CN115629550B - Self-adaptive attitude tracking control and parameter identification method for service spacecraft - Google Patents

Self-adaptive attitude tracking control and parameter identification method for service spacecraft Download PDF

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CN115629550B
CN115629550B CN202211652241.5A CN202211652241A CN115629550B CN 115629550 B CN115629550 B CN 115629550B CN 202211652241 A CN202211652241 A CN 202211652241A CN 115629550 B CN115629550 B CN 115629550B
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spacecraft
matrix
representing
attitude
angular velocity
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CN115629550A (en
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龙江
郭阳明
刘尊
马琪琪
王晓东
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Northwestern Polytechnical University
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention provides a self-adaptive attitude tracking control and parameter identification method for a service-type spacecraft, which relates to the technical field of spacecraft automatic control and parameter identification, and comprises the following steps: s1, establishing a kinematics and dynamics model of the spacecraft by adopting the corrected Rodrigues parameter as the attitude of the spacecraft; s2, setting an expected attitude of the spacecraft, and establishing a tracking error model of the attitude of the spacecraft relative to the expected attitude based on the kinematics and dynamics model of the S1; s3, carrying out attitude tracking control on the spacecraft based on the tracking error model design algorithm of the S2; the self-adaptive attitude tracking control and parameter identification method for the service-type spacecraft solves the problem of identification of on-orbit rotational inertia of the service-type spacecraft, realizes self-adaptive attitude tracking control of the service-type spacecraft and ensures the boundedness of signals of all closed-loop systems.

Description

Self-adaptive attitude tracking control and parameter identification method for service spacecraft
Technical Field
The invention relates to the technical field of spacecraft automatic control and parameter identification, in particular to a self-adaptive attitude tracking control and parameter identification method of a service type spacecraft.
Background
With the continuous development of aerospace technology, various types of spacecrafts such as artificial earth satellites, manned spacecraft, space stations, and interplanetary space vehicles have been developed, which indicates that the spacecrafts play an increasingly important role in the development and utilization of space resources. In recent years, service type spacecraft with mechanical arms and other devices have received wide attention from experts and scholars because of the ability to perform complex tasks such as capturing and cleaning space garbage for non-cooperative type spacecraft.
However, when a service-type spacecraft performs a complex task in space, the mass or center of mass of the spacecraft may change dramatically at the instant of contact with the serviced object, which undoubtedly presents difficulties and challenges to the attitude control of the spacecraft. The design of the traditional attitude control method in the past is mostly based on the precisely known moment of inertia. However, for a service spacecraft, the mass or the center of mass changes, which leads to a change in the ground-measured moment of inertia, and thus renders the conventional attitude control method ineffective. When the mass or the centroid of the spacecraft is completely unknown, that is, the rotational inertia of the spacecraft is unknown, although the influence of the unknown rotational inertia on the attitude control of the spacecraft can be compensated by introducing the adaptive estimation of the rotational inertia to the spacecraft in the prior art. However, when the spacecraft has no continuous external excitation, the adaptive estimation cannot converge to the real moment of inertia, that is, the conventional adaptive attitude control method cannot identify the unknown moment of inertia, and cannot perform adaptive attitude tracking control on the service-type spacecraft.
Based on the above, the invention provides a self-adaptive attitude tracking control and parameter identification method for a service-type spacecraft to solve the above problems.
Disclosure of Invention
The invention aims to provide a self-adaptive attitude tracking control and parameter identification method for a service-type spacecraft, which can identify unknown rotary inertia and realize self-adaptive attitude tracking control of the service-type spacecraft.
The technical scheme of the invention is as follows:
the application provides a self-adaptive attitude tracking control and parameter identification method for a service-type spacecraft, which comprises the following steps:
s1, establishing a kinematics and dynamics model of the spacecraft by adopting the corrected Rodrigues parameter as the attitude of the spacecraft;
s2, setting an expected attitude of the spacecraft, and establishing a tracking error model of the attitude of the spacecraft relative to the expected attitude based on the kinematics and dynamics model of the S1;
and S3, carrying out attitude tracking control on the spacecraft based on the tracking error model design algorithm of the S2.
Further, the kinematic and kinetic model formula in step S1 is:
Figure DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE002
represents the derivative of the modified Rodrigues parameter, <' > is determined>
Figure DEST_PATH_IMAGE003
Represents the derivative of the angular speed, is>
Figure DEST_PATH_IMAGE004
Represents a modified Rodrigues parameter, < > or >>
Figure DEST_PATH_IMAGE005
Represents angular velocity, <' > or>
Figure DEST_PATH_IMAGE006
Represents a control input of the spacecraft>
Figure DEST_PATH_IMAGE007
A matrix of moments of inertia is represented,
Figure DEST_PATH_IMAGE008
represents the Euler shaft,. Or>
Figure DEST_PATH_IMAGE009
Represents Euler angle, <' > or>
Figure DEST_PATH_IMAGE010
Represents a 3-dimensional Euclidean space, is selected>
Figure DEST_PATH_IMAGE011
A matrix of a function is represented which,
Figure DEST_PATH_IMAGE012
represents a cross-product of a 3-dimensional column vector.
Further, the formula of the tracking error model in step S2 is:
Figure DEST_PATH_IMAGE013
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE014
a derivative representing the spacecraft attitude tracking error, <' >>
Figure DEST_PATH_IMAGE015
Represents the spacecraft attitude tracking error>
Figure DEST_PATH_IMAGE016
A derivative representing the error in the tracking of the angular velocity of the spacecraft, <' >>
Figure DEST_PATH_IMAGE017
Representing a tracking error of angular velocity>
Figure DEST_PATH_IMAGE018
Which is indicative of the desired angular velocity of the vehicle,
Figure DEST_PATH_IMAGE019
represents the derivative of the desired angular speed, is>
Figure DEST_PATH_IMAGE020
Represents a control input of the spacecraft>
Figure DEST_PATH_IMAGE021
Represents a moment of inertia matrix, < > is asserted>
Figure DEST_PATH_IMAGE022
Represents angular velocity, <' > based on>
Figure DEST_PATH_IMAGE023
Represents a fork multiplier, is greater than or equal to>
Figure DEST_PATH_IMAGE024
Represents a function matrix, <' > is>
Figure DEST_PATH_IMAGE025
Representing the rotation matrix of the spacecraft.
Further, the algorithm in step S3 adopts a self-adaptive back-stepping method, which specifically includes the following steps:
s31, introducing an error variable into a tracking error model:
Figure DEST_PATH_IMAGE026
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE027
and &>
Figure DEST_PATH_IMAGE028
Represents an error variable, <' > is selected>
Figure DEST_PATH_IMAGE029
Represents the spacecraft attitude tracking error>
Figure DEST_PATH_IMAGE030
Represents a virtual control input to be devised>
Figure 273541DEST_PATH_IMAGE017
Indicating an angular velocity tracking error;
s32, for error variable
Figure 514029DEST_PATH_IMAGE027
Derivation:
Figure DEST_PATH_IMAGE031
，
Figure DEST_PATH_IMAGE032
，
wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE033
represents an error variable pick>
Figure 825187DEST_PATH_IMAGE027
Is greater than or equal to>
Figure DEST_PATH_IMAGE034
Is constant->
Figure DEST_PATH_IMAGE035
Represents the spacecraft attitude tracking error>
Figure 363485DEST_PATH_IMAGE014
Representing spacecraft attitude tracking error>
Figure 184810DEST_PATH_IMAGE035
Is greater than or equal to>
Figure DEST_PATH_IMAGE036
Represents a function matrix, <' > is>
Figure 815774DEST_PATH_IMAGE028
Represents an error variable, <' > is selected>
Figure DEST_PATH_IMAGE037
Represents a virtual control input to be devised>
Figure 988129DEST_PATH_IMAGE017
Represents an angular velocity tracking error, and>
Figure DEST_PATH_IMAGE038
representing a function matrix pickand place>
Figure 346430DEST_PATH_IMAGE024
The transposed matrix of (2);
s33, for any vector element is
Figure DEST_PATH_IMAGE039
Is greater than or equal to 3-dimensional column vector>
Figure DEST_PATH_IMAGE040
Define a matrix operator->
Figure DEST_PATH_IMAGE041
Is->
Figure DEST_PATH_IMAGE042
Thereby taking an error variable->
Figure 897628DEST_PATH_IMAGE028
Derivative and multiply the moment of inertia at both left and right ends simultaneously>
Figure 479919DEST_PATH_IMAGE021
And then the control input of the spacecraft is obtained through design>
Figure 873991DEST_PATH_IMAGE020
The calculation process is as follows:
Figure DEST_PATH_IMAGE043
，
Figure DEST_PATH_IMAGE044
，
wherein the content of the first and second substances,
Figure 550829DEST_PATH_IMAGE020
represents a control input of the spacecraft>
Figure DEST_PATH_IMAGE045
Represents a function matrix, <' > based on>
Figure 550009DEST_PATH_IMAGE027
And &>
Figure 303201DEST_PATH_IMAGE028
Represents an error variable, <' > is selected>
Figure DEST_PATH_IMAGE046
Indicates a normal number, is selected>
Figure DEST_PATH_IMAGE047
Representing an unknown parameter>
Figure DEST_PATH_IMAGE048
In combination with a predetermined number of previous evaluations>
Figure 76248DEST_PATH_IMAGE021
Represents a moment of inertia matrix, < > is asserted>
Figure DEST_PATH_IMAGE049
The cross-product operator is represented as a cross-product operator,
Figure DEST_PATH_IMAGE050
represents angular velocity, <' > or>
Figure DEST_PATH_IMAGE051
Indicating a virtual control input pick>
Figure DEST_PATH_IMAGE052
In the derivative of (C), is based on>
Figure 494459DEST_PATH_IMAGE016
Represents an angular velocity tracking error pick>
Figure 883897DEST_PATH_IMAGE017
The derivative of (a) is determined,
Figure DEST_PATH_IMAGE053
indicates angular velocity pick-up>
Figure 11253DEST_PATH_IMAGE050
Is based on the matrix operator, < > is based on>
Figure DEST_PATH_IMAGE054
Representing a variable>
Figure DEST_PATH_IMAGE055
Is based on the matrix operator, < > is based on>
Figure DEST_PATH_IMAGE056
Represents a variable->
Figure DEST_PATH_IMAGE057
Is based on the matrix operator, < > is based on>
Figure 238972DEST_PATH_IMAGE048
Representing an unknown parameter;
s34, inputting control of the spacecraft
Figure 24657DEST_PATH_IMAGE020
And substituting the tracking error model to perform attitude tracking control of the spacecraft.
Further, step S3 further includes:
and designing a rotational inertia on-orbit identification algorithm of the service spacecraft based on the tracking error model of S2 to obtain a parameter updating law of the spacecraft, and performing attitude tracking control on the spacecraft by combining the parameter updating law of the spacecraft and the control input of the spacecraft.
Compared with the prior art, the invention has at least the following advantages or beneficial effects:
(1) The method adopts the corrected Rodrigues parameters as the attitude of the spacecraft to establish a kinematics and dynamics model of the spacecraft, and sets the expected attitude of the spacecraft to establish a tracking error model of the attitude of the spacecraft relative to the expected attitude, so that an algorithm is designed to perform attitude tracking control of the spacecraft, the problem of attitude asymptotic tracking control of a service type spacecraft under the condition of unknown rotational inertia is solved, and the boundedness of signals of all closed-loop systems is ensured;
(2) According to the method, the rotational inertia in-orbit identification algorithm of the service-type spacecraft can be designed through the tracking error model, so that the identification problem of the in-orbit rotational inertia of the service-type spacecraft is solved, and the assumed condition that the parameter estimation in the traditional adaptive control can be converged to a true value only when the parameter estimation needs to meet continuous excitation is relaxed;
(3) The identification method of the invention does not need to measure the angular acceleration of the spacecraft any more, thereby reducing unnecessary measurement elements.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
FIG. 1 is a flow chart of a method for adaptive attitude tracking control and parameter identification for a service spacecraft of the present invention;
FIG. 2 is a diagram of attitude tracking error simulation for a service-type spacecraft;
FIG. 3 is an angular velocity tracking error simulation diagram for a service spacecraft;
FIG. 4 is a control input simulation diagram for a service spacecraft;
FIG. 5 is a simulation diagram of parameter identification errors for a service spacecraft;
FIG. 6 is a matrix
Figure DEST_PATH_IMAGE058
The minimum eigenvalue simulation graph of (1).
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present application, as presented in the figures, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. 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 application.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
It should be noted that, in this document, the term "comprises/comprising" or any other variation thereof is intended to cover a non-exclusive inclusion, so that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but also other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising … …" does not exclude the presence of another like element in a process, method, article, or apparatus that comprises the element.
In the description of the present application, it is also to be noted that, unless otherwise explicitly specified or limited, the terms "disposed" and "connected" are to be interpreted broadly, e.g., as being either fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present application can be understood in a specific case by those of ordinary skill in the art.
Some embodiments of the present application will be described in detail below with reference to the accompanying drawings. The embodiments and features of the embodiments described below can be combined with one another without conflict.
Example 1
Referring to fig. 1, fig. 1 is a flowchart illustrating an adaptive attitude tracking control and parameter identification method for a service-type spacecraft according to embodiment 1 of the present application.
The application provides a self-adaptive attitude tracking control and parameter identification method for a service-type spacecraft, which comprises the following steps:
s1, establishing a kinematics and dynamics model of the spacecraft by adopting the corrected Rodrigues parameter as the attitude of the spacecraft;
s2, setting an expected attitude of the spacecraft, and establishing a tracking error model of the attitude of the spacecraft relative to the expected attitude based on the kinematics and dynamics model of the S1;
and S3, carrying out attitude tracking control on the spacecraft based on the tracking error model design algorithm of the S2.
As a preferred embodiment, the kinematic and dynamic model formula in step S1 is:
Figure 60746DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 890162DEST_PATH_IMAGE002
a derivative representing a modified Rodrigues parameter, in conjunction with a signal characteristic of a characteristic in the blood vessel>
Figure 746122DEST_PATH_IMAGE003
Representing a derivative of angular velocity, based on the angular velocity of the vehicle>
Figure 834033DEST_PATH_IMAGE004
Represents a modified Rodrigues parameter, < > or >>
Figure 193470DEST_PATH_IMAGE005
Represents angular velocity, <' > or>
Figure 193787DEST_PATH_IMAGE006
Represents a control input of the spacecraft>
Figure 271464DEST_PATH_IMAGE007
A matrix of moments of inertia is represented,
Figure 664531DEST_PATH_IMAGE008
represents the Euler shaft,. Or>
Figure 144054DEST_PATH_IMAGE009
Represents the Euler angle, is greater than or equal to>
Figure 580851DEST_PATH_IMAGE010
Represents a 3-dimensional Euclidean space, <' > in greater or lesser degrees>
Figure 145825DEST_PATH_IMAGE011
A matrix of a function is represented which,
Figure 123008DEST_PATH_IMAGE012
represents a cross-product of a 3-dimensional column vector.
Order to
Figure DEST_PATH_IMAGE059
Represents dimension ^ greater or less>
Figure DEST_PATH_IMAGE060
Is based on the unit matrix of (4), then the function matrix->
Figure 643988DEST_PATH_IMAGE011
The expression of (a) is:
Figure DEST_PATH_IMAGE061
，
wherein
Figure DEST_PATH_IMAGE062
Represents a modified Rodrigues parameter, < > or >>
Figure DEST_PATH_IMAGE063
Represents a function matrix, <' > is>
Figure DEST_PATH_IMAGE064
Represents a vector pick>
Figure DEST_PATH_IMAGE065
Is transferred and is taken out>
Figure 330315DEST_PATH_IMAGE012
A cross-product operator representing a 3-dimensional column vector;
for example: for the elements of
Figure DEST_PATH_IMAGE066
Is greater than or equal to>
Figure DEST_PATH_IMAGE067
，/>
Figure DEST_PATH_IMAGE068
Then it is: />
Figure DEST_PATH_IMAGE069
，
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE070
representing a vector @>
Figure DEST_PATH_IMAGE071
In the coordinate system of (c), in combination with a coordinate system of>
Figure 743105DEST_PATH_IMAGE049
Represents a fork multiplier, is greater than or equal to>
Figure DEST_PATH_IMAGE072
Representing a transpose operation of the matrix.
As a preferred embodiment, the formula of the tracking error model in step S2 is:
Figure 914192DEST_PATH_IMAGE013
，
wherein the content of the first and second substances,
Figure 368307DEST_PATH_IMAGE014
derivative representing spacecraft attitude tracking error, based on the sum of the derivative and the derivative>
Figure 146907DEST_PATH_IMAGE015
Represents the spacecraft attitude tracking error>
Figure 686473DEST_PATH_IMAGE016
A derivative representing the error in the tracking of the angular velocity of the spacecraft, <' >>
Figure 959453DEST_PATH_IMAGE017
Representing a tracking error of angular velocity>
Figure 268075DEST_PATH_IMAGE018
Which is indicative of the desired angular velocity of the vehicle,
Figure 14314DEST_PATH_IMAGE019
represents the derivative of the desired angular speed, is>
Figure 775597DEST_PATH_IMAGE020
Represents a control input of the spacecraft>
Figure 101536DEST_PATH_IMAGE021
Represents a moment of inertia matrix, < > is asserted>
Figure 513931DEST_PATH_IMAGE022
Represents angular velocity, <' > based on>
Figure 634334DEST_PATH_IMAGE023
Represents a fork multiplier, is greater than or equal to>
Figure 882913DEST_PATH_IMAGE024
Represents a function matrix, <' > is>
Figure 746964DEST_PATH_IMAGE025
Representing the rotation matrix of the spacecraft.
Specifically, the derivation process is as follows:
assuming a desired attitude of the spacecraft
Figure DEST_PATH_IMAGE073
Is based on the system>
Figure DEST_PATH_IMAGE074
Give, wherein>
Figure DEST_PATH_IMAGE075
Indicates a desired pose pick>
Figure 921855DEST_PATH_IMAGE073
In the derivative of (C), is based on>
Figure 728006DEST_PATH_IMAGE018
Indicates a desired angular velocity, is present>
Figure DEST_PATH_IMAGE076
Indicates a desired pose pick>
Figure 729460DEST_PATH_IMAGE073
The function matrix of (2).
The attitude tracking error between the actual attitude and the desired attitude of the spacecraft can thus be expressed as:
Figure DEST_PATH_IMAGE077
，
tracking error of angular velocity
Figure DEST_PATH_IMAGE078
Can be expressed as:
Figure DEST_PATH_IMAGE079
，
wherein, the first and the second end of the pipe are connected with each other,
Figure 554459DEST_PATH_IMAGE022
represents angular velocity, <' > or>
Figure 426600DEST_PATH_IMAGE018
Indicates a desired angular velocity, is present>
Figure DEST_PATH_IMAGE080
Represents a gesture tracking error, based on the detected gesture tracking error>
Figure 606915DEST_PATH_IMAGE025
A rotation matrix representing a spacecraft;
rotation matrix of spacecraft
Figure 830086DEST_PATH_IMAGE025
Can be expressed as:
Figure DEST_PATH_IMAGE081
，
wherein the content of the first and second substances,
Figure 504781DEST_PATH_IMAGE022
represents angular velocity, <' > based on>
Figure 293745DEST_PATH_IMAGE018
Indicates a desired angular velocity, is present>
Figure 954882DEST_PATH_IMAGE080
Represents a gesture tracking error, based on the detected gesture tracking error>
Figure 399770DEST_PATH_IMAGE059
Representing dimension->
Figure 409314DEST_PATH_IMAGE060
Is selected, is selected>
Figure 521627DEST_PATH_IMAGE049
Represents a fork multiplier, <' >>
Figure DEST_PATH_IMAGE082
A transposed matrix representing an attitude tracking error; />
A tracking error model is thus obtained:
Figure 43744DEST_PATH_IMAGE013
，
order to
Figure DEST_PATH_IMAGE083
Given a vector +>
Figure 710348DEST_PATH_IMAGE067
The equation can be verified
Figure DEST_PATH_IMAGE084
And wherein:
Figure DEST_PATH_IMAGE085
，
Figure DEST_PATH_IMAGE086
，
wherein the content of the first and second substances,
Figure 149682DEST_PATH_IMAGE021
represents a moment of inertia matrix, < > is asserted>
Figure DEST_PATH_IMAGE087
Represents a vector pick>
Figure DEST_PATH_IMAGE088
Is based on the matrix operator, < > is based on>
Figure DEST_PATH_IMAGE089
Representing an unknown parameter;
thus, the attitude and angular velocity tracking error system of a spacecraft can be represented as:
Figure DEST_PATH_IMAGE090
，
it is necessary to state that the variables
Figure DEST_PATH_IMAGE091
The expression of (a) is:
Figure DEST_PATH_IMAGE092
。
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE093
represents an angular velocity tracking error, and>
Figure 929551DEST_PATH_IMAGE089
represents an unknown parameter, <' > is selected>
Figure 904460DEST_PATH_IMAGE022
Represents angular velocity, <' > based on>
Figure 386257DEST_PATH_IMAGE018
Indicates a desired angular velocity, is present>
Figure 986871DEST_PATH_IMAGE049
Represents a fork multiplier, <' >>
Figure 808197DEST_PATH_IMAGE080
Represents a gesture tracking error, based on the detected gesture tracking error>
Figure DEST_PATH_IMAGE094
Represents an angular velocity tracking error, and>
Figure 688428DEST_PATH_IMAGE020
representing control inputs of the spacecraft.
As a preferred embodiment, the algorithm in step S3 adopts an adaptive back-stepping method, which specifically includes the following steps:
s31, introducing an error variable into a tracking error model:
Figure 345937DEST_PATH_IMAGE026
wherein the content of the first and second substances,
Figure 235395DEST_PATH_IMAGE027
and &>
Figure 176806DEST_PATH_IMAGE028
Represents an error variable, <' > based on>
Figure 493518DEST_PATH_IMAGE029
Represents the spacecraft attitude tracking error>
Figure 136858DEST_PATH_IMAGE030
Indicating what is to be designedA virtual control input, <' > or>
Figure 564428DEST_PATH_IMAGE017
Indicating an angular velocity tracking error;
s32, for error variable
Figure 360346DEST_PATH_IMAGE027
Derivation:
Figure 113538DEST_PATH_IMAGE031
，/>
Figure 745639DEST_PATH_IMAGE032
，
wherein the content of the first and second substances,
Figure 976900DEST_PATH_IMAGE033
represents an error variable pick>
Figure 627325DEST_PATH_IMAGE027
In the derivative of (C), is based on>
Figure 551418DEST_PATH_IMAGE034
Is constant and is->
Figure 169350DEST_PATH_IMAGE035
The attitude tracking error of the spacecraft is represented,
Figure 1040DEST_PATH_IMAGE014
representing spacecraft attitude tracking error>
Figure 709233DEST_PATH_IMAGE035
Is greater than or equal to>
Figure 600966DEST_PATH_IMAGE036
Represents a function matrix, <' > based on>
Figure 456926DEST_PATH_IMAGE028
Indicating errorVariable(s), in combination>
Figure 780722DEST_PATH_IMAGE037
Represents a virtual control input to be devised>
Figure 405739DEST_PATH_IMAGE017
Represents an angular velocity tracking error, and>
Figure 671635DEST_PATH_IMAGE038
representing a function matrix pickand place>
Figure 749312DEST_PATH_IMAGE024
The transposed matrix of (2);
s33, for any vector element is
Figure 640914DEST_PATH_IMAGE039
Is greater than or equal to the 3-dimensional column vector->
Figure 120437DEST_PATH_IMAGE040
Define a matrix operator->
Figure 291655DEST_PATH_IMAGE041
Is->
Figure 856629DEST_PATH_IMAGE042
Thereby taking an error variable->
Figure 522228DEST_PATH_IMAGE028
Derivative and multiply the moment of inertia at both left and right ends simultaneously>
Figure 121836DEST_PATH_IMAGE021
And then the control input of the spacecraft is obtained through design>
Figure 729535DEST_PATH_IMAGE020
The calculation process is as follows:
Figure 781805DEST_PATH_IMAGE043
，
Figure 749629DEST_PATH_IMAGE044
，
wherein the content of the first and second substances,
Figure 482DEST_PATH_IMAGE020
represents a control input of the spacecraft>
Figure 779082DEST_PATH_IMAGE045
Represents a function matrix, <' > is>
Figure 318648DEST_PATH_IMAGE027
And &>
Figure 840896DEST_PATH_IMAGE028
Represents an error variable, <' > based on>
Figure 900250DEST_PATH_IMAGE046
Indicates a normal number, is selected>
Figure 849752DEST_PATH_IMAGE047
Representing an unknown parameter>
Figure 345455DEST_PATH_IMAGE048
Is evaluated based on the evaluation of->
Figure 936974DEST_PATH_IMAGE021
Represents a moment of inertia matrix, < > is asserted>
Figure 83790DEST_PATH_IMAGE049
The cross-product operator is represented as a cross-product operator,
Figure 204193DEST_PATH_IMAGE050
represents angular velocity, <' > or>
Figure 718351DEST_PATH_IMAGE051
Indicating a virtual control input pick>
Figure 582402DEST_PATH_IMAGE052
Is greater than or equal to>
Figure 396774DEST_PATH_IMAGE016
Represents an angular velocity tracking error pick>
Figure 895933DEST_PATH_IMAGE017
The derivative of (a) of (b),
Figure 428546DEST_PATH_IMAGE053
representing angular velocity>
Figure 830708DEST_PATH_IMAGE050
Is based on the matrix operator, < > is based on>
Figure 968428DEST_PATH_IMAGE054
Represents a variable->
Figure 945480DEST_PATH_IMAGE055
Is based on the matrix operator, < > is based on>
Figure 637493DEST_PATH_IMAGE056
Representing a variable>
Figure 374505DEST_PATH_IMAGE057
Is based on the matrix operator, < > is based on>
Figure 101152DEST_PATH_IMAGE048
Representing an unknown parameter;
s34, inputting control of the spacecraft
Figure 750571DEST_PATH_IMAGE020
And substituting the tracking error model to perform attitude tracking control of the spacecraft.
As a preferred embodiment, step S3 further includes:
and designing a rotational inertia on-orbit identification algorithm of the service spacecraft based on the tracking error model of S2 to obtain a parameter updating law of the spacecraft, and performing attitude tracking control on the spacecraft by combining the parameter updating law of the spacecraft and the control input of the spacecraft.
As a preferred embodiment, since for arbitrary vectors
Figure 461038DEST_PATH_IMAGE067
Equation of
Figure 470582DEST_PATH_IMAGE084
Is established, wherein>
Figure 317315DEST_PATH_IMAGE021
Represents a moment of inertia matrix, < > is asserted>
Figure DEST_PATH_IMAGE095
Represents an arbitrary vector, is>
Figure DEST_PATH_IMAGE096
Denotes unknown parameters: (
Figure 308274DEST_PATH_IMAGE085
），/>
Figure 240458DEST_PATH_IMAGE041
Represents a vector pick>
Figure 804425DEST_PATH_IMAGE095
The matrix operator of (2).
The calculation process of the rotational inertia on-orbit identification algorithm is as follows:
re-representing the attitude dynamics equations of the spacecraft:
Figure DEST_PATH_IMAGE097
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE098
a matrix operator representing the derivative of the angular velocity, device for selecting or keeping>
Figure DEST_PATH_IMAGE099
Indicating angular velocityThe matrix operator of degree->
Figure 974507DEST_PATH_IMAGE096
Represents an unknown parameter, <' > is selected>
Figure 198684DEST_PATH_IMAGE020
Represents a control input of the spacecraft>
Figure 883743DEST_PATH_IMAGE049
Represents a fork multiplier, is greater than or equal to>
Figure 235090DEST_PATH_IMAGE022
Represents angular velocity, <' > based on>
Figure DEST_PATH_IMAGE100
Representing the derivative of angular velocity;
definition matrix
Figure DEST_PATH_IMAGE101
And &>
Figure DEST_PATH_IMAGE102
To further simplify the attitude dynamics equation:
Figure DEST_PATH_IMAGE103
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE104
represents a matrix->
Figure DEST_PATH_IMAGE105
Is greater than or equal to>
Figure DEST_PATH_IMAGE106
Represents an unknown parameter, <' > is selected>
Figure 72727DEST_PATH_IMAGE020
Representing control inputs of a spacecraft;
carrying out filtering operation on the attitude dynamics equation by adopting a moment filtering technology:
Figure DEST_PATH_IMAGE107
，
Figure DEST_PATH_IMAGE108
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE109
represents the Laplace operator, and->
Figure DEST_PATH_IMAGE110
Is a normal number, based on>
Figure DEST_PATH_IMAGE111
Represents a Laplace operation, <' > based on a predetermined criterion>
Figure DEST_PATH_IMAGE112
Represents an unknown parameter, <' > is selected>
Figure 828324DEST_PATH_IMAGE020
Represents a control input of the spacecraft>
Figure 735101DEST_PATH_IMAGE104
Represents a matrix->
Figure DEST_PATH_IMAGE113
Is greater than or equal to>
Figure DEST_PATH_IMAGE114
And &>
Figure DEST_PATH_IMAGE115
Representing a defined matrix;
will matrix
Figure 781816DEST_PATH_IMAGE114
、/>
Figure 457648DEST_PATH_IMAGE115
And controlling the input->
Figure 39939DEST_PATH_IMAGE020
The filtered signals are respectively denoted as->
Figure DEST_PATH_IMAGE116
、/>
Figure DEST_PATH_IMAGE117
And &>
Figure DEST_PATH_IMAGE118
The relationship between them can be expressed as: />
Figure DEST_PATH_IMAGE119
，/>
Figure DEST_PATH_IMAGE120
，
Figure DEST_PATH_IMAGE121
Wherein->
Figure 43799DEST_PATH_IMAGE110
Is a normal number, is greater than or equal to>
Figure DEST_PATH_IMAGE122
，/>
Figure DEST_PATH_IMAGE123
And &>
Figure DEST_PATH_IMAGE124
Respectively represent->
Figure 127161DEST_PATH_IMAGE116
、/>
Figure 923079DEST_PATH_IMAGE117
And &>
Figure 676271DEST_PATH_IMAGE118
The derivative of (c).
Are respectively provided with
Figure 42793DEST_PATH_IMAGE116
、/>
Figure 539633DEST_PATH_IMAGE117
And &>
Figure 986795DEST_PATH_IMAGE118
The initial values of (a) are: />
Figure DEST_PATH_IMAGE125
，
Figure DEST_PATH_IMAGE126
，/>
Figure DEST_PATH_IMAGE127
The attitude dynamics equation of the spacecraft after filtering can be expressed as: />
Figure DEST_PATH_IMAGE128
；
Further, can be written as:
Figure DEST_PATH_IMAGE129
wherein->
Figure DEST_PATH_IMAGE130
The expression of (c) is:
Figure DEST_PATH_IMAGE131
；
therefore, after a stable linear filter is introduced,
Figure 751419DEST_PATH_IMAGE130
and &>
Figure 120083DEST_PATH_IMAGE118
Can be used to identify an unknown parameter->
Figure 155035DEST_PATH_IMAGE096
Of the signal of (1).
The approximation error is defined as:
Figure DEST_PATH_IMAGE132
，
wherein
Figure DEST_PATH_IMAGE133
；
According to
Figure DEST_PATH_IMAGE134
The approximation error can be further expressed as:
Figure DEST_PATH_IMAGE135
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE136
represents a defined approximation error, based on the value of the parameter>
Figure DEST_PATH_IMAGE137
Is expressed as->
Figure DEST_PATH_IMAGE138
，/>
Figure DEST_PATH_IMAGE139
Represents a filtered control input, <' > or>
Figure 941857DEST_PATH_IMAGE096
Represents an unknown parameter, <' >>
Figure DEST_PATH_IMAGE140
Represents an unknown parameter pick>
Figure 551699DEST_PATH_IMAGE096
Is estimated.
In summary, a parameter estimate is obtained
Figure 142080DEST_PATH_IMAGE140
The update law design formula of (1):
Figure DEST_PATH_IMAGE141
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE142
indicating a parameter estimate pick>
Figure 669139DEST_PATH_IMAGE140
Is updated law->
Figure DEST_PATH_IMAGE143
Represents a positive decision matrix>
Figure 497417DEST_PATH_IMAGE022
Represents angular velocity, <' > or>
Figure DEST_PATH_IMAGE144
Represents a cross multiplier, matrix->
Figure DEST_PATH_IMAGE145
And &>
Figure DEST_PATH_IMAGE146
Respectively indicate angular speed->
Figure 419106DEST_PATH_IMAGE022
And a variable->
Figure DEST_PATH_IMAGE147
Is based on the operator matrix, the variable->
Figure DEST_PATH_IMAGE148
Is expressed as>
Figure DEST_PATH_IMAGE149
，/>
Figure DEST_PATH_IMAGE150
Indicating a virtual control input pick>
Figure DEST_PATH_IMAGE151
Is greater than or equal to>
Figure DEST_PATH_IMAGE152
Represents an error variable, <' > based on>
Figure 106570DEST_PATH_IMAGE137
Is expressed as->
Figure DEST_PATH_IMAGE153
，/>
Figure DEST_PATH_IMAGE154
And &>
Figure DEST_PATH_IMAGE155
Is at>
Figure DEST_PATH_IMAGE156
The historical data stored at the moment in time>
Figure DEST_PATH_IMAGE157
A group number representing stored history data, greater or lesser>
Figure DEST_PATH_IMAGE158
Is expressed as->
Figure DEST_PATH_IMAGE159
，/>
Figure DEST_PATH_IMAGE160
Representing a transpose operation of the matrix.
It should be noted that two historical data matrices can be defined as follows:
Figure DEST_PATH_IMAGE161
and &>
Figure DEST_PATH_IMAGE162
To ensure parameter evaluation>
Figure 906161DEST_PATH_IMAGE140
Can converge to a true value>
Figure 182422DEST_PATH_IMAGE096
Group count of collected historical data->
Figure DEST_PATH_IMAGE163
Greater than or equal to 6, i.e. < >>
Figure DEST_PATH_IMAGE164
While ensuring that>
Figure DEST_PATH_IMAGE165
Is a full rank matrix, i.e. <' >>
Figure DEST_PATH_IMAGE166
。/>
Therefore, the attitude tracking control of the spacecraft can be carried out by combining the parameter updating law of the spacecraft and the control input of the spacecraft.
As a preferred embodiment, the stability of the spacecraft system can be analyzed by:
the Lyapunov function defining the entire closed-loop spacecraft system is:
Figure DEST_PATH_IMAGE167
，
wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE168
represents a transposed operation of the matrix, in conjunction with a transformation of the matrix, and in conjunction with a transformation of the matrix>
Figure DEST_PATH_IMAGE169
Represents an error variable, <' > is selected>
Figure 635531DEST_PATH_IMAGE143
Represents a positive decision matrix>
Figure DEST_PATH_IMAGE170
Represents a moment of inertia matrix, <' > based on>
Figure 420079DEST_PATH_IMAGE140
Represents an unknown parameter pick>
Figure 600524DEST_PATH_IMAGE096
Is estimated.
Calculating its derivative and substituting it into the control input of the spacecraft
Figure 200133DEST_PATH_IMAGE020
And parameter update law>
Figure 604569DEST_PATH_IMAGE142
The above equation can be further derived as:
Figure DEST_PATH_IMAGE171
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE172
represents a transposed operation of the matrix, in conjunction with a transformation of the matrix, and in conjunction with a transformation of the matrix>
Figure DEST_PATH_IMAGE173
、/>
Figure DEST_PATH_IMAGE174
Represents a constant +>
Figure DEST_PATH_IMAGE175
And &>
Figure 735467DEST_PATH_IMAGE169
Represents an error variable, <' > based on>
Figure DEST_PATH_IMAGE176
Indicates a positive decision matrix, based on which the decision matrix is asserted>
Figure 922866DEST_PATH_IMAGE170
Represents a moment of inertia matrix, <' > based on>
Figure DEST_PATH_IMAGE177
And &>
Figure DEST_PATH_IMAGE178
Respectively represent unknown parameters>
Figure 563932DEST_PATH_IMAGE096
Evaluation and evaluation error of (4), based on the evaluation of (4)>
Figure DEST_PATH_IMAGE179
Represents a matrix->
Figure 608112DEST_PATH_IMAGE165
The minimum eigenvalue of (c).
The matrix can be guaranteed due to the collected historical data
Figure 621112DEST_PATH_IMAGE165
Full rank, the minimum eigenvalue of the matrix is greater than 0, i.e.
Figure DEST_PATH_IMAGE180
；
Let constant
Figure DEST_PATH_IMAGE181
Then>
Figure DEST_PATH_IMAGE182
Can be further expressed as: />
Figure DEST_PATH_IMAGE183
。
Therefore, the theory of the stability of the Lyapunov function can be used to find
Figure 2414DEST_PATH_IMAGE175
，/>
Figure 311036DEST_PATH_IMAGE169
And &>
Figure 260538DEST_PATH_IMAGE178
Is bounded and->
Figure 38132DEST_PATH_IMAGE175
，/>
Figure 98492DEST_PATH_IMAGE169
And &>
Figure 527199DEST_PATH_IMAGE178
Can be consistently and asymptotically converged to 0, and further combines attitude dynamics and kinematic equations of a spacecraft and virtual control input->
Figure DEST_PATH_IMAGE184
And a control input>
Figure 913181DEST_PATH_IMAGE020
And the signals of all closed-loop systems are globally and consistently bounded, so that the stability of the spacecraft system is judged.
Example 2
In order to verify the effectiveness of the adaptive attitude tracking control and on-orbit rotational inertia identification method of the service spacecraft, provided by the invention, the effectiveness verification is carried out on the method under the Matlab/Simulink environment.
In the simulation verification process, the unknown moment of inertia of the spacecraft is set as:
Figure DEST_PATH_IMAGE185
(ii) a The desired reference track being formed by a time-varying signal
Figure DEST_PATH_IMAGE186
Generating, initial attitude of spacecraft->
Figure DEST_PATH_IMAGE187
And initial angular velocity>
Figure DEST_PATH_IMAGE188
Are respectively set to>
Figure DEST_PATH_IMAGE189
，/>
Figure DEST_PATH_IMAGE190
Evaluation of parameters->
Figure 709230DEST_PATH_IMAGE177
Is set to->
Figure DEST_PATH_IMAGE191
The control parameter is selected as->
Figure DEST_PATH_IMAGE192
，/>
Figure DEST_PATH_IMAGE193
，/>
Figure DEST_PATH_IMAGE194
，
Figure DEST_PATH_IMAGE195
In which>
Figure DEST_PATH_IMAGE196
Representing a 6-dimensional identity matrix.
The simulation results are shown in fig. 2 to fig. 6, and it can be seen from fig. 2 and fig. 3 that both the attitude tracking error and the angular velocity tracking error of the spacecraft can converge to 0, i.e. accurate attitude tracking can be realized; at the same time, fig. 4 shows that the control input of the spacecraft is bounded, i.e. that the control input is implementable in practical applications. In addition, both fig. 5 and fig. 6 show that the identification error of the unknown moment of inertia can converge to 0; therefore, the simulation results show that the attitude self-adaptive tracking control algorithm and the unknown rotational inertia identification algorithm provided by the invention are effective.
It will be appreciated that the configuration shown in the figures is merely illustrative and that an adaptive attitude tracking control and parameter identification method for a service spacecraft may include more or fewer components than shown in the figures or have a different configuration than shown in the figures. The components shown in the figures may be implemented in hardware, software, or a combination thereof.
In the embodiments provided in the present application, it should be understood that the disclosed system or method may also be implemented in other manners. The embodiments described above are merely illustrative, and the flowcharts or block diagrams in the figures, for example, illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In addition, functional modules in the embodiments of the present application may be integrated together to form an independent part, or each module may exist alone, or two or more modules may be integrated to form an independent part.
The functions, if implemented in the form of software functional modules and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk, and various media capable of storing program codes.
In summary, according to the adaptive attitude tracking control and parameter identification method for the service-type spacecraft, provided by the embodiment of the application, the corrected rodgers parameter is used as the attitude of the spacecraft to establish a kinematics and dynamics model, and meanwhile, the expected attitude of the spacecraft is set to establish a tracking error model of the attitude of the spacecraft relative to the expected attitude, so that an algorithm is designed to perform attitude tracking control on the spacecraft, the problem of attitude asymptotic tracking control of the service-type spacecraft under the condition of unknown rotational inertia is solved, and the boundedness of all closed-loop system signals is ensured; the in-orbit identification algorithm of the rotational inertia of the service spacecraft can be designed through the tracking error model, so that the identification problem of the in-orbit rotational inertia of the service spacecraft is solved, the assumed condition that parameter estimation in the traditional adaptive control can be converged to a true value only by meeting continuous excitation is relaxed, the angular acceleration of the spacecraft does not need to be measured, and unnecessary measurement elements are reduced.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
It will be evident to those skilled in the art that the application is not limited to the details of the foregoing illustrative embodiments, and that the present application may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the application being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Claims (3)

1. A self-adaptive attitude tracking control and parameter identification method for a service-type spacecraft is characterized by comprising the following steps:
s1, establishing a kinematics and dynamics model of the spacecraft by adopting the corrected Rodrigues parameter as the attitude of the spacecraft;
s2, setting an expected attitude of the spacecraft, and establishing a tracking error model of the attitude of the spacecraft relative to the expected attitude based on the kinematics and dynamics model of the S1;
s3, performing attitude tracking control on the spacecraft based on a tracking error model design algorithm of the S2;
specifically, the algorithm adopts an adaptive backstepping method, and comprises the following steps:
s31, introducing an error variable into a tracking error model:
Figure QLYQS_1
wherein the content of the first and second substances,
Figure QLYQS_2
and &>
Figure QLYQS_3
Represents an error variable, <' > is selected>
Figure QLYQS_4
Represents a tracking error of the gesture>
Figure QLYQS_5
Represents a virtual control input to be devised>
Figure QLYQS_6
Indicating an angular velocity tracking error;
s32, for error variable
Figure QLYQS_7
Derivation:
Figure QLYQS_8
，
Figure QLYQS_9
，
wherein the content of the first and second substances,
Figure QLYQS_10
represents an error variable pick>
Figure QLYQS_16
In the derivative of (C), is based on>
Figure QLYQS_19
Is constant and is->
Figure QLYQS_11
Represents the spacecraft attitude tracking error>
Figure QLYQS_14
Representing spacecraft attitude tracking error>
Figure QLYQS_17
Is greater than or equal to>
Figure QLYQS_20
Represents a function matrix, <' > is>
Figure QLYQS_12
Express errorDifference variable +>
Figure QLYQS_15
Representing a virtual control input to be devised>
Figure QLYQS_18
Represents an angular velocity tracking error, and>
Figure QLYQS_21
representation function matrix +>
Figure QLYQS_13
The transposed matrix of (2);
s33, for any vector element is
Figure QLYQS_22
Is greater than or equal to 3-dimensional column vector>
Figure QLYQS_23
Define a matrix operator->
Figure QLYQS_24
Is->
Figure QLYQS_25
Thereby taking an error variable->
Figure QLYQS_26
Derivative and multiply the moment of inertia at both left and right ends simultaneously>
Figure QLYQS_27
And then the control input of the spacecraft is obtained through design>
Figure QLYQS_28
The calculation process is as follows: />
Figure QLYQS_29
，
Figure QLYQS_30
，
Wherein, the first and the second end of the pipe are connected with each other,
Figure QLYQS_39
represents a control input of the spacecraft>
Figure QLYQS_32
Represents a function matrix, <' > is>
Figure QLYQS_35
And &>
Figure QLYQS_45
Represents an error variable, <' > is selected>
Figure QLYQS_49
Indicates a normal number, is selected>
Figure QLYQS_48
Represents an unknown parameter pick>
Figure QLYQS_51
Is evaluated based on the evaluation of->
Figure QLYQS_42
Represents a moment of inertia matrix, < > is asserted>
Figure QLYQS_46
Represents a fork multiplier, is greater than or equal to>
Figure QLYQS_31
Represents angular velocity, <' > or>
Figure QLYQS_37
Indicating a virtual control input pick>
Figure QLYQS_41
In the derivative of (C), is based on>
Figure QLYQS_44
Represents an angular velocity tracking error pick>
Figure QLYQS_47
Is greater than or equal to>
Figure QLYQS_50
Representing angular velocity>
Figure QLYQS_34
Is based on the matrix operator, < > is based on>
Figure QLYQS_36
Represents a variable->
Figure QLYQS_40
Is based on the matrix operator, < > is based on>
Figure QLYQS_43
Representing a variable>
Figure QLYQS_33
Is based on the matrix operator, < > is based on>
Figure QLYQS_38
Representing an unknown parameter;
s34, inputting control of the spacecraft
Figure QLYQS_52
Substituting the tracking error model to carry out attitude tracking control on the spacecraft;
wherein, step S3 further comprises:
designing a rotational inertia on-orbit identification algorithm of the service type spacecraft based on the tracking error model of S2 to obtain a parameter updating law of the spacecraft, and performing attitude tracking control on the spacecraft by combining the parameter updating law of the spacecraft and the control input of the spacecraft;
in particular, since for any orientationMeasurement of
Figure QLYQS_54
& -eq &>
Figure QLYQS_56
Is established, wherein>
Figure QLYQS_58
Represents a moment of inertia matrix, < > is asserted>
Figure QLYQS_55
Represents any vector, <' > based on a predetermined criterion>
Figure QLYQS_57
Denotes an unknown parameter (
Figure QLYQS_59
），/>
Figure QLYQS_60
Represents a vector pick>
Figure QLYQS_53
The matrix operator of (2);
the calculation process of the moment of inertia on-orbit identification algorithm is as follows:
re-representing the attitude dynamics equations of the spacecraft:
Figure QLYQS_61
，
wherein the content of the first and second substances,
Figure QLYQS_62
a matrix operator representing the derivative of the angular velocity, device for selecting or keeping>
Figure QLYQS_63
Matrix operator representing angular velocity>
Figure QLYQS_64
Represents an unknown parameter, <' >>
Figure QLYQS_65
Represents a control input of the spacecraft>
Figure QLYQS_66
Represents a fork multiplier, is greater than or equal to>
Figure QLYQS_67
Represents angular velocity, <' > or>
Figure QLYQS_68
Representing the derivative of angular velocity;
definition matrix
Figure QLYQS_69
And &>
Figure QLYQS_70
To further simplify the attitude dynamics equation:
Figure QLYQS_71
/>
wherein, the first and the second end of the pipe are connected with each other,
Figure QLYQS_72
represents a matrix->
Figure QLYQS_73
In the derivative of (C), is based on>
Figure QLYQS_74
Represents an unknown parameter, <' > is selected>
Figure QLYQS_75
Representing control inputs of a spacecraft;
carrying out filtering operation on the attitude dynamics equation by adopting a moment filtering technology:
Figure QLYQS_76
，
Figure QLYQS_77
，
wherein the content of the first and second substances,
Figure QLYQS_79
represents the Laplace operator, and->
Figure QLYQS_83
Is a normal number, is greater than or equal to>
Figure QLYQS_85
Represents a Laplace operation, <' > based on a predetermined criterion>
Figure QLYQS_80
Which represents the unknown parameters of the image data,
Figure QLYQS_81
represents a control input of the spacecraft>
Figure QLYQS_84
Representing a matrix +>
Figure QLYQS_86
Is greater than or equal to>
Figure QLYQS_78
And &>
Figure QLYQS_82
Representing a defined matrix;
will matrix
Figure QLYQS_95
、/>
Figure QLYQS_88
And controlling the input->
Figure QLYQS_91
The filtered signals are respectively denoted as->
Figure QLYQS_93
、/>
Figure QLYQS_97
And &>
Figure QLYQS_99
The relationship between them can be expressed as: />
Figure QLYQS_102
，/>
Figure QLYQS_96
，/>
Figure QLYQS_100
Wherein->
Figure QLYQS_87
Is a normal number, based on>
Figure QLYQS_92
，/>
Figure QLYQS_90
And &>
Figure QLYQS_94
Respectively represent->
Figure QLYQS_98
、/>
Figure QLYQS_101
And &>
Figure QLYQS_89
A derivative of (d);
are respectively provided with
Figure QLYQS_103
、/>
Figure QLYQS_104
And &>
Figure QLYQS_105
The initial values of (a) are: />
Figure QLYQS_106
，/>
Figure QLYQS_107
，/>
Figure QLYQS_108
The attitude dynamics equation of the spacecraft after filtering can be expressed as:
Figure QLYQS_109
；
further, can be written as:
Figure QLYQS_110
wherein->
Figure QLYQS_111
The expression of (a) is:
Figure QLYQS_112
；
therefore, after a stable linear filter is introduced,
Figure QLYQS_113
and &>
Figure QLYQS_114
Can be used to identify an unknown parameter->
Figure QLYQS_115
The signal of (a);
the approximation error is defined as:
Figure QLYQS_116
，
wherein
Figure QLYQS_117
；
According to
Figure QLYQS_118
The approximation error can be further expressed as:
Figure QLYQS_119
，
wherein the content of the first and second substances,
Figure QLYQS_120
represents a defined approximation error, based on the value of the parameter>
Figure QLYQS_121
Is expressed as->
Figure QLYQS_122
，
Figure QLYQS_123
Represents a filtered control input, <' > or>
Figure QLYQS_124
Represents an unknown parameter, <' >>
Figure QLYQS_125
Represents an unknown parameter pick>
Figure QLYQS_126
(ii) is estimated; />
Thereby obtaining a parameter estimate
Figure QLYQS_127
The update law design formula of (1):
Figure QLYQS_128
，
wherein, the first and the second end of the pipe are connected with each other,
Figure QLYQS_138
indicating a parameter estimate pick>
Figure QLYQS_131
Is updated law->
Figure QLYQS_134
Indicates a positive decision matrix, based on which the decision matrix is asserted>
Figure QLYQS_142
Represents angular velocity, <' > or>
Figure QLYQS_146
Representing a cross multiplier, matrix>
Figure QLYQS_148
And &>
Figure QLYQS_151
Respectively indicate angular speed->
Figure QLYQS_137
And a variable->
Figure QLYQS_141
Is based on the operator matrix, the variable->
Figure QLYQS_129
Is expressed as/>
Figure QLYQS_133
，/>
Figure QLYQS_132
Representing virtual control input>
Figure QLYQS_136
Is greater than or equal to>
Figure QLYQS_140
Represents an error variable, <' > is selected>
Figure QLYQS_144
Is expressed as->
Figure QLYQS_145
，/>
Figure QLYQS_149
And &>
Figure QLYQS_147
Is at>
Figure QLYQS_150
The historical data stored at the moment in time>
Figure QLYQS_130
A group number representing stored history data, greater or lesser>
Figure QLYQS_135
Is expressed as->
Figure QLYQS_139
，/>
Figure QLYQS_143
A transpose operation representing a matrix;
and finally, combining the parameter updating law of the spacecraft and the control input of the spacecraft to perform attitude tracking control of the spacecraft.
2. The method according to claim 1, wherein the kinematic and kinetic model equations in step S1 are:
Figure QLYQS_152
wherein the content of the first and second substances,
Figure QLYQS_154
represents the derivative of the modified Rodrigues parameter, <' > is determined>
Figure QLYQS_156
Representing a derivative of angular velocity, based on the angular velocity of the vehicle>
Figure QLYQS_159
Represents a modified Rodrigues parameter, < > or >>
Figure QLYQS_155
Represents angular velocity, <' > or>
Figure QLYQS_158
Represents a control input of the spacecraft>
Figure QLYQS_161
Represents a moment of inertia matrix, < > is asserted>
Figure QLYQS_163
Represents the Euler axis, <' > or>
Figure QLYQS_153
Represents the Euler angle, is greater than or equal to>
Figure QLYQS_157
Representing 3-dimensional euclidean spaceOr is present in>
Figure QLYQS_160
Represents a function matrix, <' > is>
Figure QLYQS_162
Represents a cross-product of a 3-dimensional column vector.
3. The method according to claim 1, wherein the tracking error model in step S2 has a formula:
Figure QLYQS_164
，
wherein the content of the first and second substances,
Figure QLYQS_165
derivative representing spacecraft attitude tracking error, based on the sum of the derivative and the derivative>
Figure QLYQS_171
Represents a tracking error of the gesture>
Figure QLYQS_174
A derivative representing the error in the tracking of the angular velocity of the spacecraft, <' >>
Figure QLYQS_166
Representing a tracking error of angular velocity>
Figure QLYQS_170
Indicates a desired gesture, and>
Figure QLYQS_173
indicates a desired angular velocity, is present>
Figure QLYQS_176
Represents the derivative of the desired angular speed, is>
Figure QLYQS_168
Represents a control input of the spacecraft>
Figure QLYQS_172
Represents a moment of inertia matrix, <' > based on>
Figure QLYQS_175
Represents angular velocity, <' > based on>
Figure QLYQS_177
Represents a fork multiplier, is greater than or equal to>
Figure QLYQS_167
Represents a function matrix, <' > based on>
Figure QLYQS_169
Representing the rotation matrix of the spacecraft. />
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