A method for determining the maximum angular momentum of a wheel system with non-zero initial angular momentum

Abstract

The present application relates to the technical field of satellite attitude control, and particularly relates to a maximum angular momentum determination method of a wheel system with non-zero initial angular momentum. The maximum angular momentum envelope surface of the momentum wheel combination can be obtained through analytical calculation, which can effectively improve the angular momentum output capacity of the momentum wheel combination, thereby improving the rapid maneuvering capability of the whole satellite and the momentum wheel anti-saturation capability, and there is no numerical iterative search process, compared with the search method, the calculation efficiency is high, the storage amount is small, and the on-board calculation is easy to realize; in addition, the obtained maximum angular momentum envelope surface has a clear boundary, and the momentum wheel output angular momentum with the maximum envelope characteristic can be accurately obtained according to the envelope surface, compared with the pseudo-inverse method, the angular momentum output capacity of the wheel system can be more fully utilized.

Description

Technical Field

[0001] This invention relates to the field of satellite attitude control technology, and in particular to a method for determining the maximum angular momentum of a gear train with non-zero initial angular momentum. Background Technology

[0002] For wheel-controlled satellites, a pseudo-inverse method is generally used for control torque distribution. This method is relatively simple and practical. However, the angular momentum output achievable through momentum wheel torque distribution based on pseudo-inverse is much smaller than the actual maximum angular momentum envelope of the wheel system. Therefore, it severely wastes the angular momentum output capability of the wheel system and significantly reduces the attitude control capability of the wheel-controlled satellite. In order to make full use of the maximum angular momentum envelope of the momentum wheel combination, the current method is to calculate the maximum angular momentum output of the wheel system in various directions based on search methods and determine the maximum angular momentum envelope surface of the entire wheel system through large-scale calculations. However, this is not suitable for the limited computing resources on the satellite.

[0003] Therefore, there is an urgent need for a new method to determine the maximum angular momentum of a gear train with non-zero initial angular momentum. Summary of the Invention

[0004] To address the problem that existing pseudo-inverse methods cannot fully utilize the angular momentum output capability of gear trains, while search methods involve excessive computation, this invention provides a method for determining the maximum angular momentum of a gear train with non-zero initial angular momentum.

[0005] In a first aspect, embodiments of the present invention provide a method for determining the maximum angular momentum of a gear train with a non-zero initial angular momentum, comprising:

[0006] Determine the angular momentum output range of each momentum wheel in the gear train and the installation vector of each momentum wheel in the coordinate system of the whole star's center of mass;

[0007] For each momentum wheel combination, the following is performed: based on the installation vectors of the two momentum wheels in the current momentum wheel combination, determine the normal vector of the maximum envelope surface formed by the current momentum wheel combination;

[0008] Based on the mounting vectors of the remaining momentum wheels (excluding the two momentum wheels in the current momentum wheel combination) and the angular momentum output range, determine the combined angular momentum on the normal vector of the maximum envelope surface when the remaining momentum wheels are saturated;

[0009] Based on the combined angular momentum, the installation vectors of the two momentum wheels in the current momentum wheel combination, and the angular momentum output range, the corner points of the envelope surface of the current momentum wheel combination are determined to determine the finite envelope surface of the current momentum wheel combination.

[0010] Based on the predetermined initial angular momentum of the combined momentum wheels of the gear train and the required direction vector of the angular momentum, the intersection point of the required direction vector with the envelope surface of the current momentum wheel combination is determined, and it is determined whether the intersection point is located within the finite envelope surface.

[0011] If yes, then determine the angular momentum corresponding to the intersection point, and allocate the maximum angular momentum output of each momentum wheel based on the angular momentum corresponding to the intersection point; if not, then change the momentum wheel combination.

[0012] Secondly, embodiments of the present invention also provide a device for determining the maximum angular momentum of a gear train with a non-zero initial angular momentum based on the method described in any embodiment of this specification, comprising:

[0013] The determination unit is used to determine the angular momentum output range of each momentum wheel in the gear train and the installation vector of each momentum wheel in the coordinate system of the whole star's center of mass.

[0014] The first calculation unit is used to perform the following for each momentum wheel combination: based on the installation vectors of the two momentum wheels in the current momentum wheel combination, determine the maximum envelope surface normal vector formed by the current momentum wheel combination;

[0015] The second calculation unit is used to determine the combined angular momentum of the remaining momentum wheels when they are saturated on the normal vector of the maximum envelope surface, based on the installation vector of the remaining momentum wheels other than the two momentum wheels in the current momentum wheel combination and the angular momentum output range.

[0016] The third calculation unit is used to determine the corner points of the envelope surface of the current momentum wheel combination based on the combined angular momentum, the installation vectors of the two momentum wheels in the current momentum wheel combination, and the angular momentum output range, so as to determine the finite envelope surface of the current momentum wheel combination.

[0017] The judgment unit is used to determine the intersection point of the demand direction vector with the envelope surface of the current momentum wheel combination based on the predetermined initial angular momentum of each momentum wheel of the gear train and the demand direction vector of the angular momentum, and to determine whether the intersection point is located within the finite envelope surface.

[0018] The loop unit is used to determine the angular momentum corresponding to the intersection point if the condition is met, and to allocate the maximum angular momentum output of each momentum wheel based on the angular momentum corresponding to the intersection point; otherwise, the momentum wheel combination is replaced.

[0019] This invention provides a method for determining the maximum angular momentum of a gear train with non-zero initial angular momentum. Through analytical calculation, the maximum angular momentum envelope of the momentum gear combination can be obtained, effectively improving the angular momentum output capability of the momentum gear combination, thereby enhancing the overall satellite's rapid maneuverability and momentum gear anti-saturation capability. Furthermore, it eliminates the need for numerical iterative search, resulting in higher computational efficiency and lower storage requirements compared to search methods, facilitating on-board computation. Additionally, the obtained maximum angular momentum envelope has clear boundaries, allowing for precise determination of the output angular momentum of the momentum gears with maximum envelope characteristics. Compared to pseudo-inverse methods, this method better utilizes the angular momentum output capability of the gear train. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart of a method for determining the maximum angular momentum of a gear train with non-zero initial angular momentum, provided by an embodiment of the present invention;

[0022] Figure 2 This is a schematic diagram illustrating the principle of determining whether an intersection point intersects with a finite envelope surface, provided by an embodiment of the present invention.

[0023] Figure 3 This is a hardware architecture diagram of a computing device provided in an embodiment of the present invention;

[0024] Figure 4 This is a structural diagram of a device for determining the maximum angular momentum of a gear train with non-zero initial angular momentum, provided by an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0026] The following describes the specific implementation of the above concept.

[0027] Please refer to Figure 1 This invention provides a method for determining the maximum angular momentum of a gear train with non-zero initial angular momentum, the method comprising:

[0028] Step 100: Determine the angular momentum output range of each momentum wheel in the gear train and the installation vector of each momentum wheel in the coordinate system of the whole star's center of mass;

[0029] Step 102: For each momentum wheel combination, perform the following: Based on the installation vectors of the two momentum wheels in the current momentum wheel combination, determine the normal vector of the maximum envelope surface formed by the current momentum wheel combination.

[0030] Step 104: Based on the installation vectors and angular momentum output ranges of the remaining momentum wheels (excluding the two momentum wheels in the current momentum wheel combination), determine the combined angular momentum on the normal vector of the maximum envelope surface when the remaining momentum wheels are saturated.

[0031] Step 106: Based on the combined angular momentum, the installation vectors of the two momentum wheels in the current momentum wheel combination, and the angular momentum output range, determine the corner points of the envelope surface of the current momentum wheel combination, so as to determine the finite envelope surface of the current momentum wheel combination;

[0032] Step 108: Based on the predetermined initial angular momentum of each momentum wheel in the gear train and the required direction vector of the angular momentum, determine the intersection point of the required direction vector with the envelope surface of the current momentum wheel combination, and determine whether the intersection point is located within the finite envelope surface.

[0033] Step 110: If yes, determine the angular momentum corresponding to the intersection point, and allocate the maximum angular momentum output of each momentum wheel based on the angular momentum corresponding to the intersection point; if no, change the momentum wheel combination.

[0034] In this embodiment of the invention, the maximum angular momentum envelope of the momentum wheel assembly can be obtained through analytical calculation, which can effectively improve the angular momentum output capability of the momentum wheel assembly, thereby enhancing the rapid maneuverability of the entire satellite and the anti-saturation capability of the momentum wheels. Moreover, there is no numerical iterative search process, which is more computationally efficient and requires less storage compared to search methods, making it easier to implement on-board calculations. In addition, the obtained maximum angular momentum envelope has a clear boundary, and the output angular momentum of the momentum wheel with the maximum envelope characteristic can be accurately obtained based on the envelope. Compared with the pseudo-inverse method, it can make fuller use of the angular momentum output capability of the wheel system.

[0035] For step 100:

[0036] In some implementations, the upper limit of the angular momentum output range of each momentum wheel in the gear train is the nominal angular momentum of the corresponding momentum wheel, and the lower limit is the negative of the nominal angular momentum of the corresponding momentum wheel.

[0037] In this embodiment, the satellite gear train generally has 4-6 momentum wheels. The angular momentum output range of each momentum wheel is roughly the same, with slight differences that can be ignored. Alternatively, the angular momentum output range of each momentum wheel can be set to be the same, or the differences can be ignored.

[0038] Regarding step 102:

[0039] In some implementations, the maximum envelope surface normal vector formed by the current momentum wheel assembly is determined based on the mounting vectors of the two momentum wheels in the current momentum wheel assembly, including:

[0040] The maximum envelope surface normal vector n formed by momentum wheel i and momentum wheel j in the current momentum wheel assembly ij for:

[0041]

[0042] Among them, w i and w j These are the installation vectors of momentum wheels i and j in the coordinate system of the entire star's center of mass, respectively.

[0043] For example, if there are 4 momentum wheels in a satellite gear train, numbered 1, 2, 3, and 4, and i and j are not equal, there are 12 momentum wheel combinations, namely momentum wheel combinations 12, 13, 14, 23, 24, 34, 21, 31, 41, 32, 42, and 43. Since the envelope surfaces generated by momentum wheel combinations 12 and 21 are in opposite directions, momentum wheel combinations 12 and 21 are two momentum wheel combinations. The other momentum wheel combinations are similar.

[0044] Regarding step 104:

[0045] In some implementations, based on the mounting vectors and angular momentum output ranges of the remaining momentum wheels (excluding the two in the current momentum wheel combination), the resultant angular momentum at the maximum envelope surface normal vector when the remaining momentum wheels are saturated is determined, including:

[0046] For all momentum wheels except the two in the current momentum wheel combination, where k ≠ i, j, the following applies:

[0047] If sign(w) is satisfied k ·n ij If ) > 0, then

[0048]

[0049] If sign(w) is satisfied k ·n ij If ) < 0, then

[0050]

[0051] The resultant angular momentum v is obtained ij for

[0052]

[0053] Where sign() performs the sign operation, n ij Let w1, ..., w be the normal vectors of the maximum envelope surface. N Let be the mounting vector of each momentum wheel in the coordinate system of the entire star's center of mass. and The intermediate resultant angular momentum is N, where N is the number of momentum wheels in the gear train and is a positive integer greater than or equal to 4. ΔH k =[ΔH k1 ,ΔH k2 ] represents the angular momentum output range of the remaining momentum wheel k, where ΔH k1 ΔH represents the lower limit of the angular momentum output range, and is a negative number. k2 This represents the upper limit of the angular momentum output range.

[0054] It should be noted that ΔH k1 It is a negative number. The calculation formula still contains a negative sign. The calculated angular momentum is positive, then the resultant angular momentum v ij The sum of the intermediate angular momentum of the two positive signs is shown in sign(w). k ·n ij The mounting direction of the momentum wheel with ) < 0 is related to sign(w) k ·n ij For momentum wheels with momentum greater than 0, the installation direction is opposite, sign(w) k ·n ij A momentum wheel with a momentum of less than 0 outputs in the opposite direction, which can be related to sign(w). k ·n ij Momentum wheels with a velocity greater than 0 output angular momentum in the same direction.

[0055] Regarding step 106:

[0056] In some implementations, the envelope corner points of the current momentum wheel assembly are determined as follows:

[0057] Let c be the four corner points of momentum wheel i and momentum wheel j in the current momentum wheel assembly. ij1 ,c ij2 ,c ij3 ,c ij4 Then the envelope surface c of the current momentum wheel combination ij The four corner points are:

[0058] c ij1 =ΔH i1 ·w i +ΔH j1 ·w j +v ij

[0059] c ij2=ΔH i1 ·w i +ΔH j2 ·w j +v ij

[0060] c ij3 =ΔH i2 ·w i +ΔH j2 ·w j +v ij

[0061] c ij4 =ΔH i2 ·w i +ΔH j1 ·w j +v ij

[0062] Where, ΔH i =[ΔH i1 ,ΔH i2 ], ΔH j =[ΔH j1 ,ΔH j2 ] represents the angular momentum output range of momentum wheel i and momentum wheel j in the current momentum wheel assembly, respectively, v ij For the resultant angular momentum, w i and w j Let be the mounting vectors for momentum wheels i and j.

[0063] In this embodiment, the maximum angular momentum envelope of each momentum wheel combination can be obtained through analytical calculation, thus determining the clear boundary of the maximum angular momentum envelope. This effectively improves the angular momentum output capability of the momentum wheel combination, thereby enhancing the overall satellite's rapid maneuverability and momentum wheel anti-saturation capability. In contrast, the search method does not know where the boundary is, and it attempts to calculate the maximum number of nearly ten thousand planes to roughly find the boundary of the envelope, resulting in an enormous computational burden that is inconvenient for on-board computation. Therefore, this embodiment not only effectively improves the angular momentum output capability of the momentum wheel combination, thereby enhancing the overall satellite's rapid maneuverability and momentum wheel anti-saturation capability, but also eliminates the need for a numerical iterative search process. Compared to the search method, it has higher computational efficiency, smaller storage requirements, and is easier to implement on-board.

[0064] Regarding step 108:

[0065] In some implementations, the intersection of the demand direction vector and the envelope of the current momentum wheel combination is determined as follows:

[0066] Let c be the finite envelope surface passing through the current momentum wheel combination. ij Given a point P0{x} s ,y s ,zs}, and the normal vector of the maximum envelope surface is n. ij The equation of the plane = {A, B, C} is:

[0067] A(x–x s )+B(y–y s )+C(z–z s ) = 0

[0068] In the formula, {x s ,y s ,z s Let {A,B,C} be the coordinates of P0 on the X, Y, and Z axes, and let {A,B,C} be the normal vector of the maximum envelope surface. ij The components of the X, Y, and Z axes, with x, y, and z intersecting at point P. t Coordinates on the X, Y, and Z axes;

[0069] Let the required direction vector be n = {p, q, r} passing through the initial angular momentum h0 = {x0, y0, z0}. Then the equation of the line is:

[0070] x = x0 + p*t

[0071] y = y0 + q*t

[0072] z = z0 + r*t

[0073] t is the variable to be determined, {x0,y0,z0} are the components of the initial angular momentum h0 along the X, Y, and Z axes, and {p,q,r} are the components of the required direction vector n along the X, Y, and Z axes.

[0074] Substituting the equation of the line into the equation of the plane, we get:

[0075] A*(x0+p*t–x s )+B*(y0+q*t–y s )+C*(z0+r*t–z s ) = 0

[0076] Right now

[0077] t=-(A*(x0–x s )+B*(y0–y s )+C*(z0–z s )) / (A*p+B*q+C*r)

[0078] Substituting t into the equation of the straight line, we can obtain the intersection point P of the required direction vector and the envelope of the current momentum wheel combination. t ={x0+p*t,y0+q*t,z0+r*t}.

[0079] In this embodiment of the invention, whether the intersection point lies within the finite envelope surface is determined in the following manner:

[0080] Calculate the intersection point P t The four corner points {P1, P2, P3, P4} of the finite envelope surface combined with the current momentum wheel are {c ij1 ,c ij2 ,c ij3 ,c ij4 The determination is made by checking whether the sum of the areas of the triangles formed by the triangles is equal to the area of ​​the finite envelope surface, i.e.:

[0081] 2S0=||P0P1×P0P2||+||P0P2×P0P3||+||P0P3×P0P4||+||P0P4×P0P1||

[0082] 2S t =||P t P1×P t P2||+||P t P2×P t P3||+||P t P3×P t P4||+||P t P4×P t P1||

[0083] Where P0 is the finite envelope surface c ij Given points on the surface, S0 is the area of ​​a finite envelope surface, S t It is the sum of the areas of the triangles formed by the four corner points of the finite envelope surface of the intersection point and the current momentum wheel combination;

[0084] Obtain the numerical calculation error ε, if |S t –S0|<<ε / 2, then the intersection point P t Located on the finite envelope surface c ij Inside;

[0085] If |S t –S0|>>ε / 2, then the intersection point P t Not located on the finite envelope surface c ij Inside.

[0086] In this embodiment, reference can be made to Figure 2 Let the four corner points of the finite envelope be {P1, P2, P3, P4}, and let P0 be a known point located within the finite envelope. The area S0 of the finite envelope can be calculated using the formula described above. t The intersection point P can be calculated using the formula above. t The sum of the areas S of the triangles formed by the four corner points {P1, P2, P3, P4} of the finite envelope surface combined with the current momentum wheel.t If S0 = S t Then determine the intersection point P. t It lies within a finite envelope. Assume the intersection point is P, which does not lie within the finite envelope. t ′, we can see the calculated S t It must not be equal to S0.

[0087] Regarding step 110:

[0088] In this step, if the intersection point lies within the finite envelope surface, it means that the current finite envelope surface is the largest finite envelope surface among all momentum wheel combinations. Then, the angular momentum h corresponding to that intersection point is... t for:

[0089] h t =t*n+h0

[0090] In the formula, t is the variable to be determined obtained in step 108, n is the required direction vector, and h0 is the initial angular momentum.

[0091] If the intersection point is not located within the finite envelope, the momentum wheel combination needs to be changed, and steps 102-110 need to be repeated until an envelope that satisfies the conditions is found, i.e., the largest finite envelope among all momentum wheel combinations. Finally, according to h t This allows you to allocate the maximum angular momentum output from each momentum wheel, specifically based on h. t The allocation will not be explained in detail here.

[0092] like Figure 3 , Figure 4 As shown, this embodiment of the invention provides a device for determining the maximum angular momentum of a gear train with a non-zero initial angular momentum. The device embodiment can be implemented by software, hardware, or a combination of both. From a hardware perspective, as... Figure 3 The diagram shown is a hardware architecture diagram of a computing device for determining the maximum angular momentum of a gear train with non-zero initial angular momentum, provided by an embodiment of the present invention. Except for... Figure 3 In addition to the processor, memory, network interface, and non-volatile memory shown, the computing device in the embodiment may also include other hardware, such as a forwarding chip responsible for processing packets. Taking software implementation as an example, such as... Figure 4 As shown, as a logical device, it is formed by the CPU of its computing device reading the corresponding computer program from the non-volatile memory into memory and running it. This embodiment provides a device for determining the maximum angular momentum of a gear train with non-zero initial angular momentum, comprising:

[0093] The determining unit 401 is used to determine the angular momentum output range of each momentum wheel in the gear train and the installation vector of each momentum wheel in the coordinate system of the whole star's center of mass.

[0094] The first calculation unit 402 is used to perform the following for each momentum wheel combination: based on the installation vectors of the two momentum wheels in the current momentum wheel combination, determine the normal vector of the maximum envelope surface formed by the current momentum wheel combination;

[0095] The second calculation unit 403 is used to determine the combined angular momentum on the maximum envelope surface normal vector when the remaining momentum wheels are saturated, based on the installation vector and angular momentum output range of the remaining momentum wheels other than the two momentum wheels in the current momentum wheel combination.

[0096] The third calculation unit 404 is used to determine the corner points of the envelope surface of the current momentum wheel combination based on the combined angular momentum, the installation vectors of the two momentum wheels in the current momentum wheel combination, and the angular momentum output range, so as to determine the finite envelope surface of the current momentum wheel combination.

[0097] The judgment unit 405 is used to determine the intersection point of the demand direction vector and the envelope surface of the current momentum wheel combination based on the predetermined initial angular momentum of the momentum wheel combination and the demand direction vector of the angular momentum, and to determine whether the intersection point is located within the finite envelope surface.

[0098] The loop unit 406 is used to determine the angular momentum corresponding to the intersection point if the condition is met, and to allocate the maximum angular momentum output of each momentum wheel based on the angular momentum corresponding to the intersection point; otherwise, the momentum wheel combination is replaced.

[0099] It is understood that the structures illustrated in the embodiments of the present invention do not constitute a specific limitation on a device for determining the maximum angular momentum of a gear train with non-zero initial angular momentum. In other embodiments of the present invention, a device for determining the maximum angular momentum of a gear train with non-zero initial angular momentum may include more or fewer component units than illustrated, or combine certain component units, or split certain component units, or arrange different component units. The illustrated components may be implemented in hardware, software, or a combination of software and hardware.

[0100] The information interaction and execution process between the various units in the above-mentioned device are based on the same concept as the method embodiment of the present invention, and the specific details can be found in the description of the method embodiment of the present invention, and will not be repeated here.

[0101] This invention also provides a computing device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements a method for determining the maximum angular momentum of a gear train with non-zero initial angular momentum according to any embodiment of this invention.

[0102] This invention also provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program causes the processor to perform a method for determining the maximum angular momentum of a gear train with non-zero initial angular momentum according to any embodiment of this invention.

[0103] Specifically, a system or apparatus equipped with a storage medium may be provided, on which software program code implementing the functions of any of the embodiments described above is stored, and the computer (or CPU or MPU) of the system or apparatus may read and execute the program code stored in the storage medium.

[0104] In this case, the program code read from the storage medium can itself implement the function of any of the above embodiments, and therefore the program code and the storage medium storing the program code constitute part of the present invention.

[0105] Examples of storage media used to provide program code include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, program code can be downloaded from a server computer via a communication network.

[0106] Furthermore, it should be clear that not only can the program code read by the computer be executed, but also the operating system or other components operating on the computer can be instructed based on the program code to perform some or all of the actual operations, thereby realizing the function of any of the embodiments described above.

[0107] Furthermore, it is understood that the program code read from the storage medium is written to the memory set in the expansion board inserted into the computer or to the memory set in the expansion module connected to the computer. Then, based on the instructions of the program code, the CPU or other components installed on the expansion board or expansion module execute some and all of the actual operations, thereby realizing the function of any of the above embodiments.

[0108] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0109] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as ROM, RAM, magnetic disk, or optical disk.

[0110] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the maximum angular momentum of a gear train with non-zero initial angular momentum, characterized in that, include: Determine the angular momentum output range of each momentum wheel in the gear train and the installation vector of each momentum wheel in the coordinate system of the whole star's center of mass; For each momentum wheel combination, the following is performed: based on the installation vectors of the two momentum wheels in the current momentum wheel combination, determine the normal vector of the maximum envelope surface formed by the current momentum wheel combination; Based on the mounting vectors of the remaining momentum wheels (excluding the two momentum wheels in the current momentum wheel combination) and the angular momentum output range, determine the combined angular momentum on the normal vector of the maximum envelope surface when the remaining momentum wheels are saturated; Based on the combined angular momentum, the installation vectors of the two momentum wheels in the current momentum wheel combination, and the angular momentum output range, the corner points of the envelope surface of the current momentum wheel combination are determined to determine the finite envelope surface of the current momentum wheel combination. Based on the predetermined initial angular momentum of the combined momentum wheels of the gear train and the required direction vector of the angular momentum, the intersection point of the required direction vector with the envelope surface of the current momentum wheel combination is determined, and it is determined whether the intersection point is located within the finite envelope surface. If yes, then determine the angular momentum corresponding to the intersection point, and allocate the maximum angular momentum output of each momentum wheel based on the angular momentum corresponding to the intersection point; if not, then change the momentum wheel combination.

2. The method according to claim 1, characterized in that, The upper limit of the angular momentum output range of each momentum wheel in the gear train is the nominal angular momentum of the corresponding momentum wheel, and the lower limit is the negative of the nominal angular momentum of the corresponding momentum wheel.

3. The method according to claim 1, characterized in that, The determination of the maximum envelope surface normal vector formed by the current momentum wheel assembly based on the installation vectors of the two momentum wheels in the current momentum wheel assembly includes: The maximum envelope surface normal vector formed by momentum wheel i and momentum wheel j in the current momentum wheel assembly for: in, and These are the installation vectors of momentum wheels i and j in the coordinate system of the entire star's center of mass, respectively.

4. The method according to claim 1, characterized in that, The determination of the combined angular momentum on the maximum envelope surface normal vector when the remaining momentum wheels are saturated, based on the mounting vectors of the remaining momentum wheels (excluding the two momentum wheels in the current momentum wheel combination) and the angular momentum output range, includes: For all momentum wheels k ≠ i, j except for the two momentum wheels in the current momentum wheel combination, the following applies: If satisfied ,but If satisfied ,but The resultant angular momentum is obtained v ij for in, To perform symbolic operations, The normal vector of the maximum envelope surface, w 1, ..., w N Let be the mounting vector of each momentum wheel in the coordinate system of the entire star's center of mass. and Let N be the intermediate resultant angular momentum, and N be the number of momentum wheels in the gear train, where N is a positive integer greater than or equal to 4. Let be the range of angular momentum output for the remaining momentum wheel k, where This represents the lower limit of the angular momentum output range, and is a negative number. This represents the upper limit of the angular momentum output range.

5. The method according to claim 4, characterized in that, The envelope corner points of the current momentum wheel assembly are determined in the following way: Let the four corner points of momentum wheel i and momentum wheel j in the current momentum wheel assembly be... c ij1 , c ij2 , c ij3 , c ij4 Then the envelope surface c of the current momentum wheel combination ij The four corner points are: c ij1 = D H i1 · w i + D H j1 · w j + v ij c ij2 = D H i1 · w i + D H j2 · w j + v ij c ij3 = D H i2 · w i + D H j2 · w j + v ij c ij4 = D H i2 · w i + D H j1 · w j + v ij Where, Δ H i = [Δ H i1 , Δ H i2 ] , Δ H j = [Δ H j1 , Δ H j2 [ ] represents the angular momentum output range of momentum wheel i and momentum wheel j in the current momentum wheel assembly, respectively. v ij The combined angular momentum, w i and w j Let be the mounting vectors for momentum wheels i and j.

6. The method according to claim 3, characterized in that, The intersection point of the demand direction vector and the envelope of the current momentum wheel combination is determined in the following way: Let c be the finite envelope surface passing through the current momentum wheel combination. ij Given a point P0{x} s , y s , z s }, and the normal vector of the maximum envelope surface is n ij The equation of the plane = {A, B, C} is: A(x – x s ) + B(y – y s ) + C(z – z s ) = 0 In the formula, {x s , y s , z s Let {A, B, C} be the coordinates of P0 on the X, Y, and Z axes, and let {A, B, C} be the normal vector of the maximum envelope surface. n ij The components of the X, Y, and Z axes, with x, y, and z intersecting at point P. t Coordinates on the X, Y, and Z axes; Let the required direction vector be n = {p, q, r} passing through the initial angular momentum h0 = {x0, y0, z0}. Then the equation of the line is: x = x0 + p*t y = y0 + q*t z = z0 + r*t t is the variable to be determined, {x0, y0, z0} are the components of the initial angular momentum h0 in the X, Y and Z axes, and {p, q, r} are the components of the required direction vector n in the X, Y and Z axes. Substituting the equation of the straight line into the equation of the plane, we get: A*(x0+ p*t – x s ) + B*(y0+ q*t – y s ) + C*(z0+ r*t – z s ) = 0 Right now t = -(A*(x0– x s ) + B*(y0– y s ) + C*(z0– z s )) / ( A*p + B*q + C*r) Substituting t into the equation of the straight line, we can obtain the intersection point P of the required direction vector and the envelope of the current momentum wheel combination. t ={x0+ p*t, y0+ q*t, z0+ r*t}.

7. The method according to claim 3, characterized in that, Whether the intersection point lies within the finite envelope is determined by the following method: Calculate the intersection point P t The four corner points {P1, P2, P3, P4} of the finite envelope surface combined with the current momentum wheel = {c ij1 ,c ij2 ,c ij3 ,c ij4 The determination is made by checking whether the sum of the areas of the triangles formed by the triangles is equal to the area of ​​the finite envelope surface, i.e.: 2S0= ||P0P1× P0P2|| + ||P0P2× P0P3|| + ||P0P3× P0P4|| + ||P0P4× P0P1|| 2S t = ||P t P1× P t P2|| + ||P t P2× P t P3|| + ||P t P3× P t P4|| + ||P t P4× P t P1|| Where P0 is the finite envelope surface c ij Given points on the surface, S0 is the area of ​​a finite envelope surface, S t The sum of the areas of the triangles formed by the intersection point and the four corner points of the finite envelope surface of the current momentum wheel combination; Obtain the numerical calculation error ε, if |S t – S0|<<ε / 2, then the intersection point P t Located on the finite envelope surface c ij Inside; If |S t – S0|>>ε / 2, then the intersection point P t Not located on the finite envelope surface c ij Inside.

8. An apparatus based on the method of any one of claims 1-7, characterized in that, include: The determination unit is used to determine the angular momentum output range of each momentum wheel in the gear train and the installation vector of each momentum wheel in the coordinate system of the whole star's center of mass. The first calculation unit is used to perform the following for each momentum wheel combination: based on the installation vectors of the two momentum wheels in the current momentum wheel combination, determine the maximum envelope surface normal vector formed by the current momentum wheel combination; The second calculation unit is used to determine the combined angular momentum of the remaining momentum wheels when they are saturated on the normal vector of the maximum envelope surface, based on the installation vector of the remaining momentum wheels other than the two momentum wheels in the current momentum wheel combination and the angular momentum output range. The third calculation unit is used to determine the corner points of the envelope surface of the current momentum wheel combination based on the combined angular momentum, the installation vectors of the two momentum wheels in the current momentum wheel combination, and the angular momentum output range, so as to determine the finite envelope surface of the current momentum wheel combination. The judgment unit is used to determine the intersection point of the demand direction vector with the envelope surface of the current momentum wheel combination based on the predetermined initial angular momentum of each momentum wheel of the gear train and the demand direction vector of the angular momentum, and to determine whether the intersection point is located within the finite envelope surface. The loop unit is used to determine the angular momentum corresponding to the intersection point if the condition is met, and to allocate the maximum angular momentum output of each momentum wheel based on the angular momentum corresponding to the intersection point; otherwise, the momentum wheel combination is replaced.

9. A computing device comprising a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program, implements the method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method of any one of claims 1-7.

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