CN111781828A - Spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control - Google Patents

Spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control Download PDF

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CN111781828A
CN111781828A CN202010551884.5A CN202010551884A CN111781828A CN 111781828 A CN111781828 A CN 111781828A CN 202010551884 A CN202010551884 A CN 202010551884A CN 111781828 A CN111781828 A CN 111781828A
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CN111781828B (en
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王祎
曹璐
常强
朱效洲
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National Defense Technology Innovation Institute PLA Academy of Military Science
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention discloses a spacecraft cluster control method based on self-adaptive nonsingular terminal sliding mode control. The method is used for realizing the flight control of the spacecraft cluster, and comprises the following steps: establishing a coordinate system, establishing a mixed Gaussian model, establishing an adaptive artificial potential energy function, determining a non-singular terminal sliding film control sliding film surface, and determining a control law of the non-singular terminal sliding film control. The method comprises the steps of analyzing and describing an outer envelope of a target spacecraft by using a Gaussian mixture model, establishing an adaptive artificial potential energy function of uncertain environment factors and target spacecraft appearance influences based on the Gaussian mixture model, and then calculating and determining a control law of nonsingular terminal sliding mode control corresponding to a tracking spacecraft by combining nonsingular terminal sliding mode control and PID control based on the adaptive artificial potential energy function so as to control a tracking reference track of the tracking spacecraft.

Description

Spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control
Technical Field
The invention relates to the technical field of spacecraft motion control, in particular to a spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control.
Background
In recent years, the number of on-orbit failure events of a spacecraft is increasing, in order to reduce the occurrence probability of the on-orbit failure events, prolong the working life of the spacecraft and improve the working performance, more and more on-orbit services are applied to the spacecraft, the close-range operation of the spacecraft is taken as a basic technology supporting the on-orbit services, and the close-range operation of the spacecraft needs to meet strict safety requirements.
With the continuous improvement of space development and application capability, a large number of spacecrafts facing various task requirements are developed and launched in succession in various countries, the structure and the composition of the spacecrafts are increasingly complex, and the technical level is continuously improved; for example, a spacecraft cluster which is composed of a plurality of closely flying spacecrafts and is used for completing a certain common task has the advantages of high flexibility, time and space coverage, high reliability, survivability and the like, and therefore the spacecraft cluster has a wider application range.
In order to ensure the safety of a spacecraft, in the process of spacecraft cluster flight, the influence of the shape of the spacecraft on the spacecraft cluster flight needs to be considered, in the current spacecraft cluster flight control process, the geometric shape of the spacecraft is usually simplified into a spherical shape or an ellipsoidal shape, but in engineering practice, the geometric shape of most spacecrafts is not a simple spherical shape or an ellipsoidal shape, and in near field operation, different geometric shapes of the spacecraft have different influences on safety control. Meanwhile, in the process of spacecraft motion, due to the fact that the knowledge of the orbit environment of the spacecraft is insufficient to a certain degree and the deviation generated by the system or equipment of the spacecraft exists, the spacecraft can be influenced by uncertain factors to a certain degree.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides a spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control.
Therefore, the invention discloses a spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control, which is used for realizing flight control of a target spacecraft and a tracking spacecraft in a spacecraft cluster, and comprises the following steps:
establishing a coordinate system: establishing an epoch J2000 earth inertia coordinate system, and establishing an orbit coordinate system of the target spacecraft on the basis of the earth inertia coordinate system;
establishing a mixed Gaussian model: acquiring position information of a plurality of characteristic points on the surface of the target spacecraft, and establishing a Gaussian mixture model of the outer envelope surface of the target spacecraft based on the position information of the plurality of characteristic points;
establishing an adaptive artificial potential energy function: based on a Gaussian mixture model, establishing a self-adaptive artificial potential energy function by combining an expected relative position of a tracked spacecraft and uncertainty factor parameters;
determining the surface of a nonsingular terminal sliding film control sliding film: determining a nonsingular terminal sliding film control sliding film surface corresponding to the tracking spacecraft by using a self-adaptive artificial potential energy function and nonsingular terminal sliding film control;
determining a control law of non-singular terminal sliding mode control: and calculating and determining a control law of the nonsingular terminal sliding mode control corresponding to the tracking spacecraft according to the nonsingular terminal sliding mode control sliding film surface and PID control.
Further, in the method for controlling a spacecraft cluster based on adaptive nonsingular terminal sliding mode control, establishing a coordinate system includes:
by using O-XIYIZIRepresenting epoch J2000 earth inertial coordinate system with earth center as origin of coordinates, XIThe axis points to epoch J2000 spring minute point, the earth equator plane is the basic plane, ZIAxial direction to the Earth's North Pole, YIAxis and XIAxis, ZIThe axes form a right-hand rectangular coordinate system;
the orbit coordinate system of the target spacecraft is represented by o-xyz, the centroid of the target spacecraft is a coordinate origin, the x axis points to the centroid of the target spacecraft from the earth geocentric, the y axis is perpendicular to the x axis in the orbit plane of the target spacecraft and points to the speed direction of the target spacecraft, the z axis is perpendicular to the orbit plane of the target spacecraft, and the z axis, the x axis and the y axis form a right-hand rectangular coordinate system.
Further, in the spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control, the outer envelope of the target spacecraft described by the plurality of characteristic points on the surface of the target spacecraft is assumed to be composed of K1Fitting a Gaussian mixture model of the Gaussian components, and expressing the probability density distribution function of the Gaussian mixture model of the outer envelope surface of the target spacecraft as follows:
Figure BDA0002542841270000021
wherein p (Z | theta) represents a probability density distribution function of the Gaussian mixture model, theta represents a parameter variable set contained in the Gaussian mixture model,
Figure BDA0002542841270000022
k-th gaussian function component, z, representing a mixture of gaussian modelsiDenotes the ith feature point, zi＝[xi,yi,zi]T，xi、yiAnd ziRespectively representing the coordinate information of the ith characteristic point in the x direction, the y direction and the z direction of the track coordinate system,
Figure BDA0002542841270000023
representing the expected value of the kth gaussian function component in the hybrid gaussian model,
Figure BDA0002542841270000024
covariance matrix representing k-th gaussian function component in mixed gaussian model, r ═ x, y, z]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, x, y and z being respectively represented byCoordinates, pi, of the pointing spacecraft in the x, y and z directions of the orbital coordinate systemkRepresents the k-th Gaussian function component of the Gaussian mixture model, pi is the circumferential ratio, e is the natural logarithm,
Figure BDA0002542841270000031
represents a 3x3 matrix
Further, in the above spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control, the adaptive artificial potential energy function based on the gaussian mixture model is represented as:
Figure BDA0002542841270000032
wherein the content of the first and second substances,
Figure BDA0002542841270000033
represents an adaptive artificial potential energy function, and r is [ x, y, z ]]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TRepresenting the expected relative position, x, of the tracking spacecraft in the orbital coordinate system of the target spacecraftf、yfAnd zfRespectively representing expected coordinates of the tracked spacecraft in the x direction, the y direction and the z direction of an orbit coordinate system, wherein pi is a circumferential rate, e is a natural logarithm, and pi isjRepresenting the jth Gaussian function component, Σ, of the Gaussian mixture modeljCovariance matrix, mu, representing the jth Gaussian function component in the Gaussian mixture modeljAnd expressing the expectation value of the jth Gaussian function component in the mixed Gaussian model, W expressing a conversion matrix, P expressing a semi-positive definite matrix and M expressing the semi-positive definite matrix.
Further, in the spacecraft cluster control method based on the adaptive nonsingular terminal sliding mode control, the tracking of the sliding film surface of the nonsingular terminal sliding mode control corresponding to the spacecraft by combining the adaptive artificial potential energy function and the nonsingular terminal sliding mode control is represented as follows:
Figure BDA0002542841270000034
wherein S ═ S1S2S3]TDenotes the slide face, S1、S2And S3Denotes the synovial surface parameter, ksA semi-positive definite matrix is represented,
Figure BDA0002542841270000035
adaptive artificial potential energy function based on mixed Gaussian model
Figure BDA0002542841270000036
The gradient is calculated for the relative position r of the tracked spacecraft, e-rf，
Figure BDA0002542841270000037
r＝[x,y,z]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TRepresenting the desired relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA0002542841270000038
representing the relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA0002542841270000039
representing the desired relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA00025428412700000310
as a positive definite matrix, ξ11、ξ12And ξ13In order to positively determine the parameters of the matrix,
Figure BDA00025428412700000311
as a positive definite matrix, ξ21、ξ22And ξ23To positively define the matrix parameters, ξ0And tau are positive auxiliary parameters, 0 < ξ0< 1,. tau. > 1, p and q are both positive and odd numbers, 1<p/q。
Further, in the method for controlling a spacecraft cluster based on adaptive nonsingular terminal sliding mode control, determining a control law of the nonsingular terminal sliding mode control includes:
improving a non-singular terminal sliding film control sliding film surface corresponding to the tracking spacecraft by using PID control to obtain the non-singular terminal sliding film control sliding film surface under the PID control;
and (3) calculating and determining a control law of the nonsingular terminal sliding mode control corresponding to the tracking spacecraft by utilizing the nonsingular terminal sliding mode control sliding film surface under the PID control.
Further, in the above spacecraft cluster control method based on adaptive non-singular terminal sliding film control, the non-singular terminal sliding film control sliding film surface under PID control is represented as:
Figure BDA0002542841270000041
wherein S isGaPNDenotes the nonsingular terminal synovial membrane control slide surface under PID control, S ═ S1S2S3]TDenotes the slide face, S1、S2And S3Denotes the synovial surface parameter, KpDenotes the proportionality constant, KiDenotes the integration constant, KdRepresenting a differential constant and t a time variable.
Further, in the spacecraft cluster control method based on the adaptive nonsingular terminal sliding mode control, a control law of the nonsingular terminal sliding mode control corresponding to the tracking spacecraft is calculated and determined according to the following formula 9;
Figure BDA0002542841270000042
wherein each parameter in formula 9 is determined by calculation using formula 10-formula 20;
Figure BDA0002542841270000043
Figure BDA0002542841270000044
ur＝(+a0)sign(S) (12)
Figure BDA0002542841270000045
Figure BDA0002542841270000051
Figure BDA0002542841270000052
Figure BDA0002542841270000053
Figure BDA0002542841270000054
Figure BDA0002542841270000055
Figure BDA0002542841270000056
Figure BDA0002542841270000057
uGaPNrepresents the control law, a0Sign (·) represents a sign function, which is constant and a positive number,
Figure BDA0002542841270000058
representing the expected relative acceleration, ω and
Figure BDA0002542841270000061
respectively representing the angular velocities andangular acceleration, mu represents the earth's gravitational constant, a and n represent the orbit major semi-axis and average angular velocity, respectively, of the target spacecraft,
Figure BDA0002542841270000062
scalar rtAnd rfRespectively representing the relative distance between the target spacecraft and the earth mass center, f representing the true perigee angle of the target spacecraft, and E representing the orbital eccentricity of the target spacecraft.
The technical scheme of the invention has the following main advantages:
the spacecraft cluster control method based on the adaptive nonsingular terminal sliding mode control analyzes and describes the outer envelope of the target spacecraft by utilizing the Gaussian mixture model, establishes the adaptive artificial potential energy function of uncertain environmental factor influence and target spacecraft appearance influence based on the Gaussian mixture model, and then determines the control law of the nonsingular terminal sliding mode control corresponding to the tracking spacecraft by combining the nonsingular terminal sliding mode control and PID control calculation based on the adaptive artificial potential energy function so as to control the tracking reference track of the tracking spacecraft.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a coordinate system according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the specific embodiments of the present invention and the accompanying drawings. It is to be understood that the described embodiments are merely a few embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme provided by the embodiment of the invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, an embodiment of the present invention provides a spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control, the method is used for implementing flight control of a target spacecraft and a tracking spacecraft in a spacecraft cluster, and the method includes the following steps:
establishing a coordinate system: establishing an epoch J2000 earth inertia coordinate system, and establishing an orbit coordinate system of the target spacecraft on the basis of the earth inertia coordinate system;
establishing a mixed Gaussian model: acquiring position information of a plurality of characteristic points on the surface of the target spacecraft, and establishing a Gaussian mixture model of the outer envelope surface of the target spacecraft based on the position information of the plurality of characteristic points;
establishing an adaptive artificial potential energy function: based on a Gaussian mixture model, establishing a self-adaptive artificial potential energy function by combining an expected relative position of a tracked spacecraft and uncertainty factor parameters;
determining the surface of a nonsingular terminal sliding film control sliding film: determining a nonsingular terminal sliding film control sliding film surface corresponding to the tracking spacecraft by using a self-adaptive artificial potential energy function and nonsingular terminal sliding film control;
determining a control law of non-singular terminal sliding mode control: and calculating and determining a control law of the nonsingular terminal sliding mode control corresponding to the tracking spacecraft according to the nonsingular terminal sliding mode control sliding film surface and PID control (proportional-integral-derivative control).
Specifically, each step in the spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control according to an embodiment of the present invention is specifically described below.
(1) Establishing a coordinate system
In the spacecraft cluster control method based on adaptive nonsingular terminal sliding film control according to an embodiment of the present invention, as shown in fig. 2, establishing a coordinate system includes:
by using O-XIYIZIRepresenting epoch J2000 earth inertial coordinate system with earth center as origin of coordinates, XIThe axis points to epoch J2000 spring minute point, the earth equator plane is the basic plane, ZIAxial direction to the Earth's North Pole, YIAxis and XIAxis, ZIThe axes form a right-hand rectangular coordinate system;
the orbit coordinate system of the target spacecraft is represented by o-xyz, the centroid of the target spacecraft is a coordinate origin, the x axis points to the centroid of the target spacecraft from the earth geocentric, the y axis is perpendicular to the x axis in the orbit plane of the target spacecraft and points to the speed direction of the target spacecraft, the z axis is perpendicular to the orbit plane of the target spacecraft, and the z axis, the x axis and the y axis form a right-hand rectangular coordinate system.
(2) Establishing a hybrid Gaussian model
Acquiring position information of a plurality of characteristic points on the surface of a target spacecraft by using a sensor, and establishing a Gaussian mixture model of the outer envelope surface of the target spacecraft based on the acquired position information of the plurality of characteristic points on the surface of the target spacecraft;
assuming that a series of feature point sample sets of the outer envelope surface of the target spacecraft are Z, Z is expressed as:
Figure BDA0002542841270000071
in the formula, ziDenotes the ith feature point, xi、yiAnd ziRespectively representing coordinate information of the ith characteristic point in the x direction, the y direction and the z direction of the track coordinate system, wherein N represents the number of the characteristic points;
meanwhile, the outer envelope of the target spacecraft described by the sample set Z of the feature points is assumed to be composed of K1Of one Gaussian componentFitting a Gaussian mixture model, the probability density distribution function p (Z | Θ) of the Gaussian mixture model can be expressed as:
Figure BDA0002542841270000081
in the formula, Θ represents a parameter variable set included in the Gaussian mixture model,
Figure BDA0002542841270000082
a k-th gaussian function component representing the gaussian mixture model,
Figure BDA0002542841270000083
representing the expected value of the kth Gaussian function component in the mixed Gaussian model corresponding to the target spacecraft surface characteristic point,
Figure BDA0002542841270000084
and (3) representing the covariance matrix of the k-th Gaussian function component in the mixed Gaussian model corresponding to the target spacecraft surface feature point, wherein r is [ x, y, z ═]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, x, y and z representing the coordinates of the tracking spacecraft in the x direction, the y direction and the z direction of the orbital coordinate system, respectively, and pikRepresents the k-th Gaussian function component of the Gaussian mixture model, pi is the circumferential ratio, e is the natural logarithm,
Figure BDA0002542841270000085
a 3x3 matrix is shown.
Wherein the content of the first and second substances,
Figure BDA0002542841270000086
πksatisfy constraints
Figure BDA0002542841270000087
ΘkRepresenting a parameter variable set, M, contained in the kth Gaussian function component in the mixed Gaussian model corresponding to the target spacecraft surface feature pointkExpressing the point of the target spacecraft surface characteristic point to correspond to the second in the Gaussian mixture modelA covariance matrix of k gaussian function components.
(3) Establishing an adaptive artificial potential energy function
Assuming that the expected relative position of the tracking spacecraft in the orbit coordinate system of the target spacecraft is rf＝[xf,yf,zf]T，xf、yfAnd zfRespectively representing expected coordinates of the tracked spacecraft in the x direction, the y direction and the z direction of the orbit coordinate system, and then based on the self-adaptive artificial potential energy function of the Gaussian mixture model
Figure BDA0002542841270000088
Can be expressed as:
Figure BDA0002542841270000089
wherein r is [ x, y, z ]]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TRepresenting the expected relative position of the tracking spacecraft in the orbit coordinate system of the target spacecraft, pi is the circumferential rate, e is the natural logarithm, pijRepresenting the jth Gaussian function component, Σ, in the Gaussian mixture modeljCovariance matrix, mu, representing the jth Gaussian function component in the Gaussian mixture modeljAnd expressing the expectation value of the jth Gaussian function component in the mixed Gaussian model, W expressing a conversion matrix, P expressing a semi-positive definite matrix and M expressing the semi-positive definite matrix.
(4) Determination of nonsingular terminal synovial membrane control slide surface
Definition vector e-rfVector of
Figure BDA0002542841270000091
The non-singular terminal sliding film control sliding film surface corresponding to the tracking spacecraft can be determined by utilizing the self-adaptive artificial potential energy function and the non-singular terminal sliding film control; specifically, the non-singular terminal synovial control slide surface corresponding to the tracking spacecraft can be represented as:
Figure BDA0002542841270000092
wherein S ═ S1S2S3]TDenotes the slide face, S1、S2And S3Denotes the synovial surface parameter, ksRepresenting a semi-positive definite matrix, ▽ representing a gradient function,
Figure BDA0002542841270000093
representing an adaptive artificial potential energy function based on a Gaussian mixture model
Figure BDA0002542841270000094
Gradient is calculated for the relative position r of the tracked spacecraft, r ═ x, y, z]T represents the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TRepresenting the desired relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA0002542841270000095
representing the relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA0002542841270000096
and
Figure BDA0002542841270000097
respectively representing the relative velocity of the tracked spacecraft in the x-direction, the y-direction and the z-direction of the orbital coordinate system,
Figure BDA0002542841270000098
representing the desired relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA0002542841270000099
and
Figure BDA00025428412700000910
respectively representing tracked spacecraftThe desired relative velocities in the x-direction, y-direction and z-direction of the orbital coordinate system,
Figure BDA00025428412700000911
as a positive definite matrix, ξ11、ξ12And ξ13In order to positively determine the parameters of the matrix,
Figure BDA00025428412700000912
as a positive definite matrix, ξ21、ξ22And ξ23To positively define the matrix parameters, ξ0And tau are positive auxiliary parameters, 0 < ξ0< 1,. tau. > 1, p and q are both positive and odd numbers, 1<p/q，ξ0The values of τ, p and q are determined in practice.
Wherein the content of the first and second substances,
Figure BDA00025428412700000913
expressed as:
Figure BDA00025428412700000914
(5) control law for determining non-singular terminal sliding mode control
Further, on the basis of the determined nonsingular terminal sliding film control sliding film surface corresponding to the tracking spacecraft, the non-singularity terminal sliding film control sliding film surface corresponding to the tracking spacecraft is improved by utilizing PID control, so that the non-singularity terminal sliding film control sliding film surface under the PID control can be obtained; specifically, the nonsingular terminal synovial membrane control slide surface under PID control can be expressed as:
Figure BDA0002542841270000101
in the formula, SGaPNDenotes the nonsingular terminal synovial membrane control slide surface under PID control, S ═ S1S2S3]TDenotes the slide face, S1、S2And S3Denotes the synovial surface parameter, KpDenotes the proportionality constant, KiDenotes the integration constant, KdRepresents a differential constantAnd t represents a time variable.
Further, on the basis of the above calculation and analysis, in an embodiment of the present invention, a control law of the nonsingular terminal sliding mode control corresponding to the tracked spacecraft may be obtained by calculation according to the following formula 9;
Figure BDA0002542841270000102
in the formula uGaPNRepresenting a control law;
each parameter in formula 9 can be determined by calculation using the following formula 10 to 20;
Figure BDA0002542841270000103
Figure BDA0002542841270000104
ur＝(+a0)sign(S) (12)
Figure BDA0002542841270000105
|e|τ-1＝((x-xf)τ-1,(y-yf)τ-1,(z-zf)τ-1)T(14)
Figure BDA0002542841270000106
Figure BDA0002542841270000111
Figure BDA0002542841270000112
Figure BDA0002542841270000113
Figure BDA0002542841270000114
Figure BDA0002542841270000115
in each of the above formulae uGaPNRepresents the control law, a0Is a constant, is a normal number, sign (·) denotes a sign function, r ═ x, y, z]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TRepresenting the desired relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA0002542841270000116
showing the relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA0002542841270000121
representing the desired relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA0002542841270000122
representing the expected relative acceleration of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure BDA0002542841270000123
and
Figure BDA0002542841270000124
representing the expected relative accelerations, ω and z, of the tracked spacecraft in the x, y and z directions, respectively, of the orbital coordinate system
Figure BDA0002542841270000125
Respectively representing the angular velocity and angular acceleration of the target spacecraft, mu representing the earth's gravitational constant, a and n representing the orbit major semi-axis and average angular velocity of the target spacecraft,
Figure BDA0002542841270000126
scalar rtAnd rfRespectively representing the relative distance between the target spacecraft and the earth mass center, f representing the true perigee angle of the target spacecraft, and E representing the orbital eccentricity of the target spacecraft.
And further, controlling the tracking reference track of the tracking spacecraft according to the determined control law of the non-singular terminal sliding mode control corresponding to the tracking spacecraft.
Therefore, in the spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control provided by the embodiment of the invention, the outer envelope of the target spacecraft is analyzed and described by using the Gaussian mixture model, the adaptive artificial potential energy function of uncertain environment factor influence and target spacecraft appearance influence is established based on the Gaussian mixture model, and then the control law of the nonsingular terminal sliding mode control corresponding to the tracking spacecraft is determined based on the adaptive artificial potential energy function and combined with the nonsingular terminal sliding mode control and PID control calculation to control the tracking reference track of the tracking spacecraft, the influence of the complex appearance of the spacecraft and the influence of the uncertain environment factor can be considered at the same time, the control precision and the adaptability are higher, the fuel can be effectively saved, and the singularity problem can be avoided.
It is noted that, in this document, relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. In addition, "front", "rear", "left", "right", "upper" and "lower" in this document are referred to the placement states shown in the drawings.
Finally, it should be noted that: the above examples are only for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (8)

1. A spacecraft cluster control method based on adaptive nonsingular terminal sliding mode control is characterized in that the method is used for realizing flight control of a target spacecraft and a tracking spacecraft in a spacecraft cluster, and the method comprises the following steps:
establishing a coordinate system: establishing an epoch J2000 earth inertia coordinate system, and establishing an orbit coordinate system of the target spacecraft on the basis of the earth inertia coordinate system;
establishing a mixed Gaussian model: acquiring position information of a plurality of characteristic points on the surface of the target spacecraft, and establishing a Gaussian mixture model of the outer envelope surface of the target spacecraft based on the position information of the plurality of characteristic points;
establishing an adaptive artificial potential energy function: based on a Gaussian mixture model, establishing a self-adaptive artificial potential energy function by combining an expected relative position of a tracked spacecraft and uncertainty factor parameters;
determining the surface of a nonsingular terminal sliding film control sliding film: determining a nonsingular terminal sliding film control sliding film surface corresponding to the tracking spacecraft by using a self-adaptive artificial potential energy function and nonsingular terminal sliding film control;
determining a control law of non-singular terminal sliding mode control: and calculating and determining a control law of the nonsingular terminal sliding mode control corresponding to the tracking spacecraft according to the nonsingular terminal sliding mode control sliding film surface and PID control.
2. The method of claim 1, wherein establishing a coordinate system comprises:
by using O-XIYIZIRepresenting epoch J2000 earth inertial coordinate system with earth center as origin of coordinates, XIThe axis points to epoch J2000 spring minute point, the earth equator plane is the basic plane, ZIAxial direction to the Earth's North Pole, YIAxis and XIAxis, ZIThe axes form a right-hand rectangular coordinate system;
the orbit coordinate system of the target spacecraft is represented by o-xyz, the centroid of the target spacecraft is a coordinate origin, the x axis points to the centroid of the target spacecraft from the earth geocentric, the y axis is perpendicular to the x axis in the orbit plane of the target spacecraft and points to the speed direction of the target spacecraft, the z axis is perpendicular to the orbit plane of the target spacecraft, and the z axis, the x axis and the y axis form a right-hand rectangular coordinate system.
3. A spacecraft clustering control method based on adaptive nonsingular terminal synovial control according to any one of claims 1 to 2, wherein an outer envelope of the target spacecraft described by a number of feature points of the target spacecraft surface is assumed to be composed of K1Fitting a Gaussian mixture model of the Gaussian components, and expressing the probability density distribution function of the Gaussian mixture model of the outer envelope surface of the target spacecraft as follows:
Figure FDA0002542841260000011
wherein p (Z | theta) represents a probability density distribution function of the Gaussian mixture model, theta represents a parameter variable set contained in the Gaussian mixture model,
Figure FDA0002542841260000012
k-th gaussian function component, z, representing a mixture of gaussian modelsiDenotes the ith feature point, zi＝[xi,yi,zi]T，xi、yiAnd ziRespectively representing the coordinate information of the ith characteristic point in the x direction, the y direction and the z direction of the track coordinate system,
Figure FDA0002542841260000021
representing the expected value of the kth gaussian function component in the hybrid gaussian model,
Figure FDA0002542841260000022
covariance matrix representing k-th gaussian function component in mixed gaussian model, r ═ x, y, z]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, x, y and z representing the coordinates of the tracking spacecraft in the x direction, the y direction and the z direction of the orbital coordinate system, respectively, and pikRepresents the k-th Gaussian function component of the Gaussian mixture model, pi is the circumferential ratio, e is the natural logarithm,
Figure FDA0002542841260000023
representing a 3x3 matrix.
4. A spacecraft clustering control method based on adaptive nonsingular terminal synovial control according to any one of claims 1 to 3, wherein the adaptive artificial potential energy function based on the gaussian mixture model is represented as:
Figure FDA0002542841260000024
wherein the content of the first and second substances,
Figure FDA0002542841260000025
represents an adaptive artificial potential energy function, and r is [ x, y, z ]]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TRepresenting the expected relative position, x, of the tracking spacecraft in the orbital coordinate system of the target spacecraftf、yfAnd zfRespectively representing expected coordinates of the tracked spacecraft in the x direction, the y direction and the z direction of an orbit coordinate system, wherein pi is a circumferential rate, e is a natural logarithm, and pi isjRepresenting the jth Gaussian function component, Σ, of the Gaussian mixture modeljCovariance matrix, mu, representing the jth Gaussian function component in the Gaussian mixture modeljAnd expressing the expectation value of the jth Gaussian function component in the mixed Gaussian model, W expressing a conversion matrix, P expressing a semi-positive definite matrix and M expressing the semi-positive definite matrix.
5. The spacecraft cluster control method based on the adaptive non-singular terminal synovial membrane control of any one of claims 1 to 4, wherein in combination with the adaptive artificial potential energy function and the non-singular terminal synovial membrane control, tracking the non-singular terminal synovial membrane control synovial surface corresponding to the spacecraft is represented as:
Figure FDA0002542841260000026
wherein S ═ S1S2S3]TDenotes the slide face, S1、S2And S3Denotes the synovial surface parameter, ksA semi-positive definite matrix is represented,
Figure FDA0002542841260000027
representing an adaptive artificial potential energy function based on a Gaussian mixture model
Figure FDA0002542841260000028
The gradient is calculated for the relative position r of the tracked spacecraft, e-rf，
Figure FDA0002542841260000029
r＝[x,y,z]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TRepresenting the desired relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure FDA00025428412600000210
representing the relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure FDA0002542841260000031
representing the desired relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft,
Figure FDA0002542841260000032
as a positive definite matrix, ξ11、ξ12And ξ13In order to positively determine the parameters of the matrix,
Figure FDA0002542841260000033
as a positive definite matrix, ξ21、ξ22And ξ23To positively define the matrix parameters, ξ0And tau are positive auxiliary parameters, 0 < ξ0< 1,. tau. > 1, p and q are both positive and odd numbers, 1<p/q。
6. The adaptive non-singular terminal synovial control based spacecraft cluster control method of any of claims 1-5, wherein determining the control law for non-singular terminal synovial control comprises:
improving a non-singular terminal sliding film control sliding film surface corresponding to the tracking spacecraft by using PID control to obtain the non-singular terminal sliding film control sliding film surface under the PID control;
and (3) calculating and determining a control law of the nonsingular terminal sliding mode control corresponding to the tracking spacecraft by utilizing the nonsingular terminal sliding mode control sliding film surface under the PID control.
7. The spacecraft cluster control method based on adaptive non-singular terminal synovial membrane control of claim 6, wherein the non-singular terminal synovial membrane control synovial membrane surfaces under PID control are represented as:
Figure FDA0002542841260000034
wherein S isGaPNDenotes the nonsingular terminal synovial membrane control slide surface under PID control, S ═ S1S2S3]TDenotes the slide face, S1、S2And S3Denotes the synovial surface parameter, KpDenotes the proportionality constant, KiDenotes the integration constant, KdRepresenting a differential constant and t a time variable.
8. The spacecraft clustering control method based on the adaptive nonsingular terminal sliding mode control according to claim 7, wherein the control law of the nonsingular terminal sliding mode control corresponding to the tracking spacecraft is determined by calculation according to the following formula 9;
Figure FDA0002542841260000035
wherein each parameter in formula 9 is determined by calculation using formula 10-formula 20;
Figure FDA0002542841260000036
Figure FDA0002542841260000037
ur＝(+a0)sign(S) (12)
Figure FDA0002542841260000041
|e|τ-1＝((x-xf)τ-1,(y-yf)τ-1,(z-zf)τ-1)T(14)
Figure FDA0002542841260000042
Figure FDA0002542841260000043
Figure FDA0002542841260000044
Figure FDA0002542841260000045
Figure FDA0002542841260000051
Figure FDA0002542841260000052
uGaPNrepresents the control law, a0Sign (·) represents a sign function, which is constant and a positive number,
Figure FDA0002542841260000053
representing the expected relative acceleration, ω and
Figure FDA0002542841260000054
respectively representing the angular velocity and angular acceleration of the target spacecraft, mu representing the earth's gravitational constant, a and n representing the orbit major semi-axis and average angular velocity of the target spacecraft,
Figure FDA0002542841260000055
scalar rtAnd rfRespectively representing the relative distance between the target spacecraft and the earth mass center, f representing the true perigee angle of the target spacecraft, and E representing the orbital eccentricity of the target spacecraft.
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