Attitude control method of SAR satellite sliding spotlight mode based on polynomial

Abstract

Aiming at the problem of attitude control of SAR satellite sliding beam mode, the present invention proposes a polynomial-based attitude control method for SAR satellite sliding beam mode. The method comprises: obtaining the projection of the three-axis pointing unit vector expected by the satellite at each discrete time point during the imaging of the sliding beam mode in the earth-fixed coordinate system according to the observation scene and satellite orbit information; converting the three-axis pointing expected by the satellite at each discrete time point during the imaging into the satellite Euler angle; fitting the satellite Euler angle at each discrete time point into a polynomial curve as the sliding beam imaging attitude curve by the least square fitting method; obtaining the attitude angular velocity curve, angular acceleration curve and angular acceleration curve according to the sliding beam imaging attitude curve, and then calculating the satellite attitude angle, angular velocity and angular acceleration at the start and end of imaging; thereby constructing the pre-imaging preset attitude curve and the post-imaging attitude return curve, and using the tracking control algorithm to realize the attitude control of the satellite over the whole process of the sliding beam mode.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite attitude control, and in particular to a polynomial-based SAR satellite sliding beam mode attitude control method, which is particularly suitable for SAR satellites that use attitude maneuvers to achieve sliding beam high-resolution imaging. Background Art

[0002] In order to meet the increasing demand for earth observation of SAR satellite systems, it is necessary to use ultra-wideband transmission signals combined with ultra-large rotation angle sliding beamforming mode to achieve high resolution in range and azimuth respectively.

[0003] In order to realize the ultra-high resolution sliding beam mode, in the prior art, Li Li proposed a method for realizing the satellite-borne SAR sliding beam mode through satellite attitude maneuvering in the patent "A satellite platform attitude maneuvering method for realizing the satellite-borne SAR ultra-high resolution sliding beam mode" (publication number: CN106291557A). The final output result of this method is the projection of the three-axis vector of the satellite platform required for imaging in the earth-fixed coordinate system. Based on the output result of this method, the three-axis Euler angle attitude required by the satellite can be further converted. However, this method can only derive the theoretical attitude of the satellite at each discrete time point during imaging, and does not contain information such as attitude angular velocity and angular acceleration, and cannot be directly applied to satellite attitude control. At the same time, it does not involve the control problem of how the satellite maneuvers from the initial attitude to the imaging attitude, and how to maneuver to the next desired attitude after the imaging is completed.

[0004] The current control method mainly uses the difference method to obtain the corresponding angular velocity and angular acceleration for attitude control. However, this requires the satellite to store the attitude angle information corresponding to each control cycle, which requires a large amount of storage space. In addition, when the attitude is differed, the angular velocity and angular acceleration data are not smooth, which can easily cause attitude jitter. Summary of the invention

[0005] Aiming at the attitude control problem of SAR satellite sliding beam mode, the present invention proposes a SAR satellite sliding beam mode attitude control method based on polynomial. Only polynomial coefficients need to be stored instead of point-by-point attitude data storage, which can reduce the storage demand of attitude data on board and ensure the continuity and stability of attitude angular velocity and angular acceleration in the whole imaging process. At the same time, the method takes into account the transition problem of the initial attitude before imaging and the next action attitude after imaging, and can be applied to the situation of multiple continuous sliding beam imaging.

[0006] The present invention is achieved through the following technical solutions.

[0007] A polynomial-based SAR satellite sliding beam mode attitude control method, comprising:

[0008] According to the observation scene and satellite orbit information, the projection of the satellite's expected three-axis pointing unit vector in the earth-fixed coordinate system at each discrete time point during the sliding beam mode imaging is obtained;

[0009] Converting the desired three-axis orientation of the satellite at each discrete time point during the imaging period into satellite Euler angles;

[0010] The least square fitting method is used to fit the satellite Euler angles at each discrete time point into a polynomial curve as the attitude curve of the sliding convergence imaging.

[0011] According to the attitude curve of the sliding convergence imaging, the attitude angular velocity curve, the angular acceleration curve and the angular jerk curve are obtained, and then the satellite attitude angle, angular velocity and angular acceleration at the start and end of imaging are calculated;

[0012] Based on the attitude angle, angular velocity, angular acceleration at the moment when the satellite sends the sliding mode command and the satellite attitude angle, angular velocity, angular acceleration, and angular jerk at the beginning of imaging, a polynomial curve is constructed as a preset attitude curve before imaging, and then the corresponding angular velocity, angular acceleration curve, and angular acceleration curve are obtained;

[0013] Based on the expected attitude angle, angular velocity, angular acceleration when the satellite completes payload shutdown and the satellite attitude angle, angular velocity, angular acceleration when imaging ends, a polynomial curve is constructed as the attitude return curve after imaging, and then the corresponding angular velocity, angular acceleration curve, and angular jerk curve are obtained;

[0014] The pre-imaging preset attitude curve, the sliding focusing imaging attitude curve and the post-imaging attitude return curve are used as control targets of the satellite control system, and a tracking control algorithm is used to realize the attitude control of the satellite in the whole process of the sliding focusing mode.

[0015] Beneficial effects of the present invention:

[0016] 1. The present invention fits the attitude during the imaging of the sliding beam mode into a polynomial curve. The satellite does not need to store the attitude data of each discrete time point, but only needs to store the polynomial coefficients to construct the complete imaging attitude process, thus reducing the demand for on-board attitude data storage;

[0017] 2. The present invention represents the posture motion of presetting before imaging, sliding imaging, and transition after imaging as polynomial curves, which can ensure that the posture angle, angular velocity, and angular acceleration change continuously when the three polynomial curves are connected end to end, so as to realize the continuous change of the motion of the control system during the execution process without causing posture jitter;

[0018] 3. The present invention adopts a polynomial attitude curve, which can directly obtain the polynomial curve corresponding to the first-order and second-order derivatives, and then obtain the angular velocity and angular acceleration at each moment, without point-by-point interpolation and differential operation, which is convenient for the rapid calculation of the tracking control algorithm;

[0019] 4. The present invention has no special requirements on the initial posture before imaging, the target posture angle, angular velocity and angular acceleration after imaging, and can adapt to sliding beam imaging tasks in various situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a flow chart of the SAR satellite sliding beam mode attitude control method based on polynomials of the present invention;

[0021] Figure 2 It is a schematic diagram of the attitude angle, angular velocity and angular acceleration curves of presetting before imaging, sliding imaging and transition after imaging in a specific implementation manner of the present invention. DETAILED DESCRIPTION

[0022] The exemplary embodiments of the present invention are described in detail below with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the accompanying drawings are only exemplary and are intended to illustrate the principles and spirit of the present invention, rather than to limit the scope of the present invention.

[0023] like Figure 1 As shown, the polynomial-based SAR satellite sliding beamforming mode attitude control method of the present invention comprises the following steps:

[0024] Step 1: According to the observation scene and satellite orbit information, the projection of the satellite's expected three-axis pointing unit vector at each discrete time point during the sliding beam mode imaging in the earth-fixed coordinate system is obtained; (hereinafter referred to as "expected three-axis pointing"); this step specifically includes:

[0025] (1) Determine the time range of the entire sliding beam imaging, that is, the time range of the satellite platform attitude maneuver, based on the observation scene position and satellite orbit information;

[0026] (2) Using SAR antenna parameters, resolution indicators, and the sub-satellite point of view at the center of the scene, determine the center rotation point during the entire satellite platform attitude maneuver;

[0027] (3) determining the desired three-axis pointing unit vector of the satellite during the imaging period according to the central rotation point of step (2) and the time range of the maneuver of step (1), thereby obtaining the precise attitude maneuver mode of the satellite platform during the entire sliding beam imaging period;

[0028] (4) According to step (3), the three-axis pointing unit vector of the satellite three-axis pointing unit vector is projected in the earth-fixed coordinate system; specifically, it is expressed in the form of a set:

[0029] {(t i ,(x i ) ECF ,(y i ) ECF ,(z i ) ECF )i=1,…,N,t img_start =t1<t2<…<t i <t i+1 <…<t N =t img_end}

[0030] Where N is the number of discrete time points, ti represents the i-th discrete time point, and t img_start is the imaging start time, t img_end is the end time of imaging; (x i ) ECF ,(y i ) ECF ,(z i ) ECF is a three-dimensional column vector representing time t i The projection of the unit vectors of the satellite's X-axis, Y-axis, and Z-axis in the Earth-fixed coordinate system.

[0031] Step 2: converting the three-axis pointing direction expected by the satellite at each discrete time point during the imaging period into the satellite Euler angle;

[0032] The Euler angle refers to the Euler angle of the satellite body relative to the orbital coordinate system, which is composed of the roll angle (rotation around the X-axis), the pitch angle (rotation around the Y-axis), and the yaw angle (rotation around the Z-axis).

[0033] In this embodiment, calculating the satellite Euler angle at time ti includes the following steps:

[0034] (1) According to t i Satellite position and speed at the moment, calculate the coordinate transformation matrix L from the geocentric inertial coordinate system to the earth-fixed coordinate system ECF_ECI_i , the coordinate transformation matrix L from the satellite orbit coordinate system to the geocentric inertial coordinate system ECI_ORB_i ; In specific implementation, the above two matrices are both 3×3 matrices, and the matrix parameters are related to the satellite orbit parameters, which are recorded in satellite orbit monographs.

[0035] (2) According to the t obtained in step 1 iThe three-axis orientation of the satellite at the moment and the coordinate transformation matrix L from the Earth-centered inertial coordinate system to the Earth-fixed coordinate system obtained in step (1) ECF_ECI_i , the coordinate transformation matrix L from the satellite orbit coordinate system to the geocentric inertial coordinate system ECI_ORB_i , obtain the coordinate transformation matrix L from the satellite orbit coordinate system to the satellite body BODY_ORB_i ; The specific formula is as follows:

[0036] L BODY_ORB_i =L BODY_ECF_i ·L ECF_ECI_i ·L ECI_ORB_i

[0037] in, (*) T Represents the transpose operation of a vector or matrix.

[0038] (3) The coordinate transformation matrix L from the satellite orbit coordinate system to the satellite body obtained in step (2) is BODY_ORB_i , get t i Satellite Euler angles at the moment.

[0039] In this embodiment, the “ZXY” Euler angle sequence is used to represent the time t i The corresponding Euler angle e i The following formula is used to obtain:

[0040]

[0041] Among them, sij represents the matrix L BODY_ORB_i The elements in the i-th row and j-th column, φi, θi, and ψi are the roll, pitch, and yaw angles at time ti, respectively.

[0042] Step 3: Using the least square fitting method, the satellite Euler angles at each discrete time point obtained in step 2 are fitted into a polynomial curve as a sliding focusing imaging attitude curve;

[0043] In this embodiment, the sliding focusing imaging posture curves include three groups, corresponding to the rolling, pitching and yaw angles respectively.

[0044] The following uses the roll angle as an example to illustrate this step, and the pitch and yaw angles can be performed in the same way.

[0045] For the roll angles corresponding to the N discrete time points obtained in step 2, fit them into a polynomial curve As shown below:

[0046]

[0047] Where K is the polynomial order, not less than 9; a j are the coefficients of each order of the polynomial, which can be obtained by the following formula:

[0048]

[0049] in(*) -1 For matrix inversion operation, A is an N×(K+1)-order matrix:

[0050]

[0051] The schematic diagram of the rolling angle attitude curve of the sliding focusing image obtained at this time is as follows Figure 2 This is shown in the “sliding convergence” portion of the top curve.

[0052] Step 4: Calculate the first-order derivative and the second-order derivative of the sliding imaging attitude curve obtained in step 3, obtain the attitude angular velocity curve, the angular acceleration curve, and the angular jerk curve, and then calculate the satellite attitude angle, angular velocity, and angular acceleration at the start and end of imaging;

[0053] The following uses the roll angle as an example to illustrate this step, and the pitch and yaw angles can be performed in the same way.

[0054] For the roll angle polynomial curve obtained in step 3 Find the first-order derivative and get the angular velocity curve As shown below:

[0055]

[0056] right Find the second-order derivative and get the angular acceleration curve As shown below:

[0057]

[0058] right Calculate the third-order derivative and get the angular acceleration curve As shown below:

[0059]

[0060] The curve diagram corresponding to formula (2) is as follows: Figure 2 The “sliding convergence imaging” part of the middle curve is shown in the following figure: Figure 2 This is shown in the “sliding convergence imaging” portion of the bottom curve.

[0061] The imaging start time t img_start Substituting into equations (1), (2), (3) and (4) respectively, we can obtain the satellite roll angle at the start of imaging: Roll angular velocity Scroll acceleration Roll jerk

[0062]

[0063]

[0064]

[0065]

[0066] The imaging end time t img_end Substitute into equation (1), equation (2), equation (3), and equation (4) respectively to obtain the satellite roll angle at the end of imaging: Roll angular velocity Scroll acceleration Roll jerk

[0067]

[0068]

[0069]

[0070]

[0071] Step 5: Based on the attitude angle, angular velocity, and angular acceleration at the time when the satellite sends the sliding mode command (referred to as the "command time") and the satellite attitude angle, angular velocity, angular acceleration, and angular jerk at the imaging start time obtained in step 4, a polynomial curve is constructed as a preset attitude curve before imaging, and then the corresponding angular velocity, angular acceleration curve, and angular jerk curve are obtained;

[0072] The following uses the roll angle as an example to illustrate this step, and the pitch and yaw angles can be performed in the same way.

[0073] The time of issuing the command is t com At the time of issuing the command, the satellite's initial roll angle, roll angular velocity, and roll angular acceleration are Then the pre-imaging posture preset curve in the rolling axis direction is for:

[0074]

[0075] Where 6 is the order of the polynomial curve, b j are the coefficients of each order of the polynomial, calculated using the following formula:

[0076]

[0077]

[0078] Where Δ = t img_start -t com .

[0079] For the polynomial rolling angle curve of formula (5), the angular velocity and angular acceleration are obtained by derivation, as shown in formula (6) and formula (7), respectively.

[0080]

[0081]

[0082] The curve diagram corresponding to formula (5) is as follows: Figure 2 As shown in the “pre-imaging preset” part of the top curve, the curve diagram corresponding to equation (6) is as follows Figure 2 The “pre-imaging preset” part of the middle curve is shown in the following figure: Figure 2 This is shown in the “Pre-Imaging Preset” portion of the bottom curve.

[0083] Step 6: Based on the expected attitude angle, angular velocity, and angular acceleration at the moment when the satellite completes payload shutdown (referred to as "shutdown moment") and the satellite attitude angle, angular velocity, and angular acceleration at the end of imaging obtained in step 4, a polynomial curve is constructed as the attitude return curve after imaging, and then the corresponding angular velocity, angular acceleration curve, and angular jerk curve are obtained;

[0084] The following uses the roll angle as an example to illustrate this step, and the pitch and yaw angles can be performed in the same way.

[0085] The shutdown time is t off At the shutdown time, the satellite expected roll angle, roll angular velocity, and roll angular acceleration are Then the post-imaging attitude return curve in the rolling axis direction is for:

[0086]

[0087] Where 6 is the order of the polynomial curve, cj is the coefficient of each order of the polynomial, and is calculated using the following formula:

[0088]

[0089]

[0090] in,

[0091] For the 6th-order polynomial rolling angle curve of formula (8), the angular velocity and angular acceleration curves can be obtained by derivation, as shown in formula (9) and formula (10) respectively.

[0092]

[0093]

[0094] The curve diagram corresponding to formula (8) in this step is as follows Figure 2 As shown in the “imaging return” part of the top curve, the curve diagram corresponding to equation (9) is as follows Figure 2 The “imaging return” part of the middle curve is shown in the following figure: Figure 2 This is shown in the “Imaging Return” portion of the bottom curve.

[0095] Step 7: taking the pre-imaging preset attitude curve, the sliding focusing imaging attitude curve, and the post-imaging attitude return curve as control targets of the satellite control system, and adopting a tracking control algorithm to realize the attitude control of the satellite in the whole process of the sliding focusing mode;

[0096] The following takes the roll angle control as an example to illustrate this step, and the pitch and yaw angle control can be performed in the same way. Figure 2 A schematic diagram of the rolling angle curve of the entire sliding process is shown, in which the angle, angular velocity and angular acceleration all change continuously.

[0097] (1) Let the current time be t, and the command time t be the relative time of the current time t. com , imaging start time t img_start , imaging end time t img_end , shutdown time t off The timing relationship of the attitude polynomial curve is used to determine which group of attitude polynomial curves should be used, and the expected rolling angle at the current time t is calculated according to the attitude polynomial curve. Angular velocity Angular acceleration

[0098] (2) The rolling angle at the current moment t measured on the satellite is The rolling angular velocity is Then calculate the current satellite X-axis direction control command torque T x (t), as shown in the following formula:

[0099]

[0100] Among them, k p is a proportional control system, k d is a differential control system, k f is the feedforward compensation coefficient, and k p ,k d ,k f >0;

[0101] (3) According to the above step (1) and sub-step (2), the control command torques in the Y-axis and Z-axis directions of the current satellite are calculated and recorded as T y (t), T z (t);

[0102] (4) According to the control command torque T in the three-axis direction x (t), T y (t), T z (t) Control the satellite attitude.

[0103] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A polynomial-based SAR satellite sliding beam mode attitude control method, characterized in that: include: According to the observation scene and satellite orbit information, the projection of the satellite's expected three-axis pointing unit vector in the earth-fixed coordinate system at each discrete time point during the sliding beam mode imaging is obtained; Converting the desired three-axis orientation of the satellite at each discrete time point during the imaging period into satellite Euler angles; The least square fitting method is used to fit the satellite Euler angles at each discrete time point into a polynomial curve as the attitude curve of the sliding convergence imaging. According to the attitude curve of the sliding convergence imaging, the attitude angular velocity curve, the angular acceleration curve and the angular jerk curve are obtained, and then the satellite attitude angle, angular velocity and angular acceleration at the start and end of imaging are calculated; Based on the attitude angle, angular velocity, angular acceleration at the moment when the satellite sends the sliding mode command and the satellite attitude angle, angular velocity, angular acceleration, angular acceleration at the beginning of imaging, a polynomial curve is constructed as a preset attitude curve before imaging; Based on the expected attitude angle, angular velocity, angular acceleration when the satellite completes payload shutdown and the satellite attitude angle, angular velocity, angular acceleration when imaging ends, a polynomial curve is constructed as a post-imaging attitude return curve; The preset attitude curve before imaging, the attitude curve of sliding focusing imaging, and the attitude return curve after imaging are used as the control targets of the satellite control system, and the tracking control algorithm is used to realize the attitude control of the satellite in the whole process of sliding focusing mode. The tracking control algorithm is used to realize the attitude control of the satellite in the whole process of sliding beam mode, which includes the following steps: (1) Let the current time be t. According to the timing relationship between the current time t and the command time, imaging start time, imaging end time, and shutdown time, determine which set of attitude polynomial curves should be used, and calculate the expected rolling angle, angular velocity, and angular acceleration at the current time t based on the attitude polynomial curves; (2) Calculate the current satellite X-axis control command torque based on the current rolling angle and rolling angular velocity measured on the satellite; (3) Calculate the control command torque in the Y-axis direction and the Z-axis direction of the current satellite according to the above steps (1) and (2); (4) Control the satellite attitude according to the control command torque in the three-axis direction.

2. The polynomial-based SAR satellite sliding beam mode attitude control method according to claim 1, characterized in that: Step 1 specifically includes: (1) Determine the time range of the entire sliding spotlight imaging, that is, the time range of the satellite platform attitude maneuver, based on the observation scene location and satellite orbit information; (2) Determine the center rotation point during the entire satellite platform attitude maneuver using SAR antenna parameters, resolution indicators, and the sub-satellite point of view at the center of the scene; (3) determining the desired three-axis pointing unit vector of the satellite during the imaging period based on the central rotation point of step (2) and the time range of the maneuver of step (1), thereby obtaining the precise attitude maneuver mode of the satellite platform during the entire sliding beam imaging period; (4) According to step (3), the three-axis pointing unit vector of the satellite three-axis pointing unit vector is projected in the earth-fixed coordinate system.

3. The polynomial-based SAR satellite sliding beam mode attitude control method according to claim 1 or 2, characterized in that: Calculate t i The satellite Euler angle at the moment comprises the following steps: (1) According to t i Satellite position and speed at all times, calculate the coordinate conversion matrix from the geocentric inertial coordinate system to the earth-fixed coordinate system, and the coordinate conversion matrix from the satellite orbit coordinate system to the geocentric inertial coordinate system; (2) According to the t obtained in step 1 i The desired three-axis orientation of the satellite at the moment and the coordinate transformation matrix from the geocentric inertial coordinate system to the earth-fixed coordinate system and the coordinate transformation matrix from the satellite orbit coordinate system to the geocentric inertial coordinate system obtained in step (1) are used to obtain the coordinate transformation matrix from the satellite orbit coordinate system to the satellite body; (3) Based on the coordinate transformation matrix from the satellite orbit coordinate system to the satellite body obtained in step (2), obtain the satellite Euler angle at time ti.

4. The polynomial-based SAR satellite sliding beam mode attitude control method according to claim 1 or 2, characterized in that: The sliding focusing imaging attitude curves include three groups, corresponding to rolling, pitching and yaw angles respectively.

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