RU2779658C1 - Method for orientation of near-earth orbiting spacecraft - Google Patents

Abstract

FIELD: space technology.

SUBSTANCE: invention relates to systems for orientation of spacecrafts (hereinafter – SC) in the Earth’s magnetic field (hereinafter – EMF). According to the invention, magnetometers measuring a magnetic induction vector (B) of EMF in a related coordinate system (hereinafter – RCS) of SC are used as sensors of SC position. A magnetic induction vector (B₀) of EMF in projections on the axis of an orbital coordinate system (hereinafter – OCS) is calculated by an analytical model of EMF. Rotation of SC relatively to OCS is equated to reverse rotation of the vector: B→A relatively to OCS, while the rotated vector A is assigned with coordinates of the vector B in RCS, by which quaternion of mutual orientation of vectors A and B₀ in OCS is calculated. The corresponding quaternion of an angular velocity is calculated by measured projections of the absolute angular velocity of SC on the axis of RCS. The method allows for restoration of orientation of SC in OCS from a random position, as well as for program orientation of SC in OCS without limitations.

EFFECT: applicability of a method to almost any types of SC, and the most effectively to SC of small sizes.

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Description

The invention relates to the field of space technology and can be used for orientation of an orbital near-Earth spacecraft (SC) relative to the orbital coordinate system (OSC) using the Earth's magnetic field (EMF) without the use of special external orientation sensors (Sun sensor, astro sensor, Earth orientation device and others).

As a triaxial orientation sensor, magnetometers (MGMs) installed along the coupled axes of the spacecraft are used.

There are known methods of spacecraft orientation [1-5, 7-15], according to which the Earth's magnetic field is used both as a reference point and as a force field to create mechanical moments that stabilize the position of the spacecraft relative to the USC.

Distinguish between passive and active methods of spacecraft orientation. Passive methods are based on the use of permanent magnets or electrostatic charges distributed over the satellite body [9, 13], interacting with the Earth's magnetic field, and additional gravitational rods, which makes it possible to bring the satellite into a certain stable position.

In active orientation methods, a mechanical moment on the spacecraft body is created by using controlled electromagnetic coils (EMCs) interacting with the EMF or flywheel control motors (FMOs) [7]. There is also a known method for stabilizing a spacecraft in a magnetic field by using a flywheel engine [8], the kinetic moment of which is located along the pitch axis of the spacecraft (along the binormal to the plane of the orbit), due to which gyroscopic moments are created that act directly on the satellite body (like a gyroorbitant), and keep, thus, the spacecraft in the plane of the orbit.

These methods of passive and active types are used for orientation of micro- and nanosatellites, because the values of the generated magnetic moments are small, the stock of stable orientation is enough only for small payloads. In addition, orientation algorithms require differentiation of the difference between the measured and calculated data on the Earth's magnetic induction vector, which degrades the accuracy and quality of the spacecraft's orientation.

магнитного поля Земли (МПЗ), магнитометрами (МГМ), установленными по осям связанной системы координат (ССК) и вычисление соответствующего этому положению вектора магнитной индукции

МПЗ в проекциях на оси ОСК по Международному аналитическому геомагнитному полю Земли.There is a known method for orienting satellites in USC [8, p. 156], including the measurement of the magnetic induction vector

of the Earth's magnetic field (EMF), magnetometers (MGM) installed along the axes of the coupled coordinate system (CCS) and the calculation of the magnetic induction vector corresponding to this position

EMF in projections on the USC axis according to the International Analytical Geomagnetic Field of the Earth.

This method is accepted as the closest analogue.

The disadvantage is the lack of the ability to orient the spacecraft relative to the USC, using the readings of magnetometers alone, without using additional data from external sensors of external information, such as solar sensors, star sensors, and the inapplicability of the method for overall and heavy spacecraft.

The technical task of the proposed technical solution is to create a SC control method capable of restoring the SC orientation relative to the USC from an arbitrary unoriented position, using the measurements of some magnetometers - according to the "blind satellite" principle and regardless of its mass and dimensions.

This method of spacecraft orientation in the Earth's magnetic field allows you to completely get rid of external information sensors and restore the spacecraft's orbital orientation at any time and in any part of the orbit.

In contrast to a close analogue, which includes measurements of the current projections of the magnetic induction vector _Вс (b _xc , b _yc , b _zc ) of the magnetic field

и

в ОСК, измеряют с помощью гироскопических датчиков угловых скоростей проекции абсолютной угловой скорости КА на оси ССК ω (ω_x, ω_y, ω_z), принимают в те же моменты времени от навигационно-баллистического обеспечения данные о параметрах угловой скорости ОСК относительно ИСК ω_o (ω_хо, ω_yo, ω_zo), определяют угловую скорость КА относительно ОСК ω_с (ω_xc, ω_yc, ω_zc) = ω-Cω_oC^T, где С - матрица, составленная из элементов кватерниона q, т - знак транспонирования, вычисляют скорость

подают сигналы управления на активные исполнительные органы КА пропорционально

где n=1, 2, 3 и поворачивают КА до совмещения показаний МГМ с расчетными значениями магнитной индукции МПЗ по соответствующим осям ОСК, завершая тем самым процесс восстановления ориентации КА.of the Earth (EMS) by magnetometers (MGMs) installed along the axes of the coupled coordinate system (CCS), and the simultaneous calculation of the magnetic induction vector B _o (b _xo , b _yo , b _zo ) of the EMF in projections onto the axes of the orbital coordinate system (OCS) using of the analytical model of the Earth's geomagnetic field (GMF), in the proposed orientation method, the rotation of the spacecraft relative to the USC is equated with the reverse rotation of the measured vector relative to the USC, while the rotated vector A (A _x , A _y , A _z ) is assigned the coordinates of the vector B in the SSC according to the rule A _x ≡B _x , A _y ≡B _y , A _z ≡B _z , which calculate the quaternion q=q ₀ +iq ₁ +jq ₂ +kq _{3 of} the mutual orientation of the vectors

and

in the USC, using gyroscopic sensors of angular velocity of the projection of the absolute angular velocity of the spacecraft on the axis of the SSC ω (ω _x , ω _y , ω _z ), receive at the same time from the navigation and ballistic support data on the parameters of the angular velocity of the USC relative to the ISC ω _o (ω _ho , ω _yo , ω _zo ), determine the angular velocity of the spacecraft relative to the USC ω _c (ω _xc , ω _yc , ω _zc ) = ω-Cω _o C ^T , where C is a matrix composed of elements of the quaternion q, t - sign of transposition, calculate speed

send control signals to the active executive bodies of the spacecraft in proportion to

where n=1, 2, 3 and turn the spacecraft until the readings of the MGM coincide with the calculated values of the magnetic induction of the EMF along the corresponding axes of the USC, thereby completing the process of restoring the orientation of the spacecraft.

Below is a practical example of the implementation of the proposed method.

The physical meaning of the VO KA method with respect to the OSC is based on the property of an invertible mapping - the isomorphism of the linear transformation of the vector coordinates with an orthogonal rotation of a 3-dimensional basis:

a=M⋅b

In accordance with this property [6], the transformation of the vector coordinates due to the rotation of the base coordinate system is equivalent to the rotation of the vector itself in the original coordinate system (ISC). In other words, we don't know what is transformed - the coordinates of the vector in the rotated coordinate system, or the coordinates of the rotated vector in the original coordinate system relative to its own initial position. In this case, both transformation matrices are the same. The difference is that as a result of rotating a vector in the original coordinate system, its transformed coordinates will also be in the original (and not in the rotated) coordinate system and will exactly correspond to its own coordinates in the rotated coordinate system.

This property formed the basis for the development of a method for restoring the orientation of the spacecraft using data from three orthogonally located magnetometers.

Orientation is restored until the calculated and measured vectors of the magnetic induction of the Earth's field coincide.

The quaternion of the mutual orientation of the vectors B _o ( _{Box Boy} B _oz ) and B _c (B _cx B _cy B _cz ), after their normalization, is conveniently calculated by the formula:

We calculate the angular velocities of the spacecraft relative to the USC

ω _c \u003d ω-C _o C ^T ,

where

C is a matrix composed of quaternion elements q (Rodrigues-Hamilton matrix), ω is a skew-symmetric matrix composed of BIUS readings, ω _o is a skew-symmetric matrix of angular velocities of the USC relative to the ISC (from ballistics data).

We calculate the angular velocities of the quaternions using the formula:

где n=1, 2, 3:

We form control signals to the executive bodies proportionally

where n=1, 2, 3:

We give control signals to the executive bodies (IO), rotate the spacecraft until A _o and B _o coincide (cosϕ = 1), completing the process of restoring the spacecraft orientation.

Note that any IO can be chosen as an IO, for example, UDM or jet engines.

Figures 1 and 2 show graphs of the orientation of the spacecraft in the process of restoring the orientation of the spacecraft from non-oriented positions in the USC.

In FIG. 1 shows small initial deviations of the spacecraft from the OSK.

In FIG. Figure 2 shows an arbitrary position of the spacecraft relative to the OSC with very large initial angular deviations of the spacecraft from the OSC.

From the graphs presented, it can be seen that the processes of restoring the orientation of the spacecraft from an unoriented position are quite fast and with good quality. The orientation accuracy was ~0.3° in angle and ~0.001°/s in angular velocity.

MGSO allows you to perform programmed turns of the spacecraft at arbitrary angles relative to the USC.

вычисляют угловую скорость КА (ССК) относительно ПСК по формуле ω_cn=ω-Sω_oS^T-SPω_n(SP)^T, где S -матрица, составленная из элементов кватерниона λ, ω_n - кососимметричная матрица программных скоростей КА, Т - знак транспонирования, после чего вычисляют скорости

подают сигналы управления на активные исполнительные органы КА пропорционально

где m=1, 2, 3 и поворачивают КА до совмещения показаний МГМ с расчетными значениями магнитной индукции МПЗ по соответствующим осям ПСК, завершая тем самым процесс программного поворота КА относительно ОСК.To implement the method according to claim 2, first set the program position of the spacecraft relative to the USC and recalculate the projections of the previously calculated vector B _o on the axes of the program basis B _n (B _xn , B _yn , B _zn )=P⋅B _o (B _xo , B _yo , B _zo ), where P is the matrix of the required orientation of the program coordinate system (PCS) relative to the CCS, the rotation of the spacecraft now relative to the CCS is equated to the reverse rotation of the measured vector B→A _n relative to the CCS, while the rotated vector A _n (A _xp , A _ur , A _zp ) assign the measured coordinates of the vector B according to the rule A _{xp ≡B} xc , A _ur ≡B _yc , A _zp ≡B _zc , calculate the quaternion of mutual orientation λ=λ ₀ +i'λ ₁ +j'λ ₂ +k'λ ₃ vectors

calculate the _angular ^velocity of the ^spacecraft ( _SSK ) _relative to the _PSK by the formula transposition sign, after which the speeds are calculated

send control signals to the active executive bodies of the spacecraft in proportion to

where m=1, 2, 3 and rotate the spacecraft until the readings of the MGM coincide with the calculated values of the magnetic induction of the EMF along the corresponding axes of the UCS, thereby completing the process of programmatic rotation of the spacecraft relative to the USC.

An illustration of the program rotation of the spacecraft is shown in figures 3 and 4. The spacecraft performs stable and high-quality program turns simultaneously at orientation angles relative to the USC ψ _p = 180°, ϑ _p = -75°, γ _p =120°. In the process of rotation, the magnetic induction vectors in the PSK and SSK systems coincide (Fig. 4).

Thus, the proposed method for the orientation of a near-Earth orbital spacecraft allows performing two functions - restoring the orientation of the spacecraft from an arbitrary unoriented position and controlling the program position of the spacecraft without restrictions on the set program angles.

Used sources

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2. Beletsky V.V., Golubkov V.V., Stepanova E.A., Khitskevich I.G. Determining the orientation of artificial satellites from measurement data. M., edition of IPM AN USSR, 1967.

3. Belokonov I.V., Kramlikh A.V. A technique for restoring the orientation of a spacecraft when combining magnetometric and radio navigation measurements. Bulletin of the Samara State Aerospace University. S.P. Queen, 2007.

4. Belyaev M.Yu. Scientific experiments on spacecraft and orbital stations. M., Mashinostroenie, 1984.

5. Vorontsov A.V., Gorbunov A.V., Karbasnikov B.V., Kozakov A.V. Approximate model of the operation of a magnetogyroscopic orbiter as part of an attitude control system of a satellite of the type "METEOR-M", M., Voprosy elektromekhaniki T. 106. 2008.

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7. Ivanov D.S., Ivlev N.A., Karpenko S.O., Ovchinnikov M.Yu., Roldugin D.S., Tkachev S.S. Flight test results of the Chibis-M microsatellite attitude control system, Space Research. 2014, volume 52, no. 3, p. 218-228.

8. Kazakov A.V. The magnetogyroscopic system is a worthy rival of the gravitational orientation system on small satellites. [Electronic resource]/. Electronic print version. publ.// jumal.vniiem.ru/

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10. Ovchinnikov M.Yu., Penkov V.I., Roldugin D.S. Magnetic systems of small satellites. M., edition of IPM RAS, 2016, 366 p.

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Claims (1)

A method for orientation of a near-Earth orbital spacecraft (SC), including measurements of the current projections of the magnetic induction vector B (B _x , B _y , B _z ) of the Earth's magnetic field (EMF) with magnetometers (MGM) installed along the axes of a coupled coordinate system (CCS), and simultaneous calculation of the magnetic induction vector B _o (B _xo , B _yo , B _zo ) EMF in projections on the axis of the orbital coordinate system (OSC) using an analytical model of the Earth's geomagnetic field (GMF), the rotation of the spacecraft, characterized in that the rotation of the spacecraft is equated relative to OSK reverse rotation of the measured vector B → A relative to the OSK, while the rotated vector A (A _x , A _y , A _z ) is assigned the coordinates of the vector B in the SSC according to the rule A _x \u003d B _x , A _y \u003d B _y , A _z \u003d B _z , which calculate the quaternion q=q ₀ +iq ₁ +iq ₂ +kq _{3 of} the mutual orientation of the vectors

and

in the USC, using gyroscopic sensors of angular velocity of the projection of the absolute angular velocity of the spacecraft on the axis of the SSC ω (ω _x , ω _y , ω _z ), receive at the same time from the navigation and ballistic support data on the parameters of the angular velocity of the USC relative to the original system coordinates (ISC) ω _o (ω _ho , ω _yo , ω _zo ), determine the angular velocity of the spacecraft relative to the USC ω _c (ω _xc , ω _yc , ω _zc )=ω-Cω _o C ^T , where C is a matrix composed of elements of the quaternion q, T is the sign of the transposition, calculate the speed

send control signals to the active executive bodies of the spacecraft in proportion to

where n=1, 2, 3, and turn the spacecraft until the readings of the MGM coincide with the calculated values of the magnetic induction of the EMF along the corresponding axes of the USC, thereby completing the process of restoring the orientation of the spacecraft, or set the program position of the spacecraft relative to the USC and recalculate the projections of the previously calculated vector B _o on the axis of the program basis B _n (B _xn , B _yn , B _zn )=Р⋅В _o (B _xo , B _yo , B _zo ), where Р is the matrix of the required orientation of the program coordinate system (PCS) relative to the CCS, the rotation of the spacecraft is now already with respect to the UCS, it is equated to the reverse rotation of the measured vector B → A _n relative to the UCS, while the rotated vector A _n (A _xp , A _yp , A _zp ) is assigned the measured coordinates of the vector B according to the rule A _{xp ≡B} xc , A _ur = B _yc , A _zp =In _zc , calculate the quaternion of mutual orientation λ=λ ₀ +i'λ ₁ +j'λ ₂ +k'λ ₃ vectors

and

calculate the angular _velocity of the ^spacecraft ( _SSK ) _relative ^to the _PSK by the formula transposition sign, after which the speeds are calculated

send control signals to the active executive bodies of the spacecraft proportionally

where m=1, 2, 3, and rotate the spacecraft until the readings of the MGM coincide with the calculated values of the magnetic induction of the EMF along the corresponding axes of the UCS, thereby completing the process of programmatic rotation of the spacecraft relative to the USC.

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