Design method of attitude dimension reduction for dual-satellite formation tracking and aiming joint tracking

Abstract

The present invention provides a dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method, which includes the following steps: Step 1: Based on the orbital information of the satellite obtained by ground measurement and control and the target satellite obtained by tracking and aiming measurement, establish the orbital recursion of the satellite and the target satellite, obtain the relative position of the satellite and the target satellite in the geocentric inertial system, and establish a relative motion model of the two satellites; Step 2: Establish a unique non-singular tracking imaging rectangular coordinate system as a reference coordinate system for attitude determination; Step 3: Convert inter-satellite data to the reference coordinate system and establish an attitude equation; Step 4: Differentiate the motion equation of the reference coordinate system, derive a motion characteristic description method, and combine it with the angular velocity calculation method of the attitude reference coordinate system to complete the description of the motion characteristics of the reference coordinate system. The present invention can expand the application scope of target satellite tracking and imaging, making it effective under more complex orbits and more flexible formation distances.

Description

Technical Field

[0001] The present invention belongs to the field of autonomous satellite formation, and in particular relates to a method for designing attitude dimension reduction in joint tracking of two-satellite formation motion and aiming. Background Art

[0002] The development of aerospace technology requires that satellites can autonomously realize tasks such as formation, space rendezvous and docking, on-orbit satellite capture and maintenance, and deep space exploration, and attitude tracking technology is its key technology. Attitude tracking refers to the satellite completing the tracking and attitude aiming of the target satellite through the onboard computer, onboard relative measurement equipment, and ground orbit determination data. The onboard relative measurement equipment includes microwave radar and imaging camera, etc., so there is no need for response information from the target satellite, and it provides the line-of-sight distance and two line-of-sight angle information to the target satellite. In the approach imaging mission condition of the target satellite, the target satellite moves faster, and in a short period of time, the target motion trajectory forms a plane with a certain flatness in the formation binary satellite orbit system (such as Figure 1 As shown in Figure 1, the trajectory of the motion is approximately within a plane. By offsetting the satellite system in the orbital system, the imaging camera's optical axis motion plane can be rotated to the target's motion plane, reducing the two-dimensional projection of the target motion to a one-dimensional projection. This allows the satellite to track and control the target with only one-dimensional attitude maneuvers. The high-dynamic tracking capability of the satellite's rotation is utilized to continuously track and monitor the target. Summary of the Invention

[0003] The purpose of the present invention is to provide a dual-star formation tracking and aiming joint tracking attitude dimensionality reduction design method, which can expand the application scope of target star tracking and imaging, making it effective in more complex orbits and more flexible formation distances.

[0004] To achieve the above-mentioned object, the present invention provides a dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method, which comprises the following steps: step 1: establishing orbital recursion of the satellite and the target star based on the orbital information of the satellite obtained by ground measurement and control and the target star obtained by tracking and aiming measurement, obtaining the relative position of the satellite and the target star in the geocentric inertial system, and establishing a relative motion model of the two stars; step 2: establishing a unique non-singular tracking imaging rectangular coordinate system as a reference coordinate system for attitude determination; step 3: converting inter-satellite data into the reference coordinate system and establishing an attitude equation; step 4: performing differentiation on the motion equation of the reference coordinate system, deriving a motion characteristic description method, and combining the angular velocity calculation method of the attitude reference coordinate system to complete the description of the motion characteristics of the reference coordinate system.

[0005] Preferably, the relative motion model of the two stars is represented by a target azimuth vector, and the target azimuth vector is obtained in the following two ways: 1. When ground orbit determination data is available, the orbit determination information of the target star and the satellite is directly used, and the orbit determination information of the target star and the satellite is directly used, combined with the attitude information of the satellite output by the star sensor and the installation matrix of each sensor on the satellite, to establish a first target azimuth vector; 2. When ground orbit determination data is not available and relative navigation on the satellite is available, the relative position relationship between the satellite and the target star is obtained by the relative navigation filtering result, and a second target azimuth vector is established.

[0006] Preferably, when the ground measurement track is valid, the first target orientation vector is expressed as follows:

[0007]

[0008] in: The expression of the first target azimuth vector of the satellite pointing to the target star in the geocentric inertial system; is the expression of the satellite's absolute position in the Earth-centered inertial system; is the expression of the absolute position of the target star in the geocentric inertial system.

[0009] Preferably, when the ground orbit determination is invalid and the relative navigation of the satellite is valid, the second target azimuth vector is expressed as follows:

[0010] A io =R z (-Ω)R x (-i)R z (-(ω+f))*R z (-pi / 2)R x (pi / 2)=[A iox A ioy A ioz ] 3×3

[0011]

[0012] in, The target azimuth vector of the satellite pointing to the target star is expressed in the geocentric inertial system; is the tracking measurement value; Ω,i,(ω+f) is the orbit parameter, ω is the argument of perigee, f is the true anomaly, Ω is the right ascension of the ascending node, and i is the orbit inclination, which is obtained by orbit recursion; R i (), i = x, y, z represents rotation around the x-axis, y-axis, and z-axis, and the rotation angle is the value in the brackets; A io is the attitude transformation matrix from the satellite orbit coordinate system to the Earth-centered inertial system.

[0013] Preferably, in step 2, the Y axis of the reference coordinate system is obtained by cross-producting the target pointing vector m beats ago and the target pointing vector of the current beat. Each coordinate axis of the reference coordinate system can be described by the following formula:

[0014]

[0015]

[0016]

[0017] in, are the expressions of the target azimuth vector of the satellite pointing to the target star in the geocentric inertial system at the current beat and m beats ago, respectively.

[0018] Preferably, the attitude conversion matrix from the Earth-centered inertial system to the reference coordinate system is:

[0019] A ti =[X i Y i Z i ] T .

[0020] Wherein, the subscript t represents the reference coordinate system, and the subscript i represents the Earth-centered inertial system.

[0021] Preferably, the expression for describing the posture in the reference coordinate system using the posture quaternion difference method in step 3 is as follows:

[0022]

[0023] Among them, q bt is the attitude quaternion of the satellite's own system to the reference coordinate system; q it Quaternion for attitude conversion from geocentric inertial system to reference coordinate system; The quaternion estimate of the inertial to satellite system is output from the star sensor + gyro Kalman filter. The subscript b in the expression represents the satellite system.

[0024] Preferably, the method for calculating the angular velocity of the reference coordinate system in step 4 includes the following formula for solving the rotational angular velocity:

[0025]

[0026] Among them, (ω ti ) t Angular velocity of the reference coordinate system; (ω ti ) t (k+1) is the angular velocity of the current beat reference coordinate system; q ti (k+1),q ti(k) are the quaternions of the current beat and the previous beat of the reference coordinate system relative to the geocentric inertial system; T s It is the time interval from k beat to k+1 beat, which is generally the control cycle of the control system.

[0027] Preferably, the angular velocity of the satellite relative to the reference coordinate system is expressed in the satellite system as:

[0028] (ω tb ) b =(ω ib ) b -A bt (ω it ) t

[0029] Among them, (ω ib ) b is the angular velocity of the satellite relative to the Earth's inertial system expressed in the satellite's own system, (ω it ) t is the angular velocity of the reference coordinate system, A bt is the attitude transformation matrix from the satellite's local coordinate system to the reference coordinate system.

[0030] In summary, compared with the prior art, the design method for attitude dimensionality reduction of dual-satellite formation tracking and aiming combined tracking provided by the present invention has the following beneficial effects: (1) The present invention solves the influence of uncertainty and rapidity of following the target satellite on the control, and uses the ground measurement and control / navigation and attitude sensor measurement data to obtain the angle required for continuous tracking of the dynamic target through the attitude tracking algorithm; (2) By solving the angular velocity information of the attitude reference system, the target angular motion trajectory is predicted, and a feedforward control link is introduced to improve the closed-loop stable control accuracy; (3) The present invention provides an attitude quaternion difference method, which has the advantages of simple calculation and less calculation amount on the satellite. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Schematic diagram of a plane with a certain flatness formed by the target motion trajectory of the present invention in the formation binary orbit system;

[0032] Figure 2 This is a flow chart of the dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method of the present invention;

[0033] Figure 3 The reference coordinate system selected for the dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method of the present invention;

[0034] Figure 4 This is a schematic diagram of a satellite formation to which the dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method of the present invention is applicable. DETAILED DESCRIPTION

[0035] The following will be combined with the appended Figure 1 ~Attached Figure 4 , the technical solutions, structural features, objectives achieved and effects in the embodiments of the present invention are described in detail.

[0036] It should be noted that the drawings are in a very simplified form and use non-precise proportions. They are only used to conveniently and clearly assist in explaining the embodiments of the present invention, and are not used to limit the conditions for the implementation of the present invention. Therefore, they have no substantive technical significance. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the efficacy and purpose that can be achieved by the present invention.

[0037] It should be noted that, in the present invention, relational terms such as first and second, etc. are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only the elements explicitly listed, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0038] Since attitude measurement, ground measurement and control / relative navigation and relative pointing attitude determination are the prerequisites for completing joint tracking control, the present invention provides a dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method, such as Figure 1 As shown, the following steps are included:

[0039] Step 1: Based on the orbital information of the satellite obtained by ground measurement and control and the target satellite obtained by tracking and aiming, establish the orbital recursion of the satellite and target satellite, obtain the relative position of the satellite and target satellite in the geocentric inertial system, and establish the relative motion model of the two satellites;

[0040] Step 2: Establish a unique tracking imaging rectangular coordinate system without singularity as the reference coordinate system for attitude determination;

[0041] Step 3: Convert the intersatellite data to the reference coordinate system and establish the attitude equation;

[0042] Step 4: Differentiate the motion equation of the reference coordinate system, derive the motion characteristics description method, and combine it with the calculation method of the angular velocity of the attitude reference coordinate system to complete the description of the motion characteristics of the reference coordinate system.

[0043] Among them, such as Figure 1As shown, in the step 1, due to the relatively fast relative motion speed of satellite 2 and target star 1, the motion trajectory of target star 1 has a certain flatness in the binary orbit system composed of target star orbit 11 and satellite orbit 21 in a short time. The offset of satellite 2 in satellite orbit 21, that is, the motion plane of the camera optical axis on satellite 2 is rotated to the target motion plane, so that the two-dimensional projection of the motion of target star 1 is reduced to a one-dimensional projection, so that satellite 2 only needs one-dimensional attitude maneuver to complete the tracking and pointing control of target star 1, thus completing the dimensionality reduction design.

[0044] Furthermore, the relative motion model of the two satellites is represented by a target azimuth vector, and the target azimuth vector is obtained by the following two methods: 1. When ground orbit determination data is available, the orbit determination information of the target star and the satellite is directly used, combined with the attitude information of the satellite output by the star sensor and the installation matrix of each sensor on the satellite, to establish a first target azimuth vector; 2. When ground orbit determination data is not available and relative navigation on the satellite is available, the relative position relationship between the satellite and the target star is obtained by the relative navigation filtering result, and a second target azimuth vector is established.

[0045] When the ground measurement track is valid, the first target orientation vector is expressed as follows:

[0046]

[0047] in: is the expression of the first target azimuth vector of satellite 2 pointing to target satellite 1 in the geocentric inertial system; is the expression of the absolute position of satellite 2 in the geocentric inertial system; is the expression of the absolute position of target satellite 1 in the geocentric inertial system.

[0048] When the ground orbit determination is invalid and the relative navigation of the satellite is valid, the second target azimuth vector is expressed as follows:

[0049] A io =R z (-Ω)R x (-i)R z (-(ω+f))*R z (-pi / 2)R x (pi / 2)=[A iox A ioy A ioz ] 3×3

[0050]

[0051] in, is the expression of the second target azimuth vector from satellite 2 to target satellite 1 in the geocentric inertial system; is the measurement value of the tracking and aiming unit on satellite 1; Ω,i,(ω+f) are orbital parameters, Ω is the right ascension of the ascending node, i is the orbital inclination, ω is the argument of perigee, and f is the true anomaly, which is obtained by orbit recursion; R i (), i = x, y, z represents rotation around the x-axis, y-axis, and z-axis, and the rotation angle is the value in the brackets; pi = 3.141592; A io is the attitude transformation matrix from the satellite orbit coordinate system to the Earth-centered inertial system.

[0052] Furthermore, the core of the design for attitude determination relative to the target satellite is to establish a tracking imaging coordinate system based on the target azimuth vector and the relative position information of the two satellites as the attitude reference coordinate system. This is described in step 2: establishing a unique, non-singular tracking imaging rectangular coordinate system as the reference coordinate system for attitude determination. The coordinate axes of this reference coordinate system are selected to ensure that the camera optical axis vector is perpendicular to the plane of the target satellite's trajectory.

[0053] The normal n between the camera optical axis vector and the target star motion trajectory plane is calculated using the following formula:

[0054]

[0055]

[0056]

[0057] in, is the unit vector of the normal line of the trajectory plane; t0 is the time when the satellite points to the target star vector at the starting point of tracking; r0=(x0 y0 z0) T is the coordinate of the tracking starting point at time t0 in the binary orbit system; t′0 is the time when the satellite points to the target star vector at any point near the tracking starting point; r′0=(x′0y′0z′0) T It is the coordinate of any point near the tracking starting point at time t'0 in the binary orbit system.

[0058] Specifically, in step 2, the Y axis of the reference coordinate system is obtained by cross-producting the target pointing vector m beats ago and the target pointing vector of the current beat. If the value of m is set to 20, then the coordinate axes of the reference coordinate system can be described by the following formula:

[0059]

[0060]

[0061]

[0062] in, are the expressions of the target azimuth vector of satellite 2 pointing to target satellite 1 in the geocentric inertial system at the current beat and m beats (assuming m = 20) respectively. It should be noted that the beat refers to the control period of satellite 2, which is related to the design of satellite 2 and is a fixed value; for example, if the control period is 0.5s, 20 beats is 10s, that is, They are the expressions of the target azimuth vector of satellite 2 pointing to target satellite 1 in the geocentric inertial system in the current control period and 10s ago respectively.

[0063] Furthermore, the attitude conversion matrix from the Earth-centered inertial system to the reference coordinate system is:

[0064] A ti =[X i Y i Z i ] T

[0065] Wherein, the subscript t represents the reference coordinate system, and i represents the Earth-centered inertial system.

[0066] Once the "tracking and imaging" attitude reference is established in step 2, that is, the attitude reference coordinate system is established, the formation tracking and aiming joint tracking task for target satellite 1 can be equivalent to conventional "attitude determination." The original tracking and aiming joint task is relatively complex, integrating orbit calculation, attitude calculation, and control. However, through the design and selection of the attitude reference system, the present invention transforms attitude and orbit joint control into simple attitude determination and control, completing the tracking and imaging task through attitude determination.

[0067] Furthermore, the expression for describing the posture in the reference coordinate system using the posture quaternion difference method in step 3 is as follows:

[0068]

[0069] Among them, q bt is the attitude quaternion of the satellite's own system to the reference coordinate system; q it Quaternion for attitude conversion from geocentric inertial system to reference coordinate system; The quaternion estimate of the inertial output from the star sensor + gyro Kalman filter to the satellite body; the subscript b in the expression represents the satellite body system.

[0070] In order to complete continuous tracking, imaging, and monitoring of the target satellite and ensure high-precision and high-stability tracking and imaging quality for the satellite platform, it is necessary to describe the motion characteristics of the reference coordinate system to provide information for subsequent angular motion trajectory estimation and feedforward control of the target satellite.

[0071] Specifically, the method for calculating the angular velocity of the reference coordinate system in step 4 includes the following formula for solving the rotational angular velocity:

[0072]

[0073] Among them, (ω ti ) t Angular velocity of the reference coordinate system; (ω ti ) t (k+1) is the angular velocity of the current beat reference coordinate system; q ti (k+1),q ti (k) are the quaternions of the current beat and the previous beat of the reference coordinate system relative to the geocentric inertial system; T s It is the time interval from k beat to k+1 beat, which is generally the control cycle of the control system.

[0074] Furthermore, the angular velocity of the satellite relative to the reference coordinate system is expressed in the satellite system as:

[0075] (ω tb ) b =(ω ib ) b -A bt (ω it ) t

[0076] Among them, (ω ib ) b is the angular velocity of the satellite relative to the Earth's inertial system expressed in the satellite's own system, (ω it ) t is the angular velocity of the reference coordinate system, A bt is the attitude transformation matrix from the satellite's local coordinate system to the reference coordinate system.

[0077] In summary, compared with the existing technology, the present invention obtains the orbital information of the satellite and target satellite through ground-based measurement and control, and then obtains the coefficients of the on-board autonomous orbit recursion and the target satellite recursion through fitting. The on-board orbit recursion and the target satellite orbit recursion are then performed to obtain the relative position information of the two satellites in the geocentric inertial system. At the same time, when there is no ground-based orbit measurement and control support, the autonomous navigation on the satellite can output the relative position information of the satellite and the target satellite in the orbital system. Then, based on the relative pointing attitude, the tracking imaging coordinate system is established based on the relative position information of the two satellites as the attitude reference coordinate system. Using the measurement data of the attitude sensor, the attitude equation is established, and the attitude angle and attitude angular velocity information of the satellite system relative to the reference coordinate system are calculated. This expands the application scope of target satellite tracking and imaging, making it effective in more complex orbits and more flexible formation distances.

[0078] Although the present invention has been described in detail through the above preferred embodiments, it should be understood that the above description is not intended to limit the present invention. After reading the above description, various modifications and substitutions of the present invention will become apparent to those skilled in the art. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method, characterized by: include: Step 1: Based on the orbital information of the satellite obtained by ground measurement and control and the target satellite obtained by tracking and aiming, the orbital recursion of the satellite and the target satellite is established, the relative position of the satellite and the target satellite in the geocentric inertial system is obtained, and the relative motion model of the two satellites is established; Step 2: Establish a unique tracking imaging rectangular coordinate system without singularity as the reference coordinate system for attitude determination; Step 3: Convert the intersatellite data to the reference coordinate system and establish the attitude equation; Step 4: Differentiate the motion equation of the reference coordinate system, derive the motion characteristics description method, and combine it with the calculation method of the angular velocity of the attitude reference coordinate system to complete the description of the motion characteristics of the reference coordinate system; The relative motion model of the two satellites is represented by a target azimuth vector, which is obtained by the following two methods:

1. When ground orbit data is available, directly use the orbit information of the target star and the satellite, directly use the orbit information of the target star and the satellite, combine the attitude information of the satellite output by the star sensor and the installation matrix of each sensor on the satellite, and establish a first target azimuth vector; 2. When ground-based orbit determination data is unavailable but relative navigation on the satellite is available, the relative position relationship between the satellite and the target satellite is obtained based on the relative navigation filtering result, and a second target azimuth vector is established; When the ground measurement track is valid, the first target orientation vector is expressed as follows: in: The first target azimuth vector pointing from the satellite to the target star is expressed in the geocentric inertial system When the ground orbit determination is invalid and the relative navigation of the satellite is valid, the second target azimuth vector is expressed as follows: A io =R z (-Ω)R x (-i)R z (-(ω+f))*R z (-pi / 2)R x (pi / 2)=[A iox A ioy A ioz ] 3×3 in, The target azimuth vector of the satellite pointing to the target star is expressed in the geocentric inertial system; is the tracking measurement value; Ω,i,(ω+f) is the orbit parameter, Ω is the right ascension of the ascending node, i is the orbit inclination, ω is the argument of perigee, f is the true anomaly, R i (), i = x, y, z represents the rotation around the x-axis, y-axis, and z-axis, and the rotation angle is the value in the brackets; it is obtained by recursion of the orbit; A io is the attitude transformation matrix from the satellite orbit coordinate system to the Earth-centered inertial system; In the step 2, the Y axis of the reference coordinate system is obtained by cross-producting the target pointing vector m beats ago and the target pointing vector of the current beat. The coordinate axes of the reference coordinate system can be described by the following formula: in, are the expressions of the target azimuth vector of the satellite pointing to the target star in the geocentric inertial system at the current beat and m beats ago, respectively.

2. The dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method according to claim 1, characterized in that: The attitude conversion matrix from the Earth-centered inertial system to the reference coordinate system is: A ti =[X i Y i Z i ] T Wherein, the subscript t represents the reference coordinate system, and the subscript i represents the Earth-centered inertial system.

3. The dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method according to claim 2, characterized in that: The expression for describing the posture in the reference coordinate system using the posture quaternion difference method in step 3 is as follows: Among them, q bt is the attitude quaternion of the satellite's own system to the reference coordinate system; q it Quaternion for attitude conversion from geocentric inertial system to reference coordinate system; The quaternion estimate of the inertial to satellite system is output from the star sensor + gyro Kalman filter. The subscript b in the expression represents the satellite system.

4. The dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method according to claim 3, characterized in that: The calculation method of the angular velocity of the reference coordinate system described in step 4 includes the following formula for solving the rotational angular velocity: Among them, (ω ti ) t Angular velocity of the reference coordinate system; (ω ti ) t (k+1) is the angular velocity of the current beat reference coordinate system; q ti (k+1),q ti (k) are the quaternions of the current beat and the previous beat of the reference coordinate system relative to the geocentric inertial system; T s It is the time interval from k beat to k+1 beat, which is generally the control cycle of the control system.

5. The dual-satellite formation tracking and aiming joint tracking attitude dimensionality reduction design method according to claim 4, characterized in that: The angular velocity of the satellite relative to the reference coordinate system is expressed in the satellite system as: (oh tb ) b =(ω ib ) b -A bt (oh it ) t Among them, (ω ib ) b is the angular velocity of the satellite relative to the Earth's inertial system expressed in the satellite's own system, (ω it ) t is the angular velocity of the reference coordinate system, A bt is the attitude transformation matrix from the satellite's local coordinate system to the reference coordinate system.

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