 281641DEST_PATH_IMAGE018
denotes to the first
Figure 796936DEST_PATH_IMAGE019
The speed of rotation of the individual rotors,
Figure 719892DEST_PATH_IMAGE020
the air resistance coefficient is expressed as a ratio of,
Figure 29651DEST_PATH_IMAGE021
indicating the distance of the motor from the center of the quadrotors,
Figure 834796DEST_PATH_IMAGE022
representing the moment of inertia of the rotor.
Time-varying actuator faults are modeled as
Figure 888202DEST_PATH_IMAGE023
Wherein the content of the first and second substances,
Figure 416398DEST_PATH_IMAGE024
the input torque to be designed is represented,
Figure 897058DEST_PATH_IMAGE025
wherein, in the step (A),
Figure 455078DEST_PATH_IMAGE026
representing a time-varying efficiency factor, is,
Figure 984280DEST_PATH_IMAGE027
indicating a time-varying bias fault when
Figure 944145DEST_PATH_IMAGE028
，
Figure 595707DEST_PATH_IMAGE029
Is a first time
Figure 562394DEST_PATH_IMAGE030
The four-rotor aircraft has no faults.
Considering unmodeled uncertainty and time-varying actuator failures, the model of the ith four-rotor aircraft was reconstructed as:
Figure 957604DEST_PATH_IMAGE141
wherein, the first and the second end of the pipe are connected with each other,
Figure 709659DEST_PATH_IMAGE033
and
Figure 532122DEST_PATH_IMAGE142
is a variable of the state of the vehicle,
Figure 502219DEST_PATH_IMAGE036
，
Figure 638802DEST_PATH_IMAGE037
，
Figure 307681DEST_PATH_IMAGE038
，
Figure 487995DEST_PATH_IMAGE039
the uncertainty is represented by a representation of the time,
Figure 242325DEST_PATH_IMAGE040
；
Figure 244916DEST_PATH_IMAGE041
and is and
Figure 705984DEST_PATH_IMAGE143
。
the communication topological relation in the step S2 is as follows: the follower is marked as
Figure 870249DEST_PATH_IMAGE043
The pilot is marked as 0,
Figure 111875DEST_PATH_IMAGE044
undirected graph for topology between followers
Figure 340993DEST_PATH_IMAGE045
By node assembly
Figure 718885DEST_PATH_IMAGE046
Edge collector
Figure 319630DEST_PATH_IMAGE047
And an adjacency matrix
Figure 720656DEST_PATH_IMAGE048
Wherein, in the process,a ij is the connection weight; for the
Figure 65049DEST_PATH_IMAGE049
If, if
Figure 297448DEST_PATH_IMAGE050
Then, then
Figure 256045DEST_PATH_IMAGE051
Otherwise
Figure 206684DEST_PATH_IMAGE052
；
Figure 89189DEST_PATH_IMAGE053
Four-rotor aircraft
Figure 379356DEST_PATH_IMAGE054
And four-rotor aircraft
Figure 321904DEST_PATH_IMAGE030
Can exchange information with each other; four-rotor aircraft
Figure 759839DEST_PATH_IMAGE030
Is described as a neighbor set
Figure 131521DEST_PATH_IMAGE055
(ii) a Let the degree matrix be
Figure 338511DEST_PATH_IMAGE056
Wherein, in the step (A),
Figure 451961DEST_PATH_IMAGE057
defining a Laplace matrix as
Figure 314875DEST_PATH_IMAGE058
(ii) a By using
Figure 539183DEST_PATH_IMAGE059
Representing a pilot adjacency matrix for
Figure 866259DEST_PATH_IMAGE060
If four rotors
Figure 71981DEST_PATH_IMAGE030
Can receive the information of four rotors of the pilot,
Figure 484508DEST_PATH_IMAGE061
otherwise, otherwise
Figure 450190DEST_PATH_IMAGE062
。
The formation attitude tracking error system in step S3 is defined as follows:
Figure 631772DEST_PATH_IMAGE063
wherein, the first and the second end of the pipe are connected with each other,
Figure 87025DEST_PATH_IMAGE064
and
Figure 409684DEST_PATH_IMAGE065
in order to track the error, the tracking error is,
Figure 975794DEST_PATH_IMAGE066
is a virtual controller.
Based on equation (3), the derivative of the system (4) is expressed as:
Figure 277463DEST_PATH_IMAGE067
wherein, the first and the second end of the pipe are connected with each other,
Figure 841299DEST_PATH_IMAGE068
and
Figure 962839DEST_PATH_IMAGE069
for the purpose of the overall uncertainty term,
Figure 332640DEST_PATH_IMAGE070
and is and
Figure 675766DEST_PATH_IMAGE144
。
the virtual controller in step S4 is constructed as follows:
to ensure that the states satisfy the time-varying all-state constraint, the time-varying barrier Lyapunov function is constructed as
Figure 472821DEST_PATH_IMAGE072
Wherein the content of the first and second substances,
Figure 81657DEST_PATH_IMAGE073
and
Figure 927253DEST_PATH_IMAGE074
is a normal number for all
Figure 937934DEST_PATH_IMAGE075
Definition of
Figure 905890DEST_PATH_IMAGE076
And
Figure 693367DEST_PATH_IMAGE077
in order to estimate the error, the error is estimated,
Figure 404971DEST_PATH_IMAGE078
and
Figure 270159DEST_PATH_IMAGE079
are respectively
Figure 346700DEST_PATH_IMAGE080
And
Figure 930128DEST_PATH_IMAGE081
the estimated value of (c), and in addition,
Figure 445423DEST_PATH_IMAGE081
is that
Figure 352068DEST_PATH_IMAGE082
The upper bound of (a) is,
Figure 661826DEST_PATH_IMAGE083
is a smooth, bounded function and is simply represented as
Figure 732550DEST_PATH_IMAGE084
It can be seen that
Figure 785957DEST_PATH_IMAGE085
In the collection
Figure 563420DEST_PATH_IMAGE086
Is continuously differentiable.
Order to
Figure 44080DEST_PATH_IMAGE087
To obtain
Figure 602100DEST_PATH_IMAGE088
Derived from the principle of neural network
Figure 882034DEST_PATH_IMAGE089
Wherein, in the step (A),
Figure 576321DEST_PATH_IMAGE090
as a weight matrix, the weight matrix is,
Figure 493461DEST_PATH_IMAGE091
in order to activate the function(s),
Figure 210882DEST_PATH_IMAGE092
is an error, and
Figure 606091DEST_PATH_IMAGE093
in addition, in the case of a single-layer,
Figure 420463DEST_PATH_IMAGE094
。
wherein, the first and the second end of the pipe are connected with each other,
Figure 429876DEST_PATH_IMAGE095
is a constant and, in addition,
Figure 696909DEST_PATH_IMAGE096
is a bounded continuous function.
Then, a virtual controller is developed
Figure 895810DEST_PATH_IMAGE145
Wherein the content of the first and second substances,
Figure 502371DEST_PATH_IMAGE129
is constant, and
Figure 495735DEST_PATH_IMAGE099
wherein, in the step (A),
Figure 250065DEST_PATH_IMAGE100
is a small constant, and furthermore, the adaptation law is given as
Figure 672562DEST_PATH_IMAGE101
Wherein, the first and the second end of the pipe are connected with each other,
Figure 195948DEST_PATH_IMAGE102
and is made of
Figure 625792DEST_PATH_IMAGE103
Is a normal number.
Substituting the formulas (8) - (11) into the formula (7) to obtain
Figure 805101DEST_PATH_IMAGE104
By applying the Young inequality and selecting
Figure 80224DEST_PATH_IMAGE146
Then the formula (12) is changed to
Figure 723695DEST_PATH_IMAGE106
Wherein the content of the first and second substances,
Figure 245812DEST_PATH_IMAGE147
and is made of
Figure 974734DEST_PATH_IMAGE108
。
A first order differentiator is used to estimate
Figure 53548DEST_PATH_IMAGE066
Which is determined by the following formula
Figure 489209DEST_PATH_IMAGE110
Wherein the content of the first and second substances,
Figure 260856DEST_PATH_IMAGE111
in the state of the mobile communication terminal, the state,
Figure 211494DEST_PATH_IMAGE112
is a normal number of the blood vessel which is,
Figure 782415DEST_PATH_IMAGE066
is to
Figure 134899DEST_PATH_IMAGE113
Is estimated by the estimation of (a) a,
Figure 77447DEST_PATH_IMAGE114
is the estimation error.
The actual controller design process in step S5 is as follows:
the Lyapunov function is constructed as follows
Figure 453065DEST_PATH_IMAGE148
Wherein the content of the first and second substances,
Figure 873682DEST_PATH_IMAGE116
is a normal number, and is,
Figure 346251DEST_PATH_IMAGE117
in order to estimate the error, the error is estimated,
Figure 646652DEST_PATH_IMAGE118
is composed of
Figure 571882DEST_PATH_IMAGE119
The estimated value of (c), and in addition,
Figure 796190DEST_PATH_IMAGE120
is that
Figure 795370DEST_PATH_IMAGE121
The upper bound of (c).
Definition of
Figure 79721DEST_PATH_IMAGE122
Is obviously provided with
Figure 492248DEST_PATH_IMAGE123
Using neural network techniques, there are
Figure 520247DEST_PATH_IMAGE124
Wherein
Figure 381456DEST_PATH_IMAGE125
In addition, in the case of a single-layer,
Figure 571129DEST_PATH_IMAGE126
in which
Figure 470952DEST_PATH_IMAGE127
Is a constant.
The actual controller is then designed to
Figure 974745DEST_PATH_IMAGE149
Wherein the content of the first and second substances,
Figure 276414DEST_PATH_IMAGE129
is constant, and
Figure 636988DEST_PATH_IMAGE150
wherein
Figure 211057DEST_PATH_IMAGE130
For a small constant, the adaptation law is given as
Figure 580859DEST_PATH_IMAGE151
Wherein, the first and the second end of the pipe are connected with each other,
Figure 471455DEST_PATH_IMAGE152
and is made of
Figure 268509DEST_PATH_IMAGE133
Is a normal number.
Order to
Figure 815028DEST_PATH_IMAGE146
And the formulae (16) to (20) are substituted for the formula (15) to obtain
Figure 988521DEST_PATH_IMAGE135
（21）
Wherein the content of the first and second substances,
Figure 999202DEST_PATH_IMAGE136
and is
Figure 780207DEST_PATH_IMAGE153
And satisfy
Figure 814022DEST_PATH_IMAGE138
From the formula (21), yield
Figure 525626DEST_PATH_IMAGE139
And four rotor attitude systems are all semi-global and ultimately bounded.
The structure of the heterogeneous quad-rotor aircraft formation attitude fault-tolerant control algorithm of the embodiment of the invention is shown in fig. 2.
The communication topological relation between the four-rotor aircrafts in the heterogeneous four-rotor aircraft formation is shown in FIG. 3, and the expected attitude of a pilot is
Figure 390814DEST_PATH_IMAGE154
. In addition to this, the present invention is,
Figure 339791DEST_PATH_IMAGE155
. Assume actuator failure modes are:
Figure 923219DEST_PATH_IMAGE156
simulation results under the heterogeneous quad-rotor aircraft formation attitude fault-tolerant control method of the embodiment of the invention are shown in fig. 4-9. Fig. 4-6 show the tracking performance for constrained roll, pitch and yaw angles, respectively, and fig. 7-9 show the trajectories for constrained roll, pitch and yaw rates, respectively. As shown in fig. 4-6, each follower can achieve high precision tracking of the pose of the pilot. 4-9 also demonstrate state variables
Figure 110618DEST_PATH_IMAGE157
And
Figure 721990DEST_PATH_IMAGE158
the time-varying all-state constraint of (a) is always followed under the presented fault-tolerant control method. From the simulation results, the attitude tracking target of the pilot is realized, and the performance of the method provided by the embodiment of the invention is verified.
According to the heterogeneous quad-rotor aircraft formation attitude fault-tolerant control method provided by the embodiment of the invention, the influence of various adverse factors on the dynamics of the quad-rotor aircraft is considered, wherein the adverse factors comprise system uncertainty, actuator faults and time-varying full-state constraint, and the method is more practical than the traditional constant full-state constraint controller and can expand the actual application range; a time-varying Lyapunov function is introduced to ensure that the attitude variable of the aircraft always obeys the time-varying all-state constraint; a distributed fault-tolerant control algorithm is designed for the heterogeneous four-rotor aircraft, so that the attitude of the four-rotor aircraft of a pilot can be tracked quickly and accurately under the condition that time-varying execution faults exist.
In the description of the present invention, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or to imply that the number of technical features indicated is significant. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. The meaning of "plurality" is two or more unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "above," and "over" a second feature may be directly on or obliquely above the second feature, or simply mean that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Moreover, various embodiments or examples and features of various embodiments or examples described in this specification can be combined and combined by one skilled in the art without being mutually inconsistent.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps in the process, and alternate implementations are included within the scope of the preferred embodiment of the present invention in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present invention.
The logic and/or steps represented in the flowcharts or otherwise described herein, such as an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present invention may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a separate product, may also be stored in a computer-readable storage medium.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (1)

1. A heterogeneous four-rotor aircraft formation attitude fault-tolerant control method is characterized by comprising the following steps:
constructing a heterogeneous four-rotor aircraft formation attitude dynamics model under the influence of time-varying faults and uncertain functions, wherein the heterogeneous four-rotor aircraft formation comprises n +1 four-rotor aircraft, the n +1 four-rotor aircraft comprises a pilot and n followers, the model comprises a dynamic equation of an attitude angle and an attitude angle rate, and n is a positive integer;
determining a communication topological relation between the four-rotor aircrafts in the heterogeneous four-rotor aircraft formation by using an undirected graph theory;
constructing a formation attitude tracking error system of a follower according to the attitude information of the pilot;
designing a virtual controller for the attitude angle ring of each follower based on inversion control and a time-varying barrier Lyapunov function;
developing an actual controller according to the attitude angular rate loop of the virtual controller to the follower,
wherein, the model of ith four rotor crafts does:
Figure FDA0003814147580000011
wherein σ i ＝[φ i ，θ i ，ψ i ] T And phi is i ，θ i And psi i Respectively roll angle, pitch angle and yaw angle, omega i ＝[p i ，q i ，r i ] T Wherein p is i ，q i And r i Respectively roll, pitch and yaw rates,
Figure FDA0003814147580000012
is a matrix of the inertia, and the inertia matrix,
Figure FDA0003814147580000013
representing a control input, f i Is air friction force, G i In order to realize the moment of the gyro,
Figure FDA0003814147580000014
in order to be able to disturb the flow,
Figure FDA0003814147580000015
is omega i Of an inverse symmetric matrix, M (σ) i ) Is composed of
Figure FDA0003814147580000016
By using a small attitude angle approximation, the model of the ith four-rotor aircraft is reconstructed as:
Figure FDA0003814147580000021
wherein the content of the first and second substances,
Figure FDA0003814147580000022
Figure FDA0003814147580000023
where a =1,2,3,4 denotes the rotational speed of the a-th rotor, k if Denotes the coefficient of air resistance,/ i Shows the distance of the motor from the center of the four rotors, J ir The moment of inertia of the rotor is represented,
time-varying actuator faults are modeled as
Figure FDA0003814147580000024
Wherein u is i The input torque to be designed is represented,
Figure FDA0003814147580000025
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003814147580000026
Figure FDA0003814147580000027
which is representative of a time-varying efficiency factor,
Figure FDA0003814147580000028
indicating a time-varying bias fault when
Figure FDA0003814147580000029
Figure FDA00038141475800000210
The ith four-rotor aircraft is not in fault,
considering unmodeled uncertainty and time-varying actuator failures, the model of the ith four-rotor aircraft was reconstructed as:
Figure FDA00038141475800000211
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00038141475800000212
Figure FDA00038141475800000213
the uncertainty is represented by a representation of the time,
Figure FDA00038141475800000214
and is
Figure FDA00038141475800000215
Figure FDA00038141475800000216
The communication topological relation is as follows:
followers are labeled 1, 2.. N, pilots are labeled 0, topology among n followers is used with an undirected graph
Figure FDA0003814147580000031
By node assembly
Figure FDA0003814147580000032
Edge set
Figure FDA0003814147580000033
And adjacency matrix
Figure FDA0003814147580000034
For i, j ∈ V, if (i, j) ∈ ε, then a ij =1, otherwise a ij ＝0；
Figure FDA0003814147580000035
Figure FDA0003814147580000036
The information of the four-rotor aircraft j and the information of the four-rotor aircraft i can be mutually exchanged; the neighbor set of a quad-rotor aircraft i is described as
Figure FDA0003814147580000037
Let the degree matrix be
Figure FDA0003814147580000038
Figure FDA0003814147580000039
Wherein the content of the first and second substances,
Figure FDA00038141475800000310
defining a Laplace matrix as
Figure FDA00038141475800000311
By using
Figure FDA00038141475800000312
Representing the pilot adjacency matrix, for i ∈ V, if quad-rotor i can receive the pilot quad-rotationInformation of the wing, b i =1, otherwise b i ＝0，
The formation attitude tracking error system is defined as follows:
Figure FDA00038141475800000313
wherein the content of the first and second substances,
Figure FDA00038141475800000314
in the form of a virtual controller, the controller,
based on equation (3), the derivative of the system (4) is expressed as:
Figure FDA00038141475800000315
wherein the content of the first and second substances,
Figure FDA00038141475800000316
and
Figure FDA00038141475800000317
for the purpose of the overall uncertainty term,
Figure FDA00038141475800000318
Figure FDA00038141475800000319
and is provided with
Figure FDA00038141475800000320
The virtual controller is constructed by the following steps:
to ensure that the states satisfy the time-varying all-state constraints, the time-varying barrier Lyapunov function is constructed as
Figure FDA00038141475800000321
Wherein, c i1 ，c i2 And c i3 Is a normal number, defined for all r =1,2,k =1,2,3
Figure FDA0003814147580000041
Figure FDA0003814147580000042
And
Figure FDA0003814147580000043
in order to estimate the error, the error is estimated,
Figure FDA0003814147580000044
and
Figure FDA0003814147580000045
are respectively
Figure FDA0003814147580000046
And
Figure FDA0003814147580000047
the estimated time of (c) may, in addition,
Figure FDA0003814147580000048
is that
Figure FDA0003814147580000049
The upper bound of (a) is,
Figure FDA00038141475800000410
is a smooth, bounded function and is simply represented as
Figure FDA00038141475800000411
It can be seen that
Figure FDA00038141475800000412
In the collection
Figure FDA00038141475800000413
Is continuously micro-adjustable in the (1) phase,
order to
Figure FDA00038141475800000414
To obtain
Figure FDA00038141475800000415
Derived from the principle of neural network
Figure FDA00038141475800000416
Wherein the content of the first and second substances,
Figure FDA00038141475800000417
as a weight matrix, the weight matrix is,
Figure FDA00038141475800000418
in order to activate the function(s),
Figure FDA00038141475800000419
is an error, and
Figure FDA00038141475800000420
in addition to this, the present invention is,
Figure FDA00038141475800000421
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00038141475800000422
is a constant and, in addition,
Figure FDA00038141475800000423
is a bounded continuous function;
then, a virtual controller is developed
Figure FDA00038141475800000424
Wherein the content of the first and second substances,
Figure FDA00038141475800000425
is constant, and
Figure FDA00038141475800000426
wherein the content of the first and second substances,
Figure FDA00038141475800000427
Figure FDA00038141475800000428
is a small constant, and furthermore, the adaptation law is given as
Figure FDA00038141475800000429
Figure FDA0003814147580000051
Figure FDA0003814147580000052
Wherein the content of the first and second substances,
Figure FDA0003814147580000053
and h is i1 ，h i2 ，h i3 Is a normal number;
substituting the formulas (8) - (11) into the formula (7) to obtain
Figure FDA0003814147580000054
By applying the Young inequality and selecting
Figure FDA0003814147580000055
Then the formula (12) becomes
Figure FDA0003814147580000056
Wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003814147580000057
Figure FDA0003814147580000058
and is
Figure FDA0003814147580000059
A first order differentiator is used to estimate
Figure FDA00038141475800000510
It is determined by the following formula
Figure FDA00038141475800000511
Figure FDA00038141475800000512
Figure FDA00038141475800000513
Wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00038141475800000514
in the state of the mobile communication terminal, the state,
Figure FDA00038141475800000515
is a normal number, and is,
Figure FDA00038141475800000516
is to
Figure FDA00038141475800000517
Is estimated by the estimation of (a) a,
Figure FDA00038141475800000518
is the error of the estimation that is,
the actual controller design process is as follows:
the Lyapunov function is constructed as follows
Figure FDA0003814147580000061
Wherein, c i4 ，c i5 ，c i6 ，c i7 Is a normal number, and is,
Figure FDA0003814147580000062
in order to estimate the error, the error is estimated,
Figure FDA0003814147580000063
is composed of
Figure FDA0003814147580000064
The estimated value of (c), and in addition,
Figure FDA0003814147580000065
is that
Figure FDA0003814147580000066
The upper bound of (c);
definition of
Figure FDA0003814147580000067
Is obviously provided with
Figure FDA0003814147580000068
Using neural network techniques, there are
Figure FDA0003814147580000069
Wherein
Figure FDA00038141475800000610
In addition, in the case of the present invention,
Figure FDA00038141475800000611
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00038141475800000612
is a constant;
the actual controller is then designed to
Figure FDA00038141475800000613
Wherein the content of the first and second substances,
Figure FDA00038141475800000614
is constant, and
Figure FDA00038141475800000615
wherein
Figure FDA00038141475800000616
Figure FDA00038141475800000617
For a small constant, the adaptation law is given as
Figure FDA00038141475800000618
Figure FDA00038141475800000619
Figure FDA0003814147580000071
Figure FDA0003814147580000072
Wherein the content of the first and second substances,
Figure FDA0003814147580000073
Figure FDA0003814147580000074
Figure FDA0003814147580000075
and h is i4 ，h i5 ，h i6 ，h i7 Is a normal number;
order to
Figure FDA0003814147580000076
And substituting formulae (16) to (20) for formula (15) to obtain
Figure FDA0003814147580000077
Wherein the content of the first and second substances,
Figure FDA0003814147580000078
M＝M 1 +M 2 and is and
Figure FDA0003814147580000079
Figure FDA00038141475800000710
Figure FDA00038141475800000711
and satisfy
Figure FDA00038141475800000712
From the formula (21), yield
Figure FDA00038141475800000713
And four rotor attitude systems are all semi-global and ultimately bounded.
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