Method for controlling a cluster of gyroscopic actuators to generate angular momentum

Abstract

A method for controlling a set of gyroscopic actuators of a satellite, distributed into two coplanar subsets, is described, the method comprising: Receiving a setpoint angular momentum, Determining an angular momentum to be provided by each coplanar subset (, ), from a distribution parameter, between the two subsets, of a component of the setpoint angular momentum along an axis () common to the two planes, r being a scalar comprising the lowest admissible value and the highest admissible value of the contribution of one of the coplanar subsets to the component of the setpoint angular momentum along the axis common to the two planes, determining a tilt angle value of each gyroscopic actuator of a subset, from the angular momentum to be provided by said subset, and Issuing a command to each gyroscopic actuator comprising the respective tilt angle value determined.Figure from the summary: Figure 2.

Description

Title of the invention: Method for controlling a cluster of gyroscopic actuators to generate angular momentum. Technical field

[0001] The present disclosure relates to a method of controlling a set of gyroscopic actuators to make these actuators achieve a set angular momentum. Previous technique

[0002] A gyroscopic actuator 10, also called a gyrodyne, or in English CMG for "Control Moment Gyro", is schematically represented in [Fig. 1] and comprises a flywheel 11 which is driven in rotation, about an axis of rotation x, by a motor (not shown) at a high constant rotational speed, and an orientation device 12 for the rotation axis x of the flywheel in a plane. In [Fig. 1], the orientation device 12 for the rotation axis x of the flywheel is adapted to drive the rotation axis x in rotation with respect to an orthogonal axis z. The rotation of the flywheel about its rotation axis x creates a constant angular momentum which is a function of the rotational speed of the flywheel 11 and its moment of inertia about the rotation axis.When a velocity is applied to the orientation of the x-axis of rotation of the flywheel, a gyroscopic torque results from the transfer of angular momentum between the flywheel and its support.

[0003] It is known, for example from the publication by Michel Llibre, "Gyroscopic Actuators for Attitude Control of Satellites", February 16, 2009, to use gyroscopic actuators for the attitude control of a satellite. In this case, the tilt axis of the flywheel is linked to the satellite frame, so that the rotation axis of the flywheel is movable relative to the satellite frame, and the gyroscopic torque generated by the gyroscopic actuator is transmitted to the satellite frame and makes it possible to control a rotation speed of the satellite by the principle of conservation of angular momentum of the assembly comprising the satellite and the gyroscopic actuator(s).

[0004] A drawback of using gyroscopic actuators for attitude control concerns singularities, which are configurations of the gyroscopic actuators in which there exists a direction such that, regardless of the angular velocity of the tilt angle commanded to the gyroscopic actuators, the gyroscopic torque produced is always orthogonal to the direction considered, so that for this configuration it is not possible to achieve control of the gyroscopic actuators allowing instantaneous control of the rotation speed of the satellite.

[0005] The use of gyroscopic actuators for the attitude control of a satellite therefore implies reducing singular configurations as much as possible, in order to increase the operational capabilities of this attitude control solution.

[0006] Furthermore, some control laws used to control the tilt angle of gyroscopic actuators, in order to produce a setpoint angular momentum, are not deterministic, in that they do not allow a specific configuration of gyroscopic actuator tilt angles to be associated with a setpoint angular momentum. This can result in the need to stop an ongoing mission in order to desaturate the gyroscopic actuators and return them to their initial configuration, which impacts the successful execution of the mission and entails additional costs for satellite operation. Summary

[0007] This disclosure improves the situation.

[0008] In particular, one purpose of the present disclosure is to propose a method for controlling a set of gyroscopic actuators of a satellite, which makes it possible to increase the operational capabilities of a satellite during a mission.

[0009] Another purpose of the present disclosure is to propose a method in which the control of gyroscopic actuators, for a given setpoint angular momentum, is deterministic.

[0010] Another purpose of the present disclosure is to propose attitude control of a satellite that is applicable with a variable number of gyroscopic actuators.

[0011] Another purpose of this disclosure is to enable the range of angular momentum capacity of all gyroscopic actuators to be adapted according to the needs of the mission.

[0012] In this regard, a method is proposed for controlling a set of gyroscopic actuators of a satellite, for the realization by the gyroscopic actuators of a setpoint angular momentum, each gyroscopic actuator comprising a flywheel capable of being driven in rotation about an axis of rotation so as to produce angular momentum, and a device for orienting the axis of rotation at an angle θ, the gyroscopic actuators being distributed in two coplanar subsets, each coplanar subset comprising at least two gyroscopic actuators configured to generate a respective angular momentum contained in the same plane of the subset, the respective planes of the two subsets being non-coplanar, the control method comprising: - the reception of a dimensionless setpoint angular momentum to be generated by all gyroscopic actuators, - the determination of an angular momentum to be provided by each coplanar subset, from the dimensionless setpoint angular momentum and a distribution parameter chosen according to a predetermined sequence of distribution parameters, between the two coplanar subsets, of a component of the setpoint angular momentum along an axis common to the two planes, in which the parameter r is a scalar between a minimum value and a maximum value corresponding respectively to the lowest admissible value and the highest admissible value of the contribution of one of the coplanar subsets to the component of the setpoint angular momentum along the axis common to the two planes, - the determination of a tilt angle value for each gyroscopic actuator of a coplanar sub-assembly, based on the angular momentum to be provided by said coplanar sub-assembly, and - the emission of a command from each gyroscopic actuator including the respective determined tilt angle value.

[0013] In embodiments, the distribution parameter has at least one predetermined value depending on the mission of the satellite.

[0014] In embodiments, the predetermined distribution parameter has a value profile that varies over time during a satellite mission.

[0015] In some embodiments, the parameter r is defined as follows: yPxY = (1 - r) - U rv?xy j æ ± ± j Amin' x Æmax xPxz = x - XPxy where ^pxy and xpxz are respectively the angular momenta generated, along the common axis (^.) of the two planes, by the two coplanar subsets, xPxY is the lowest admissible value of the contribution of a subset to said component of the setpoint angular momenta along the common axis (xs) of the two planes, and is the highest admissible value of the contribution of the subset to the component (A) of the setpoint angular momentum along the axis (xç) common to the two planes.

[0016] In embodiments, & is defined as Eq. 2 JT: [0, ZlTp © c K3 (7 —• A = z) cos sine, iePxy / , sin^i <ePxz and we define vp*Y and as Amin nm = max ( - \lNy 2 -y 2 ; x - ^^- 2 2 ) Eq. 6: ; x + ^Nz2-z2 )

[0017] In embodiments, determining an angle value for each gyroscopic actuator of a coplanar subassembly from the angular momentum to be provided by said subassembly comprises: - the determination of a direction of angular momentum to be provided by each gyroscopic actuator, based on the angular momentum to be provided by the sub-assembly, and at least one predetermined parameter, defining an angular separation between the angular momentum to be provided by a reference gyroscopic actuator and the angular momentum to be provided by the sub-assembly, and - the determination of a tilt angle value for each gyroscopic actuator from the corresponding angular momentum direction.

[0018] In embodiments, wherein the step of determining a direction of angular momentum to be generated by each gyroscopic actuator comprises: - determining the direction of the angular momentum of a reference gyroscopic actuator from a first angular separation parameter and the direction of the angular momentum to be provided by the subassembly, and - if a coplanar subset includes more than two gyroscopic actuators, the iterative implementation of: • the determination of a residual angular momentum to be provided by the gyroscopic actuators of the sub-assembly, excluding the reference gyroscopic actuator, and • Determining the direction of an angular momentum of an additional reference gyroscopic actuator from an additional angular separation parameter between the moment kinetic energy to be provided by the additional reference gyroscopic actuator and the direction of the residual angular momentum.

[0019] According to another object, a method for controlling a set of gyroscopic actuators of a satellite is described, each gyroscopic actuator comprising a flywheel capable of being driven in rotation about an axis of rotation so as to produce an angular momentum, and a device for tilting the axis of rotation according to an angle of inclination o,

[0020] the gyroscopic actuators being distributed into two coplanar subsets, one of the subsets comprising a gyroscopic actuator configured to generate an angular momentum contained in a first plane, and the other subset comprising at least two gyroscopic actuators configured to generate a respective angular momentum contained in the same second plane of the subset, the first and second planes being non-coplanar,

[0021] the method comprising: - the reception of a dimensionless setpoint angular momentum to be generated by all gyroscopic actuators, - The determination of an angular momentum to be provided by each coplanar subset, based on the setpoint angular momentum, and a distribution parameter, chosen according to a predetermined sequence of distribution parameters between the two coplanar subsets of gyroscopic actuators, of a component of the setpoint angular momentum (along an axis common to the two planes, in which the parameter r is a scalar chosen between a minimum value and a maximum value corresponding respectively to the lowest permissible value and the highest permissible value of the contribution of one of the coplanar subsets to the setpoint angular momentum along the axis common to the two planes, and - the determination of a tilt angle value for each gyroscopic actuator of a coplanar sub-assembly, based on the determined angular momentum to be provided by said coplanar sub-assembly, and - the emission of a command from each gyroscopic actuator including the respective determined tilt angle value.

[0022] According to another object, a computer program product is described, comprising code instructions for implementing one of the processes according to the preceding description, when executed by a computer.

[0023] According to another object, a computer is described, configured for the implementation of one of the methods according to the preceding description, for the attitude control of a satellite.

[0024] According to another object, a satellite is described, comprising: - a set of gyroscopic actuators, each gyroscopic actuator comprising a flywheel capable of being driven in rotation about an axis of rotation so as to produce angular momentum, and a device for orienting the axis of rotation at an angle θ, the gyroscopic actuators being distributed into two coplanar subsets, each coplanar subset comprising at least two gyroscopic actuators configured to generate angular momentum h; contained in the same respective plane of the subset, the respective planes of the two subsets being non-coplanar, and - a satellite control device, adapted to implement one of the control methods according to the preceding description.

[0025] The proposed control method makes it possible to determine, for a given angular momentum to be provided by a gyroscopic actuator array formed of two coplanar sub-assemblies, a position, i.e., an angle, of each gyroscopic actuator. This determination is made according to a specific method, notably based on a distribution parameter, between the two sub-assemblies, of a component along an axis common to the planes of the two sub-assemblies, of the given angular momentum to be provided by the array. The control of the gyroscopic actuators, based on a given value of the setpoint angular momentum, developed according to the precise and deterministic method, is advantageously reproducible in ground simulation and makes it possible to know exactly the state of the gyroscopic actuator array.

[0026] Furthermore, determining a value for the distribution parameter associated with the distribution method makes it possible to precisely delimit the areas to be avoided, corresponding to singular or low-controllability angular momentum zones of the cluster. Consequently, the distribution parameter in the distribution method according to the invention can be determined as needed to correspond to angular momentum outside the exclusion zones. Thus, depending on the mission requirements, it is possible to determine a value for the distribution parameter for the method according to the invention that allows the singular zones to be positioned outside the angular momentum values ​​required for mission execution, thereby increasing the satellite's operational capabilities. Brief description of the drawings

[0027] Other features, details and advantages will become apparent from reading the detailed description below and from analyzing the accompanying drawings, in which: Fig. 1

[0028] [Fig.1] represents a schematic diagram of a gyroscopic actuator. Fig. 2

[0029] [Fig.2] schematically represents the layout of an example assembly of gyroscopic actuators. Fig. 3a

[0030] [Fig.3a] represents an example of an angular momentum capacity domain of a set of gyroscopic actuators comprising a subset of three coplanar gyroscopic actuators and a subset of two coplanar gyroscopic actuators. Fig. 3b

[0031] [Fig.3b] represents an example of an angular momentum capacity domain of a set of gyroscopic actuators comprising two subsets of two coplanar gyroscopic actuators. Fig. 4

[0032] [Fig.4] is a graphical representation of the distribution parameter r of the contribution, to the x component of the angular momentum to be provided by the set of gyroscopic actuators, by one of the two subsets of actuators. Fig. 5

[0033] [Fig.5] represents the angles of two actuators of a coplanar subset determined from the component of angular momentum in the plane of the subset. Fig. 6a

[0034] [Fig.6a] represents an example of the set of singular configurations of a cluster of 2 x 2 CMG for a first value of the distribution parameter r. Fig. 6b

[0035] [Fig.6b] represents another example of an ensemble of singular configurations of a 2 x 2 CMG cluster for another value of the distribution parameter r. Fig. 7a

[0036] [Fig.7a] represents an example of the angular momenta of a subset of three coplanar gyroscopic actuators to obtain a first value of a component of a setpoint angular momentum in the plane of the actuators. Fig. 7b

[0037] [Fig.7b] represents an example of the angular momenta of a subset of three coplanar gyroscopic actuators to obtain a second value of a component of a setpoint angular momentum in the plane of the actuators. Fig. 8a

[0038] [Fig.8a] schematically represents the main steps of a process according to a method of implementation. Fig. 8b

[0039] [Fig.8b] schematically represents the main steps of a process according to another embodiment. Fig. 9

[0040] [Fig.9] schematically represents a satellite in orbit around the Earth, for which the method for controlling gyroscopic actuators can be implemented.

[0041] Detailed description of at least one embodiment

[0042] In the present, the terms "gyroscopic actuator" or "CMG" may be used interchangeably to refer to a gyroscopic actuator.

[0043] The assembly G of gyroscopic actuators distributed into two sub-assemblies described below may be referred to as a "cluster" of gyroscopic actuators.

[0044] The notation Ny + Nz CMG will be used to designate the configuration of a gyroscopic actuator array, where Ny and Nz respectively denote the number of gyroscopic actuators in each of the two coplanar subsets. The notation "2x2 CMG" can also be used, which corresponds to the "2 + 2 CMG" configuration.

[0045] With reference to Figure 2, an example of the configuration of a set G of gyroscopic actuators 10 of a satellite is schematically represented. As described previously with reference to Figure 1, each gyroscopic actuator 10, or MGA, comprises a flywheel 11 capable of being driven in rotation about an axis of rotation, so as to produce a constant angular momentum of magnitude h, and a device for orienting the axis of rotation of the flywheel at an angle θ. The angle θ therefore also corresponds to the orientation of the angular momentum produced by the gyroscopic actuator. In Figure 2, each arrow in a plane Pxy and Pxz schematically represents the angle of the axis of rotation of the flywheel of a gyroscopic actuator, i.e., the direction of the angular momentum of the actuator. For the purposes of this disclosure, all gyroscopic actuators 10 in the assembly are assumed to be identical, and therefore have the same angular momentum h.

[0046] As schematically represented in [Fig. 2], the set G of gyroscopic actuators 10 is divided into two coplanar subsets. In a coplanar subset, the gyroscopic actuators of the same subset are configured so that the angular momentum of each gyroscopic actuator can be oriented in the same plane, i.e., with respect to the same axis that is orthogonal to said plane. Although the two planes corresponding to the two coplanar subsets may be orthogonal, this is not a limiting case. However, the two planes of the two subsets are not parallel.

[0047] Each coplanar subset can comprise between two and four gyroscopic actuators, for example, two or three gyroscopic actuators. However, the number of gyroscopic actuators is not necessarily the same for both subsets. This disclosure therefore applies, for example, to the cases 2x2 CMG, 2 + 3 CMG, 3 + 3 CMG, etc. Furthermore, this disclosure also applies to a special case described in more detail below, denoted 1 + 2 CMG, in which one subset comprises at least two coplanar gyroscopic actuators, and the other subset comprises only one gyroscopic actuator. This case may correspond, in particular, to a failure of one gyroscopic actuator in one of the two subsets of an initial 2 x 2 CMG configuration.

[0048] Returning to [Fig.2], it represents the example of a configuration with four gyroscopic actuators 10 distributed in two subsets of two gyroscopic actuators each, and arranged in two distinct non-coplanar planes.

[0049] By convention, a direct normalized frame of reference is defined, linked to the set of gyroscopic actuators and formed by the three unit vectors çx^y^z^ defined as follows: - The line forming the intersection of the two planes carries the unit vector Xg? - The unit vector is orthogonal to Xg inside the first plane, named PXY, - The unit vector Z g is orthogonal to X5 inside the second plane, called PYZ.

[0050] The orientation of the vectors is defined such that the frame 7?$= so^ direct. This coordinate system is not necessarily orthogonal; it is only so if the angle between the two planes is equal to 90 degrees.

[0051] In each plane, the angle formed by the axis of rotation of a gyroscopic actuator i of a subset with respect to a common origin for all gyroscopic actuators defined by the vector Xs is denoted. By convention, the sign is positive towards the direction vector of each plane (Ig for PXY, Zg for Pxz). In the example shown in Figure 3, the angles (CF| ; 02 z ^3 / ^4) of the four gyroscopic actuators are therefore represented with 0^0; 02 < 0; 03 < 0; 04 < 0

[0052] With these assumptions and notations, the angular momentum jj&rappe generated by the cluster G of gyroscopic actuators is expressed as follows, as a function of the angles: ( Hx = JlŒfCOSffj) Eq. 1: h®r(,PFe = HxXg + HyYg + HzZg with = h(SiepXYsinffJ , Hz = h(2ïepxz sin where in this equation we have noted i G PXy the set of gyroscopic actuators i belonging to the coplanar subset of plane P^y and Î ^XZ the set of gyroscopic actuators i belonging to the coplanar subset of plane P^z.

[0053] The dimensionless angular momentum A = (x; y; z) = hsrappe / h is defined as the ratio between the physical angular momentum generated by the cluster ^cluster _ , . [Nms] and the individual angular momentum of the CMG A. x xj yj z / It is assumed that the gyroscopic actuators are free to rotate and are therefore not subject to any physical or software limit, so that ff = ( CTp* ... ; ) can reach any value in the space where N corresponds to the number of gyroscopic actuators in the set. By managing the modulo 2, we can restrict this gimbal angular space to ]-tt, jt]n for example, or equivalently to [0,27dN, without loss of generality.

[0054] The dimensionless angular momentum generated by the cluster is obtained as the image of a by a non-linear function 2T towards a subset 2) dcR3, defined as follows: Eq. 2 Jf: [O, ZTTp © C R3 A = (X; y; z) fePxz

[0055] The space © containing the set of angular momenta realizable by the cluster G is called the angular momentum capacity domain (dimensionless). A necessary and sufficient condition for the existence of a solution is written: Eq. 3: 3 xpæ;xps |xp® + xpxz = x ; + y2 <Ny2 ; xpxz‘ + z2<Nz2 Where xpxy is the contribution to x of the subset of coplanar gyroscopic actuators of the plane P^y, and is the contribution to x of the subset of coplanar gyroscopic actuators of the plane P\ / ; Ny is the number of gyroscopic actuators of the coplanar subset of the plane Pjçy and Nz is the The number of gyroscopic actuators in the coplanar subset of the Pxz plane. From this, we deduce the domain ® dimensionless angular momentum (X', y; Z) achievable by the cluster, defined by the following system of three inequalities: Eq. 4:2) = fx. y, z E [ Jyj < jV¥ : |zj < ; |x] < IA\.2 - y2 4- 1¾2 — z2 1 l ■ -v V ■ I

[0056] With reference to Figures 3a and 3b, the angular momentum domain achievable by a cluster formed respectively of 2 + 3 CMGs and 2 x 2 CMGs is represented; that is, for [Fig. 3a], a cluster in which one subset comprises two gyroscopic actuators and the other comprises three gyroscopic actuators, and for [Fig. 3b], a cluster of two subsets of two gyroscopic actuators. In both cases, terminal disks are observed at + / - Z and + / - Y, the radius of which varies according to the number of gyroscopic actuators in the subset considered.

[0057] Returning to equation 2, this equation describes the relationship between the angles of the gyroscopic actuators and the (dimensionalless) angular momentum generated by the cluster. This system can be explicitly inverted, allowing the determination of all solutions enabling the realization of a given dimensionless angular momentum (x; y; z), subject to feasibility due to the maximum angular momentum capacity of the cluster (i.e., it is necessary that £6 ®). This system includes one degree of freedom related to the distribution of angular momentum between the two planes.

[0058] Considering an angular momentum * to be provided by the array of gyroscopic actuators, this angular momentum is distributed into two components JjPxy and ^pxz respectively in the two planes Pxy and ^XZ- aa^ns^ • — = ^PxY + ^Pxz-

[0059] We therefore introduce a distribution parameter r, between the two coplanar subsets, of the component of the angular momentum A along the direction common to the two subsets, that is to say the component x along the xc axis, according to the preceding notations.

[0060] The parameter r is defined as follows: x p xy = (1 - r) 1¾ + r Eq. 5. J v mm max x p yz = x - x p xy

[0061] Where represents the lowest possible contribution of the gyroscopic actuators of the coplanar subset corresponding to the plane P^y to the component x along the axis Xç of the total angular momentum to be generated by the set, and is the highest possible contribution.

[0062] According to the above notation, j^xy _ XPXY + y, Ji22 = xPxz + Z

[0063] These minimum and maximum contributions of the CMG contribution of the Pxy plane the x component are given by the following equation: Eq. 6: = max( - ; x- JnT-z^) iiiin \ yja ' v / ^àx=min(^V y 2 -y 2 ;x+^ z 2 -z 2 ) "and 0 < r < 1

[0064] The distribution parameter r is, for example, a scalar between 0 and 1, which can be seen as a distribution slider for the x component of the total angular momentum Æ provided by the gyroscopic actuators: - The value r = 0 positions the contribution of the plane's gyroscopic actuators to the x component at its lowest permissible value xPL, and therefore that of the plane Pxz at its maximum value. - The value r=l positions the contribution of the gyroscopic actuators of the Pxy plane to the x component at its highest permissible value, and therefore that of the Pxz plane at its minimum value. - A choice r = 0.5 positions the contributions of the two subsets of the planes Pxy ct PXZ at the middle of the admissible distribution interval.

[0065] With reference to Figure 4, the meaning of the distribution parameter r is graphically represented in the case of a 2 x 2 CMG example. In this case, solving the problem of realizing a given dimensionless angular momentum using all the gyroscopic actuators requires that the distribution solutions in (xp-; xPxz) satisfy the following constraints from Equation 4 introduced above, applied to the 2x2 CMG case: x p xv+x p xz = x with |x p xy| < ^4-y 2 and |x p xz| <^4-z 2

[0066] Graphically, these conditions are represented as illustrated in Figure 4. The segment between vpxy and xSiX represents the range of values ​​of the min max parameter distribution r.

[0067] The choice of the parameter ra has an impact on the localization of the angular momentum singularities that can be generated by the set of gyroscopic actuators. The torque generated by the set of gyroscopic actuators around a given position is expressed by differentiating the angular momentum as follows: Ç$ = -hÀ with A - (x;ÿX)-

[0068] This equation can be reformulated as a matrix equation showing the local Jacobian of the linear function^; dependent on the angles of the gyroscopic actuators, J( <f) : = avec

[0069] In the case, for example, of a set of 2 x 2 gyroscopic actuators, the Jacobian is of dimension 3 x 4, and defined as follows: / — 81« | COSO4 \ 0 — s'iiKT^X O CGS <74 /

[0070] The Jacobian depends on the state of the angles of the gyroscopic actuators and is therefore not constant. A particular situation arises if, for a certain state of the cluster defined by the position, the torques generated, regardless of the velocity control, are always orthogonal to a certain direction U. The configuration Gs of the cluster is then said to be singular, and the direction Us, which is uncontrollable, is called the singular direction for this configuration.

[0071] The singularity of a configuration of angles of the gyroscopic actuators °s is equivalent to the existence of at least one zero singular value of the local Jacobian matrix which is in turn equivalent to the fact that the determinant of the matrix Jtc'JJ^J is zero.

[0072] Since the determinant is a continuous function, and the Jacobian is also continuous at 0, this determinant constitutes an interesting and practical metric of the "distance to singularity" for a given configuration in cardan space.

[0073] The controllability index p2 for a cluster state 0 is thus defined as follows, ^(<7) = In summary, a cluster configuration for which p2 = 0 is singular. In such a case, it is not possible to locally achieve any instantaneous torque control with finite cardan speeds; there exists at least one direction of the controlled torque that is not physically realizable.

[0074] However, the value of the distribution parameter ra plays an important role in the localization of singular configurations. With reference to Figures 6a and 6b, two examples of areas of reduced controllability, where are areas corresponding to the singular configurations of the assembly, are shown in the angular momentum capability domain for an array of gyroscopic actuators composed of 2x2 CMGs, for two different values ​​of this parameter. Figure 6a represents the case r = 0.5, where the singularities are located in the center of the angular momentum capability domain, and Figure 6b represents the case r = 0.75, where the singularities are located further out at the periphery of this domain. Depending on the nature of the mission planned for the satellite, and the associated requirements for the satellite's attitude control, a more appropriate value of r can therefore be selected.If necessary, a temporal sequence of different successive values ​​of r can also be predicted during the mission.

[0075] With the parameter r defined, the system (Eq. 2) can be reformulated as follows, by to show the distribution of the x component between the two planes: Eq. 7 COS (Fi = X Pxz sin (Fi = z

[0076] In this "separate" form, the system can be solved. We will now present how the system is solved as a function of the configurations of all the gyroscopic actuators. Case of 2x2 CMG configuration

[0077] In the case of the 2x2 CMG configuration, and using the notations of [Fig.2] for the indices of the gyroscopic actuators, equation 5 is reformulated as follows: Eq. 8 cosox-l- cosa2 = x p " si <r1+sin<r2 = y cos 3 + cos 4 = sinog + sina4 = z with xpxy+xpxz = x

[0078] And these solutions are obtained in angles of the gyroscopic actuators (J = ( (Fp <J2; Oÿ £F4) comme suit en fonction de la commande * = (y y; z) de moment cinétique de grappe et de la répartition choisie (x^XY* X^xz), Eq. 9 C1.2 = ArgOr1^ 4- jy) ± acos ct3 4 = ArgGPxz 4- jz) ± acos kPjiY +jy! 2 + jz] 2 with + xPxz = x

[0079] According to (Eq. 9), if we place ourselves in one of the two planes, for example PXy without restriction of generality, the realization of a dimensionless angular momentum control (x^y; y) is carried out by positioning the rotation axes of the gyroscopic actuators according to the following angles: (a = Arg(xPKY + jy) + jy | S = acos--------- 2

[0080] Figure 5 graphically represents the components a (median angle of the two gyroscopic actuators of the subset) and 6 (half-differential angle between the two gyroscopic actuators of the subset).

[0081] A parameter y2CMG g { - 1 ; 1} can be introduced here, which corresponds to the sign of the angular displacement of a reference gyroscopic actuator, index 1, by relation to the direction of the angular momentum to be generated by the coplanar sub-assembly h XY: eq. 11 - 04 = a + ÿzcw G ,6 a2=ap 2 CMG6

[0082] Once the parameter y2CMG is fixed, the position of the second gyroscopic actuator is completely determined. In the case where 1^^11 = 0' 6 = 90, deget a can take any value.

[0083] Thus, the angles of the gyroscopic actuators of a coplanar subset of two actuators can be determined. This is true for the 2x2 CMG configuration but also for all 2 + N CMG configurations comprising a subset of two gyroscopic actuators.

[0084] Case of N + N configurations, CMG where Av and / or N is greater than 2

[0085] In the case where at least one coplanar subset of gyroscopic actuators comprises three or more actuators (the example from hereafter is always taken from the P^y plane without loss of generality), there exists one (or more) additional degree(s) of freedom for the distribution of the angular momentum component generated by the subset. Figures 7a and 7b show two examples of angular momentum to be generated by a coplanar subset of three gyroscopic actuators, with several possible angles θ for the actuators. Gyroscopic mechanisms enable the generation of these angular momenta. Depending on the value of Ny, the number of additional degrees of freedom can exceed one. Beyond two, each additional CMG provides one additional degree of freedom for generating angular momentum in the planar subset.

[0086] To characterize the additional degree of freedom in the plane of 3 CMG, it is proposed to consider a reference gyroscopic actuator CMGref, as well as the angular separation between the angular momentum to be provided by the reference gyroscopic actuator and the angular momentum to be provided by the coplanar subset. The maximum value 6max of this angular separation occurs when the two other gyroscopic actuators are aligned and is given for || / jPxY|| < 3: SmaX - acos (||F^H ~ Il || > 1 Smax - otherwise

[0087] In the following, the gyroscopic actuator index 1 is considered to be the reference actuator. The parameter ySCMG g [ _ |] qUi is introduced and parameterized the angular deviation between the angular momentum of the reference CMG with respect to the direction of the angular momentum to be provided by the coplanar subset ^pxy &!=(*+y3CMG6max

[0088] Once ySCMG has been determined or fixed, there remains one degree of freedom which corresponds to the two possible permutations of the remaining CMGs. It then suffices to apply the method described above to a subset of two coplanar actuators once the contribution of the reference gyroscopic actuator has been removed, i.e.

[0089] hours = eq. 12 v res / x hj es j [sin(a1) / (f2=ares+yZCMGGres a3=ares_ y2CMG^res

[0090] With: there res = atan2(hy es , h rx es )

[0091] In the case of a coplanar subset comprising more than three gyroscopic actuators, this approach can be implemented iteratively as follows: - We determine the parameter yNCMG £ [ - 1, 1 ] which parameterizes the angle of the angular deviation between the direction of the angular momentum of a first reference gyroscopic actuator with respect to the direction of the angular momentum to be provided by the coplanar subset ^pxy - We consider the remaining angular momentum h1 es once we have removed the contribution of the reference CMG, that is to say , res i»Pxy COS ( Oref ) We determine the parameter ylV-1 CMG g [ _ 1, 1 ] which parameterizes the angle of the angular deviation between the first remaining CMG, considered as a second reference gyroscopic actuator, with respect to the direction of the remaining angular momentum h , The remaining angular momentum is considered after removing the contribution of the second reference CMG, iterating these steps until only two gyroscopic actuators remain between which the remaining angular momentum can be distributed. The angles of these two gyroscopic actuators are then determined, and then, taking into account the parameter values yN-1 CMG. yNCMG qUi have been fixed, we can determine the contributions of the successive reference CMGs. Case of the configuration Ny = 1 and Nz > 2 CMG

[0092] As previously stated, the case where one of the coplanar subassemblies comprises only a single gyroscopic actuator may correspond to a failure case. In this case, the necessary and sufficient condition for the existence of a solution is written, under the non-limiting assumption that the coplanar subassembly reduced to a single CMG corresponds to the PXY plane:

[0093] 3 IP<;XPÏ / | XPxy + XPxz = XP»'2 + y2=l; Xpxz2 + z2<

[0094] The difference with the previous cases is that the amplitude of the angular momentum in the PXY plane of the gyroscopic actuator alone cannot be modulated. Thus, the inequality concerning capacity in the PXY plane is transformed into equality. Solving this equation gives two solutions: ^PXY = ±Vi-y2'

[0095] In the case of a single gyroscopic actuator in one of the planes (in this case PXY), the contribution of the gyroscopic actuator of the PXY plane to the component A of the total angular momentum A generated by the cluster therefore only accepts two solutions. Thus, the distribution parameter r can only take two possible values: 0 or H ' = \ / 1 - A max V 1 J f and r = 0 or r = 1

[0096] In view of the foregoing, and with reference to Figures 8a and 8b, the principles set forth above are used in a method for controlling a set G of gyroscopic actuators 10 of a satellite S, to cause these gyroscopic actuators to generate a set angular momentum and thus enable attitude control of the satellite. The satellite S is equipped with such a set of gyroscopic actuators 10 distributed in two subsets, where, if a subset comprises at least two gyroscopic actuators 10, the subset is coplanar, and with a control device 20 for said actuators, schematically represented in [Fig. 9].

[0097] The satellite in which this method is implemented can, for example, be an Earth observation satellite, carrying at least one observation instrument. The satellite can be intended to be operated in low Earth orbit (LEO), medium Earth orbit (MEO), or geostationary orbit (GEO).

[0098] In some embodiments, the satellite mission is determined a priori, so that a setpoint attitude (which may vary over time) for the satellite is determined a priori for the entire duration of the mission, and that the requirements in terms The torque generated by all the gyroscopic actuators to maintain or change the satellite's attitude is also known. Based on these requirements, at least one value, or a time sequence of values, of the setpoint angular momentum is determined.

[0099] Furthermore, one or more values ​​of the distribution parameter r introduced above is or are predetermined. The sequence of values ​​may, for example, represent a curve of successive discrete values, or successive levels, or be constant. The sequence may be continuous or discontinuous.

[0100] The value sequence can be determined, in particular, according to the mission requirements and the arrangement of singularity zones (or areas of reduced controllability) related to the choice of parameter r. In some embodiments, the value of parameter r can be constant for the entire duration of the mission. Alternatively, parameter r can exhibit a value profile that varies over time during the mission. Alternatively, the torque requirements to be generated by all the gyroscopic actuators can be determined during the mission and, depending on these requirements, one or more values ​​of the distribution parameter r can be determined.

[0101] Depending on the configuration of the gyroscopic actuator set, one or more parameters y, equal to -1 or 1, fixing the angular separation between a reference gyroscopic actuator and the direction of the angular momentum to be generated by a coplanar subset, is also determined. As described above concerning the parameters y2CMG, y3CMG, etc., the number of parameters y depends on the number of gyroscopic actuators in the subset, and more particularly there is a number Nl of parameters y fixed for a subset of N gyroscopic actuators.

[0102] The process includes a step 100 of receiving a setpoint angular momentum cluster = ( H ) to be provided by the set G of gyroscopic actuators 10, that is to say, this setpoint angular momentum must be jointly generated by all the gyroscopic actuators. This setpoint angular momentum can be reduced to the dimensionless angular momentum â = (x;y;z) = introduced above. The setpoint angular momentum can for example, having been determined from an instantaneous torque to be supplied by the gyroscopic actuators.

[0103] The method then comprises, starting from the received setpoint angular momentum, implementing an inversion 200 of this setpoint angular momentum to determine the angles o of the set of gyroscopic actuators 10 enabling the generation this angular momentum of the setpoint, and the sending of a setpoint to the gyroscopic actuators with an indication of the angle to adopt.

[0104] In some embodiments, steps 100 and 200, which determine the angle values ​​of the gyroscopic actuators, are carried out by a ground station T, which then communicates the gyroscopic actuator angle values ​​to be used to the satellite S. The ground station may, for example, include at least one processor and at least one electronic memory (not shown) in which a computer program product is stored, in the form of code instructions to be executed to carry out steps 100 and 200 of the method. In one variant, the ground station includes one or more programmable logic circuits, such as FPGAs, PLDs, etc., and / or specialized integrated circuits (ASICs) adapted to carry out these steps.

[0105] Alternatively, steps 100 and 200, as well as step 300 of sending a command to the gyroscopic actuators, are implemented by the control device 20 on board the satellite, which may also include at least one or more processors (CPU, DSP, GPU, FPGA, ASIC, etc.) and a memory (magnetic hard drive, electronic memory, optical disk, etc.) in which are stored the code instructions executed by the processor, as well as the values ​​of the parameters determined for the implementation of the mission.

[0106] The inversion step 200 includes determining the angle o of each gyroscopic actuator from the setpoint angular momentum and the distribution parameter r. The parameter r allows determining 210 the contribution xPxY, jfpxz of each coplanar subset to the x component of the angular momentum along the axis common to the two planes, by application of equation 5 above, where the minimum and maximum permissible contributions of the subset are determined as a function of the number of gyroscopic actuators and the setpoint angular momentum by equation 6.

[0107] Consequently, the angles of the gyroscopic actuators of each sub-assembly are determined from the angular momentum to be provided by each sub-assembly, i.e. xPxY + y for the sub-assembly corresponding to the P^y plane, and XPxz + Z for the sub-assembly corresponding to the Py / - plane.

[0108] In embodiments, this determination 220 of an angle value of each gyroscopic actuator from the angular momentum to be provided by each subassembly comprises: - The determination 221 of an angle of at least one reference gyroscopic actuator, from the angular momentum to be provided by the sub-assembly and at least one parameter y defining an angular separation between the moment kinetic energy to be provided by this reference gyroscopic actuator and the angular momentum of the subassembly, and - The determination 223 of an angle value of each other gyroscopic actuator of the subset from the angle of the reference gyroscopic actuator.

[0109] With reference to Figure 8a, in cases where the satellite comprises at least one subset of two coplanar gyroscopic actuators, the determination of the angle o, of each actuator of this subset is carried out by application of Equation 11 introduced above, where the reference gyroscopic actuator has an angle ^1.

[0110] With reference to [Fig. 8b], when the satellite comprises at least one subset of three or more gyroscopic actuators, the determination 220 of the angle o.dc each actuator of that subset comprises: - The determination 221 of an angle of a first reference gyroscopic actuator, from the angular momentum to be provided by the sub-assembly JjPxy and at least one parameter yNCMG defining an angular separation between the angular momentum to be provided by this reference gyroscopic actuator and the angular momentum of the sub-assembly, - The iterative implementation, until the number of gyroscopic actuators excluding the reference gyroscopic actuator(s) reaches two, of the following steps: • determination 222 of a residual angular momentum hres to be provided by the gyroscopic actuators of the sub-assembly except for the reference gyroscopic actuator(s), • determination (221) of the direction of an angular momentum of an additional reference gyro actuator from parameters yiV-lCMG defining the sign of an angular separation between the angular momentum to be provided by the additional reference gyro actuator and the direction of the residual angular momentum. We thus iteratively reduce to a case of two residual gyroscopic actuators, where it is possible to determine the angles of these actuators during a step 223 as in the case described above with reference to [Fig.2]. The angles of the reference gyroscopic actuators are then deduced from the values ​​of the y parameters.

Claims

1. Demands Method for controlling an assembly (G) of gyroscopic actuators (10) of a satellite (S), for generating a setpoint angular momentum by the gyroscopic actuators, each gyroscopic actuator (10) comprising a flywheel (11) capable of being driven in rotation about an axis of rotation so as to produce angular momentum, and an orientation device (12) for the axis of rotation at an angle θ, the gyroscopic actuators being distributed into two coplanar sub-assemblies, each coplanar sub-assembly comprising at least two gyroscopic actuators configured to generate a respective angular momentum contained within the same plane of the sub-assembly, the respective planes of the two sub-assemblies being non-coplanar, the control method comprising: - The reception (100) of a dimensionless setpoint angular momentum ( a K'z)) to be generated by the set of gyroscopic actuators, - The determination (210) of an angular momentum to be provided by each coplanar subset ( / jPxY, / |Pxz), from the dimensionless setpoint angular momentum and a distribution parameter (r) chosen according to a predetermined sequence of distribution parameters, between the two coplanar subsets, of a component (x) of the setpoint angular momentum along an axis (^s) common to the two planes, in which the parameter r is a scalar between a minimum value and a maximum value corresponding respectively to the lowest admissible value (ypxY ) and the highest admissible value (x^y) of the contribution of one of the coplanar subsets to the component (x) of the setpoint angular momentum along the axis common to the two planes,The determination (220) of a tilt angle value (Oj) of each gyroscopic actuator of a coplanar subset, from the angular momentum (jjPxy, j^pxy) to be provided by said coplanar subset, and - The emission (300) of a command of each gyroscopic actuator comprising the respective determined tilt angle value (o;).

2. A method according to claim 1, wherein the distribution parameter (r) has at least one predetermined value depending on the mission of the satellite.

3. A method according to any one of claims 1 or 2, wherein the predetermined distribution parameter (r) exhibits a time-varying value profile during a satellite mission.

4. A method according to any one of the preceding claims, wherein the parameter r is defined as follows: VPXY' = (1 - r)YPXY ra < ± ± ; Amin' * Amax

5.

6. °where xPxY and xPxz are respectively the angular moments generated, along the common axis (¾) of the two planes, by the two coplanar subsets, ypxy is the lowest admissible value of the contribution of a subset to said component of the setpoint angular moment along the common axis (¾) of the two planes, is the highest admissible value of the contribution of the subset to the component (x) of the setpoint angular moment along the common axis (¾) of the two planes. A method according to the preceding claim, wherein * is defined as Eq. 2 ïf: [0, 2711" D c R3 a —> h = (x; y; z) Z = Sin<7( and in which we define vpxy and as min max Eq.Q. = max(-^N y 2 -y 2 ; x-^N^-z 2 ) ^^ = min(^y 2 -y 2 '.x+^N^-z 2} .et 0 < r < 1 A method according to any one of the preceding claims, wherein the determination (220) of an angle value of each gyroscopic actuator of a coplanar subassembly from the angular momentum to be provided by said subassembly comprises: - The determination of a direction of angular momentum (hi) to be provided by each gyroscopic actuator, from the angular momentum to be provided by the subset (hPXY, hPxz), and at least one predetermined parameter (y), defining an angular separation between the angular momentum to be provided by a reference gyroscopic actuator and the angular momentum to be provided by the subset, and - Determining a tilt angle value for each gyroscopic actuator from the corresponding angular momentum direction.

7. A method according to claim 5, wherein the step of determining a direction of angular momentum to be generated by each gyroscopic actuator comprises: - determining the direction of angular momentum of a reference gyroscopic actuator from a first angular separation parameter and the direction of angular momentum to be provided by the subassembly, and - if a coplanar subassembly comprises more than two gyroscopic actuators, the iterative implementation of: • determining a residual angular momentum to be provided by the gyroscopic actuators of the subassembly, except for the reference gyroscopic actuator,and • the determination of the direction of an angular momentum of an additional reference gyroscopic actuator from an additional angular separation parameter between the angular momentum to be provided by the additional reference gyroscopic actuator and the direction of the residual angular momentum.

8. A method for controlling an array of gyroscopic actuators of a satellite, each gyroscopic actuator comprising a flywheel capable of being driven in rotation about an axis of rotation so as to produce angular momentum, and a device for tilting the axis of rotation at an angle of inclination θ, the gyroscopic actuators being distributed into two coplanar sub-assemblies, one of the sub-assemblies comprising a gyroscopic actuator configured to generate angular momentum contained in a first plane, and the other sub-assembly comprising at least two gyroscopic actuators configured to generate respective angular momentum contained in the same second plane of the sub-assembly, the first and second planes being non-coplanar, the method comprising: - The reception (100) of a dimensionless setpoint angular momentum h(x,y,z) to be generated by the set of gyroscopic actuators, - The determination (210) of an angular momentum to be provided by each coplanar subset ( / jPxY, / |Pxz), from the setpoint angular momentum, and a distribution parameter (r), chosen according to a predetermined sequence of distribution parameters between the two coplanar subsets of gyroscopic actuators, of a component of the setpoint angular momentum (hx) along an axis common to the two planes, in which the parameter r is a scalar chosen between a minimum value and a maximum value corresponding respectively to the lowest admissible value and the highest admissible value of the contribution of one of the coplanar subsets to the setpoint angular momentum along the axis common to the two planes,and - The determination (220) of a tilt angle value (Oi) of each gyroscopic actuator of a coplanar subset, from the determined angular momentum ( / jPxY, j^xz), to be provided by said coplanar subset, and - The emission (400) of a command of each gyroscopic actuator comprising the respective determined tilt angle value (o;).,

9. Product computer program, comprising code instructions for implementing the method according to any one of the preceding claims, when executed by a computer.

10. Computer, configured for the implementation of the method according to any one of claims 1 to 8, for the attitude control of a satellite.

11. Satellite (S), comprising: an assembly (G) of gyroscopic actuators (10), each gyroscopic actuator (10) comprising a flywheel (11) capable of being driven in rotation about an axis of rotation so as to produce angular momentum, and a device (12) for orienting the axis of rotation at an angle θ, the gyroscopic actuators (10) being distributed into two coplanar subassemblies, each coplanar subassembly comprising at least two gyroscopic actuators configured to generate angular momentum h; contained in the same respective plane of the subassembly, the respective planes of the two subassemblies being non-coplanar, and a control device (T,20) of the satellite, adapted to implement the control method according to any one of claims 1 to 8.

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