Space target anti-missing tracking control method and system for video satellite

Abstract

The present invention discloses a space target anti-missing tracking control method and system for a video satellite. First, based on the perspective projection principle, the corresponding relationship between the position coordinates of the space target in the geocentric inertial system and the projection position of the image plane is established; then, the attitude kinematic equation and attitude dynamic equation of the video satellite are established; next, the attitude error quaternion and attitude error angular velocity of the video satellite are calculated based on the projection position of the space target; then, the imaging restriction area is designed in the image plane, and a logarithmic convex potential function described by the error quaternion is constructed; finally, an anti-missing tracking controller is designed based on the potential function and the error angular velocity to control the satellite attitude. The present invention can stably visually track the space target, and can prevent the target projection from deviating from the image plane during the tracking control process, effectively solving the problem of space target missing, and has fast response speed, good stability and control convergence.

Description

Technical Field

[0001] The invention belongs to the field of video satellite design, and in particular relates to a space target anti-missing tracking control method and system for a video satellite. Background Art

[0002] The current space environment is becoming increasingly complex, and the importance of space target observation missions is becoming increasingly prominent. In order to make up for the shortcomings of ground observation methods, countries are vigorously developing space surveillance technology. Video satellites have unique advantages such as short development cycle, fast response speed, and high-resolution real-time continuous imaging. They are widely used in ground target observation such as disaster monitoring, resource census, and moving target monitoring, as well as space target observation.

[0003] Typical small video satellites in the world include LAPAN-TUBSAT, Sumbandia and Tiantuo-2. They all adjust the satellite attitude in real time to keep the target in the field of view of the onboard camera at all times, thus achieving continuous tracking and video imaging of the target.

[0004] Usually, video satellites use a method based on position information to track targets. The attitude error and angular velocity error of the video satellite are calculated through the target position information, and then the actuator is controlled to achieve satellite attitude maneuvering and gaze tracking. Since this method requires obtaining the target's prior position information, it is only applicable to cooperative target tracking. However, many space targets such as space debris and faulty spacecraft are non-cooperative targets. Their real-time position information cannot be accurately obtained, and target tracking cannot be performed using the position-based method.

[0005] The image-based space target tracking method uses the real-time deviation of the target projection in the image plane as control feedback, which does not rely on the target's prior position information. Visual servo control through camera images has a wide range of applications in robots, drones and other fields. In the field of video satellite applications, the document "Design of the image-based satellite attitude control algorithm" (author: Zdesar A, Klancar G, Music G; conference: XXIV International Conference on Information IEEE Computer Society; year: 2013) proposed an attitude control algorithm based on image feedback for the attitude tracking problem of earth observation satellites, and realized the pointing tracking of ground targets; the document "Image-based attitude maneuvers for space debris tracking" (author: Felicetti L, Emami MR; journal: Aerospace science and technology; year: 2018; volume (issue): 76 (5); page number: 58-71) realized the motion prediction and continuous tracking of space debris based on images; the document "Spacecraft Staring Attitude Control for Ground Targets Using an Uncalibrated Camera" (author: 20.Song C., Fan C., Song, H., Wang, M; Journal: Aerospace; Year: 2022; Volume (Issue): 9(6); Page Number: 283) uses an uncalibrated camera to complete the gaze tracking of ground targets; the patent "A video satellite attitude control method for tracking and imaging non-cooperative targets" (Inventors: Xiang Junhua, Zhang Xueyang, Cui Kaikai, etc.; Country: China; Publication Number: CN 106097397 A; Publication Date: 2016.11.09) provides an attitude control method for the tracking and imaging of non-cooperative moving targets by video satellites. However, none of the above documents considers how to ensure that the target always falls within the field of view. Since there is usually an initial angular velocity in the satellite attitude maneuver and the target orbital motion, when the target first enters the field of view, there may be a large relative motion between the target and the video satellite, and the target may leave the camera field of view, resulting in tracking failure. Summary of the invention

[0006] The present invention proposes a space target anti-missing tracking control method and system for a video satellite, aiming to solve the problem that when a target first enters the camera field of view and has a large relative angular velocity in a video satellite visual tracking application, the target field of view is easily lost.

[0007] The technical solution of the present invention is as follows:

[0008] A space target anti-missing tracking control method for a video satellite is proposed. e ) performs attitude control on the video satellite, including the following steps:

[0009] S1. Based on the perspective projection principle, the corresponding relationship between the position coordinates of the space target in the geocentric inertial system and the projection position of the image plane is established;

[0010] S2. Further establish the attitude kinematic equation and attitude dynamic equation of the video satellite;

[0011] S3. Calculate the attitude error quaternion and attitude error angular velocity of the video satellite based on the image plane projection position of the space target;

[0012] S4, designing an imaging restriction area in the image plane, and constructing a logarithmic convex potential function described by the attitude error quaternion;

[0013] S5. Based on the logarithmic convex potential function and the attitude error angular velocity of the video satellite, an anti-missing visual tracking controller for the video satellite is designed.

[0014] Preferably, the mathematical expression of the corresponding relationship between the position coordinates of the space target in the geocentric inertial system and the image plane projection position in step S1 is:

[0015]

[0016] Where u and v are the horizontal and vertical coordinates of the target projection point in the pixel coordinate system; u0 and v0 are the horizontal and vertical coordinates of the pixel point where the camera optical axis intersects the image plane; du and dv are the horizontal and vertical sizes of the pixel point; f is the focal length of the camera; i R iT is the position coordinate of the space target in the Earth-centered inertial system; i R ib is the position coordinate of the video satellite in the geocentric inertial system; is the transformation matrix from the geocentric inertial system to the satellite body coordinate system; c It is the Z-axis coordinate of the space target in the camera coordinate system.

[0017] Preferably, the attitude kinematic equation of the video satellite established in step S2 is:

[0018]

[0019] Where q is the attitude quaternion of the video satellite, ω is the description of the angular velocity of the satellite body coordinate system relative to the geocentric inertial system in the satellite body coordinate system; the superscript · represents the derivative of the variable, and the symbol Represents quaternion multiplication operation;

[0020] The attitude dynamics equation of the established video satellite is:

[0021]

[0022] Where J is the moment of inertia matrix of the video satellite, u c is the attitude control torque.

[0023] Preferably, the calculation formula of the attitude error quaternion of the video satellite in step S3 is:

[0024]

[0025] Where q e is the attitude error quaternion of the video satellite; a is the Euler axis vector, and the expression of a is:

[0026]

[0027] where r t =(x pt y pt f) T is the target position direction vector in the camera coordinate system, r o =(00f) T is the optical axis direction vector in the camera coordinate system, x pt =(u-u0)·du,y pt =(v-v0)·dv, u and v are the horizontal and vertical coordinates of the target projection point in the pixel coordinate system; u0 and v0 are the horizontal and vertical coordinates of the pixel point where the camera optical axis intersects the image plane; du and dv are the horizontal and vertical sizes of the pixel point; f is the focal length of the camera. θ is the Euler angle, and the expression of θ is:

[0028]

[0029] Where arccos represents the inverse cosine function.

[0030] The calculation process of the attitude error angular velocity of the video satellite is:

[0031] First, solve the video satellite's expected attitude quaternion q d , whose expression is:

[0032]

[0033] In the formula, the superscript * represents the conjugate of the vector, and q represents the attitude quaternion of the video satellite.

[0034] Then calculate the expected angular velocity ω of the video satellite d , whose expression is:

[0035]

[0036] Where superscript · is the derivative of the variable, superscript T is the transpose of the matrix; Ξ(q d ) is the desired attitude quaternion q d The matrix described is expressed as:

[0037]

[0038] Where q d0 and q d1 ,q d2 ,q d3 Represent the desired attitude quaternion q d A scalar and a vector of three elements.

[0039] Finally, solve the attitude error angular velocity ω of the video satellite e for:

[0040] ω e =ω-A(q e )ω d ,

[0041] Where ω is the description of the angular velocity of the satellite body coordinate system relative to the Earth's center inertial system in the satellite body coordinate system; A(q e ) is the error quaternion q e The transformation matrix represented by satisfies the following relationship:

[0042]

[0043] where q e0 is the scalar error quaternion, q ev is the vector of error quaternion; I 3×3 represents the third-order identity matrix, the superscript × is a skew-symmetric operator, for any vector x = (x1 x2 x3) T , there is an expression:

[0044]

[0045] Furthermore, step S4 includes the following sub-steps:

[0046] S41, Design imaging restriction area:

[0047] The maximum inscribed circle of the rectangular field of view is taken as the target imaging restriction area, that is, the target image plane projection position is always required to be within the area to ensure that the target does not leave the field of view and has a good observation field of view. The advantage of designing the imaging restriction area in this way is that the range constraint of the target imaging projection position can be converted into the target position direction vector r in the camera coordinate system t and the optical axis direction vector r o The angle constraint is set to facilitate the establishment of the connection with the satellite attitude. The following relationship should be satisfied:

[0048] 0≤θ<θ max

[0049] In the inequality, θ is the real-time position direction vector r of the target in the camera coordinate system t and the optical axis direction vector r o The angle between max is the target position direction vector r in the camera coordinate system when the projection position of the target in the image plane is at the boundary of the restricted area b and the optical axis direction vector r o The angle between , is expressed as:

[0050]

[0051] Where u s and v s are the number of horizontal and vertical pixels on the image plane, du and dv are the horizontal and vertical sizes of the pixels, f is the focal length of the camera; arctan is the inverse tangent function.

[0052] S42, based on the restricted area, construct the following error quaternion q e The logarithmic convex potential function V(q e ):

[0053]

[0054] Where q e is the attitude error quaternion, q e0 is the attitude error quaternion q e scalar; k1 is a positive constant, a is a positive constant and makes Uniformly distributed between 0 and 1;

[0055] When the image plane projection position of the space target is within the imaging restriction area, the logarithmic convex potential function satisfies V(q e )≥0, and if and only if the error quaternion q e =(1 0) T When the potential function V(q e) obtains the local minimum value, which is also the global minimum value, which is zero; when the image plane projection position of the space target approaches the boundary of the restricted area, the logarithmic convex potential function V(q e ) approaches infinity.

[0056] Further, in step S5, the designed video satellite anti-missing visual tracking controller is:

[0057]

[0058] In the formula, u c is the control torque output by the anti-missing controller; k2 is the positive constant; q e is the attitude error quaternion; ω e is the angular velocity of the attitude error; ω is the description of the angular velocity of the satellite body coordinate system relative to the geocentric inertial system in the satellite body coordinate system; ω d is the expected angular velocity; is the potential function V(q e ) first-order gradient; J is the moment of inertia of the video satellite; the superscript * indicates the conjugate of the quaternion; the superscript · is the derivative of the variable; the symbol represents quaternion multiplication; vec(·) represents the vector part of (·); A(q e ) is the error quaternion q e The transformation matrix represented by satisfies:

[0059]

[0060] where q e0 is the scalar of the error quaternion, q ev is the vector of error quaternion; I 3×3 Represents the third-order identity matrix. The superscript “×” is a skew-symmetric operator. For any vector x=(x1 x2 x3) T , there is an expression:

[0061]

[0062] In addition, the present invention also proposes a space target anti-missing tracking control system for a video satellite, comprising a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to execute the steps of the space target anti-missing tracking control method for the video satellite, or the memory stores a computer program programmed or configured to execute the space target anti-missing tracking control method for the video satellite.

[0063] The present invention also proposes a video mini-satellite, comprising a satellite body, wherein the satellite body comprises a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to execute the steps of the space target anti-missing tracking control method of the video mini-satellite, or the memory stores a computer program programmed or configured to execute the space target anti-missing tracking control method of the video mini-satellite.

[0064] The present invention also proposes a computer-readable storage medium, in which a computer program programmed or configured to execute the space target anti-missing tracking control method of the video satellite is stored.

[0065] Compared with the prior art, the beneficial effects of the technical solution of the present invention are mainly reflected in the following aspects:

[0066] The present invention can stably visually track non-cooperative targets in space, and can prevent the target projection from deviating from the image plane during the tracking control process, effectively solving the problem of space target miss, and has fast response speed, good stability and control convergence. The present invention can provide technical reference and support for the design of video satellite tracking controller for space target anti-miss. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0068] Figure 1 The following is a basic flow chart of the method according to the embodiment of the present invention.

[0069] Figure 2 Schematic diagram of the internal perspective projection principle of the camera in an embodiment of the present invention.

[0070] Figure 3 Schematic diagram of external imaging of a camera in an embodiment of the present invention.

[0071] Figure 4 Schematic diagram of the imaging restriction area in the field of view designed for an embodiment of the present invention.

[0072] Figure 5 This is a partial change diagram of the error quaternion vector in the anti-missing tracking control according to an embodiment of the present invention.

[0073] Figure 6 This is a diagram showing the variation of the error angular velocity in the anti-missing tracking control according to an embodiment of the present invention.

[0074] Figure 7 The imaging results in the anti-missing tracking control of the embodiment of the present invention are: (a) trajectory diagram of the projection position of the space target on the image plane; (b) deviation change diagram of the projection pixel position of the space target on the image plane.

[0075] Figure 8 Variable changes in the anti-missing tracking control according to an embodiment of the present invention: (a) graph of potential function value changes; (b) graph of camera optical axis deviation angle changes.

[0076] Fig. 9 This is a diagram of the control torque variation in the anti-off-target tracking control according to an embodiment of the present invention. DETAILED DESCRIPTION

[0077] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0078] For the sake of clarity, the meanings of the relevant variable symbols used in the present invention are shown in Table 1 below.

[0079] Table 1 Meaning of variables or symbols

[0080]

[0081]

[0082] 1. Overall concept of the present invention

[0083] As a new type of target imaging observation satellite, video satellites have unique advantages such as short R&D cycle, fast response speed, and high-resolution real-time continuous imaging capabilities. They are widely used in disaster prediction, resource survey, moving target monitoring and other fields.

[0084] In order to solve the problem that the target field of view is easily lost when the target first enters the camera field of view in the case of a large relative angular velocity in the video satellite visual tracking application, the present invention proposes a space target anti-missing tracking control method for the video satellite, and the overall idea is as follows:

[0085] Firstly, the correspondence between the position coordinates of the target position in the geocentric inertial system and the image plane projection position is established based on the perspective projection principle in combination with the position, attitude and onboard camera parameters of the video satellite. Then, the attitude kinematic equation and attitude dynamic equation of the video satellite are further established. Next, the attitude error quaternion and attitude error angular velocity of the video satellite are calculated based on the image plane projection position of the space target. Next, the imaging restriction area is designed in the image plane, and the logarithmic convex potential function described by the error quaternion is constructed. Finally, based on the logarithmic convex potential function and the attitude error angular velocity of the video satellite, the anti-missing tracking controller of the video satellite is designed, and the stability of the closed-loop system is proved by the Barbalat lemma. The effectiveness of the control method is verified by numerical simulation.

[0086] 2. Specific implementation steps of the present invention

[0087] Based on the above general idea, the specific implementation process of the control method of the present invention includes the following steps: Figure 1 The five steps S1-S5 shown are described in detail as follows:

[0088] Step S1, based on the perspective projection principle, establish a corresponding relationship between the position coordinates of the space target in the geocentric inertial system and the projection position of the image plane;

[0089] First, define the relevant coordinate system:

[0090] Earth-centered inertial system O i -X i Y i Z i : Select J2000.0 coordinate system, the origin of the coordinate system is O i Located at the center of the earth, i X i Pointing to the J2000.0 mean vernal equinox, O i Z i The axis points to the pole of the J2000.0 flat equator, O i Y i With O i X i Axis and O i Z i The axes form a right-handed coordinate system.

[0091] Satellite body coordinate system O b -X b Y b Z b :Origin of coordinate system O b Located at the satellite's center of mass, the three coordinate axes are along the three directions of the satellite's main inertia axis.

[0092] Pixel coordinate system O'-uv: The origin of the coordinate system O' is located at the upper left corner of the image plane, the O'u axis and the O'v axis are parallel to the rows and columns of the image plane respectively, and the coordinate unit is pixel. Generally speaking, the image plane is a rectangle.

[0093] Camera coordinate system O c -X c Y c Z c :Coordinate origin O c Located in the optical center of the camera, O c Z c The axis direction coincides with the camera optical axis and points perpendicularly to the camera image plane; c X c Axis and O c Y c The axes are parallel to the O'u axis and O'v axis in the pixel coordinate system and have the same direction.

[0094] Then, based on the perspective projection principle, a camera internal and external parameter model is established to show how the space target described in the geocentric inertial system is projected onto the image plane of the satellite camera through imaging geometry:

[0095] like Figure 2 As shown, the internal projection of the camera reflects the conversion relationship between the three-dimensional coordinates of the space target in the camera coordinate system and the two-dimensional coordinates in the pixel coordinate system.

[0096] The focal length of the camera is f; the coordinates of the pixel point where the camera optical axis intersects the image plane are (u0 v0) T , which is usually at the center of the image plane; du and dv are the horizontal and vertical dimensions of the pixel respectively; the position coordinates of the space target in the camera coordinate system are c R cT =(x c y c z c ) T , expressed in pixel coordinates as (uv) T According to the pinhole imaging perspective projection principle, using homogeneous coordinate representation, we have:

[0097]

[0098] Where Π∈R 3×4 It is a matrix determined by the intrinsic parameters of the camera.

[0099] like Figure 3 As shown in , the camera external imaging model describes the conversion relationship between the coordinates of the target in the inertial system and the coordinates in the camera system. i R ib is the position coordinate of the video satellite in the geocentric inertial system, i RiT is the position coordinate of the space target in the geocentric inertial system, b R bT The vector pointing from the video satellite to the space target is expressed in the satellite body coordinate system. Based on the geometric relationship, we have:

[0100]

[0101] In the formula represents the transformation matrix from the geocentric inertial system to the satellite body coordinate system, and T represents the transformation matrix determined by the position and attitude of the video satellite.

[0102] Without loss of generality, assuming that the camera has been accurately calibrated and the camera coordinate system coincides with the satellite body coordinate system, the following relationship exists:

[0103] c R cT = b R bT (3)

[0104] Combining equations (1), (2) and (3), we have:

[0105]

[0106] Where M = Π·T∈R 3×4 is a matrix determined by the video satellite and camera parameters. is the i-th row vector of matrix M, equation (4) can be rewritten as:

[0107]

[0108]

[0109] Step S2, establishing the video satellite attitude kinematics and dynamics equations;

[0110] 1) Attitude kinematics equation

[0111] The attitude kinematic equation of the video satellite describes the relationship between various motion parameters.

[0112] Euler's rotation theorem shows that the attitude of a rigid satellite can be determined by rotating it around an axis vector e∈R 3×1 Rotate the angle γ∈R to change from a given direction to any other direction. The axis vector e is the Euler axis vector, and the angle γ is the Euler angle. The present invention uses the quaternion from the geocentric inertial system to the satellite body coordinate system Describes the satellite attitude, where q0 is the scalar quaternion q, q v =(q1 q2 q3) Tis the vector of quaternion q. The quaternion q has the following relationship with the Euler axis vector e and the Euler angle γ:

[0113]

[0114] In the formula, the Euler axis vector e is a unit direction vector, so the quaternion satisfies the normalization condition ||q||=1.

[0115] The attitude kinematic equation described by the quaternion q is:

[0116]

[0117] Where ω∈R 3×1 is the description of the angular velocity of the satellite body coordinate system relative to the geocentric inertial system in the satellite body coordinate system. The superscript “·” indicates the derivative of the variable. Represents a quaternion multiplication operation.

[0118] 2) Posture dynamics equation

[0119] The video small satellite attitude dynamics equation describes the relationship between the applied torque and attitude motion.

[0120] The video satellite adopts the rigid body assumption and ignores the interference torque. The attitude dynamics equation is:

[0121]

[0122] Where J∈R 3×3 is the moment of inertia matrix of the video satellite, u c ∈R 3×1 is the attitude control torque.

[0123] Step S3, calculating the attitude error quaternion and attitude error angular velocity of the video satellite based on the image plane projection position of the space target;

[0124] 1) Error quaternion solution

[0125] Combination Figure 2 The perspective projection model shown in the figure, the target position direction vector in the camera coordinate system is represented by r t , it is related to c R cT Collinear, and have:

[0126] r t =(x pt y pt f) T (10)

[0127] Where x pt and pt Respectively represent the target projection point in the camera coordinate system Oc X c Axis and O c Y c The coordinates of the axes have the following relationship:

[0128]

[0129] Note o is the direction vector of the camera optical axis in the camera coordinate system:

[0130] r o =(0 0 f) T (12)

[0131] The purpose of attitude control is to make the projection of the target in the image plane located at the center. The attitude error can be defined as the direction vector r from the target position in the camera coordinate system. t To the camera optical axis direction vector r o Therefore, the video satellite’s attitude error quaternion q e It can be expressed as:

[0132]

[0133] Where a is the Euler axis vector and θ is the Euler angle, both of which can be expressed as r t and r o express:

[0134]

[0135]

[0136] Where arccos is the inverse cosine function.

[0137] 2) Error angular velocity solution

[0138] The angular velocity of the attitude error cannot be directly obtained through the target projection position at a certain moment, but it can be solved through the continuous change of pixel coordinates over a period of time.

[0139] Combining the attitude quaternion q of the video satellite and the error quaternion q obtained by formula (13) e , the desired attitude quaternion q can be obtained d , whose expression is:

[0140]

[0141] The superscript “*” in the formula represents the conjugate quaternion, that is, for the error quaternion have:

[0142]

[0143] where q e0 Scalar representing the error quaternion, q ev =(q e1 q e2 q e3 ) T Vector representing the error quaternion.

[0144] For the expected quaternion q d Differentiation The expected angular velocity ω of the video satellite can be calculated by the following formula d :

[0145]

[0146] The superscript "T" in the formula indicates the transpose of the matrix, Ξ(q d ) can be defined by the following formula:

[0147]

[0148] Where q d0 and q d1 ,q d2 ,q d3 Represent the desired attitude quaternion q d A scalar and a vector of three elements.

[0149] Therefore, the error angular velocity ω e It can be obtained by the following formula:

[0150] ω e =ω-A(q e )ω d (20)

[0151] Where A(q e ) represents the error quaternion q e The transformation matrix represented by satisfies the following relationship:

[0152]

[0153] Where I 3×3 Represents the third-order identity matrix, the superscript "×" represents the skew-symmetric operator, for any vector x = (x1 x2x3) T ,have:

[0154]

[0155] Step S4, designing an imaging restriction area in the image plane, and constructing a logarithmic convex potential function described by the attitude error quaternion;

[0156] The target imaging restricted area selection is shown as follows Figure 4As shown in the figure, the black frame boundary is the image plane boundary, and the gray shadow area (the maximum inscribed circle of the rectangular field of view) is selected as the target projection position restriction area, that is, the target imaging pixel point is always required to be located in the gray shadow area to ensure that the target does not leave the field of view and has a good observation field of view. In order to facilitate the establishment of the connection between the projection restriction area and the satellite attitude, considering that the camera is fixed to the satellite body, the present invention converts the target imaging projection range constraint into the target position direction vector r under the camera system t and the optical axis direction vector r o Angle constraint. Figure 4 As shown in , when the target image is located at the boundary of the restricted area, the target position direction vector in the camera coordinate system is r b . r b With the optical axis vector r o The angle is θ max , which is the maximum allowable angle between the optical axis and the target under satellite attitude control. From the geometric relationship:

[0157]

[0158] Where u s and v s They represent the number of horizontal and vertical pixels on the image plane respectively, and arctan represents the inverse tangent function.

[0159] Therefore, the Euler angle θ obtained by equation (15) should satisfy:

[0160] 0≤θ<θ max (twenty four)

[0161] Obviously, θ max is a quantity not greater than the camera's field of view, which is less than 90°, so we can get:

[0162]

[0163] Then when the target projection satisfies the constraint condition, that is, the imaging position is within the restricted area, the set of error quaternions Q e satisfy:

[0164]

[0165] Based on the inequality condition expressed by equation (25), the present invention constructs a method consisting of the error quaternion q e The logarithmic potential function described by:

[0166]

[0167] Where k1 is a positive constant, a is a positive constant and makes Uniformly distributed between 0 and 1.

[0168] According to the error quaternion q e Definition, formula (27) can be rewritten as:

[0169]

[0170] Combined with the mathematical condition that the target projection is within the restricted area, when When (1-q e0 )=0 and is equal to a certain real constant, so V(q e )=0; when q e ∈Q e And q e ≠(1 0) T When V(q e )>0, and when the projection position approaches the boundary of the restricted range, θ→θ max ,at this time So the potential function will approach infinity. So q e =(1 0) T is the global minimum point of the potential function.

[0171] The following proves that the designed potential function is a convex function, so that q e =(1 0) T It is also a local minimum point, which ensures that there is a potential energy decreasing trend that makes the target projection gradually converge to the desired position.

[0172] For a multivariable function, to prove that it is a convex function, we can prove that its Hessian matrix (second-order gradient matrix) is positive. The first-order gradient matrix of the potential function is:

[0173]

[0174] Further calculating the gradient of formula (29), we get the Hessian matrix (second-order gradient):

[0175]

[0176] Multiply both sides of formula (30) by and q e , and when the video satellite attitude meets the constraints, compared with q e0 For example, q e1 ,q e2 and q e3 can all be considered zero, and the equation can be simplified to:

[0177]

[0178] According to the value range of each variable, it is easy to get Therefore, the positive definiteness of the Hessian matrix is ​​proved and the designed potential function is a convex function.

[0179] Step S5, designing a video satellite anti-missing visual tracking controller based on the logarithmic convex potential function and the attitude error angular velocity of the video satellite;

[0180] The purpose of the video satellite anti-missing visual tracking controller designed in the present invention is to eliminate the attitude quaternion error and angular velocity error, and to ensure that the target projection is always located in the imaging restriction area during the control process. e ) and error angular velocity ω e , construct the augmented function V t as follows:

[0181]

[0182] It is obvious that V t ≥0, combined with attitude kinematics, dynamic equations and formula (20), V t The derivative with respect to time is:

[0183]

[0184] Where vec(·) represents the vector part of (·).

[0185] The anti-missing tracking controller designed by the present invention is as follows:

[0186]

[0187] Where k2 is a positive constant.

[0188] The basic idea of ​​the controller design is to provide a large control torque to prevent the target from leaving the field of view when the error angular velocity is large or the target perspective projection deviates from the expected position and approaches the boundary of the restricted area. When the target projection approaches the center of the image plane when approaching the expected posture, a very small control torque is provided to eliminate the deviation caused by the orbital motion of the target and the video satellite, and maintain visual tracking of the moving target.

[0189] The stability analysis of the controller is carried out, and the designed anti-missing tracking control law is substituted into equation (33), and the expression can be obtained:

[0190]

[0191] So the function V t is monotonically decreasing, since V t ≥0, so 0≤V t ≤V t (0), that is, Vt is bounded. Take V t The second derivative of :

[0192]

[0193] Since V t is bounded, so we can get q e and ω e are all bounded. Due to the boundedness of the above variables, we can determine is also bounded. According to Barbalat's lemma, we can get:

[0194]

[0195] Right now:

[0196]

[0197] Substituting equation (20) and attitude control law (34) into the attitude dynamics equation, we get:

[0198]

[0199] According to the conclusion Easy to get Therefore, from formula (39), we can get Combining the expression (29), we can conclude that Therefore, the stability of the proposed potential function-based anti-missing tracking controller is demonstrated, and the closed-loop system is asymptotically stable and can achieve the desired attitude control target.

[0200] 3. Simulation Analysis and Effect Verification

[0201] The anti-missing tracking control method proposed in the present invention was numerically simulated and verified by MATLAB software.

[0202] 1) Main simulation parameters

[0203] The orbital elements of the video satellite and space target are shown in Table 1:

[0204] Table 1 Orbital elements of video small satellites and space targets

[0205]

[0206] The parameters of the onboard camera are shown in Table 2:

[0207] Table 2 Camera parameter table

[0208] f <![CDATA[u s ]]> <![CDATA[v s ]]> <![CDATA[u0]]> <![CDATA[v0]]> du dv 0.8m 3200 2900 1600 1450 <![CDATA[7×10 -6 m]]> <![CDATA[7×10 -6 m]]>

[0209] Satellite moment of inertia:

[0210] Video satellite initial attitude quaternion: (-0.2251 -0.9241 0.2653 -0.1718) T ;

[0211] Video satellite initial angular velocity: (0.8365 0.9740 0) T ° / s.

[0212] The potential function and controller parameters are taken as:

[0213] a=10000k1=10k2=8

[0214] The reaction force flywheel installed orthogonally along the satellite body axis is used as the attitude control actuator of the present invention, and the maximum value of its output control torque is 0.6N·m.

[0215] 2) Simulation results and analysis

[0216] Under the designed simulation parameter conditions, the simulation results of anti-missing tracking control are as follows: Figure 5-Figure 9 shown.

[0217] From the above simulation diagram, we can get:

[0218] Figure 5 At the initial moment, the video satellite is only at O b X b and O b Y b There are certain initial error quaternions in both directions. This is because the distance from the video satellite to the space target cannot be obtained based on the pixel coordinates of the projection point on the image plane. The visual tracking of the video satellite to the space target is a kind of optical axis pointing control that does not rely on distance information. After the video satellite has adjusted its attitude for 7.8 seconds, the attitude error is eliminated, the optical axis points to the space target and maintains a stable tracking state. It can also be seen from the figure that the deviation at the initial moment is relatively small, because the image-based non-cooperative target tracking is based on the premise that the target appears in the image plane. Due to the limitation of the field of view, the pointing control of the optical axis of the camera on the video satellite is a small angle adjustment.

[0219] Figure 6 At the initial moment, at O b X b Direction and O b Y b There is a relatively large initial error angular velocity in the direction, indicating that there is a large relative motion between the video satellite and the target. At this time, the target can easily leave the camera's visual plane and cause loss of vision. As time changes, the error angular velocity ω eIt is gradually eliminated under the action of the anti-missing controller and finally converges to 0, achieving stable tracking.

[0220] Figure 7 In the figure, (a) is the trajectory of the projection position of the space target on the image plane. It can be seen from the figure that the target appears in the image plane at the initial moment. Due to the large error angular velocity, the target produces a relative motion that deviates from the image plane. However, under the action of the potential function-based anti-missing controller, the target imaging position is always kept within the restricted area and eventually reaches the desired projection position. (b) is a graph showing the change in the projection position deviation of the space target on the image plane. It can also be seen that as the video satellite attitude is adjusted, the pixel deviation gradually decreases and is eventually completely eliminated.

[0221] Figure 8 In the figure, (a) is the real-time change curve of the potential function value, and (b) is the change of the camera optical axis angle deviation. It can be seen from the figure that the two curves have the same trend, which illustrates the corresponding relationship between the deviation angle and the potential function value. The larger the deviation, the larger the potential function value. When the directivity deviation angle decreases to 0, the potential function converges to 0 and remains stable. Therefore, the system can run from high to low along the potential function, avoiding the regional restriction boundary and approaching the global equilibrium point of the system. There are two upward changes in the process of the two curves sliding downward. This is due to the large relative motion of the video satellite and the overshoot in the control process. As the error angular velocity and overshoot are gradually eliminated, the downward trend of the curve change is restored.

[0222] Fig. 9 In the process, the change of control torque is affected by the potential function and the error angular velocity. When the error angular velocity is large in the initial stage and the target projection is close to the edge of the restricted area, the potential function value increases, the control torque rises and reaches the maximum output amplitude; when the angular velocity error gradually decreases and the potential function gradually decreases, the control output torque gradually decreases. After the system reaches the global equilibrium point, the control torque is maintained at a very small value to eliminate the slight attitude deviation caused by the orbital motion of the space target and the video satellite.

[0223] Therefore, it can be concluded that the control method designed by the present invention is simple and effective, which can make the projection of the target in the field of view always located in the restricted area and finally reach the expected coordinate position, and the image error converges to zero. The method proposed by the present invention is of great significance for the visual image capture and anti-missing tracking control of space targets with large relative motion with the video satellite, which is conducive to strengthening the space situation awareness capability of the video satellite.

[0224] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A method for preventing a space target from missing a target and tracking a video satellite. When performing anti-missing tracking control on a space target, a potential function V(q e ) performs attitude control on the video satellite, and is characterized in that: The function expression of the anti-missing visual tracking controller is: In the formula, u c is the control torque output by the anti-missing visual tracking controller; k2 is the positive constant; q e is the attitude error quaternion of the video satellite; ω e is the angular velocity of the video satellite’s attitude error; ω is the description of the angular velocity of the satellite body coordinate system relative to the geocentric inertial system in the satellite body coordinate system; ω d is the expected angular velocity; is the potential function V(q e ) first-order gradient; J is the moment of inertia of the video satellite; the superscript * represents the conjugate of the variable; the superscript · represents the derivative of the variable; the symbol represents quaternion multiplication; vec(·) represents the vector part of the variable; A(q e ) is the error quaternion q e The transformation matrix represented by , and satisfies: where q e0 is the scalar error quaternion, q ev is the error quaternion; I 3×3 Represents the third-order identity matrix, the superscript × represents the skew-symmetric operator, for any vector x = (x1 x2 x3) T , there is an expression:

2. The space target anti-missing tracking control method of the video satellite according to claim 1, characterized in that: The preset potential function V(q e ) is constructed as follows: First, design the imaging restriction area of ​​the video satellite: The maximum inscribed circle of the rectangular field of view is taken as the target imaging restriction area. It is required that the projection position of the target image plane is always within the area to ensure that the target does not leave the field of view and has a good observation field of view. The real-time position direction vector r of the target in the camera coordinate system is t and the optical axis direction vector r o The angle θ should satisfy the following relationship: 0≤θ<θ max , In the formula, θ max is the target position direction vector r in the camera coordinate system when the projection position of the target in the image plane is at the boundary of the restricted area b and the optical axis direction vector r o The angle, θ max The expression is: In the formula, u s and v s are the number of horizontal and vertical pixels on the image plane, du and dv are the horizontal and vertical sizes of the pixels, f is the focal length of the camera; arctan is the inverse tangent function; Then, according to the imaging restriction area, the error quaternion q is constructed as follows e The potential function V(q e ): Where q e is the vector of attitude error quaternion, q e0 is the attitude error quaternion q e scalar; k1 is a positive constant, a is a positive constant and makes Uniformly distributed between 0 and 1; V(q e ) is a logarithmic convex potential function; when the image plane projection position of the space target is within the imaging restriction area, the potential function satisfies V(q e )≥0, and if and only if the error quaternion q e =(1 0) T When the potential function V(q e ) obtains the local minimum value, which is also the global minimum value and is zero; when the image plane projection position of the space target approaches the boundary of the restricted area, the potential function V(q e ) approaches infinity.

3. The space target anti-missing tracking control method of the video satellite as claimed in claim 1, characterized in that: The use of a preset potential function V(q e ) also includes the following steps before the anti-missing visual tracking controller performs attitude control on the video satellite: S1. Based on the perspective projection principle, the corresponding relationship between the position coordinates of the space target in the geocentric inertial system and the projection position on the image plane is established; S2. Establish the attitude kinematic equation and attitude dynamic equation of the video satellite; S3. Based on the image plane projection position of the space target, the attitude error quaternion and attitude error angular velocity of the video satellite are calculated.

4. The space target anti-missing tracking control method of the video satellite as claimed in claim 3 is characterized in that: The mathematical expression of the corresponding relationship between the position coordinates of the space target in the geocentric inertial system and the image plane projection position in step S1 is: Where u and v are the horizontal and vertical coordinates of the target projection point in the pixel coordinate system respectively; u0 and v0 are the horizontal and vertical coordinates of the pixel point where the camera optical axis intersects the image plane; du and dv are the horizontal and vertical sizes of the pixel point; f is the focal length of the camera; i R iT is the position coordinate of the space target in the geocentric inertial system; i R ib is the position coordinate of the video satellite in the geocentric inertial system; is the transformation matrix from the geocentric inertial system to the satellite body coordinate system; c It is the Z-axis coordinate of the space target in the camera coordinate system.

5. The space target anti-missing tracking control method of the video satellite as claimed in claim 3 is characterized in that: The attitude kinematic equation of the video satellite established in step S2 is: Where q is the attitude quaternion of the video satellite, ω is the description of the angular velocity of the satellite body coordinate system relative to the geocentric inertial system in the satellite body coordinate system; the superscript "·" represents the derivative of the variable, and the symbol Represents quaternion multiplication operation; The attitude dynamics equation of the established video satellite is: Where J is the moment of inertia matrix of the video satellite, u c is the attitude control torque.

6. The space target anti-missing tracking control method of the video satellite as claimed in claim 3 is characterized in that: The calculation formula of the attitude error quaternion of the video satellite in step S3 is: Where q e is the attitude error quaternion of the video satellite; a is the Euler axis vector, and the expression of a is: where r t =(x pt y pt f) T is the target position direction vector in the camera coordinate system, r o =(0 0 f) T is the optical axis direction vector in the camera coordinate system, x pt =(u-u0)·du,y pt =(v-v0)·dv, where u and v are the horizontal and vertical coordinates of the target projection point in the pixel coordinate system respectively; u0 and v0 are the horizontal and vertical coordinates of the pixel point where the camera optical axis intersects the image plane; du and dv are the horizontal and vertical sizes of the pixel point; f is the focal length of the camera, θ is the Euler angle, and the expression of θ is: Where arccos represents the inverse cosine function, The calculation process of the attitude error angular velocity of the video satellite is: First, solve the video satellite's expected attitude quaternion q d , the expression is: In the formula, the superscript * represents the conjugate of the vector, q represents the attitude quaternion of the video satellite, Then calculate the expected angular velocity ω of the video satellite d , the expression is: Where superscript · is the derivative of the variable, superscript T is the transpose of the matrix; Ξ(q d ) is the desired attitude quaternion q d The matrix described is expressed as: Where q d0 and q d1 ,q d2 ,q d3 Represent the desired attitude quaternion q d The scalar and vector of three elements, Finally, solve the attitude error angular velocity ω of the video satellite e for: oh e =ω-A(q e )oh d , Where ω is the description of the angular velocity of the satellite body coordinate system relative to the Earth's center inertial system in the satellite body coordinate system; A(q e ) is the error quaternion q e The transformation matrix represented by satisfies the following relationship: where q ev is the vector of error quaternions.

7. A potential function-based video satellite space target anti-missing tracking control system, comprising a microprocessor and a memory connected to each other, characterized in that: The microprocessor is programmed or configured to execute the steps of the space target anti-missing tracking control method for the video satellite as described in any one of claims 1 to 6, or the memory stores a computer program programmed or configured to execute the space target anti-missing tracking control method for the video satellite as described in any one of claims 1 to 6.

8. A video satellite, comprising a satellite body, wherein the satellite body comprises a microprocessor and a memory connected to each other, characterized in that: The microprocessor is programmed or configured to execute the steps of the space target anti-missing tracking control method for the video satellite as described in any one of claims 1 to 6, or the memory stores a computer program programmed or configured to execute the space target anti-missing tracking control method for the video satellite as described in any one of claims 1 to 6.

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