A Calculation Method for the Earth-Pointing Rotation Angle of a Spaceborne Three-Axis Turntable

Abstract

The present invention provides a method for calculating the rotation angle of a spaceborne three-axis turntable for earth pointing. According to the relationship between the load main axis vector and the earth pointing target vector, the expected quaternion for earth pointing is calculated, and then the expected quaternion is converted into Euler angles according to a specified rotation sequence to obtain the pitch, azimuth, and roll angles of the three-axis turntable. The above method realizes the precise pointing of the load to the ground target. The method is easy to implement in engineering, and the pointing accuracy meets the working accuracy requirements of common imaging and communication loads. At the same time, it can also be simplified and applied to two-dimensional rotation mechanisms, having great engineering application value.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and particularly relates to a method for calculating the rotation angle of a spaceborne three-axis turntable for earth pointing. Background Art

[0002] With the development of space technology, the number of artificial satellites has increased significantly, and the functions of the payloads carried on the satellites have gradually become richer. For artificial earth satellites, their payloads often perform earth-pointing tasks, such as remote sensing imaging of the earth or measurement and control communication with ground stations. To ensure the normal execution of the satellite's earth-pointing tasks, it is necessary to accurately point the main axis of the payload at the ground target. The payloads can be mounted fixedly on the satellite body, and different pointing directions of the payload main axis are achieved through the attitude change of the satellite; or they can be fixed on the servo mechanism, and the pointing direction of the main axis is changed by the rotation of the servo mechanism. For some lightweight satellite payloads, it has gradually become an actual need and development direction to use a spaceborne two-axis / three-axis turntable to achieve different earth-pointing directions. Therefore, accurately calculating the pitch angle, azimuth angle, and roll angle of a spaceborne three-axis turntable during the satellite's earth-pointing task is a common engineering problem.

[0003] In view of the above problems, the present invention proposes a method for calculating the rotation angle of a spaceborne three-axis turntable for earth pointing. Based on the relationship between the main axis vector of the payload and the earth-pointing target vector, the expected quaternion for earth pointing is calculated, and then the expected quaternion is converted into Euler angles according to a specified rotation sequence to obtain the pitch, azimuth, and roll angles of the three-axis turntable. The above method realizes the accurate pointing of the payload at the ground target, is easy to implement in engineering, the pointing accuracy meets the working accuracy requirements of common imaging and communication payloads, and can also be simply applied to two-dimensional rotation mechanisms, having great engineering application value. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems in the prior art, and proposes a method for calculating the rotation angle of a spaceborne three-axis turntable for earth pointing.

[0005] The present invention is realized through the following technical solutions. The present invention proposes a method for calculating the rotation angle of a spaceborne three-axis turntable for earth pointing, and the method specifically includes:

[0006] Step 1: Obtain the position of the ground target in the WGS-84 coordinate system according to the longitude, latitude, and altitude information of the ground mission target;

[0007] Step 2: Convert the position of the ground target in the WGS-84 coordinate system to the position in the inertial coordinate system;

[0008] Step 3: Calculate the target vector of the turntable main axis in the inertial coordinate system;

[0009] Step 4: Calculate the current attitude quaternion of the three-axis turntable;

[0010] Step 5: Convert the target vector in the inertial coordinate system to the turntable coordinate system;

[0011] Step 6: Calculate the desired quaternion Q of the main axis in the turntable coordinate system d ;

[0012] Step 7: Convert the desired quaternion to the rotation angles of the three-axis turntable according to the specified rotation sequence.

[0013] Further, in Step 1, according to the longitude, latitude, and altitude information of the target ground station, obtain the position of the ground station in the WGS-84 coordinate system;

[0014] The position information of the communication ground station is described as longitude λ, latitude L, and altitude h in the geographic coordinate system. Transform the position information of the ground station to the position information R in the World Geodetic System WGS-84 WGS_ground as:

[0015]

[0016] where: R N is the curvature of the meridian; f is the flattening of the earth.

[0017] Further, in Step 2, convert the position R of the ground station in the WGS-84 coordinate system WGS_ground to the position R in the inertial system J2000_ground .

[0018] Further, in Step 3, calculate the target vector of the communication payload in the inertial coordinate system. Subtract the position R J2000_ground of the target ground station from the position R J2000_self of the satellite itself to obtain the target vector of the communication payload in the inertial system as:

[0019] r1 = R J2000_ground - R J2000_self , (2).

[0020] Further, in Step 4, the current attitude quaternion Q of the three-axis turntable servo :

[0021]

[0022] where: Q ib is the current attitude quaternion of the satellite; Q Ins is the installation quaternion from the satellite to the servo turntable coordinate system.

[0023] Further, in Step 5, transform the turntable quaternion Q servo to the attitude rotation matrix T servo , and calculate the projection vector r of the laser communication optical axis in the turntable coordinate systemlaser is:

[0024] r laser = T servo r1, (4).

[0025] Furthermore, in step 6, according to the axis-angle transformation theory, the optical axis Z-axis of the communication terminal rotates around the rotation axis r rorate by the rotation angle θ to point to the target. The rotation axis r rorate is:

[0026] r rorate = r z × r laser , (5)

[0027] The included angle θ between the coordinate system Z-axis and r laser is:

[0028] θ = arctan(r rorate , r z · r laser ), (6)

[0029] Then the desired attitude quaternion of the communication terminal Z-axis pointing to the target vector is:

[0030]

[0031] Furthermore, in step 7, there are 12 rotation sequences for Euler angles. Taking the Z-Y-X order as an example, the Euler angles, that is, rotating α, β, γ angles around the X-Y-Z of the fixed coordinate system in sequence, are converted into quaternions:

[0032]

[0033] According to formula (8), the inverse solution is obtained, that is, the conversion from the quaternion q = (q0, q1, q2, q3) to Euler angles is:

[0034]

[0035] The Euler angles α, β, γ are the rotation angles of the corresponding actuators, namely the pitch angle, azimuth angle, and roll angle.

[0036] The present invention also provides an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of the method for calculating the rotation angle of a spaceborne three-axis turntable for earth pointing are implemented.

[0037] The present invention also provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the method for calculating the rotation angle of a spaceborne three-axis turntable for earth pointing are implemented.

[0038] The present invention has the following beneficial effects:

[0039] The calculation method of the rotation angle of the spaceborne three-axis turntable for ground pointing designed by the present invention can achieve accurate pointing of the satellite payload to the ground target through accurate calculation of the turntable rotation angle, ensuring the normal and efficient progress of the satellite payload's ground mission. Moreover, the method of the present invention has strong scalability. It can be adjusted by 12 different rotation sequences of Euler angles to achieve different rotation sequences, or the rotation angle solution of the two-dimensional turntable can be simplified by removing a certain rotation angle. In summary, the calculation method of the present invention has a simple principle, high solution accuracy, is easy to implement, and has strong scalability, and can be applied to engineering practice. Description of the Drawings

[0040] Figure 1 It is a schematic diagram for solving the rotation angle of the ground mission;

[0041] Figure 2 It is the verification effect diagram of ground pointing for the embodiment. Detailed Embodiment

[0042] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0043] The purpose of the present invention is to provide a calculation method for the rotation angle of a spaceborne three-axis turntable for ground pointing, and the basic principle is:

[0044] First, through two coordinate system transformations, the longitude, latitude, and altitude information of the ground target in the geographical coordinate system is transformed into the position information in the J2000 protocol inertial coordinate system. In the inertial coordinate system, the expected pointing vector of the satellite payload to the ground target can be obtained by combining the satellite's own position information. By converting the target vector into the turntable coordinate system, the expected rotation quaternion in the turntable coordinate system can be calculated from the relationship between the payload main axis vector and the expected pointing vector. Finally, from the solution relationship between the rotation quaternion and the Euler angles, the three expected rotation angle information of the pitch angle, azimuth angle, and roll angle can be solved according to the specified rotation sequence. The spaceborne three-axis turntable rotates according to the above rotation angle information to achieve accurate pointing to the ground target.

[0045] Combined with Figure 1 - Figure 2 , the present invention proposes a calculation method for the rotation angle of a spaceborne three-axis turntable for ground pointing, and the method specifically includes:

[0046] Step 1: Obtain the position of the ground target in the World Geodetic System (WGS)-84 based on the longitude, latitude, and altitude information of the ground mission objective;

[0047] Step 2: Convert the position of the ground target in the WGS-84 to the position in the inertial system;

[0048] Step 3: Calculate the target vector of the turntable spindle in the inertial coordinate system;

[0049] Step 4: Calculate the current attitude quaternion of the three-axis turntable;

[0050] Step 5: Convert the target vector in the inertial coordinate system to the turntable coordinate system;

[0051] Step 6: Calculate the desired quaternion Q of the spindle in the turntable coordinate system d ;

[0052] Step 7: Convert the desired quaternion to the rotation angles of the three-axis turntable according to the specified rotation sequence.

[0053] The present invention realizes the calculation method of the earth-pointing rotation angle of the spaceborne three-axis turntable through the following technical solutions. Taking the communication between a certain satellite payload and a ground station as an example, the satellite is in a sun-synchronous orbit at an altitude of 535 km, the ground station is located within the coverage range near the satellite's sub-satellite point, and the satellite adopts a three-axis earth-stabilized attitude. The calculation is divided into the following steps:

[0054] Step 1: Obtain the position of the ground target in the WGS-84 based on the longitude, latitude, and altitude information of the ground mission objective.

[0055] In Step 1, obtain the position of the ground station in the WGS-84 based on the longitude, latitude, and altitude information of the target ground station;

[0056] The position information of the communication ground station is described as longitude λ, latitude L, and altitude h in the geographic coordinate system. Transform the position information of the ground station to the position information R in the World Geodetic System (WGS)-84 WGS_ground as:

[0057]

[0058] where: R N is the meridian curvature; f is the flattening of the earth.

[0059] Step 2: Convert the position of the ground target in the WGS-84 to the position in the inertial system.

[0060] In Step 2, convert the position R of the ground station in the WGS-84 WGS_ground to the position R in the inertial system J2000_ground .

[0061] Step 3: Calculate the target vector of the turntable spindle in the inertial coordinate system.

[0062] In Step 3, calculate the target vector of the communication payload in the inertial coordinate system. Subtract the position R J2000_ground of the target ground station from the position R J2000_self of this satellite to obtain the target vector of the communication payload in the inertial system as:

[0063] r1 = R J2000_ground - R J2000_self , (2).

[0064] Step 4: Calculate the current attitude quaternion of the three-axis turntable.

[0065] In Step 4, the current attitude quaternion Q servo of the three-axis turntable is:

[0066]

[0067] where: Q ib is the current attitude quaternion of the satellite; Q Ins is the installation quaternion from the satellite to the servo turntable coordinate system.

[0068] Step 5: Convert the target vector in the inertial coordinate system to the turntable coordinate system.

[0069] In Step 5, transform the turntable quaternion Q servo into the attitude rotation matrix T servo , and calculate the projection vector r laser of the laser communication optical axis in the turntable coordinate system as:

[0070] r laser = T servo r1, (4).

[0071] Step 6: Calculate the desired quaternion Q d of the spindle in the turntable coordinate system.

[0072] In Step 6, according to the axis-angle transformation theory, the Z-axis of the communication terminal optical axis can point to the target by rotating an angle θ around the rotation axis r rorate . The rotation axis r rorate is:

[0073] r rorate = r z × r laser , (5)

[0074] The angle θ between the Z-axis of the coordinate system and r laser is:

[0075] θ = arctan(r rorate , rz ·r laser ), (6)

[0076] Then the desired attitude quaternion of the communication terminal's Z-axis pointing to the target vector is:

[0077]

[0078] Step 7: Convert the desired quaternion to the rotation angle of the turntable according to the specified rotation order.

[0079] In Step 7, there are 12 rotation orders for Euler angles. Taking the Z-Y-X order as an example, the Euler angles, that is, rotating by α, β, γ angles around the X-Y-Z of the fixed coordinate system in sequence, are converted to quaternions:

[0080]

[0081] Find the inverse solution according to formula (8), that is, the conversion from the quaternion q=(q0, q1, q2, q3) to Euler angles is:

[0082]

[0083] The Euler angles α, β, γ are the rotation angles of the corresponding actuators, namely the pitch angle, azimuth angle, and roll angle.

[0084] Take the calculated pitch angle, azimuth angle, and roll angle as the input of the three-axis turntable, and the obtained pointing is correct, and the optical axis of the communication payload accurately points to the ground station. Conduct a quantitative analysis on the pointing result. Take the solution result in the simulation software as the true value, and compare the angle calculated according to the above algorithm with the true value. The deviation is within 0.01°, and the deviation is within the error tolerance range of common ground tasks.

[0085] The present invention also proposes an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the method for calculating the rotation angle of a spaceborne three-axis turntable for ground pointing.

[0086] The present invention also proposes a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, they implement the steps of the method for calculating the rotation angle of a spaceborne three-axis turntable for ground pointing.

[0087] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read only memory (ROM), a programmable ROM (PROM), an erasable programmable ROM (EPROM), an electrically erasable programmable ROM (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DRRAM). It should be noted that the memory of the method described in the present invention is intended to include but not limited to these and any other suitable types of memory.

[0088] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wirelessly (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that the computer can access or a data storage device such as a server, data center, etc. that contains one or more integrated available media. The available media can be magnetic media (such as floppy disks, hard disks, magnetic tapes), optical media (such as high-density digital video discs (DVDs)), or semiconductor media (such as solid state discs (SSDs)), etc.

[0089] In the implementation process, each step of the above method can be completed by the integrated logic circuit of the hardware in the processor or the instructions in the form of software. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as being executed by the hardware processor or completed by the combination of the hardware and software modules in the processor. The software module can be located in a mature storage medium in the art such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, registers, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.

[0090] It should be noted that the processor in the embodiments of the present application may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method embodiments can be completed by the integrated logic circuit in the hardware of the processor or instructions in the form of software. The above-mentioned processor may be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps and logic block diagrams disclosed in the embodiments of the present application. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as being executed and completed by a hardware decoding processor, or executed and completed by a combination of hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0091] The above has introduced in detail a method for calculating the rotation angle of a spaceborne three-axis turntable pointing to the ground. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A calculation method for the rotation angle of a spaceborne three-axis turntable pointing to the ground, characterized in that The method specifically includes the following: Step 1: Obtain the position of the ground target in the WGS-84 coordinate system according to the latitude, longitude, and altitude information of the ground mission target; Step 2: Convert the position of the ground target in the WGS-84 coordinate system to the position in the inertial coordinate system; Step 3: Calculate the target vector of the turntable spindle in the inertial coordinate system; Step 4: Calculate the current attitude quaternion of the three-axis turntable; Step 5: Convert the target vector in the inertial coordinate system to the turntable coordinate system; Step 6: Calculate the desired quaternion Q of the spindle in the rotary table coordinate system d ; Step 7: Convert the desired quaternion to the rotation angles of the three-axis turntable according to the specified rotation sequence; In step 3, calculate the target vector of the communication payload in the inertial coordinate system, and subtract the position R of the target ground station J2000_ground from the position R of this satellite J2000_self to obtain the target vector of the communication payload in the inertial system as follows: r1 = R J2000_ground -R J2000_self , (2); In step 4, the current attitude quaternion Q of the three-axis turntable servo : Where: Q ib is the current attitude quaternion of the satellite; Q Ins is the installation quaternion from the satellite to the servo turntable coordinate system; In step 5, the turntable quaternion Q servo is transformed into the attitude rotation matrix T servo , and the projection vector r laser of the optical axis of laser communication in the turntable coordinate system is calculated as follows: r laser ＝T servo r1, (4)； In step 6, according to the axis-angle transformation theory, the optical axis Z-axis of the communication terminal rotates around the rotation axis r rorate by the rotation angle θ to point to the target, and the rotation axis r rorate is: r rorate ＝r z ×r laser , (5) The included angle θ between the Z-axis of the coordinate system and r laser is: θ = arctan(r rorate , r z ·r laser ), (6) Then the desired attitude quaternion for the Z-axis of the communication terminal to point to the target vector is:

2. The method according to claim 1, characterized in that In Step 1, obtain the position of the ground station in the WGS-84 coordinate system according to the latitude, longitude, and altitude information of the target ground station; The position information of the communication ground station is described as longitude λ, latitude L, and altitude h in the geographical coordinate system. The position information of the ground station is transformed into the position information R in the World Geodetic System WGS-84 WGS_ground It is as follows: In the formula: R N is the meridian curvature; f is the flattening of the earth.

3. The method according to claim 2, wherein In step 2, the ground station position R in the WGS-84 coordinate system WGS_ground is converted to the position R in the inertial coordinate system J2000_ground .

4. The method according to claim 3, characterized in that In Step 7, there are 12 rotation sequences for Euler angles. Taking the Z-Y-X sequence as an example, convert the Euler angles, that is, rotate by angles α, β, and γ around the X-Y-Z of the fixed coordinate system in sequence, to quaternions: Obtain the inverse solution according to formula (8), that is, the conversion from the quaternion q=(q0, q1, q2, q3) to Euler angles is: The Euler angles α, β, and γ are the rotation angles of the corresponding actuators, namely the pitch angle, azimuth angle, and roll angle.

5. An electronic device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method described in any one of claims 1-4.

6. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, it implements the steps of the method described in any one of claims 1-4.

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