Method for determining available angular momentum space during partial failure of control moment gyroscope group

Abstract

The invention discloses a method for determining an available angular momentum space during partial failure of a control moment gyroscope group. The method can be applied to a control moment gyroscope group control system with a pentagonal pyramid structure. According to the method, the shape and the position of an angular momentum available space when only three control moment gyroscopes in the six control moment gyroscopes are available are given. According to the method, complex trajectory optimization and singular avoidance problems are simplified into simple geometric problems, and finally a visual analysis structure is obtained and can be directly used as binding parameters for on-satellite calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite control moment gyros, and in particular to a method for determining the available angular momentum space when part of the control moment gyro group fails. Background Art

[0002] With the continuous development of space technology, the types of satellite missions are becoming more and more diverse, and the design of the control system is becoming more and more targeted. Among them, the application of control moment gyros well meets the agile maneuvering requirements of some satellites. For long-life and frequently maneuvering spacecraft, the pentagonal pyramid configuration composed of 6 control moment gyros is the best configuration of the control moment gyro group. The configuration efficiency, failure efficiency, controllability efficiency, and singularity loss rate in this configuration are much better than those of other common configurations (such as the pyramid configuration, the quadrangular pyramid configuration, etc.). To ensure that the system has sufficient control ability and singularity avoidance ability, generally at least 4 out of 6 control moment gyros are used for control. However, when only 3 out of 6 control moment gyros are available (for example, the total power limit does not allow the use of more control moment gyros, or only 3 control moment gyros can work), the control ability of the system will be greatly reduced. Therefore, it is necessary to clarify the available angular momentum space in the case of partial failure to make the best use of the existing control ability as much as possible and ensure the long-term stable operation of the system. Summary of the Invention

[0003] The present invention provides a method for determining the available angular momentum space when part of the control moment gyro group fails, which is applied to the control moment gyro group control system with a pentagonal pyramid configuration. This method gives the shape and position of the available angular momentum space when only 3 out of 6 control moment gyros are available, and provides a design idea for the bias angular momentum design and control strategy when part of the control moment gyro group fails.

[0004] In a first aspect, a method for determining the available angular momentum space when part of the control moment gyro group fails is provided. The control moment gyro group is composed of 6 control moment gyros to form a pentagonal pyramid configuration. The installation coordinate system of the control moment gyro group is Oa-XaYaZa, and the single control moment gyro coordinate system is Oi-XiYiZi, where i is the number of the control moment gyro. OiYi represents the forward rotation direction of the frame, OiZi represents the angular momentum direction when the inner rotor rotates forward, and OiXi represents the torque direction generated by the instantaneous forward rotation of the frame. When the frame angle is 0, the OiXi axis is parallel to the XaOaYa plane, and the included angle between the OiYi axis and the OaZa axis is an obtuse angle. The included angle between the frame axes of any two control moment gyros is 63.4349°. The frame axis of the No. 1 control moment gyro is located in the XaOaYa plane, the frame axis of the No. 6 control moment gyro points to the -OaZa direction, and the No. 1, 2, 3, 4, and 5 control moment gyros are arranged in sequence around the OaZa axis. Projecting along the -OaZa direction, the No. 1, 2, 3, 4, and 5 control moment gyros are arranged counterclockwise, including:

[0005] Determine the numbers and rotation-related parameters of the three selected control moment gyros;

[0006] According to the numbers of the three selected control moment gyros, determine the corresponding configurations, and reorder the numbers of the three selected control moment gyros;

[0007] According to the numbers of the three sorted control moment gyros and the corresponding configurations, calculate the azimuth vectors to determine the center and magnitude of the available angular momentum space.

[0008] Combined with the first aspect, in some implementation manners of the first aspect, according to the numbers of the three selected control moment gyros, determine the corresponding configurations, including:

[0009] When the numbers of the three selected control moment gyros are any one of the following, the corresponding configuration is a type-I configuration: 123, 234, 345, 145, 125, 146, 136, 246, 256, 356;

[0010] When the numbers of the three selected control moment gyros are any one of the following, the corresponding configuration is a type-II configuration: 126, 236, 346, 456, 156, 124, 235, 134, 245, 135.

[0011] Combined with the first aspect, in some implementation manners of the first aspect, the corresponding relationship for reordering the type-I configuration is:

[0012] If it is 123 before sorting, it is 312 after sorting;

[0013] If it is 234 before sorting, it is 423 after sorting;

[0014] If it is 345 before sorting, it is 534 after sorting;

[0015] If it is 145 before sorting, it is 145 after sorting;

[0016] If it is 125 before sorting, it is 251 after sorting;

[0017] If it is 146 before sorting, it is 416 after sorting;

[0018] If it is 136 before sorting, it is 136 after sorting;

[0019] If it is 246 before sorting, it is 246 after sorting;

[0020] If it is 256 before sorting, it is 526 after sorting;

[0021] If it is 356 before sorting, it is 356 after sorting.

[0022] In combination with the first aspect, in some implementations of the first aspect, the correspondence of the reordering of the second-class configuration is as follows:

[0023] If the number before sorting is 126, then the number after sorting is 126;

[0024] If the number before sorting is 236, then the number after sorting is 236;

[0025] If the number before sorting is 346, then the number after sorting is 346;

[0026] If the number before sorting is 456, then the number after sorting is 456;

[0027] If the number before sorting is 156, then the number after sorting is 516;

[0028] If the number before sorting is 124, then the number after sorting is 142;

[0029] If the number before sorting is 235, then the number after sorting is 253;

[0030] If the number before sorting is 134, then the number after sorting is 314;

[0031] If the number before sorting is 245, then the number after sorting is 425;

[0032] If the number before sorting is 135, then the number after sorting is 531.

[0033] In combination with the first aspect, in some implementations of the first aspect, according to the numbers of the three control moment gyros after sorting and the corresponding configurations, calculate the azimuth vector, including:

[0034] If the number of the control moment gyro in the a-th position after sorting is i, then the azimuth vector corresponds to G i where a = 1, 2, 3, and G i is the i-th column of the moment direction matrix G0 of the control moment gyro group.

[0035] In combination with the first aspect, in some implementations of the first aspect, for the second-class configuration, when a = 2, and the numbers of the three selected control moment gyros are any of the following, the azimuth vector 124, 235, 134, 245, 135; for other cases of the second-class configuration and the first-class configuration, the azimuth vector

[0036] In combination with the first aspect, in some implementations of the first aspect, for the first-class configuration, the available angular momentum space is 1 annular space + 2 spherical spaces; the central plane of the available annular space passes through the vector g4 and is perpendicular to the vector g5, and the two available spherical spaces are on the vector g5 and the reverse extension line of the vector g5. The calculation process of the vector g4 is as follows:

[0037]

[0038] g4 = g4 / |g4|

[0039] The vector g5 is obtained by rotating the azimuth vector about the vector g4 by an angle θ,

[0040] θ = 180° - acos(cos(63.4349°)cos(72°)).

[0041] Combined with the first aspect, in some implementations of the first aspect, for a certain type of configuration, determine the maximum value of the outer singular envelope in the direction of g5 The maximum value of the outer singular envelope in the direction perpendicular to g5 The maximum value of the inner singular envelope in the direction of g5 The maximum value of the inner singular envelope in the direction perpendicular to g5

[0042] Determine the distance between the centers of the two spherical available spaces from the coordinate center The radius of the sphere The radius of the central circle of the ring of the annular available space The radius of the ring

[0043] Combined with the first aspect, in some implementations of the first aspect, for a second type of configuration, the available angular momentum space is 8 spherical spaces; two spherical available spaces are on the vector g5 and the extended line in the opposite direction of the vector g5, two spherical available spaces are on the vector g 10 and the vector g 10 on the extended line in the opposite direction, two spherical available spaces are on the vector g 13 and the vector g 13 on the extended line in the opposite direction, two spherical available spaces are on the vector g 16 and the vector g 16 on the extended line in the opposite direction; the calculation process of the vector g5 is as follows:

[0044]

[0045] g5 = g5 / |g5|

[0046] The vector g 10 is the normal of the plane formed by the vector g9 and the vector g8, the vector g8 is the normal of the plane formed by the vector g5 and the positioning vector The calculation process of the vector g9 is as follows:

[0047]

[0048] g9 = g9 / |g9|, β is the angle between the vector g5 and the positioning vector ;

[0049] Vector g 13 is vector g 12 and vector g 11 form the normal direction of the plane. Vector g 11 is the normal direction of the plane formed by vector g5 and the positioning vector Vector g 12 The calculation process is as follows:

[0050]

[0051] g 12 = g 12 / |g 12 |

[0052] Vector g 16 is vector g 15 and vector g 14 form the normal direction of the plane. Vector g 14 is the normal direction of the plane formed by vector g5 and the positioning vector Vector g 15 The calculation process is as follows:

[0053]

[0054] g 15 = g 15 / |g 15 |.

[0055] Combined with the first aspect, in some implementations of the first aspect, determine the maximum value of the outer singular envelope in the direction of g5 g 10 、g 13 、g 16 the maximum value of the outer singular envelope in the direction the maximum value of the inner singular envelope in the direction of g5 g 10 、g 13 、g 16 the maximum value of the inner singular envelope in the direction

[0056] Two spherical available spaces on g5 and the reverse extension line of g5, the center of the sphere is at a distance from the coordinate center Sphere radius

[0057] The remaining 6 spherical available spaces, the center of the sphere is at a distance from the coordinate center Sphere radius

[0058] Compared with the prior art, the solution provided by the present invention at least includes the following beneficial technical effects:

[0059] The present invention mainly utilizes the symmetry of the regular dodecahedron, classifying the situation where only 3 out of 6 control moment gyros are available into two major categories; re - sorting the selected control moment gyros for unified subsequent calculation methods; calculating the relevant geometric relationships based on the frame - axis vectors of the available control moment gyros to obtain the orientation of the available angular - momentum space; and determining the specific shape and position of the available angular - momentum space according to the singular distribution of the control - moment - gyro group. The present invention simplifies the complex trajectory - optimization and singularity - avoidance problems into simple geometric problems, and finally obtains an intuitive analytical structure, which can be directly used as the binding parameters for on - satellite calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flowchart for determining the available angular - momentum space when part of the control - moment - gyro group fails.

[0061] Figure 2 It is a schematic diagram of the "123" - type configuration.

[0062] Figure 3 It is a schematic diagram of the "126" - type configuration.

[0063] Figure 4 It is a schematic diagram of the partial singular distribution of the control - moment - gyro group in the "123" - type configuration.

[0064] Figure 5 It is a schematic diagram of the partial singular distribution of the control - moment - gyro group and the distribution of the available angular - momentum space in the "123" - type configuration.

[0065] Figure 6 It is a schematic diagram of the partial singular distribution of the control - moment - gyro group in the "126" - type configuration.

[0066] Figure 7 It is a schematic diagram of the partial singular distribution of the control - moment - gyro group and the distribution of the available angular - momentum space in the "126" - type configuration.

[0067] Figure 8 It is a schematic diagram of the installation of the control - moment - gyro group in the pentagonal - pyramid configuration. DETAILED DESCRIPTION OF THE INVENTION

[0068] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0069] As Figure 1 shown, the present invention provides a method for determining the available angular - momentum space when part of the control - moment - gyro group fails, and the specific steps are as follows.

[0070] 1. Determine the relevant parameters of the selected control - moment - gyro group.

[0071] According to the installation characteristics and selection of the control moment gyroscope group, determine the frame axis direction matrix G, the moment direction matrix A and the angular momentum direction matrix B when the frame angle is 0; according to the rotation characteristics of the inner rotor of the control moment gyroscope, determine the nominal angular momentum h0 of the inner rotor.

[0072] 2. Reorder the selected 3 control moment gyroscopes according to the combination to which they belong.

[0073] According to the geometric characteristics of the regular dodecahedron, divide all 20 combinations of 3 control moment gyroscopes into two types of configurations, namely "123" and "126", with 10 combinations in each type. See Table 1 for details. To unify the method of calculating the azimuth vector, different combinations of control moment gyroscopes under different classifications need to be arranged in a certain order. For the "126" type of configuration, it is necessary to specify the direction of the frame axis vector of the No. 2 control moment gyroscope in the new order, which is achieved by multiplying the frame axis coefficient. +1 means the same direction as the original vector, and -1 means the opposite direction to the original vector.

[0074] 3. Calculate the azimuth vector. Calculate the vector that can describe the azimuth of the available angular momentum space according to the frame axis.

[0075] 4. Determine the center and size of the available angular momentum space. Determine the singular point distribution according to the moment direction matrix, angular momentum direction matrix and nominal angular momentum of the inner rotor obtained in step 1. According to the criterion that the available angular momentum space is as large as possible and the outer envelope has no intersection with the singular points, determine the geometric center and size of the available angular momentum space according to the azimuth vector calculated in step 3 and the singular distribution of the control moment gyroscope combination. The methods of calculating the azimuth vector for the "123" and "126" types of configurations are different.

[0076] The following takes the common pentagonal pyramid configuration control moment gyroscope group as an example to introduce the specific implementation steps of the algorithm.

[0077] Establish the installation coordinate system Oa-XaYaZa of the control moment gyroscope group, and establish the single control moment gyroscope coordinate system Oi-XiYiZi (i = 1, 2,..., 6), where OiYi represents the positive rotation (counterclockwise) direction of the frame, OiZi represents the angular momentum direction when the inner rotor rotates positively (counterclockwise), and OiXi represents the moment direction generated by the instantaneous positive rotation of the frame. It is agreed that when the frame angle is 0, the OiXi axis is parallel to the XaOaYa plane, and the included angle between the OiYi axis and the OaZa axis is an obtuse angle. See Figure 8 , the included angle between the frame axes of any two control moment gyroscopes is 63.4349°. The frame axis of the No. 1 control moment gyroscope is located in the XaOaYa plane, the frame axis of the No. 6 control moment gyroscope points to the -OaZa direction, and the No. 1, 2, 3, 4, and 5 control moment gyroscopes are arranged in sequence around the OaZa axis. Projected along the -OaZa direction, the No. 1, 2, 3, 4, and 5 control moment gyroscopes are arranged counterclockwise.

[0078] Step 1: Determine the relevant parameters of the selected control moment gyroscope group.

[0079] When not considering the selected combination, the torque direction matrix of the control moment gyroscope group is G0, and the dimension of this matrix is 3×6. Each column element corresponds to the component of the OiYi axis in the Oa-XaYaZa system when the frame angle is 0. The order from left to right is 1→6.

[0080] G0 = [G1 G2... G6]

[0081] When not considering the selected combination, the torque direction matrix of the control moment gyroscope group is A0, and the dimension of this matrix is 3×6. Each column element corresponds to the component of the OiXi axis in the Oa-XaYaZa system when the frame angle is 0. The order from left to right is 1→6; the angular momentum direction matrix of the control moment gyroscope group is B0, and the dimension of this matrix is 3×6. Each column element corresponds to the component of the OiZi axis in the Oa-XaYaZa system when the frame angle is 0. The order from left to right is 1→6.

[0082] Let k cmg_i be the selection flag of the i-th control moment gyroscope, where 1 means selected and 0 means not selected. In the embodiment provided in this application, only 3 out of 6 control moment gyroscopes are available.

[0083] After being arranged in the form of a diagonal matrix (dimension 6×6), we have

[0084]

[0085] When considering the selected combination, when the frame angle is 0, the torque direction matrix A and the angular momentum direction matrix B are respectively

[0086] A = A0k cmg

[0087] B = B0k cmg

[0088] According to the rotation characteristics of the inner rotor of the control moment gyroscope, that is, the moment of inertia J (scalar, unit: kg·m 2 ) and the nominal rotational speed W (scalar, unit: rpm), determine the nominal angular momentum h0 of the inner rotor (scalar, unit: Nms)

[0089]

[0090] Step 2: Divide the combination of 3 control moment gyroscopes into two categories: "123" and "126".

[0091] The vectors formed by each column of G0 drawn in the Oa-XaYaZa system are set to have equal lengths, all equal to X (for example, the lengths are equal after unit normalization). Define the vector formed by the i-th column of G0 as the first vector i. With the vertex of the first vector i as the center, draw a regular pentagon with a side length of 2X*tan(63.4349° / 2)tan36° in the plane perpendicular to the first vector i; iterate through i = 1 to 6 to obtain the 1st to 6th regular pentagons; connect the 6 regular pentagons to get half of a regular dodecahedron.

[0092] Draw equal-length reverse vectors for each column of G0 in the Oa-XaYaZa system; that is, define the equal-length reverse vector of each column of G0 as the second vector i, and the second vector i is equal in length and opposite in direction to the first vector i. With the vertex of the second vector i as the center, draw a regular pentagon with a side length of 2X*tan(63.4349° / 2)tan36° in the plane perpendicular to the second vector i; iterate through i = 1 to 6 to obtain the 7th to 12th regular pentagons; connect the 7th to 12th regular pentagons and the previously obtained half of the regular dodecahedron to finally get a regular dodecahedron.

[0093] When 3 control moment gyros work, the following two types of configurations can be obtained: One type of configuration: can be called the "123" type series connection, including 123, 234, 345, 145, 125, 146, 136, 246, 256, 356; The second type of configuration: can be called the "126" type aggregation, including 126, 236, 346, 456, 156, 124, 235, 134, 245, 135.

[0094] Step 3: Reorder the control moment gyro combination, and the result is shown in Table 1.

[0095] Table 1

[0096]

[0097] Taking the 123 combination of the first type of configuration as an example, specify the vector in the new order

[0098] Taking the 126 combination of the second type of configuration as an example, specify the vector in the new order

[0099] Taking the 124 combination of the second type of configuration as an example, specify the vector in the new order

[0100] Step 4: Calculate the azimuth vector.

[0101] For the first type of configuration: the "123" type series connection, as Figure 2 shown, the calculation process of the intermediate vector g4 is as follows:

[0102]

[0103] g4 = g4 / |g4|

[0104] The intermediate vector g5 is obtained by rotating around g4 by an angle θ,

[0105] θ = 180° - acos(cos(63.4349°)cos(72°))

[0106] Rotation quaternion

[0107]

[0108] Rotation matrix

[0109]

[0110] The calculation process of the intermediate vector g5 is as follows:

[0111] g5 = E 53 g3

[0112] g5 = g5 / |g5|

[0113] The calculation process of the intermediate vector g6 is as follows:

[0114] g6 = g4 × g5

[0115] g6 = g6 / |g6|

[0116] For the type II configuration: the "126" type aggregation, such as Figure 3 shown, the calculation process of the intermediate vector g5 (the center of the three frame axis vectors) is as follows:

[0117]

[0118] g5 = g5 / |g5|

[0119] The included angle between g5 and is β,

[0120]

[0121] The intermediate vector g8 (the normal of the plane formed by g5 and )

[0122]

[0123] g8 = g8 / |g8|

[0124] The intermediate vector g9 (in the plane formed by g5 and and in the plane formed by g5 and in the middle)

[0125]

[0126] g9 = g9 / |g9|

[0127] Intermediate vector g 10 (Normal to the plane formed by g9 and g8)

[0128] g 10 = g9 × g8

[0129] g 10 = g 10 / |g 10 |

[0130] Intermediate vector g 11 (g5 and Normal to the plane formed)

[0131]

[0132] g 11 = g 11 / |g 11 |

[0133] Intermediate vector g 12 (In the plane formed by g5 and , in the middle between g5 and )

[0134]

[0135] g 12 = g 12 / |g 12 |

[0136] Intermediate vector g 13 (g 12 and g 11 Normal to the plane formed)

[0137] g 13 = g 12 × g 11

[0138] g 13 = g 13 / |g 13 |

[0139] Intermediate vector g 14 (g5 and Normal to the plane formed)

[0140]

[0141] g14 = g 14 / |g 14 |

[0142] Intermediate vector g 15 (within the plane formed by g5 and and in the middle between g5 and )

[0143]

[0144] g 15 = g 15 / |g 15 |

[0145] Intermediate vector g 16 (normal to the plane formed by g 15 and g 14 )

[0146] g 16 = g 15 ×g 14

[0147] g 16 = g 16 / |g 16 |

[0148] Step 5: Determine the center and magnitude of the available angular momentum space.

[0149] First, find the singular points. The meaning of singular points is that when the control moment gyro group is at the current frame angle combination, the output torque direction is perpendicular to the command torque direction. The specific steps for searching are as follows:

[0150] Establish a spherical coordinate system in the Oa-XaYaZa system. Randomly select points within the spherical coordinate system by artificial setting to search for singular points. The randomly selected command torque unit vector u satisfies:

[0151]

[0152] λ represents the longitude, and the range is [0, 2π]; represents the latitude, and the range is

[0153] For the i-th control moment gyro, the corresponding frame angles in the singular state are

[0154]

[0155] A i represents the i-th column of matrix A, and B i represents the i-th column of matrix B.

[0156] For the control moment gyroscopes not selected, δ i = 0.

[0157] Each control moment gyroscope has 2 frame angles that can reach the singular state. In the case of selecting 3 gyroscopes, there are a total of 2 3 = 8 combinations. Calculate the total angular momentum of each combination

[0158]

[0159] According to the above process, uniformly traverse the points on the sphere of longitude and latitude to obtain the distribution of the total angular momentum of the control moment gyroscopes in the singular state, and then determine the geometric center and size of the available angular momentum space. According to the distribution of the singular points, for the "123" type configuration, the available angular momentum space is 1 annular space + 2 spherical spaces; for the "126" type configuration, the available angular momentum space is 8 spherical spaces. The geometric center and size of the available angular momentum space can meet the following principles: the available angular momentum space is as large as possible, and the outer envelope has no intersection with the singular points.

[0160] See Figure 4 and Figure 5 , for the positioning of the available angular momentum space of the "123" type series connection, according to the distribution of the total angular momentum H of the singular points, determine the maximum value of the outer singular envelope in the g5 direction The maximum value of the outer singular envelope in the direction perpendicular to g5 The maximum value of the inner singular envelope in the g5 direction The maximum value of the inner singular envelope in the direction perpendicular to g5 Determine that the two spherical available spaces are on g5 and the reverse extension line of g5. The center distance of the spheres from the coordinate center is (H1 + H3) / 2 = 1.975h0, and the sphere radius is (H1 - H3) / 2 = 0.95h0; the central plane of the annular available space passes through g4 and is perpendicular to g5. The radius of the central circle of the annulus is (H2 + H4) / 2 = 0.6h0, and the annulus radius is (H2 - H4) / 2 = 0.5h0. g4, g5, and g6 form a coordinate system that can describe the position of the annulus.

[0161] See Figure 6 and Figure 7 , for the positioning of the available angular momentum space of the "126" type aggregation, according to the distribution of the total angular momentum H of the singular points, determine that the maximum value of the outer singular envelope in the g5 direction is H5 = 0.75max(||H||) = 1.8h0, g 10 , g 13 , g 16 The maximum value of the outer singular envelope in the direction is H6 = max(||H||) = 2.4h0; the maximum value of the inner singular envelope in the g5 direction is H7 = 0.125max(||H||) = 0.3h0, g 10 , g 13 , g 16The maximum value of the inner singular envelope in the direction H8 = 0.375max(||H||) = 0.9h0. There are two spherical available spaces on the reverse extension line of g5 and g5, the center distance from the coordinate center is (H5 + H7) / 2 = 1.05h0, and the spherical radius is (H5 - H7) / 2 = 0.75h0; there are two spherical available spaces on the reverse extension line of g 10 and g 10 's reverse extension line, the center distance from the coordinate center is (H6 + H8) / 2 = 1.65h0, and the spherical radius is (H6 - H8) / 2 = 0.75h0; there are two spherical available spaces on the reverse extension line of g 13 and g 13 's reverse extension line, the center distance from the coordinate center is (H6 + H8) / 2 = 1.65h0, and the spherical radius is (H6 - H8) / 2 = 0.75h0; there are two spherical available spaces on the reverse extension line of g 16 and g 16 's reverse extension line, the center distance from the coordinate center is (H6 + H8) / 2 = 1.65h0, and the spherical radius is (H6 - H8) / 2 = 0.75h0.

[0162] Although the present invention is disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention should be determined by the scope defined in the claims of the present invention.

Claims

1. A method for determining the available angular momentum space when a part of a control moment gyro group fails. The control moment gyro group consists of six control moment gyros in a pentagonal pyramid configuration. The installation coordinate system of the control moment gyro group is Oa-XaYaZa, and the single control moment gyro coordinate system is Oi-XiYiZi, where i is the number of the control moment gyro. OiYi represents the positive rotation direction of the frame, OiZi represents the angular momentum direction when the inner rotor rotates positively, and OiXi represents the torque direction generated by the instantaneous positive rotation of the frame. When the frame angle is 0, the OiXi axis is parallel to the XaOaYa plane, and the angle between the OiYi axis and the OaZa axis is an obtuse angle. The angle between the frame axes of any two control moment gyros is 63.4349°. The frame axis of the No. 1 control moment gyro is located in the XaOaYa plane, and the frame axis of the No. 6 control moment gyro points in the -OaZa direction. The No. 1, 2, 3, 4, and 5 control moment gyros are arranged in sequence around the OaZa axis. When projected along the -OaZa direction, the No. 1, 2, 3, 4, and 5 control moment gyros are arranged counterclockwise. It is characterized in that, Including: Determine the numbers and rotation-related parameters of the selected 3 control moment gyroscopes; According to the numbers of the selected 3 control moment gyroscopes, determine the corresponding configurations, and reorder the numbers of the selected 3 control moment gyroscopes; According to the numbers of the 3 control moment gyroscopes after sorting and the corresponding configurations, calculate the azimuth vector, and determine the center and magnitude of the available angular momentum space.

2. The method according to claim 1, characterized in that, According to the numbers of the selected 3 control moment gyroscopes, determine the corresponding configurations, including: When the numbers of the selected 3 control moment gyroscopes are any of the following, the corresponding configuration is a type-I configuration: 123, 234, 345, 145, 125, 146, 136, 246, 256, 356; When the numbers of the selected 3 control moment gyroscopes are any of the following, the corresponding configuration is a type-II configuration: 126, 236, 346, 456, 156, 124, 235, 134, 245, 135.

3. The method according to claim 1, wherein The corresponding relationship of reordering for type-I configurations is: If it is 123 before sorting, it is 312 after sorting; If it is 234 before sorting, it is 423 after sorting; If it is 345 before sorting, it is 534 after sorting; If it is 145 before sorting, it is 145 after sorting; If it is 125 before sorting, it is 251 after sorting; If it is 146 before sorting, it is 416 after sorting; If it is 136 before sorting, it is 136 after sorting; If it is 246 before sorting, it is 246 after sorting; If it is 256 before sorting, it is 526 after sorting; If it is 356 before sorting, it is 356 after sorting.

4. The method according to claim 1, characterized in that The corresponding relationship of reordering for type-II configurations is: If it is 126 before sorting, it is 126 after sorting; If it is 236 before sorting, it is 236 after sorting; If it is 346 before sorting, it is 346 after sorting; If it is 456 before sorting, it is 456 after sorting; If it is 156 before sorting, it is 516 after sorting; If it is 124 before sorting, it is 142 after sorting; If it is 235 before sorting, it is 253 after sorting; If it is 134 before sorting, it is 314 after sorting; If it is 245 before sorting, it is 425 after sorting; If it is 135 before sorting, it is 531 after sorting.

5. The method according to claim 1, characterized in that According to the numbers of the 3 control moment gyroscopes after sorting and the corresponding configurations, calculate the azimuth vector, including: If the control moment gyro number in the a-th position after sorting is i, then the azimuth vector corresponds to G i , where a = 1, 2, 3, and G i is the i-th column of the moment direction matrix G0 of the control moment gyro group.

6. The method according to claim 5, wherein For the second-class configuration, when a = 2 and the numbers of the three selected control moment gyroscopes are any one of the following, the azimuth vector 124, 235, 134, 245, 135; for other cases of the second-class configuration and the first-class configuration, the azimuth vector 7. The method according to claim 5 or 6, characterized in that For a class of configurations, the available angular momentum space is 1 toroidal space + 2 spherical spaces; the central plane of the available toroidal space passes through vector g4 and is perpendicular to vector g5, and the two available spherical spaces are on vector g 5 and the reverse extension line of vector g5. The calculation process of vector g4 is as follows: g4 = g4 / |g4| The vector g5 is obtained by rotating the azimuth vector about the vector g4 by an angle of θ. θ = 180° - acos(cos(63.4349°)cos(72°)).

8. The method according to claim 7, wherein For type-I configurations, determine that the maximum value of the outer singular envelope in the g5 direction H1 = max(||H||) = 2.925h0, and the maximum value of the outer singular envelope in the direction perpendicular to g5 H2 = 0.376H1 = 1.1h0; the maximum value of the inner singular envelope in the g5 direction H3 = 0.35H1 = 1.025h0, and the maximum value of the inner singular envelope in the direction perpendicular to g5 H4 = 0.034H1 = 0.1h0; Determine that the center distance of the centers of the two spherical available spaces from the coordinate center is (H1 + H3) / 2 = 1.975h0, and the spherical radius is (H1 - H3) / 2 = 0.95h0; the radius of the center circle of the annular available space is (H2 + H4) / 2 = 0.6h0, and the annular radius is (H2 - H4) / 2 = 0.5h0.

9. The method according to claim 5 or 6, characterized in that, For the second-class configuration, the available angular momentum space is eight spherical spaces; two spherical available spaces are on the vector g5 and the reverse extension line of the vector g5, two spherical available spaces are on the vector g 10 and the vector g 10 and the reverse extension line of the vector g 13 and the vector g 13 and the reverse extension line of the vector g 16 and the vector g 16 and the reverse extension line of the vector g; the calculation process of the vector g5 is as follows: g5 = g5 / |g5| Vector g 10 is the normal of the plane formed by vector g9 and vector g8, and vector g8 is the normal of the plane formed by vector g5 and the positioning vector The calculation process of vector g9 is as follows: g9 = g9 / |g9|, where β is the angle between vector g5 and the positioning vector ; Vector g 13 is vector g 12 and vector g 11 form the normal of the plane. Vector g 11 is the normal of the plane formed by vector g5 and the positioning vector Vector g 12 The calculation process is as follows: g 12 = g 12 / |g 12 | vector g 16 is vector g 15 and vector g 14 form the normal direction of the plane. Vector g 14 is the normal direction of the plane formed by vector g5 and the positioning vector Vector g 15 The calculation process is as follows: g 15 = g 15 / |g 15 |。 10. The method according to claim 9, wherein Determine that the maximum value of the outer singular envelope in the g5 direction H5 = 0.75max(||H||) = 1.8h0, g 10 and g 13 and g 16 The maximum value of the outer singular envelope in the g6 direction H6 = max(||H||) = 2.4h0; the maximum value of the inner singular envelope in the g5 direction H7 = 0.125max(||H||) = 0.3h0, g 10 and g 13 and g 16 The maximum value of the inner singular envelope in the g8 direction H8 = 0.375max(||H||) = 0.9h0; Two spherical available spaces on the reverse extension line of g5 and g5, the center distance from the coordinate center is (H5 + H7) / 2 = 1.05h0, and the sphere radius is (H5 - H7) / 2 = 0.75h0; The remaining six spherical available spaces, the center distance from the coordinate center is (H6 + H8) / 2 = 1.65h0, and the sphere radius is (H6 - H8) / 2 = 0.75h0.

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