Method for determining target frame angle of control moment gyroscope group under multiple constraints

Abstract

The invention discloses a method for determining a target frame angle of a control moment gyroscope group under multiple constraints. The method can be applied to a control moment gyroscope group control system with a pentagonal pyramid structure. According to the method, the total angular momentum of the control moment gyroscope group reaches the target angular momentum, and meanwhile, the control moment gyroscope group can have high output capacity. According to the method, a complex optimization problem is simplified into a multi-constraint Newton iteration problem, the algorithm is simple and efficient, and the method is suitable for satellite on-orbit real-time calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite control moment gyroscopes, and particularly to a method for determining the target frame angle of a group of control moment gyroscopes under multiple constraints. Background Art

[0002] With the continuous development of space technology, the tasks of satellites have become increasingly complex. Among them, the tasks of earth observation are growing day by day. To meet the observation requirements, satellites need to have the ability of rapid maneuvering and rapid stabilization after reaching the target position; correspondingly, the attitude control system needs to have strong control ability, and generally uses a group of control moment gyroscopes as the main on-board actuators. As an angular momentum exchange device, a control moment gyroscope generates a gyroscopic torque by driving the inner rotor to rotate through the rotation of the outer frame, thereby changing the direction of the inner rotor angular momentum. When used in conjunction with the on-board angular momentum unloading device, the outer frame of the control moment gyroscope will reciprocate near the same frame angle. Long-term rotation at the same position will exacerbate the wear of the bearing and slip ring components, generate wear debris, affect the product life, and further affect the long-term stable operation ability of the control system. Therefore, it is necessary to regularly change the target frame angle position to make the friction more uniform and dispersed. Summary of the Invention

[0003] The present invention provides a method for determining the target frame angle of a group of control moment gyroscopes under multiple constraints, which can be applied to the control system of a group of control moment gyroscopes with a pentagonal pyramid configuration. While meeting the requirement that the total angular momentum of the group of control moment gyroscopes reaches the target angular momentum, this method can enable the group of control moment gyroscopes to have strong output ability.

[0004] In a first aspect, there is provided a method for determining the target frame angle of a group of control moment gyroscopes under multiple constraints, including:

[0005] Setting a target angular momentum and a target singularity measure;

[0006] Checking whether the setting of the target angular momentum is valid according to the relevant parameters of the control moment gyroscopes selected in the group of control moment gyroscopes;

[0007] When the setting of the target angular momentum is valid, checking whether the target angular momentum and the target singularity measure are both set validly;

[0008] Based on whether the target angular momentum and the target singularity measure are both set validly, outputting the last iteration result as the target frame angle.

[0009] In combination with the first aspect, in some implementation manners of the first aspect, the method further includes:

[0010] Driving the control moment gyroscopes selected in the group of control moment gyroscopes to rotate to the target frame angle according to the output target frame angle.

[0011] Combined with the first aspect, in some implementations of the first aspect, the target angular momentum H t is defined in the installation coordinate system Op-XpYpZp of the control moment gyro group and satisfies:

[0012]

[0013] where h0 is the nominal angular momentum of the inner rotor and N is the number of control moment gyros currently selected.

[0014] Combined with the first aspect, in some implementations of the first aspect, the target singularity measure D t satisfies:

[0015] D t = k h0 k D D max

[0016] D max is the maximum singularity measure, N is the number of control moment gyros currently selected;

[0017] The coefficient k h0 satisfies: H t is the target angular momentum and h0 is the nominal angular momentum of the inner rotor;

[0018] The coefficient k D satisfies:

[0019] Combined with the first aspect, in some implementations of the first aspect, during the process of verifying whether the target angular momentum setting is valid, a set of gimbal angles is randomly generated as the initial value. According to the relevant parameters of the selected control moment gyros and the randomly generated gimbal angles, the total angular momentum H and the torque output matrix C are calculated. When the total angular momentum H does not reach the target angular momentum, the gimbal angles are continuously iterated. If the total angular momentum H reaches the target angular momentum within the limited number of times, it is considered that the setting is valid. If it fails to reach within the limited number of times, a new set of gimbal angles is regenerated as the initial value and the above steps are repeated. If no valid result is iterated after randomly generating the gimbal angles multiple times, it is considered that the target angular momentum setting is invalid and the process is exited.

[0020] Combined with the first aspect, in some implementations of the first aspect, the method uses the Newton iteration method to verify whether the target angular momentum setting is valid, including:

[0021] Clear the counter K1 and start loop 1;

[0022] In loop 1, a set of gimbal angles δ = [δ1 … δ i … δ6] T is randomly generated, and δ iRestricted within the range of [0, 2π), clear the counter K2 and start Loop 2;

[0023] In Loop 2, calculate the total angular momentum in the installation coordinate system Op-XpYpZp of the control moment gyro group where, H i is the i-th column of the angular momentum output matrix H in the Op-XpYpZp system of the control moment gyro group 36 of H 36 = h0(Asinδ + Bcosδ)=[H1…H i …H6], h0 is the nominal angular momentum of the inner rotor, A is the torque direction matrix when the frame angle is 0, and B is the angular momentum direction matrix when the frame angle is 0.

[0024]

[0025] If |H - H t | ≤ 1e-6, then the target angular momentum H t is set to be valid, and Loop 1 and Loop 2 are exited;

[0026] If |H - H t | > 1e-6, then iterate the frame angle δ = δ - Q1(H - H t ), increment the counter K2 by 1, and continue to execute Loop 2; where, Q1 is the pseudo-inverse matrix of is the partial derivative matrix of the total angular momentum H with respect to the frame angle δ, C is the torque output matrix in the Op-XpYpZp system of the control moment gyro group,

[0027] C = Acosδ - Bsinδ;

[0028] If the counter K2 exceeds the judgment threshold, increment the counter K1 by 1 and continue to execute Loop 1; if the counter K1 exceeds the judgment threshold, exit Loop 1 and prompt to reset the target angular momentum H t .

[0029] In combination with the first aspect, in some implementations of the first aspect, during the process of verifying whether the target angular momentum and the target singularity measure are both set effectively, based on the fact that the target angular momentum is set effectively, a set of gimbal angles is randomly generated as the initial value. According to the relevant parameters of the selected control moment gyro and the randomly generated gimbal angles, the total angular momentum H, the torque output matrix C, and the singularity measure D are calculated. When the total angular momentum H and the singularity measure D do not simultaneously reach the set target, the gimbal angles are continuously iterated. If the total angular momentum H and the singularity measure D simultaneously reach the set target within the specified number of times, it is considered that the setting is effective. If they do not reach the target simultaneously within the specified number of times, a new set of gimbal angles is regenerated as the initial value and the above steps are repeated. If no effective result is iterated after randomly generating the gimbal angles multiple times, it is considered that the target singularity measure is set ineffectively, and the process is exited.

[0030] In combination with the first aspect, in some implementations of the first aspect, the method uses the Newton iteration method to verify whether the target angular momentum and the target singularity measure are both set effectively;

[0031] Clear the counter K3 and start loop 3;

[0032] In loop 3, randomly generate a set of gimbal angles δ = [δ1…δ i …δ6] T , and limit δ i within the range of [0, 2π). Clear the counter K4 and start loop 4;

[0033] In loop 4, calculate the total angular momentum in the installation coordinate system Op-XpYpZp of the control moment gyro group, and calculate the singularity measure D = e 11 (e 22 e 33 -e 23 e 32 ) + e 12 (e 23 e 31 -e 21 e 33 ) + e 13 (e 21 e 32 -e 22 e 31 ); H i is the i-th column of the angular momentum output matrix H 36 in the Op-XpYpZp system of the control moment gyro group, H 36 = h0(Asinδ + Bcosδ) = [H1 … H i …H6], h0 is the nominal angular momentum of the inner rotor, A is the torque direction matrix when the gimbal angle is 0, and B is the angular momentum direction matrix when the gimbal angle is 0.

[0034]

[0035] e mn is an element of the singular metric matrix E, m = 1, 2, 3, n = 1, 2, 3, C is the torque output matrix in the Op-XpYpZp system of the control moment gyro group, C = Acosδ - Bsinδ;

[0036] If |H - H t | ≤ 1e-6 and |D - D t | ≤ 1e-6, then the target angular momentum H t and the target singular metric D t are both set to be valid, and the loop 3 and loop 4 are exited; if |H - H t | > 1e-6 or |D - D t | > 1e-6, then the iteration frame angle counter K4 is incremented by 1, and loop 4 continues to execute; where,

[0037] Q2 is the pseudo-inverse matrix of the total partial derivative matrix P, Q2 = P T (PP T ) -1 ,

[0038] The partial derivative matrix of the total angular momentum H with respect to the frame angle δ The partial derivative of the singular metric D with respect to the frame angle δ The partial derivative of the singular metric D with respect to the i-th frame angle δ i of is the partial derivative matrix of the singular metric matrix E with respect to the i-th frame angle of the elements, s = 1, 2, 3, t = 1, 2, 3,

[0040]

[0041] A i represents the i-th column of matrix A, B i represents the i-th column of matrix B;

[0042] If the counter K4 exceeds the judgment threshold, the counter K3 is incremented by 1, and loop 4 continues to execute; if the counter K3 exceeds the judgment threshold, loop 3 is exited, and a prompt is given to reset the target singular metric D.

[0043] Combined with the first aspect, in some implementation manners of the first aspect, the nominal angular momentum of the inner rotor J is the moment of inertia of the inner rotor of the control moment gyro, and W is the nominal rotational speed of the inner rotor of the control moment gyro.

[0044] Combined with the first aspect, in certain implementations of the first aspect, when the frame angle is 0, the moment direction matrix A = A0k cmg When the frame angle is 0, the angular momentum direction matrix B = B0k cmg , k cmg is used to represent the selected control moment gyro k cmg_i is the selection flag for the i-th control moment gyro, 1 means selected, 0 means not selected;

[0045] A0 is the moment direction matrix of the control moment gyro group. The i-th column element of A0 represents the component of the OiZi axis of the single-axis coordinate system Oi-XiYiZi of the i-th control moment gyro in the Op-XpYpZp system when the frame angle is 0;

[0046] B0 is the angular momentum direction matrix of the control moment gyro group. The i-th column element of B0 represents the component of the OiYi axis of the single-axis coordinate system Oi-XiYiZi of the i-th control moment gyro in the Op-XpYpZp system when the frame angle is 0.

[0047] Compared with the prior art, the solution provided by the present invention has at least the following beneficial technical effects:

[0048] The present invention mainly uses the Newton iteration method to determine whether the total angular momentum of the control moment gyro group can reach the target angular momentum according to the angular momentum output ability of the selected combination of the current control moment gyro group; on this basis, according to the angular momentum output ability and moment output ability of the selected combination of the current control moment gyro group, it is determined whether the control moment gyro group is far enough from the force singularity state to generate gyroscopic moments in any direction. The present invention simplifies the complex optimization problem into a multi-constraint Newton iteration problem, with a simple algorithm principle and small computational complexity, suitable for on-board real-time calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is the flowchart for calculating the target frame angle of the control moment gyro group under multiple constraints.

[0050] Figure 2 is the schematic diagram of the combined singularity measure and angular momentum change of 6 control moment gyros considering only angular momentum constraints.

[0051] Figure 3 is the schematic diagram of the frame angle change of 6 control moment gyros considering only angular momentum constraints.

[0052] Figure 4 is the schematic diagram of the combined singularity measure and angular momentum change of 6 control moment gyros considering both angular momentum and singularity measure constraints.

[0053] Figure 5Schematic diagram of the frame angle change of six control moment gyroscopes considering both angular momentum and singular metric constraints simultaneously.

[0054] Figure 6 Schematic diagram of the installation of a control moment gyroscope group in a pentagonal pyramid configuration. Specific implementation manner

[0055] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0056] As Figure 1 shown, the present invention provides a method for determining the target frame angle of a control moment gyroscope group under multiple constraints, and the specific steps are as follows.

[0057] Step 1), determine the relevant parameters of the selected control moment gyroscope group.

[0058] According to the installation characteristics of the control moment gyroscope group, determine the torque direction matrix A and the angular momentum direction matrix B when the frame angle is 0; when determining the torque direction matrix A and the angular momentum direction matrix B when the frame angle is 0, it is necessary to combine the installation characteristics of the control moment gyroscope group with the actual selection situation, and the columns corresponding to the unselected control moment gyroscopes in matrices A and B are all 0. According to the number of selected control moment gyroscopes, determine the maximum singular metric D indicating the output ability of the control moment gyroscope group max ; according to the rotation characteristics of the inner rotor of the control moment gyroscope, determine the nominal angular momentum h0 of the inner rotor.

[0059] Step 2), set the target angular momentum and the target singular metric.

[0060] According to the system usage requirements such as unloading and bias momentum, set the target angular momentum H t ; referring to the maximum singular metric D max set the target singular metric D t . Generally, there is a correlation between the setting range of the target angular momentum and the number of selected control moment gyroscopes; the setting range of the target singular metric is related to the number of selected control moment gyroscopes and the setting situation of the target angular momentum.

[0061] Step 3), use the Newton iteration method to verify whether the setting of the target angular momentum is valid.

[0062] Randomly generate a set of frame angles as the initial value, calculate the three-axis combined angular momentum H and the torque output matrix C according to the relevant parameters and the frame angles obtained in the first step, iterate the frame angles before the three-axis combined angular momentum reaches the target angular momentum, if it can be reached within the limited number of times, it is considered that the setting is valid, if it cannot be reached within the limited number of times, regenerate a set of frame angles as the initial value and repeat the above steps. If no effective result can be iterated after multiple random generations, it is considered that the setting is invalid and the process is exited.

[0063] Use a double loop. The outer loop sets the upper limit of the number of times to generate random initial values, and the inner loop iterates the gimbal angles. The partial derivative matrix in the Newton iteration method is the partial derivative of the angular momentum with respect to the gimbal angles. The judgment basis is whether the total angular momentum of the control moment gyro group reaches the target angular momentum.

[0064] Step 4), use the Newton iteration method to verify whether the setting of the target singularity measure is valid.

[0065] Use the Newton iteration method to verify whether the setting of the target singularity measure is valid: On the basis that the target angular momentum setting is valid, randomly generate a set of gimbal angles as the initial values. Calculate the three-axis combined angular momentum H, the torque output matrix C, and the singularity measure D according to the relevant parameters and gimbal angles obtained in the first step. Iterate the gimbal angles before the three-axis combined angular momentum and the singularity measure reach the set targets simultaneously. If it can be achieved within the limited number of times, it is considered that the setting is valid. If it cannot be achieved within the limited number of times, regenerate a set of gimbal angles as the initial values and repeat the above steps. If no valid result can be iterated after multiple random generations, it is considered that the setting is invalid and the process is exited.

[0066] Use a double loop. The outer loop sets the upper limit of the number of times to generate random initial values, and the inner loop iterates the gimbal angles. The partial derivative matrix in the Newton iteration method is the matrix synthesized by the partial derivative of the angular momentum with respect to the gimbal angles and the partial derivative of the singularity measure with respect to the gimbal angles. The judgment basis is that both the total angular momentum of the control moment gyro group reaches the target angular momentum and the singularity measure of the control moment gyro group reaches the target singularity measure.

[0067] Step 5), output the target gimbal angles.

[0068] On the basis that the target angular momentum and the target singularity measure are set validly, output the last iteration result as the target gimbal angles.

[0069] The following takes the common pentagonal pyramid configuration control moment gyro group (as Figure 6 shown) as an example to introduce the specific implementation steps of the algorithm.

[0070] In order to obtain a uniform and symmetric momentum envelope, the angle between the frame axes of any two control moment gyros is equal, which is β = 63.4349°. The bottom angle of the pentagonal pyramid is η = 360° / 5 = 72°. Establish the installation coordinate system Op-XpYpZp of the control moment gyro group, and establish the single control moment gyro coordinate system Oi-XiYiZi (i = 1, 2,..., 6). Among them, OiXi represents the positive rotation (counterclockwise) direction of the frame, OiYi represents the angular momentum direction when the inner rotor rotates positively (counterclockwise), and OiZi represents the torque direction generated by the instantaneous positive rotation of the frame. It is agreed that when the gimbal angle is 0, the OiZi axis is parallel to the plane XpOpYp, and the angle between the OiYi axis and the OpZp axis is an acute angle.

[0071] Step 1, determine the relevant parameters of the selected control moment gyro group.

[0072] When not considering the selected combination, the torque direction matrix of the control moment gyro group is A0, and the dimension of this matrix is 3×6. Each column element corresponds to the component of the OiZi axis in the Op-XpYpZp system when the gimbal angle is 0, and the order from left to right is 1→6; the angular momentum direction matrix of the control moment gyro group is B0, and the dimension of this matrix is 3×6. Each column element corresponds to the component of the OiYi axis in the Op-XpYpZp system when the gimbal angle is 0, and the order from left to right is 1→6.

[0073] Let k cmg_i be the selection flag of the i-th control moment gyro, 1 means selected, and 0 means not selected.

[0074] After being arranged into a diagonal matrix (dimension 6×6) form, there is

[0075]

[0076] When considering the selected combination, when the gimbal angle is 0, the torque direction matrix A and the angular momentum direction matrix B are respectively

[0077] A = A0k cmg

[0078] B = B0k cmg

[0079] The number of selected torque gyros is

[0080]

[0081] The maximum singular metric D max (scalar)

[0082]

[0083] According to the rotation characteristics of the inner rotor of the control moment gyro, that is, the moment of inertia J (scalar, unit: kg·m 2 ) and the nominal rotational speed W (scalar, unit: rpm), the nominal angular momentum h0 of the inner rotor (scalar, unit: Nms) is determined

[0084]

[0085] Step 2: Set the target angular momentum and the target singular metric.

[0086] According to the system usage requirements such as unloading, bias momentum, etc., set the target angular momentum H t (dimension 3×1, unit: Nms, default value is [0; 0; 0]), defined in the Op-XpYpZp system. For the case of N≥4, generally required

[0087]

[0088] According to the target angular momentum H t and the maximum singular metric D max Set the target singular metric D t (scalar, default value is 0). For the case of N≥4, it is generally required that

[0089] D t = k h0 k D D max

[0090]

[0091] The values of H t and D t can be appropriately adjusted according to the actual situation.

[0092] It should be understood that N≥3. For the case of N = 3, D t takes the default value 0, and directly sets the target singular metric valid flag, without performing the validity check of the target singular metric setting. The target angular momentum H t is then set manually according to the actual situation.

[0093] Step 3: Use the Newton iteration method to check whether the target angular momentum setting is valid.

[0094] When the target angular momentum setting is invalid (default state), clear the counter K1 and start loop 1.

[0095] Randomly generate a set of frame angles δ = [δ1 δ2 …… δ6] T (dimension 6×1, unit: rad), limit δ i within the range of [0, 2π), clear the counter K2, and start loop 2.

[0096] Sine (diagonal) matrix (dimension 6×6)

[0097]

[0098] Cosine (diagonal) matrix (dimension 6×6)

[0099]

[0100] The angular momentum output matrix (dimension 3×6) in the control moment gyro group Op-XpYpZp system is

[0101] H 36 = h0(Asinδ + Bcosδ) = [H1 H2……H6]

[0102] In the formula, H i corresponds to the matrix H36 The i-th column of

[0103] The torque output matrix (dimension 3×6) of the control moment gyro group in the Op-XpYpZp system is

[0104] C = Acosδ - Bsinδ

[0105] The total angular momentum of the control moment gyro group in the Op-XpYpZp system is

[0106]

[0107] If |H - H t | ≤ 1e-6, then set the target angular momentum setting to be valid, exit Loop 1 and Loop 2, which means the target angular momentum can be achieved, and proceed to Step 4; if |H - H t | > 1e-6, then perform the following operations and continue to execute Loop 1 and Loop 2.

[0108] The partial derivative matrix of angular momentum with respect to the gimbal angle (dimension 3×6)

[0109]

[0110] The corresponding pseudo-inverse matrix is (dimension 6×3)

[0111] Q = P T (PP T ) -1

[0112] Iterative gimbal angle

[0113] δ = δ - Q(H - H t )

[0114] Restrict δ i to the range [0, 2π), and increment the counter K2 by 1.

[0115] If the counter K2 exceeds the judgment threshold (default is 50, can be modified), increment the counter K1 by 1 and restart Loop 2; if the counter K1 exceeds the judgment threshold (default is 3, can be modified), exit Loop 1 and prompt to reset the target angular momentum.

[0116] Step 4: Use the Newton iteration method to verify whether the target singularity measure setting is valid.

[0117] When the target angular momentum setting is valid but the target singularity measure setting is invalid (default state), clear the counter K3 and start Loop 3.

[0118] Randomly generate a set of gimbal angles δ = [δ1 δ2... δ6] T (dimension 6×1, unit: rad), and for δ iRestricted within the range of [0, 2π), clear the counter K4 and start loop 4.

[0119] Sine (diagonal) matrix (dimension 6×6)

[0120]

[0121] Cosine (diagonal) matrix (dimension 6×6)

[0122]

[0123] The angular momentum output matrix (dimension 3×6) in the Op-XpYpZp system of the control moment gyro group is

[0124] H 36 = h0(Asinδ + Bcosδ) = [H1 H2 …… H6]

[0125] Where, H i Corresponds to the i-th column of matrix H 36 of.

[0126] The torque output matrix (dimension 3×6) in the Op-XpYpZp system of the control moment gyro group is

[0127] C = Acosδ - Bsinδ

[0128] The total angular momentum in the Op-XpYpZp system of the control moment gyro group is (dimension 3×1)

[0129]

[0130] Singular metric matrix (dimension 3×3)

[0131]

[0132] Singular metric (dimension 1×1)

[0133] D = e 11 (e 22 e 33 -e 23 e 32 ) + e 12 (e 23 e 31 -e 21 e 33 ) + e 13 (e 21 e 32 -e 22 e 31 )

[0134] If |H - H t | ≤ 1e-6 and |D - Dt If |≤1e-6, then set the target singular metric setting to be valid and exit Loop 3 and Loop 4; if |H - H t | > 1e-6 or |D - D t | > 1e-6, then perform the following steps.

[0135] Partial derivative matrix of angular momentum with respect to the frame angle (dimension 3×6)

[0136]

[0137] Partial derivative matrix of the singular metric matrix with respect to the i-th frame angle (dimension 3×3)

[0138]

[0139] In the formula, A i represents the i-th column of matrix A, and B i represents the i-th column of matrix B.

[0140] Partial derivative of the singular metric with respect to the i-th frame angle (dimension 1×1)

[0141]

[0142] Partial derivative of the singular metric with respect to the frame angle (dimension 1×6)

[0143]

[0144] Total partial derivative matrix (dimension 4×6)

[0145]

[0146] The corresponding pseudo-inverse matrix is (dimension 6×4)

[0147] Q = P T (PP T ) -1

[0148] Iterative frame angle

[0149]

[0150] Restrict δ i to the range [0, 2π), and increment the counter K4 by 1.

[0151] If the counter K4 exceeds the judgment threshold (default is 50, can be modified), increment the counter K3 by 1 and restart Loop 4; if the counter K3 exceeds the judgment threshold (default is 3, can be modified), exit Loop 3 and prompt to reset the target singular metric.

[0152] Step 5. Output the target frame angle.

[0153] Based on the effectiveness of both the target angular momentum and the target singularity metric settings, the result of the last iteration is output as the target frame angle, i.e., δ0 = δ.

[0154] Figure 2 It is a schematic diagram of the singularity metric and angular momentum change of a combination of 6 control moment gyros considering only angular momentum constraints. Figure 3 It is a schematic diagram of the frame angle change of 6 control moment gyros considering only angular momentum constraints. Figure 4 It is a schematic diagram of the singularity metric and angular momentum change of a combination of 6 control moment gyros considering both angular momentum and singularity metric constraints. Figure 5 It is a schematic diagram of the frame angle change of 6 control moment gyros considering both angular momentum and singularity metric constraints. By periodically executing the above steps 1 to 5, the present invention can change the setting of the target frame angle irregularly, ensuring that if the frame angle is not changed and the control rate works, there will be other actuators, ensuring that the control moment gyro group moves near multiple frame angles, thereby reducing wear and extending the product life.

[0155] Although the present invention is disclosed above in 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 by the claims of the present invention.

Claims

1. A method for determining the target gimbal angle of a control moment gyroscope group under multiple constraints, characterized in that, Including: Set the target angular momentum and the target singularity metric; According to the relevant parameters of the selected control moment gyroscopes in the control moment gyroscope group, verify whether the setting of the target angular momentum is valid; When the setting of the target angular momentum is verified to be valid, verify whether the target angular momentum and the target singularity metric are both set validly; Based on whether the target angular momentum and the target singularity metric are both set validly, use the last iteration result as the output of the target frame angle.

2. The method according to claim 1, characterized in that, The method further includes: According to the output target frame angle, drive the selected control moment gyroscopes in the control moment gyroscope group to rotate to the target frame angle.

3. The method according to claim 1, wherein Target angular momentum H t Defined in the installation coordinate system Op-XpYpZp of the control moment gyro group, satisfying: h0 is the nominal angular momentum of the inner rotor, and N is the number of currently selected control moment gyroscopes.

4. The method according to claim 1, characterized in that Target singularity metric D t Satisfy: D t = k h0 k D D max D max is the maximum singular metric, N is the number of currently selected control moment gyroscopes; Coefficient k h0 Satisfies: H t is the target angular momentum, and h0 is the nominal angular momentum of the inner rotor; Coefficient k D Satisfy:

5. The method according to claim 1, characterized in that, During the process of verifying whether the setting of the target angular momentum is valid, randomly generate a set of frame angles as the initial value. According to the relevant parameters of the selected control moment gyroscopes and the randomly generated frame angles, calculate the total angular momentum H and the torque output matrix C. Continuously iterate the frame angles when the total angular momentum H does not reach the target angular momentum. If the total angular momentum H reaches the target angular momentum within the limited number of times, it is considered that the setting is valid. If it fails to reach within the limited number of times, regenerate a set of frame angles as the initial value and repeat the above steps. If no valid result is iterated after randomly generating frame angles multiple times, it is considered that the setting of the target angular momentum is invalid, and the process exits.

6. The method according to claim 1, characterized in that, The method uses the Newton iteration method to verify whether the setting of the target angular momentum is valid, including: Clear the counter K1 and start loop 1; In loop 1, a set of frame angles δ = [δ1 … δ i … δ6] is randomly generated. T , δ is i restricted to the range [0, 2π), the counter K2 is cleared, and loop 2 starts; In Loop 2, calculate the total angular momentum in the installation coordinate system Op-XpYpZp of the control moment gyro group where H i is the i-th column of the angular momentum output matrix H in the Op-XpYpZp system of the control moment gyro group 36 and H 36 = h0(A sinδ + B cosδ) = [H1 … H i … H6], where h0 is the nominal angular momentum of the inner rotor, A is the torque direction matrix when the frame angle is 0, and B is the angular momentum direction matrix when the frame angle is 0 If |H - H t | ≤ 1e - 6, then the target angular momentum H t is set to be valid, and loop 1 and loop 2 are exited; If |H - H t | > 1e-6, then the iterative frame angle δ = δ - Q1(H - H t ), the counter K2 is incremented by 1, and loop 2 is continued; where Q1 is the pseudo-inverse matrix of, is the partial derivative matrix of the total angular momentum H with respect to the frame angle δ, C is the torque output matrix in the Op-XpYpZp system of the control moment gyro group, C = Acosδ - Bsinδ; If the counter K2 exceeds the judgment threshold, the counter K1 is incremented by 1, and loop 1 continues to execute; if the counter K1 exceeds the judgment threshold, loop 1 is exited, and a prompt to reset the target angular momentum H is given t .

7. The method according to claim 1, characterized in that During the process of verifying whether the target angular momentum and the target singularity metric are both set validly, based on the valid setting of the target angular momentum, randomly generate a set of frame angles as the initial value. According to the relevant parameters of the selected control moment gyroscopes and the randomly generated frame angles, calculate the total angular momentum H, the torque output matrix C, and the singularity metric D. Continuously iterate the frame angles when the total angular momentum H and the singularity metric D do not both reach the set target. If the total angular momentum H and the singularity metric D both reach the set target within the limited number of times, it is considered that the setting is valid. If it fails to reach both within the limited number of times, regenerate a set of frame angles as the initial value and repeat the above steps. If no valid result is iterated after randomly generating frame angles multiple times, it is considered that the setting of the target singularity metric is invalid, and the process exits.

8. The method according to claim 1, wherein The method uses the Newton iteration method to verify whether the target angular momentum and the target singularity metric are both set validly; Clear the counter K3 and start loop 3; In loop 3, a set of frame angles δ = [δ1 … δ i … δ6] is randomly generated. T δ is restricted within the range of [0, 2π), the counter K4 is cleared, and loop 4 starts; i ​ In loop 4, calculate the total angular momentum in the installation coordinate system Op-XpYpZp of the control moment gyro group and calculate the singularity metric D = e 11 (e 22 e 33 -e 23 e 32 ) + e 12 (e 23 e 31 -e 21 e 33 ) + e 13 (e 21 e 32 -e 22 e 31 ); H i is the i-th column of the angular momentum output matrix H 36 in the Op-XpYpZp system of the control moment gyro group, H 36 = h0(A sinδ + B cosδ) = [H1 … H i …H6], h0 is the nominal angular momentum of the inner rotor, A is the torque direction matrix when the frame angle is 0, and B is the angular momentum direction matrix when the frame angle is 0 e mn is the element of the singular metric matrix E, where m = 1, 2, 3 and n = 1, 2, 3. C is the torque output matrix in the Op-XpYpZp system of the control moment gyro group, and C = Acosδ - Bsinδ; If |H - H t | ≤ 1e - 6 and |D - D t | ≤ 1e - 6, then the target angular momentum H t and the target singular metric D t are both set to be valid, and loop 3 and loop 4 are exited; if |H - H t | > 1e - 6 or |D - D t | > 1e - 6, then the iteration frame angle counter K4 is incremented by 1, and loop 4 continues to execute; where Q2 is the pseudo-inverse matrix of the total partial derivative matrix P, Q2 = P T (PP T ) -1 , Partial derivative matrix of the total angular momentum H with respect to the frame angle δ Partial derivative of the singular metric D with respect to the frame angle δ Partial derivative of the singular metric D with respect to the i-th frame angle δ i Partial derivative Is the partial derivative matrix of the singular metric matrix E with respect to the i-th frame angle Elements of, s = 1, 2, 3, t = 1, 2, 3, A i represents the i-th column of matrix A, B i represents the i-th column of matrix B; If the counter K4 exceeds the judgment threshold, increment the counter K3 by 1 and continue to execute loop 4; if the counter K3 exceeds the judgment threshold, exit loop 3 and prompt to reset the target singularity metric D.

9. The method according to any one of claims 3, 4, 6, and 8, characterized in that Inner rotor nominal angular momentum J is the moment of inertia of the inner rotor of the control moment gyro, and W is the nominal rotational speed of the inner rotor of the control moment gyro.

10. The method according to claim 6 or 8, characterized in that, When the frame angle is 0, the torque direction matrix A = A0k cmg When the frame angle is 0, the angular momentum direction matrix B = B0k cmg , k cmg is used to represent the selected control moment gyroscope , k cmg_i is the selection flag for the i-th control moment gyroscope, 1 means selected, 0 means not selected; A0 is the torque direction matrix of the control moment gyroscope group. The i-th column element of A0 represents the component of the OiZi axis of the single-axis coordinate system Oi-XiYiZi of the i-th control moment gyroscope in the Op-XpYpZp system when the frame angle is 0; B0 is the angular momentum direction matrix of the control moment gyroscope group. The i-th column element of B0 represents the component of the OiYi axis of the single-axis coordinate system Oi-XiYiZi of the i-th control moment gyroscope in the Op-XpYpZp system when the frame angle is 0.

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