JP2020050272A - Gimbal profile generation device, gimbal profile generation program, and gimbal profile generation method - Google Patents

Abstract

To provide a gimbal profile generation device which provide gimbal profile generation ensuring convergence without using high-load calculation method for numerically obtaining a convergence direction such as the Newton method.SOLUTION: In a gimbal profile generation device 100, a posture rate calculator 91 calculates a posture rate based on the amount of posture change of a spacecraft. An inverse kinematics calculation unit 95 calculates the first angular momentum of the spacecraft using the calculated posture rate, and second angular momentum of the spacecraft based on a gimbal rotation angle obtained from a gimbal steady state indicating a state in which the three-axis total angular momentum of all CMGs in the coast section is zero and an angular momentum envelope of CMGs. The inverse kinematics calculation unit 95 calculates an initial value of an intermediate gimbal rotation angle based on a gimbal rotation angle change obtained by multiplying a difference between the first angular momentum and the second angular momentum by a matrix that converts an angular momentum time derivative into a gimbal rotation angular velocity.SELECTED DRAWING: Figure 10

Description

  The present invention relates to an apparatus, a program, and a method for generating a gimbal profile that is a profile of a target gimbal rotation angle of a control moment gyro (hereinafter, referred to as “CMG”).

  CMG is an actuator for controlling the three-axis attitude of a spacecraft such as an artificial satellite. Each CMG has one or more gimbal axes and a wheel that rotates around a spin axis orthogonal to the gimbal axis. The CMG is an actuator that changes angular momentum by rotating a wheel rotating around a spin axis around a gimbal axis. Hereinafter, the rotation angle about the gimbal axis is referred to as a gimbal rotation angle or a gimbal angle. In order to change the attitude of the spacecraft, it is necessary to change the gimbal angle. However, the attitude of the spacecraft is changed by planning the amount of change in the gimbal angle as a “CMG gimbal target profile” in advance. There is a method (for example, Patent Document 1).

  In a method such as Patent Document 1 in which a CMG gimbal target profile is planned in advance, the CMG gimbal target profile calculates a gimbal angle and the like required for attitude change on a feedforward basis based on a target attitude change amount of the satellite. In this calculation process, the attitude angular velocity of the spacecraft is calculated from the gimbal angle, and the calculated attitude angular velocity is time-integrated by numerical calculation to calculate the attitude angle. Further, the gimbal angle correction and the posture angle calculation are repeated until the calculated posture angle matches the desired posture change amount. In order to provide the above-mentioned calculation function in the on-board computer of the spacecraft, it is necessary to reduce the repetitive calculation load of the time integration and the calculation of the attitude angle, in particular, to the extent that the on-board computer can calculate. Further, since the calculation function repeatedly repeats time correction by gimbal angle correction and numerical calculation to calculate the attitude angle, it is necessary to guarantee the stability (convergence) of the numerical calculation.

Patent No. 5484262

  In a conventional gimbal target profile generator, a posture angle obtained by time integration and a desired posture change amount are matched by using a calculation method for numerically obtaining a convergence direction (gimbal angle correction direction) such as Newton's method. Let me. Therefore, there is a problem in that the processing load is large and the convergence of the numerical convergence operation is guaranteed.

The gimbal profile generation device of the present invention includes:
A coast, which is used for attitude control of a spacecraft having a plurality of control moment gyros and is located between a first transition section, a second transition section, and the first transition section and the second transition section. A gimbal profile generation device that generates a gimbal profile having a gimbal rotation angle divided into sections and
An attitude rate calculation unit that calculates an attitude rate of the spacecraft based on an attitude change amount required for the spacecraft,
A gimbal steady state in which the first angular momentum of the spacecraft is calculated using the attitude rate calculated by the attitude rate calculation unit, and the three-axis total angular momentum of all the control moment gyros in the coast section is zero. A second angular momentum of the spacecraft is calculated based on a gimbal rotation angle obtained from the state and a control moment gyro angular momentum envelope, and an angular momentum time is calculated as a difference between the first angular momentum and the second angular momentum. An inverse kinematics calculation unit that calculates an initial value of the intermediate gimbal rotation angle based on a gimbal rotation angle change amount obtained by multiplying a matrix that converts the derivative into a gimbal rotation angular velocity;
An attitude for calculating an attitude angle of the spacecraft based on a time integration of an initial value of the intermediate gimbal rotation angle, and calculating an attitude error of the spacecraft from the attitude angle and an attitude angle required for the spacecraft. An error calculator.

  Since the gimbal profile generation device of the present invention includes the inverse kinematics calculation unit, the gimbal profile can be generated without increasing the processing load even when the intermediate gimbal angle is not given.

FIG. 5 is a diagram of the first embodiment and shows a CMG gimbal target profile for realizing the attitude change of the spacecraft. FIG. 5 is a diagram of the first embodiment and shows a posture rate profile. FIG. 4 is a diagram of the first embodiment, showing a CMG gimbal target profile, a posture rate profile, a momentum of the entire CMG, and a posture angle. FIG. 5 is a diagram of the first embodiment and shows a comparative example of a method of generating a CMG gimbal target profile by the gimbal profile generation device 100. FIG. 4 is a diagram of the first embodiment and is a perspective view of the CMG 200; FIG. 3 is a diagram of the first embodiment and shows a hardware configuration of the gimbal profile generation device 100. FIG. 4 is a diagram of the first embodiment and shows a CMG gimbal target profile generated by the gimbal profile generation device 100. 5 is a flowchart of the first embodiment, showing an operation of generating a CMG gimbal target profile by the gimbal profile generation device 100. FIG. 4 is a diagram of the first embodiment and shows a speed profile of a trapezoidal shape. FIG. 3 is a diagram of the first embodiment and shows a functional configuration of the gimbal profile generation device 100. 9 is a flowchart of the first embodiment, showing the content of step S20. 9 is a flowchart of the first embodiment, showing the contents of steps S30 and S40. FIG. 9 is a diagram of the first embodiment and shows a modification.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the drawings, the same or corresponding portions are denoted by the same reference numerals. In the description of the embodiments, the description of the same or corresponding portions will be omitted or simplified as appropriate.
In the following embodiments, vectors, matrices, and tensors appear.
Vectors are shown in bold. In some cases, vectors are expressed as <V> for convenience. <V> means the vector V.
Matrices and tensors are shown in bold. Further, the matrix and the tensor may be expressed as [W] for convenience. [W] means a matrix W or a tensor W.

Embodiment 1 FIG.
Hereinafter, the gimbal profile generation device 100 according to the first embodiment will be described with reference to FIGS.
FIG. 1 shows an example of a CMG gimbal target profile for realizing the attitude change of the spacecraft. CMG gimbal target profile of FIG. 1, a transition section A to change the gimbal angles from any of the gimbal angle start theta ₀ to Shitacoas, the coast section to maintain the intermediate gimbal angle Shitacoast, any of the gimbal angle end from the intermediate gimbal angle Shitacoast And a transition section B in which the gimbal angle is changed. θcoast is hereinafter referred to as an intermediate gimbal angle.

  FIG. 2 shows a posture rate profile. When the CMG gimbal target profile shown in FIG. 1 is used, the total angular momentum of the three axes of all CMGs at the intermediate gimbal angle θcoast is close to a state close to zero (this state is referred to as “steady state of gimbal angle”). For example, an attitude rate close to the attitude rate profile shown in FIG. 2 can be obtained. At this time, the attitude angle obtained by time-integrating the attitude rate profile shown in FIG. 2 is an approximate attitude change amount of the spacecraft.

In order to achieve the desired attitude change, it is assumed that the posture condition of attitude change start phi ₀ and attitude change termination phi _f is given.
FIG. 3 is a diagram obtained by adding a graph of the momentum and the posture angle of the entire CMG to the case of the CMG gimbal target profile of FIG. 1 and the posture rate profile of FIG. If the orientation condition is given, from the posture condition, the gimbal angle of attitude change beginning and attitude change termination (hereinafter referred to as starting gimbal angle theta ₀ and terminating the gimbal angle theta _f) is calculated by using any technique be able to.

Given the starting gimbal angle θ ₀ and the ending gimbal angle θ _f , the conditions that can be changed to achieve the desired attitude change in the spacecraft using the CMG gimbal target profile shown in FIG. Only the angle θcoast.
FIG. 4 is a comparative example of a method of generating a CMG gimbal target profile by the gimbal profile generation device 100. In the process of step S01, an intermediate gimbal angle initial value is calculated by an arbitrary method, and is set as an initial value of the intermediate gimbal angle nominal value. The process of step S02 is performed by changing the intermediate gimbal angle with respect to the intermediate gimbal angle nominal value using the intermediate gimbal angle nominal value and the value obtained by slightly changing the intermediate gimbal angle from the nominal value. The change amount of the end posture and the convergence direction of the intermediate gimbal angle (the direction in which the end posture achieves the desired posture change) are obtained and updated to the direction in which the intermediate gimbal angle converges. This is a numerical method such as the Newton method. In the comparative example of FIG. 4, for example, the intermediate gimbal angle θcoast is obtained by using an arithmetic technique (Newton method or the like) for numerically obtaining the convergence direction (gimbal angle correction direction) by slightly changing the intermediate gimbal angle θcoast. In the comparative example of FIG. 4, in addition to obtaining the attitude angle by time integration, an arithmetic load for calculating the convergence direction numerically is added. Therefore, the comparative example in FIG. 4 has a problem that the processing load is high and it is difficult to guarantee the convergence of the numerical convergence operation.

  The gimbal profile generation device 100 described in the first embodiment solves the problem described in FIG. 4 by generating a CMG gimbal target profile shown in FIG. 7 described later.

  FIG. 5 is a perspective view of the CMG 200. The CMG 200 will be described simply. The CMG 200 is controlled by a CMG gimbal target profile generated by the gimbal profile generation device 100. The CMG 200 is used for attitude control of a spacecraft such as an artificial satellite. The CMG 200 includes a wheel 210 that rotates at high speed around a spin axis 211 and a gimbal 220 that supports the wheel 210 and rotates around a gimbal axis 221 perpendicular to the spin axis 211. The rotation angle around the gimbal axis 221 is the gimbal rotation angle 222.

  In the CMG 200, the wheel 210 generates angular momentum about the spin axis 211 by rotating at high speed. By rotating the gimbal 220 around the gimbal axis 221 and rotating the direction of the angular momentum of the wheel 210, a reaction torque acts on the spacecraft. The spacecraft uses this reaction torque for attitude control.

*** Configuration description ***
FIG. 6 shows a hardware configuration of the gimbal profile generation device 100. The configuration of the gimbal profile generation device 100 will be described with reference to FIG. The gimbal profile generation device 100 is a computer. The gimbal profile generation device 100 includes the processor 10 and other hardware such as the memory 20, the auxiliary storage device 30, the input interface 40, and the output interface 50. The processor 10 is connected to other hardware via a signal line 60, and controls the other hardware.

  The gimbal profile generation device 100 includes, as functional elements, an attitude rate calculation unit 91, a first quantization unit 92, a second quantization unit 93, an envelope surface calculation unit 94, an inverse kinematics calculation unit 95, and a gimbal rotation angle update unit 96. , An attitude error calculation unit 97 and a correction unit 98. The posture rate calculation unit 91, the first quantization unit 92, the second quantization unit 93, the envelope surface calculation unit 94, the inverse kinematics calculation unit 95, the gimbal rotation angle update unit 96, the posture error calculation unit 97, and the correction unit 98 Is realized by a gimbal profile generation program which is software.

  The processor 10 is a device that executes a gimbal profile generation program. The gimbal profile generation program includes a posture rate calculation unit 91, a first quantization unit 92, a second quantization unit 93, an envelope calculation unit 94, an inverse kinematics calculation unit 95, a gimbal rotation angle update unit 96, a posture error calculation unit. 97 is a program for realizing the correction unit 98. The processor 10 includes a posture rate calculation unit 91, a first quantization unit 92, a second quantization unit 93, an envelope surface calculation unit 94, an inverse kinematics calculation unit 95, a gimbal rotation angle update unit 96, a posture error calculation unit 97, An IC (Integrated Circuit) that performs the processing of the correction unit 98. Specific examples of the processor 10 are a CPU (Central Processing Unit), a DSP (Digital Signal Processor), and a GPU (Graphics Processing Unit).

  The memory 20 is a storage device that temporarily stores data. Specific examples of the memory 20 are an SRAM (Static Random Access Memory) and a DRAM (Dynamic Random Access Memory). The memory 20 holds the operation result of the processor 10.

  The auxiliary storage device 30 is a storage device for storing data. A specific example of the auxiliary storage device 30 is an HDD (Hard Disk Drive). The auxiliary storage device 30 includes an SD (Secure Digital) memory card, a CF (Compact Flash), a NAND flash, a flexible disk, an optical disk, a compact disk, a Blu-ray (registered trademark) disk, and a DVD (Digital Versatile Disk). It may be a portable recording medium.

  The input interface 40 acquires information from an external device. The output interface 50 outputs information to an external device.

  The gimbal profile generation program is read from the memory 20 by the processor 10 and executed by the processor 10. The memory 20 stores not only a gimbal profile generation program but also a program for executing other control calculations and the like. The processor 10 executes a gimbal profile generation program while executing a program for executing other control calculations and the like. The gimbal profile generation program and a program for executing other control calculations and the like may be stored in the auxiliary storage device 30. The gimbal profile generation program and other programs for executing control calculations and the like stored in the auxiliary storage device 30 are loaded into the memory 20 and executed by the processor 10. A part or all of the use of an OS (Operating System) and a program for performing a gimbal profile generation program and other control calculations may be incorporated in the OS (Operation System).

  The gimbal profile generation device 100 may include a plurality of processors instead of the processor 10. The plurality of processors share execution of the gimbal profile generation program. Each processor is a device that executes a gimbal profile generation program, similarly to the processor 10.

  Data, information, signal values, and variable values used, processed, or output by the gimbal profile generation program are stored in the memory 20, the auxiliary storage device 30, the register in the processor 10, or the cache memory.

  The gimbal profile generation program includes a posture rate calculation unit 91, a first quantization unit 92, a second quantization unit 93, an envelope calculation unit 94, an inverse kinematics calculation unit 95, a gimbal rotation angle update unit 96, a posture error calculation unit. This is a program that causes a computer to execute each process, each procedure, or each process in which the “unit” of each unit of the 97 and the correction unit 98 is replaced with “process”, “procedure”, or “process”. The gimbal profile generation method is a method performed by the gimbal profile generation device 100, which is a computer, executing a gimbal profile generation program.

  The gimbal profile generation program may be provided by being stored in a computer-readable recording medium, or may be provided as a program product.

FIG. 7 shows a CMG gimbal target profile generated by the gimbal profile generation device 100. The CMG gimbal target profile is a gimbal profile. The gimbal profile generation device 100 generates the gimbal profile of FIG. The gimbal profile of FIG. 7 is used for attitude control of a spacecraft having a plurality of control moment gyros, and is a first transition section Δt _trans from the origin to time t1, and a second transition section from time t2 to time t3. is a transition period △ having a t _trans, the gimbal angle of rotation is divided into a certain △ t _coast in the coasting section located between the first transition section and second transition section. Although not a required equals one △ _{t trans} by a second transition section from the first is the transition section △ _{t trans} and time t2 until time t1 to time t3, for convenience of description, necessary to distinguish Because there is no い ず_れ , they are all described as △ t _trans .
FIG. 8 is a flowchart illustrating an operation of generating the CMG gimbal target profile by the gimbal profile generation device 100. FIG. 8 shows the correspondence between the processing steps in FIG. Steps S10 to S40 shown in FIG. 7 are as follows. In step S10, an initial value of the intermediate gimbal angle is calculated using the reverse motion angle. In addition, the quantization guarantees the convergence. In step S20, correction is performed using the Jacobian matrix. In step S30, the error that could not be compensated in steps S10 and S20 is superimposed on the coast section as an error correction profile. In step S40, the error that could not be compensated in steps S10, S20, and S30 is added to the start of the target attitude, and the error is suppressed by feedback control before the driving is completed.

Prior to the description of FIGS. 7 and 8, a technique commonly used in FIGS. 7 and 8 will be described. The angular momentum <h> and torque <τ> of the entire CMG can be obtained as follows.

ただし、式５中の［Ａ^＋（θ）］は、例えば［Ａ（θ）］の擬似逆行列等、以下の式６、式７を同時に満足する任意の行列である。［Ａ^＋（θ）］の算出方法は本発明の対象範囲を超えるため、説明は省略する。

Here, [A ⁺ (θ)] in Expression 5 is an arbitrary matrix that satisfies the following Expressions 6 and 7 simultaneously, such as a pseudo inverse matrix of [A (θ)]. The method of calculating [A ⁺ (θ)] is beyond the scope of the present invention, and a description thereof will be omitted.

  Next, a method of approximately calculating a posture profile corresponding to the gimbal target profile will be described.

FIG. 9 shows a speed profile of a trapezoidal shape. When the intermediate gimbal angle θcoast is not given, a posture profile is generated using the trapezoidal velocity profile shown in FIG. At this time, the constant angular acceleration in the trapezoidal velocity profile is obtained by setting the posture rate corresponding to the CMG angular momentum envelope (described later) to the gimbal angle between the gimbal angle obtained from the CMG angular momentum envelope and the start gimbal angle or the end gimbal angle. The average value of the value obtained by dividing by the time required to change while satisfying the angle change constraint and the value of the angular acceleration that can be output to the posture change direction side in the gimbal angle steady state is used. This is referred to as a “method of calculating angular acceleration when no intermediate gimbal value is given”.
The maximum posture rate in the trapezoidal velocity profile is calculated from the constant angular acceleration obtained by the average value and the desired posture change amount. The angular momentum is calculated by multiplying the maximum attitude rate calculated above by the inertia tensor of the spacecraft. The gimbal angle corresponding to the angular momentum calculated above was obtained from the combination of the zero angular momentum and the gimbal steady state, or the angular momentum and the CMG angular momentum envelope corresponding to the CMG angular momentum envelope (nearly good). The starting point is a combination of gimbal angles (a value close to the gimbal angle is good), and the calculation is performed using inverse kinematics (Equation 5).
In the calculation process, the maximum posture rate (and the angular momentum calculated from the maximum posture rate) in the posture driving direction and the trapezoidal velocity profile can be originally an arbitrary value because it is calculated from a desired posture change amount. The calculation is performed by performing quantization at intervals of.
By the quantization, the calculation condition for the calculation is suppressed to a finite number for any desired posture change amount. Convergence can be assured by verifying / confirming convergence (a solution is required) under all conditions with respect to the calculation conditions suppressed to a finite number.

  When the intermediate gimbal angle θcoast is given, each posture change amount of the transition section A, coast section, and transition section B obtained based on the given intermediate gimbal angle θcoast can be calculated by time integration.

  In the time integration, the angular momentum is calculated from the gimbal angle based on Equation 1, the calculated angular momentum is multiplied by the inverse matrix of the inertial tensor of the spacecraft, the attitude rate is calculated, and the calculated attitude rate is integrated over time. Calculate the attitude angle. This posture angle calculation method is referred to as “posture angle calculation method using an intermediate gimbal”.

The approximate posture profile when the intermediate gimbal angle θcoast is given is used to approximately calculate the posture profile when the intermediate gimbal angle θcoast is changed. In the calculation of the posture profile, the transition section A and the transition section B use the posture change amount calculated based on the given intermediate gimbal angle θcoast. With respect to the posture change amount of the _coast section Δt _coast , the desired posture change amount is a posture change amount obtained by subtracting the posture change amount of the transition section A and the transition section B from the desired posture change amount of the whole posture change. From the amount and the coast section time Δt _coast , the coast section's posture rate is calculated using the fact that the desired posture change amount of the coast section is given by Equation 8 when expressed in quaternion Δqcoast.

*** Explanation of operation ***
Next, based on the above description, the operation of the gimbal profile generation device 100 will be described with reference to FIGS. 7, 8, 10, 11, and 12. The operation of the gimbal profile generation device 100 corresponds to a gimbal profile generation method. The operation of the gimbal profile generation device 100 corresponds to the processing of a gimbal profile generation program.

FIG. 10 shows a functional configuration of the gimbal profile generation device 100.
FIG. 11 shows the contents of step S20.
FIG. 12 shows the contents of steps S30 and S40. 11 and 12, solid arrows indicate the flow of processing, and dotted arrows indicate output and input of information. The black diamond represents the determination processing of the attitude error calculation unit 97. The posture error calculation unit 97 determines whether the posture error is within a specified value, and indicates that the process may be completed if the posture error is within the specified value.

<Step S10>
Step S10 will be described with reference to FIGS. 7, 8, and 10. In step S10, the gimbal profile generation device 100 calculates an intermediate gimbal angle initial value using inverse kinematics. When using inverse kinematics, the use of quantization guarantees the convergence of the calculation of the initial gimbal angle initial value (allows for preliminary verification under all conditions). Hereinafter, step S10 will be described.

In the process of step S10, the attitude profile calculation and the gimbal angle calculation when the intermediate gimbal angle is not given are used.
The following (1) to (7) are the process of calculating the intermediate gimbal angle initial value 95a.

(1) The posture rate calculator 91 acquires the input information 90a. Input information 90a is, including the beginning of the attitude conditions and termination attitude conditions of the spacecraft, the beginning of the gimbal angle θ ₀ and the end of the gimbal angle θ _f, the attitude change time of the spacecraft.
(2) The attitude rate calculator 91 calculates the attitude rate of the spacecraft based on the attitude change amount required for the spacecraft. Specifically, it is as follows.
The posture rate calculation unit 91 generates a posture rate 91a of the coast section from the acquired input information 90a. Attitude rate calculation unit 91, the speed of the constant angular acceleration <alpha> and using the drive angle theta _r and the drive time T, analytically maximum angular velocity omega _{m (part} speed of the trapezoidal speed pattern becomes constant trapezoidal speed pattern ). The method of obtaining the constant angular acceleration <α> used here is obtained by the “calculation method of angular acceleration when no intermediate gimbal value is given” described with reference to FIG. 9, and the following two average values are used. .
The posture rate corresponding to the CMG angular momentum envelope surface (described later) ÷ the time that satisfies the constraint of the CMG gimbal change.The angular acceleration that can be output to the posture change direction side in the gimbal angle steady state. (3) The first quantization unit 92 The posture rate 91a in the coast section is obtained, the posture rate 91a is quantized at arbitrary intervals, and the quantized posture rate 92a is output.
(4) The second quantization unit 93 acquires the input information 90a, calculates the Euler axis (drive direction) and the drive amount based on the input information 90a, and quantizes the drive direction and the drive amount at arbitrary intervals. The converted information 93a is output.
(5) The envelope calculation unit 94 outputs the gimbal angle 94a obtained from the gimbal angle steady state and the CMG angular momentum envelope using the information 93a output from the second quantization unit 93. The envelope surface calculation unit 94 has a function of, when a certain three-axis direction vector (drive direction) is input, outputting a three-axis angular momentum and a CMG gimbal angle corresponding to a CMG angular momentum envelope.

(6) The inverse kinematics calculation unit 95 acquires the quantized attitude rate 92a from the first quantization unit 92, and the gimbal angle steady state and the CMG angular momentum envelope obtained from the envelope surface calculation unit 94. The corner 94a is obtained.
(7) The inverse kinematics calculation unit 95 calculates the intermediate gimbal angle initial value 95a using the obtained two data. Inverse kinematics calculation unit 95 calculates the angular momentum at <h> = [I] * <ω IN> when the quantized orientation rate is input and <omega _IN>. Here, * indicates multiplication. The gimbal angle corresponding to <h> is obtained by Expression 5. <H (θ ₀ + △ θ)> in Equation 5 corresponds to <h>. Also, <θ ₀ > in Equation 5 is of two types, and corresponds to the gimbal angle 94 a obtained from the gimbal angle steady state and the CMG angular momentum envelope. Actually, the inverse kinematics calculation unit 95 calculates the interval between <h (θ ₀ + △ θ)> and <h (θ ₀ )> a plurality of times. For example, 0.1 <h>, 0.2 <h>,. . . , <H>, and gradually change the gimbal angle.
As described above, the inverse kinematics calculation unit 95 calculates <h (θ ₀ + θ)>, which is the first angular momentum of the spacecraft, using the attitude rate calculated by the attitude rate calculation unit 91.
The inverse kinematics calculation unit 95 calculates the gimbal rotation angle obtained from the gimbal steady state in which the three-axis total angular momentum of all control moment gyros in the coast section is zero and the angular momentum envelope of the control moment gyro. <H (θ ₀ )>, which is the second angular momentum of the spacecraft, is calculated.
The inverse kinematics calculation unit 95 converts the angular momentum time derivative into a difference between the first angular momentum <h (θ ₀ + θ)> and the second angular momentum <h (θ ₀ )> to a matrix [gimbal rotation angular velocity]. A ⁺ (θ)], an initial value θ of the intermediate gimbal rotation angle is calculated based on the gimbal rotation angle change amount obtained by multiplication. The inverse kinematics calculation unit 95 calculates the first angular momentum of the spacecraft using the quantized attitude rate, and calculates the second angular momentum of the spacecraft based on the quantized gimbal rotation angle. calculate.

(8) The above (1) to (7) are the process of calculating the intermediate gimbal angle initial value 95a.

<Step S20>
In step S20, a posture profile calculation method when the intermediate gimbal angle θcoast is given is used.
In step S20, the terminal posture is calculated using the intermediate gimbal angle. The intermediate gimbal angle is updated using the Jacobi matrix around the intermediate gimbal angle and the approximate posture profile. Update is performed an arbitrary number of times (convergence determination is unnecessary).
In the following steps, the gimbal profile generation device 100 generates a gimbal target profile based on the intermediate gimbal angle initial value 95a obtained in step S10, and calculates the terminal attitude by time integration of the gimbal target profile.

In step S21, the attitude error calculation unit 97 calculates the attitude angle of the spacecraft based on the time integration of the initial value of the intermediate gimbal rotation angle, and calculates the attitude angle of the spacecraft from the attitude angle and the attitude angle required for the spacecraft. Calculate the attitude error. This will be specifically described below.
The posture error calculator 97 acquires the input information 90a and the intermediate gimbal angle initial value 95a. When the intermediate gimbal angle is given, the attitude error calculation unit 97 calculates the attitude change amount of the spacecraft in the transition section A, coast section, and transition section B obtained based on the given intermediate gimbal angle. It can be calculated by integration. In this case, a posture angle calculation method using an intermediate gimbal is used. That is, in the time integration, the angular momentum is calculated from the gimbal angle based on Equation 1, the calculated angular momentum is multiplied by the inverse matrix of the inertia tensor of the spacecraft, the attitude rate is calculated, and the calculated attitude rate is integrated over time. Calculate the attitude angle. The attitude error calculator 97 calculates an attitude error from the spacecraft end attitude condition included in the input information 90a and the difference between the attitude angles obtained in step S21. The posture error calculator 97 outputs a posture error 97b.

ステップＳ２２においては、中間ジンバル角θｃｏａｓｔが与えられている前提での算出となるため、式１０から得られる姿勢レート変化量＜△ω＞は微小値として考えることができる。

ステップＳ２２ではジンバル回転角更新部９６は、式９又は式１２のいずれかを用いて中間ジンバル角の更新を行う。 In step S22, when the attitude error calculated by the attitude error calculation section 97 is equal to or larger than the threshold, the gimbal rotation angle update section 96 determines the time required for the coast section and the amount of attitude change required for the spacecraft in the coast section. Based on this, the posture rate corresponding to the coast section is calculated.
Attitude error calculation section 97 updates the initial value of the intermediate gimbal rotation angle based on the calculated attitude rate and the initial value of the intermediate gimbal rotation angle.
Specifically, it is as follows.
The gimbal rotation angle update unit 96 acquires the input information 90a, the posture error 97b, and the intermediate gimbal angle initial value 95a. The gimbal rotation angle update unit 96 calculates the posture rate <ω _coast > of the _coast section by using Expression 8 in order to compensate the posture error 97b by correcting the intermediate gimbal angle. Calculated from the calculated attitude rate < _ωcoast > and a given intermediate gimbal angle (calculate angular momentum from gimbal angle based on Equation 1, and multiply the calculated angular momentum by the inverse matrix of the inertia tensor of the spacecraft) Based on the calculated attitude rate <ω> and the inertia tensor [I] of the spacecraft, the gimbal rotation angle update unit 96 calculates the correction amount <△ θ> of the intermediate gimbal angle by using Expression 9 obtained by modifying Expression 5. I do.

In step S22, since the calculation is performed on the premise that the intermediate gimbal angle θcoast is given, the amount of change in the posture rate <△ ω> obtained from Expression 10 can be considered as a small value.

In step S22, the gimbal rotation angle update unit 96 updates the intermediate gimbal angle using either Equation 9 or Equation 12.

  In step S23, it is determined whether it is repetition or completion. If completed, the process of step S20 is completed. If not, the process proceeds to step S24.

In step S24, the same processing as in step S21 is performed. In step S24, the attitude error calculation unit 97 calculates the attitude angle of the spacecraft based on the time integration of the intermediate gimbal rotation angle updated by the gimbal rotation angle update unit 96.
The attitude error calculator 97 calculates an attitude error of the spacecraft from the calculated attitude angle and the attitude angle required for the spacecraft. Specifically, it is as follows.
In step S24, the intermediate gimbal angle 96a calculated by the gimbal rotation angle update unit 96 is input to the attitude error calculation unit 97.
In step S24, the posture error calculator 97 acquires the input information 90a and the intermediate gimbal angle 96a. When the intermediate gimbal angle is given, the attitude error calculation unit 97 calculates the attitude change amount of the spacecraft in the transition section A, coast section, and transition section B obtained based on the given intermediate gimbal angle. It can be calculated by integration.
In this case, a posture angle calculation method using an intermediate gimbal is used. That is, in the time integration, the angular momentum is calculated from the gimbal angle based on Equation 1, the calculated angular momentum is multiplied by the inverse matrix of the inertia tensor of the spacecraft, the attitude rate is calculated, and the calculated attitude rate is integrated over time. Calculate the attitude angle. The attitude error calculation unit 97 calculates an attitude error from the spacecraft end attitude condition included in the input information 90a and the difference between the attitude angles obtained in step S24. The posture error calculator 97 outputs a posture error 97b.

In step S25, the same processing as in step S22 is performed. In step S25, the intermediate gimbal angle 96a calculated by the gimbal rotation angle updating unit 96 is input to the gimbal rotation angle updating unit 96. The gimbal rotation angle updating unit 96 performs the same processing as in step S22.
That is, in step S25, the gimbal rotation angle updating unit 96 determines the time required for the coast section and the space time in the coast section when the posture error calculated by the posture error calculation unit 97 from the updated intermediate gimbal rotation angle is equal to or larger than the threshold. The attitude rate corresponding to the coast section is calculated based on the attitude change amount required for the aircraft. The gimbal rotation angle updating unit 96 updates the intermediate gimbal rotation angle as a constant value that does not change over time based on the intermediate gimbal rotation angle and the calculated attitude rate.

  In step S26, it is determined whether it is repetition or completion. If completed, the process of step S20 is completed. If not, the process proceeds to step S24. Generally, as the number of repetitions increases, the correction amount <△ θ> of the intermediate gimbal angle θcoast gradually decreases and tends to converge.

<Step S30>
In step S30, an error between the terminal attitude and the desired attitude change amount is determined based on the intermediate gimbal angle obtained in step S20, and an intermediate gimbal angle error correction profile is determined based on the Jacobian matrix around the intermediate gimbal angle. , Superimposed on the middle gimbal angle (applied to the coast section).
Step S30 will be described with reference to FIGS. Step S30 includes steps S31 to S33.

  In step S31, the posture error calculator 97 acquires the input information 90a and the intermediate gimbal angle. The intermediate gimbal angle here is the final value in step S20. The attitude error calculation unit 97 calculates the attitude angle and the attitude error using the input information 90a and the intermediate gimbal angle and using the attitude angle calculation method using the intermediate gimbal, as in step S21. The posture error calculator 97 outputs a posture error 97a and a posture profile.

なお、式１３、式１４、式１５は時間多項式にて表現されており、それぞれの時間微分量を容易に得ることが出来る。
ステップＳ３０では、コースト区間の始端と終端のジンバル角を補正前後で変化させないため、遷移区間Ａ及び遷移区間Ｂにおける姿勢変更量を変化させずに、全体の姿勢変更量を変化させることができる。 In step S32, the correction unit 98 calculates the attitude angle of the spacecraft based on the intermediate gimbal rotation angle of the coast section updated by the gimbal rotation angle updating unit 96. The correction unit 98 calculates a correction amount of the intermediate gimbal rotation angle in the updated coast section from the calculated attitude angle of the spacecraft.
Specifically, it is as follows.
In step S32, the correction unit 98 acquires the input information 90a and the attitude error 97a and the attitude profile from the attitude error calculation unit 97. The correction unit 98 corrects the gimbal angle in the coast section without changing the gimbal angles at the start and end of the coast section in order to compensate for the calculated error. The fact that the gimbal angles at the start and end of the coast section are not changed corresponds to the situation where the posture rates at the start and end of the coast section are not changed. Therefore, under the condition that the posture rates at the start and end of the coast section (the posture rates at the start and end in this case are the same), the correction unit 98 calculates an error compensation posture profile for correcting the error amount. At this time, the attitude rate correction amount is minute as shown in Expression 11, and the Euler rate can be used, and an error-compensated attitude profile can be given by the Euler angles and Euler rates shown in Expressions 13 and 14. . However, Expressions 13 and 14 represent only one of the Euler angles and Euler rates, and the other two components can be similarly expressed. Δφ is the amount of change in the attitude of the entire error compensation attitude profile, which coincides with the error amount. In addition, t represents the elapsed time from the start of the coast section.

Expressions 13, 14, and 15 are expressed by a time polynomial, and the time differential amount can be easily obtained.
In step S30, since the gimbal angles at the start and end of the coast section are not changed before and after the correction, the entire posture change amount can be changed without changing the posture change amount in the transition section A and the transition section B.

<Step S40>
In step S40,
The attitude error calculation unit 97 reflects the correction amount calculated by the correction unit 98 on the intermediate gimbal rotation angle updated by the gimbal rotation angle update unit 96. The attitude error calculator 97 calculates the attitude angle of the spacecraft based on the time integration of the intermediate gimbal rotation angle reflecting the correction amount. The attitude error calculation unit 97 calculates the attitude error of the spacecraft from the calculated attitude angle and the attitude angle required for the spacecraft, and calculates the calculated attitude error as an intermediate gimbal rotation angle reflecting the correction amount. The gimbal profile is added to the start point of the gimbal rotation angle in the first transition section. That is, the posture error calculation unit 97 adds the calculated posture error to the start end of the target posture profile. Specifically, it is as follows.
In step S40, based on the CMG gimbal target profile obtained in step S30, an error between the target attitude profile, the end attitude, and a desired attitude change amount is obtained, and the error is added to the target attitude profile (posture change). This is equivalent to changing the target posture condition at the start end).
In step S40, the posture error calculation unit 97 acquires the input information 90a, the intermediate gimbal angle 96a of the final value in step S20, and acquires the gimbal angle 98a corresponding to the error compensation posture profile from the correction unit 98. Attitude error calculation section 97 acquires input information 90a and intermediate gimbal angle 96a. When the intermediate gimbal angle is given, the attitude error calculation unit 97 calculates the attitude change amount of the spacecraft in the transition section A, coast section, and transition section B obtained based on the given intermediate gimbal angle. It can be calculated by integration. In this case, a posture angle calculation method using an intermediate gimbal is used. That is, in the time integration, the angular momentum is calculated from the gimbal angle based on Equation 1, the calculated angular momentum is multiplied by the inverse matrix of the inertia tensor of the spacecraft, the attitude rate is calculated, and the calculated attitude rate is integrated over time. Calculate the attitude angle. The attitude error calculator 97 calculates the attitude error amount from the spacecraft end attitude condition included in the input information 90a and the difference between the attitude angles obtained in step S24. Attitude error calculation section 97 adds the calculated error amount to the target attitude profile to obtain a final target attitude profile. Specifically, the posture error calculation unit 97 adds the calculated error amount to the start end of the target posture profile.

  The posture error calculation unit 97 adds the calculated error amount to the target posture profile. Therefore, at the posture change start end, the target posture changes by the calculated error amount. If it changes, it can be followed in the attitude feedback control, so there is no problem. Conversely, since the error from the desired posture change amount can be suppressed to zero at the posture change end, various performances such as posture control accuracy and posture stability immediately after the posture change can be improved.

*** Effect of Embodiment 1 ***
The gimbal profile generating apparatus 100 uses an arithmetic method for numerically obtaining a convergence direction (gimbal angle correction direction), such as the Newton method, in order to match the desired attitude change amount with the attitude angle obtained by time integration. Instead, an arithmetic method for obtaining the convergence direction (gimbal angle correction direction) by an approximate analytical solution from Equations 9 to 12 is used. Therefore, the calculation load can be reduced as compared with the conventional method. In addition, by performing quantization on the CMG gimbal target profile generation process, convergence stability can be guaranteed.
The gimbal profile generation apparatus 100 can generate a gimbal angle profile using Equations 3 to 5 even when no intermediate gimbal angle is given.
From step S20 to step S40, the gimbal profile generation device 100 can repeat the calculation an arbitrary number of times, but does not need to perform the convergence calculation and does not need to consider the convergence. In step S10, convergence is guaranteed by quantization as described above. As described above, the gimbal profile generation device 100 according to the first embodiment ensures convergence.

<Modification>
In the first embodiment, the function of the gimbal profile generation device 100 is realized by software. However, as a modification, the function of the gimbal profile generation device 100 may be realized by hardware.
FIG. 13 is a diagram illustrating a configuration of a gimbal profile generation device 100 according to a modification of the first embodiment. The electronic circuit 99 in FIG. 13 includes a posture rate calculator 91, a first quantizer 92, a second quantizer 93, an envelope calculator 94, an inverse kinematics calculator 95, a gimbal rotation angle update unit 96, a posture error. It is a dedicated electronic circuit that realizes the functions of the calculation unit 97 and the correction unit 98, and the functions of the memory 20, the auxiliary storage device 30, the input interface 40, and the output interface 50. The electronic circuit 99 is, specifically, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, a logic IC, a GA, an ASIC, or an FPGA. GA is an abbreviation for Gate Array.
ASIC is an abbreviation for Application Specific Integrated Circuit. FPGA is an abbreviation for Field-Programmable Gate Array. The functions of the components of the gimbal profile generation device 100 may be realized by one electronic circuit, or may be realized by being distributed to a plurality of electronic circuits. As another modification, some functions of the components of the gimbal profile generation device 100 may be realized by an electronic circuit, and the remaining functions may be realized by software.

  Each of the processor and the electronic circuit is also called a processing circuitry. That is, in the gimbal profile generation device 100, the posture rate calculation unit 91, the first quantization unit 92, the second quantization unit 93, the envelope surface calculation unit 94, the inverse kinematics calculation unit 95, the gimbal rotation angle update unit 96, the posture The functions of the error calculator 97 and the corrector 98 are realized by the processing circuitry. Alternatively, the posture rate calculation unit 91, the first quantization unit 92, the second quantization unit 93, the envelope surface calculation unit 94, the inverse kinematics calculation unit 95, the gimbal rotation angle update unit 96, the posture error calculation unit 97, and the correction unit The function of each unit of 98, the function of the memory 20, the auxiliary storage device 30, the function of the input interface 40, and the function of the output interface 50 may be realized by the processing circuitry.

  Although the first embodiment has been described above, one of the first embodiments may be partially implemented. Alternatively, two or more of the first embodiment may be partially combined for implementation. The present invention is not limited to the first embodiment, and various changes can be made as needed.

  Reference Signs List 10 processor, 20 memory, 30 auxiliary storage device, 40 input interface, 50 output interface, 60 signal lines, 90a input information, 91 attitude rate calculation section, 91a attitude rate, 92 first quantization section, 92a quantized attitude Rate, 93 second quantization unit, 93a information, 94 envelope surface calculation unit, 94a gimbal angle, 95 inverse kinematics calculation unit, 95a intermediate gimbal angle initial value, 96 gimbal rotation angle update unit, 96a intermediate gimbal angle, 97 attitude Error calculator, 97a attitude error, 97b attitude error, 98 corrector, 98a gimbal angle, 99 electronic circuit, 100 gimbal profile generator, 200 gimbal, 201 spin axis, 202 gimbal axis, 203 gimbal rotation angle.

Claims (9)

A coast, which is used for attitude control of a spacecraft having a plurality of control moment gyros and is located between a first transition section, a second transition section, and the first transition section and the second transition section. A gimbal profile generation device that generates a gimbal profile having a gimbal rotation angle divided into sections and
An attitude rate calculation unit that calculates an attitude rate of the spacecraft based on an attitude change amount required for the spacecraft,
A gimbal steady state in which the first angular momentum of the spacecraft is calculated using the attitude rate calculated by the attitude rate calculation unit, and the three-axis total angular momentum of all the control moment gyros in the coast section is zero. A second angular momentum of the spacecraft is calculated based on a gimbal rotation angle obtained from the state and a control moment gyro angular momentum envelope, and an angular momentum time is calculated as a difference between the first angular momentum and the second angular momentum. An inverse kinematics calculation unit that calculates an initial value of the intermediate gimbal rotation angle based on a gimbal rotation angle change amount obtained by multiplying a matrix that converts the derivative into a gimbal rotation angular velocity;
An attitude for calculating an attitude angle of the spacecraft based on a time integration of an initial value of the intermediate gimbal rotation angle, and calculating an attitude error of the spacecraft from the attitude angle and an attitude angle required for the spacecraft. A gimbal profile generation device including an error calculation unit. The gimbal profile generation device includes:
When the attitude error calculated by the attitude error calculation unit is equal to or greater than a threshold, the attitude error corresponds to the coast interval based on the time required for the coast interval and the amount of attitude change required for the spacecraft in the coast interval. Calculate the posture rate to do,
The gimbal profile generation device according to claim 1, further comprising: a gimbal rotation angle update unit that updates the initial value of the intermediate gimbal rotation angle based on the initial value of the intermediate gimbal rotation angle and the calculated posture rate. The attitude error calculation unit,
The attitude angle of the spacecraft is calculated based on the time integration of the intermediate gimbal rotation angle updated by the gimbal rotation angle updating unit, and the calculated attitude angle and the attitude angle required for the spacecraft are 3. The gimbal profile generation device according to claim 2, wherein the attitude error of the spacecraft is calculated. The gimbal rotation angle update unit,
When the attitude error calculated by the attitude error calculation unit from the updated intermediate gimbal rotation angle is equal to or greater than a threshold, the time required for the coast interval, the amount of attitude change required for the spacecraft in the coast interval, Calculating an attitude rate corresponding to the coast section based on the intermediate gimbal rotation angle and updating the intermediate gimbal rotation angle as a constant value that does not change with time based on the calculated attitude rate. Item 3. The gimbal profile generation device according to item 3. The gimbal profile generation device further includes:
The attitude angle of the spacecraft is calculated based on the intermediate gimbal rotation angle of the coast section updated by the gimbal rotation angle update unit, and the intermediate gimbal of the coast section updated from the calculated attitude angle of the spacecraft. The gimbal profile generation device according to claim 4, further comprising a correction unit that calculates a correction amount of the rotation angle. The attitude error calculation unit,
The correction amount calculated by the correction unit is reflected in the intermediate gimbal rotation angle updated by the gimbal rotation angle update unit, and the correction amount is reflected based on a time integration of the intermediate gimbal rotation angle. Calculating an attitude angle, calculating an attitude error of the spacecraft from the calculated attitude angle and the attitude angle required for the spacecraft, and adding the calculated attitude error to the beginning of a target attitude profile. Item 6. The gimbal profile generation device according to item 5. The inverse kinematics calculation unit,
The method according to claim 1, wherein a first angular momentum of the spacecraft is calculated using the attitude rate that is quantized, and a second angular momentum of the spacecraft is calculated based on the gimbal rotation angle that is quantized. The gimbal profile generation device according to claim 6. A coast, which is used for attitude control of a spacecraft having a plurality of control moment gyros and is located between a first transition section, a second transition section, and the first transition section and the second transition section. In a gimbal profile generation program that generates a gimbal profile having a gimbal rotation angle divided into sections,
A process of calculating the attitude rate of the spacecraft based on the attitude change amount required for the spacecraft;
A first angular momentum of the spacecraft is calculated using the calculated attitude rate, and a gimbal steady state indicating a state in which the three-axis total angular momentum of all the control moment gyros in the coast section is zero and a control moment gyro are calculated. A second angular momentum of the spacecraft is calculated based on the gimbal rotation angle obtained from the angular momentum envelope and the difference between the first angular momentum and the second angular momentum is used to convert the angular momentum time derivative into a gimbal rotation angular velocity. A process of calculating an initial value of the intermediate gimbal rotation angle based on a gimbal rotation angle change amount obtained by multiplying the matrix to be converted;
A process of calculating an attitude angle of the spacecraft based on a time integration of an initial value of the intermediate gimbal rotation angle, and calculating an attitude error of the spacecraft from the attitude angle and an attitude angle required for the spacecraft. A gimbal profile generation program that causes a computer to execute A coast, which is used for attitude control of a spacecraft having a plurality of control moment gyros and is located between a first transition section, a second transition section, and the first transition section and the second transition section. In a gimbal profile generation method in which a computer generates a gimbal profile having a gimbal rotation angle divided into sections,
Computer
Calculate the attitude rate of the spacecraft based on the attitude change amount required for the spacecraft,
A first angular momentum of the spacecraft is calculated using the calculated attitude rate, and a gimbal steady state indicating a state in which the three-axis total angular momentum of all the control moment gyros in the coast section is zero and a control moment gyro are calculated. A second angular momentum of the spacecraft is calculated based on the gimbal rotation angle obtained from the angular momentum envelope and the difference between the first angular momentum and the second angular momentum is used to convert the angular momentum time derivative into a gimbal rotation angular velocity. Calculate the initial value of the intermediate gimbal rotation angle based on the gimbal rotation angle change obtained by multiplying the matrix to be converted,
A gimbal that calculates an attitude angle of the spacecraft based on a time integration of an initial value of the intermediate gimbal rotation angle, and calculates an attitude error of the spacecraft from the attitude angle and an attitude angle required for the spacecraft. Profile generation method.

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