Satellite systems

Abstract

This invention provides a satellite system capable of controlling the translational and rotational motions of multiple satellites using a simple control method. [Solution] A satellite system including N element satellites (where N is a natural number of 2 or more) that perform formation flight, wherein each element satellite is equipped with n coils (where n is a natural number of 4 or more), and the n coils equipped with each element satellite are arranged such that at least three of the magnetic force vectors generated by each of the n coils do not lie on the same plane, and at least three of the torque vectors generated by each of the n coils do not lie on the same plane, and the degrees of freedom of the translational and rotational motion of the N element satellites are represented by N S And N represents the controllable degrees of freedom based on n coils. C In relation to N S ≤N C Satisfying N S It is defined as 6N-6 when N is 2 or greater, and N C This is defined as nN-1 when N is 2, and nN when N is 3 or greater.

Description

[Technical Field]

[0001] This disclosure relates to satellite systems. [Background technology]

[0002] It has been proposed to deploy a large number of small satellites in space and move them in orbit in formation flight while controlling their relative positions. For example, Patent Document 1 describes how a large number of small satellites performing formation flight constitute a phased array antenna system, which relays communications between ground-based communication devices. In such satellite systems, each satellite is equipped with a coil, and the translation and rotation of the satellites are controlled by the magnetic force emitted by the coil. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Patent No. 7416468 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] However, when controlling a large number of satellites, complex methods were sometimes required, such as dividing them into groups of a few nearby satellites and then performing time-division control, or using different AC frequencies for coil control for each group. In particular, as the number of satellites increases, the frequency and the number of divisions in time division increase significantly, making it easier for issues such as robustness and time synchronization accuracy to arise.

[0005] One objective of this disclosure is to provide a satellite system capable of controlling the translational and rotational motions of multiple satellites using a simple control method. [Means for solving the problem]

[0006] The satellite system according to the present disclosure is a satellite system including N element satellites (N is a natural number of 2 or greater) that perform formation flight, wherein each element satellite included in the N element satellites includes n coils (n is a natural number of 4 or greater), the n coils provided in each element satellite included in the N element satellites are arranged such that among magnetic force vectors respectively generated by the n coils, at least three magnetic force vectors do not lie on the same plane, and among torque vectors respectively generated by the n coils, at least three torque vectors do not lie on the same plane, N representing the degrees of freedom of translational and rotational motion of the N element satellites S and N representing the controllable degrees of freedom based on the n coils C satisfy the relationship N S ≦N C , wherein N S is defined as 6N-6 when N is 2 or greater, and N C is defined as nN-1 when N is 2 and nN when N is 3 or greater. Effects of the Invention

[0007] According to the present disclosure, it is possible to provide a satellite system capable of controlling translational motion and rotational motion of a plurality of satellites by a simple control method. Brief Description of the Drawings

[0008] [Figure 1] It is a conceptual diagram showing a schematic configuration of a satellite system 1 according to the present embodiment. [Figure 2] It is a block diagram showing an example of a functional configuration of an element satellite 10 according to the present embodiment. [Figure 3] It is a diagram for explaining an example of an arrangement of coils 12 included in the element satellite 10 according to the present embodiment. [Figure 4A] It is a diagram for explaining another example of an arrangement of coils 12 included in the element satellite 10 according to the present embodiment. [Figure 4B] It is a diagram for explaining another example of an arrangement of coils 12 included in the element satellite 10 according to the present embodiment. [Figure 5]It is a diagram for explaining still another example of the arrangement of coils 12 provided in the element satellite 10 according to the present embodiment. MODE FOR CARRYING OUT THE INVENTION

[0009] Embodiments of the present disclosure will be described with reference to the accompanying drawings.

[0010] (1) Outline of Satellite System 1 FIG. 1 is a conceptual diagram for explaining the outline of the satellite system 1 according to the present embodiment.

[0011] The satellite system 1 includes a plurality of element satellites 10. At least a part of the plurality of element satellites 10 included in the satellite system 1 are arranged in an array. The arrangement method of the element satellites 10 is not particularly limited, and may be, for example, a linear arrangement, a planar arrangement, a lattice arrangement, a concentric arrangement, or the like. In the present disclosure, when distinguishing individual element satellites 10 or configurations included in individual element satellites 10, reference signs such as "A" and "B" may be added in some cases.

[0012] In the present embodiment, a micro element satellite is used as the element satellite 10. For example, the size of one element satellite 10 is several cm to several tens of cm. The total number N of element satellites 10 constituting the satellite system 1 is not particularly limited as long as it is a natural number of 2 or more. The total number N of the element satellites 10 may be several hundreds, several thousands, or tens of thousands or more. The distance between adjacent element satellites 10 is, for example, several cm to several tens of cm. The distance between adjacent element satellites 10 may be approximately equal to the wavelength, or may be shorter than the wavelength (e.g., assumed frequency band = 0.8 GHz to 60 GHz). The altitude of each element satellite 10 is, for example, about several hundred km to 1,000 km.

[0013] Satellite system 1 may, for example, constitute a phased array antenna system. Satellite system 1 may receive transmission signals transmitted from transmitter 3. Satellite system 1 may also transmit transmission signals to receiver 4. Satellite system 1 may relay communication between transmitter 3 and receiver 4. That is, satellite system 1 may generate a transmission signal based on a signal generated by receiving a transmission signal from transmitter 3 and transmit it to receiver 4. Transmitter 3 and receiver 4 may be, for example, mobile stations such as smartphones. In this case, at least some element satellites 10 of satellite system 1 may form a service link with the mobile station (transmitter 3 and / or receiver 4). Alternatively, for example, transmitter 3 and receiver 4 may be base stations. In this case, at least some element satellites 10 of satellite system 1 may form a feeder link or service link with the base station (transmitter 3 and / or receiver 4). Transmitter 3 and receiver 4 may be provided together in a single device.

[0014] (2) Functional configuration of the element satellite 10 Figure 2 is a block diagram showing an example of the functional configuration of the element satellite 10 according to this embodiment. The element satellite 10 comprises a control device 11, n coils 12 (12-1, 12-2, ..., 12-n) (where n is a natural number of 4 or more), an antenna 13, an antenna 14, and a transmitting / receiving circuit 15.

[0015] The control device 11 is a device that controls the operation of the entire element satellite 10. The control device 11 includes one or more processors 111 (hereinafter simply referred to as "processor 111") and one or more storage devices 112 (hereinafter simply referred to as "storage devices 112"). The processor 111 includes a CPU (Central Processing Unit), etc., and performs various information processing. The storage devices 112 store various information necessary for processing by the processor 111. The storage devices 112 also store the control program. The control program is a computer program executed by the processor 111, and the functions of the control device 11 are realized through the cooperation of the processor 111 and the storage devices 112. The control program may be recorded on a computer-readable recording medium.

[0016] The n coils 12 are a mechanism for adjusting the position and attitude of the element satellites 10 under the control of the control device 11. In the case of ultra-small element satellites 10 performing formation flight, the n coils 12 may be configured as electromagnets. Each of the n coils 12 has current flowing through it under the control of the control device 11 and functions as an electromagnet. The electromagnets can adjust the relative positions between neighboring element satellites 10 using magnetic force, and control them to maintain a desired array shape. In particular, the n coils 12 may be controlled by the control device 11 by a predetermined simple control method described later. The arrangement of the n coils 12 in the element satellites 10 will be described later.

[0017] The current value of each of the n coils 12 may be calculated using a predetermined algorithm. This calculation may be performed individually by the control device 11 of each of the N element satellites 10, or by the control device 11 of one or more specific element satellites 10 among the N element satellites 10. Alternatively, this calculation may be performed by an external device of the satellite system 1. The calculated current values ​​may be obtained by communication between the element satellite 10 and other element satellites 10 or the external device.

[0018] The outline of the predetermined algorithm described above is explained below. The input values ​​include the required values ​​for acceleration and angular acceleration of each element satellite 10. From these required values, the current value that should flow through each of the coils 12 provided by the N element satellites 10 is calculated in reverse. In this reverse calculation, the control device 11 uses conventional techniques such as the dipole approximation and the Biot-Savart law when determining force and torque from the coil current. From the candidate combinations of current values ​​that realize the required values ​​for acceleration and angular acceleration of each element satellite 10, the current value with the lowest power consumption is determined as the final current value using a predetermined optimization method as appropriate. The optimization method is not particularly limited and may include, for example, the gradient method or a neural network method using deep learning.

[0019] Antenna 13 is an example of an antenna element that receives radio waves (an example of a signal) transmitted from a transmission source (transmitter 3, etc.) and outputs them to the transmit / receive circuit 15. Antenna 13 also outputs radio waves to an external device (receiver 4, etc.) based on the signal generated by the transmit / receive circuit 15. Antenna 13 may, together with antennas 13 on other element satellites 10, constitute a phased array antenna for transmission and / or reception.

[0020] Antenna 14 is an example of an antenna element and is used for communication between element satellites 10. Antenna 14 may, for example, receive radio waves transmitted from other element satellites 10 (e.g., other adjacent element satellites 10 in the satellite group) and supply signals based on these to the control device 11. Antenna 14 may also, for example, transmit signals supplied from the control device 11 as radio waves directed towards other element satellites 10 (e.g., other adjacent element satellites 10 in the satellite group). Note that antenna 14 may be integrated with antenna 13 into a single antenna element.

[0021] The transmitting / receiving circuit 15 performs predetermined signal processing on the signal generated when the antennas (antennas 13 and 14, etc.) of the element satellite 10 receive radio waves. The transmitting / receiving circuit 15 also outputs the processed signal to the antennas (antennas 13 and 14, etc.) of the element satellite 10, causing the antennas to emit radio waves to the outside.

[0022] The signal processing (amplification, phase shift, modulation, demodulation, etc.) performed by the transmitting / receiving circuit 15 is controlled, for example, by the control device 11, so that the excitation weight of the antenna 13 becomes a predetermined value. In this case, the control device 11 controls the transmitting / receiving circuit 15 so that the excitation weight of the antenna 13 becomes a desired value, for example, based on excitation weight control information. The control device 11 may, for example, receive excitation weight control information transferred from other element satellites 10 via the antenna 14 and store it in one or more storage devices 112. The control device 11 may, for example, transfer excitation weight control information to other element satellites 10 via the antenna 14. The excitation weight control information may be calculated to compensate for differences in the position of the element satellites 10 and variations in individual element satellites 10 (including information measured before the launch of the element satellites 10). The excitation weight control information may be calculated by the control device 11 or obtained from other devices (other element satellites 10 or ground devices, etc.).

[0023] (3) Arrangement of coil 12 (3-1) Conditions for the arrangement of coil 12 (a) and (b) The arrangement of the n coils 12 in the element satellite 10 according to this embodiment will now be described. The n coils 12 provided in the element satellite 10 may be arranged such that the following conditions (a) and (b) are satisfied. The force vector that contributes as a translational force to the element satellite 10 from the force based on the magnetic dipole emitted by the coil 12 is called the magnetic force vector. The force vector that contributes as a rotational force to the element satellite 10 from the force received by the magnetic dipole emitted by the coil 12 is called the torque vector.

[0024] Condition (a): "At least three magnetic field vectors do not lie on the same plane." When condition (a) is met, the "at least three magnetic field vectors" will include vectors in three linearly independent directions in three-dimensional space. Therefore, it becomes possible to control the translational motion of the element satellite 10 with respect to three independent degrees of freedom in three-dimensional space.

[0025] Condition (b): "At least three torque vectors do not lie on the same plane." When condition (b) is met, the "at least three torque vectors" include vectors in three linearly independent directions in three-dimensional space. Therefore, it becomes possible to control the rotational motion of the element satellite 10 with respect to three independent degrees of freedom in three-dimensional space.

[0026] (3-2) Three-dimensional distributed arrangement of coils When conditions (a) and (b) are met, the coils are arranged in a three-dimensional distributed configuration, which in turn makes it possible to achieve complete 6-degree-of-freedom control. The mathematical explanation for this is provided below.

[0027] Expression of force The force vector f acting on a magnetic dipole vector μ placed in a magnetic field vector B is expressed as the negative gradient of the potential energy U of the magnetic dipole vector μ, as shown in equation (1) below.

[0028]

number

[0029] Using vector calculus identities, equation (1) can be expanded as follows:

[0030]

number

[0031] Here, μ is treated as a constant vector independent of position.

[0032] Physical prerequisites Assume a situation where a coil having a magnetic moment vector μ is placed in a magnetic field vector B applied from the outside. At this time, it is physically natural to assume that there is no current serving as a magnetic field source at the position vector r where the coil is located. That is, if the current density vector is denoted by J, it can be considered that J=0 at the coil position. From Ampère's law (one of Maxwell's equations), ∇×B=0 holds. As a result, the second term on the right-hand side of Equation (2) becomes zero, and the expression of force is simplified as follows.

[0033] [Formula]

[0034] In the following analysis, based on this physically reasonable assumption, Equation (3) is used as the expression for force.

[0035] Gradient tensor and skew-symmetric matrix To simplify the analysis, a magnetic field gradient tensor G is defined as follows.

[0036] [Formula]

[0037] Note that the transpose matrix G of this magnetic field gradient tensor G T can be used to express the force vector f as follows.

[0038] [Formula]

[0039] Further, as shown below, any vector v=(v x ,v y ,v z ) TWe define a skew-symmetric matrix [v] as a matrix that transforms the vector product (cross product) of a matrix into the product of a matrix and a vector.

[0040]

number

[0041] Using the skew-symmetric matrix [v], the torque vector τ can be expressed as follows:

[0042]

number

[0043] Single-point model A 6-dimensional generalized force vector F, which combines force and torque, is defined as F[f T ,τ T ] T This is defined as follows. Using the above matrix, the linear mapping from the magnetic dipole vector μ to the generalized force vector F can be represented by a single matrix M.

[0044]

number

[0045] Since the transformation matrix M is a 6x3 matrix, its rank is at most 3.

[0046] From the fundamental principles of linear algebra, the generated vector group {F i The dimension (rank) of the space spanned by {μ} is determined by the rank of the transformation matrix M and the input vector group {μ}. i It is restricted by both ranks of}. Specifically, the following relationship holds:

[0047]

number

[0048] In a single-point application model, the rank of each term is evaluated as follows: • System transformation capability: Since M is a 6x3 matrix, its rank is rank(M) ≤ 3. • Input diversity: μ i Since it is a 3-dimensional vector, the rank of its set is rank{μ i}≦3.

[0049] Therefore, from equation (9), the rank achievable with the single-point application model is as follows:

[0050]

number

[0051] This is even if the input {μ i Enriching} in 3D (rank{μ i Even if}=3), the system's conversion capability rank(M) is limited to three dimensions, meaning that the degrees of freedom for the generated force / torque will never exceed 3.

[0052] Extended model: Introduction of point of action shift Let's consider a more realistic case where the center of the coil (the position of the dipole) and the center point of the object on which the force acts do not coincide. We represent this geometric "deviation" as a three-dimensional real vector in R. i Let's assume that this shift in the point of application results in force f i The additional torque R generated by i ×f i This occurs. Therefore, the total torque τ i It is given by the following equation.

[0053]

number

[0054] As a result, the generalized force vector F i and the dipole vector μ i The relationship can be expressed as follows, using a different transformation matrix Mi for each coil:

[0055]

number

[0056] Rank analysis and derivation of degrees of freedom The set of generalized forces that can be generated across the entire system {F i Evaluate the rank of matrix M. i This can be written as the sum of a fixed part and a variable part that depends on the coil arrangement.

[0057]

number

[0058] The overall rank of the system is determined by the dimension of the space spanned by these matrices. Here, we define the linear independence of the coil displacement vector group as r.

[0059]

number

[0060] Linear mapping Φ:R→[R]×G T Since rank(Φ)≦3, the dimension of the space spanned by the variation caused by the shift can be estimated as follows.

[0061]

number

[0062] Therefore, the upper limit of the overall system rank (controllable degrees of freedom) is given by the sum of the rank of the fixed part (maximum 3) and the rank of the variable part (maximum min(3,r)).

[0063]

number

[0064] This equation represents the "performance limit" determined by the physical arrangement of the system. To maximize this performance, the input side also needs to have sufficient diversity. That is, rank{μ i Independently driving the coils so that}=3 is a prerequisite for achieving the theoretical maximum rank.

[0065] Case-by-case analysis and conclusions Based on the above upper bound formula, the maximum rank values ​​corresponding to the spatial arrangement r of the coil are summarized in the table below.

[0066] [Table 1]

[0067] From the above, the importance of the spatial arrangement of coils in force and torque control of magnetic dipole systems has been mathematically demonstrated, starting from physically valid fundamental principles. The magnetic field gradient tensor G is full rank, and the coil displacement vector group {R i If the coils are three-dimensionally independent (r=3), the rank of the generalized force vector generated by the system can reach its maximum value of 6. This theoretically supports the idea that a spatially dispersed coil arrangement, rather than concentrating the points of application, is essential to achieve 6-degree-of-freedom manipulation that completely controls the position and orientation of an object.

[0068] (4) Control of Satellite System 1 The satellite system 1 according to this embodiment is configured so that the N element satellites 10 provided by the satellite system 1 can be controlled by a predetermined simple control method. Here, the predetermined simple control method may exclude control methods based on frequency division. That is, the predetermined simple control method may include a method of controlling all the coils 12 provided by the N element satellites 10 using AC in the same frequency range. Also, the predetermined simple control method may exclude control methods based on time division. That is, the predetermined simple control method may include a method of simultaneously controlling all the coils 12 provided by the N element satellites 10. Also, the predetermined simple control method may exclude control methods that group the N element satellites 10. That is, the predetermined simple control method may include a method of independently controlling each of the N element satellites 10.

[0069] Here, we will explain the number of coils 12 that each of the N element satellites 10 should have in order to control the N element satellites 10 using the predetermined simple control method described above. First, the n coils 12 that each of the N element satellites 10 has should satisfy the above-mentioned conditions (a) and (b). That is, it should be possible to independently control the six degrees of freedom of translational and rotational motion of each element satellite 10.

[0070] Let "motional degrees of freedom Ns" be the degrees of freedom for the translational and rotational motion of the N element satellites 10 that make up satellite system 1. Here, the degrees of freedom for the translational motion of each element satellite 10 are in three directions in three-dimensional space, and the degrees of freedom for the rotational motion of each element satellite 10 are in three directions around each of those three directions. Therefore, if we consider each element satellite 10 independently, the sum of the degrees of freedom for the translational and rotational motion of the N element satellites 10 is 6N. Here, since momentum and angular momentum are conserved in satellite system 1, the total motional degrees of freedom Ns for satellite system 1 is the sum of the degrees of freedom for the translational and rotational motion of each element satellite 10 minus 6 degrees of freedom. That is, the motional degrees of freedom Ns is 6N-6.

[0071] Next, for satellite system 1, the degree of freedom of the controllable coil 12 is defined as "controllable degree of freedom Nc". When N is 3 or greater, the controllable degree of freedom Nc is nN, which is the total number of coils 12 in satellite system 1. When N is 2, it becomes a two-body problem involving two element satellites 10, so the controllable degree of freedom Nc is nN-1, which is the total number of coils 12 in satellite system 1 minus 1.

[0072] Here, in order for N element satellites 10 to be controlled by a predetermined simple control method, it is sufficient that the degree of freedom of motion Ns ≤ the degree of freedom of control Nc. Below, we will explain the number of coils 12 n for each value that the number of element satellites 10 N can take under this condition.

[0073] When N=2, the degrees of freedom of motion Ns=6N-6=6×2-6=6 The values ​​of n such that control degrees of freedom Nc ≥ motion degrees of freedom Ns = 6 are 2n-1 ≥ 6, which means n ≥ 7 / 2. Therefore, n is 4 or greater. Therefore, if the satellite system 1 comprises two element satellites 10, each element satellite 10 must be equipped with four or more coils in order to control the two element satellites 10 by a predetermined simple control method.

[0074] When N=3, the degrees of freedom of motion Ns=6N-6=6×3-6=12. The value of n such that the degrees of control Nc ≥ degrees of freedom of motion Ns=12 is 3n ≥ 12, which means n ≥ 4. Therefore, n is 4 or greater. Consequently, if satellite system 1 has three element satellites 10, in order to be able to control the three element satellites 10 by a predetermined simple control method, each element satellite 10 needs to have four or more coils.

[0075] When N=4, the degrees of freedom of motion Ns=6N-6=6×4-6=18. The value of n such that the degrees of control Nc ≥ degrees of freedom of motion Ns=18 is 4n ≥ 18, so n ≥ 4.5. Therefore, n is 5 or greater. Consequently, if satellite system 1 has four element satellites 10, in order to be able to control the four element satellites 10 by a predetermined simple control method, each element satellite 10 needs to have five or more coils.

[0076] When N=5, the degrees of freedom of motion Ns=6N-6=6×5-6=24. The value of n such that the degrees of control Nc ≥ degrees of freedom of motion Ns=24 is 5n ≥ 24, so n ≥ 4.8. Therefore, n is 5 or greater. Consequently, if satellite system 1 has 5 element satellites 10, in order to be able to control the 5 element satellites 10 by a predetermined simple control method, each element satellite 10 needs to have 5 or more coils.

[0077] When N=6, the degrees of freedom of motion Ns=6N-6=6×6-6=30. The value of n such that the degrees of control Nc ≥ degrees of freedom of motion Ns=30 is 6n ≥ 30, which means n ≥ 5. Therefore, n is 5 or greater. Consequently, if satellite system 1 has 6 element satellites 10, in order to be able to control the 6 element satellites 10 by a predetermined simple control method, each element satellite 10 needs to have 5 or more coils.

[0078] Let's consider the case where N≧7. If the control degrees of freedom Nc≧ and the motion degrees of freedom Ns, then nN≧6N-6. Therefore, n≧6-6 / N. Since N≧7, 6-6 / N≧6-6 / 7=36 / 7. Thus, n is 6 or greater. Consequently, if satellite system 1 has seven or more element satellites 10, in order to be able to control these seven or more element satellites 10 by a predetermined simple control method, each element satellite 10 needs to have six or more coils.

[0079] (5) Specific examples of the arrangement of coil 12 The arrangement of the coil 12 in the element satellite 10 according to this embodiment will be described below.

[0080] (5-1)Specific Example 1 Figure 3 is a diagram illustrating an example of the arrangement of coils 12 in the element satellite 10 according to this embodiment. The element satellite 10 comprises six coils 12a1, 12a2, 12a3, 12a4, 12a5, and 12a6. Figure 3 shows a hypothetical approximate cube 20 in which the six coils 12a1 to 12a6 are arranged. As shown in Figure 3, the vertices of the approximate cube 20 are A, B, C, D, E, F, G, and H. The shape of the hypothetical approximate cube 20 may be the same as or approximate to a geometrically exact cube.

[0081] The element satellite 10 may have a shape that encloses a hypothetical approximate cube 20 on which six coils 12a1 to 12a6 are arranged. For example, the element satellite 10 itself may have the shape of the approximate cube 20, or the approximate cube 20 may be enclosed inside the element satellite 10 which has any shape. In particular, the approximate cube 20 may be placed inside the element satellite 10 such that the center of gravity of the approximate cube 20 coincides with the center of gravity of the element satellite 10.

[0082] As shown in Figure 3, the six coils 12a1, 12a2, 12a3, 12a4, 12a5, and 12a6 may be arranged on at least a portion of the faces of the roughly cube 20. Specifically, as shown in Figure 3, coil 12a1 may be arranged on approximately half of face ABCD on the side of edge AD, coil 12a2 on approximately half of face EFGH on the side of edge FG, coil 12a3 on approximately half of face ABFE on the side of edge AE, coil 12a4 on approximately half of face DCGH on the side of edge CG, coil 12a5 on approximately half of face BCGF on the side of edge BC, and coil 12a6 on approximately half of face ADHE on the side of edge HE. Here, each of the coils 12a1 to 12a6 arranged in this manner may be fixed inside the element satellite 10 in any manner. That is, each of the coils 12a1 to 12a6 may be attached to a support frame or holder formed on the inner wall of the housing of the element satellite 10. Note that the illustration is just one example, and the coil arrangement is not limited to these examples.

[0083] When current flows through coil 12a1, a magnetic dipole is generated from coil 12a1. As shown in Figure 3, a magnetic dipole vector μa1 is defined as the vector representing this magnetic dipole, originating from the center C1 of coil 12a1 and pointing in the direction normal to the plane ABCD. Similarly, a magnetic dipole vector μa2 is defined originating from the center C2 of coil 12a2 and pointing in the direction normal to the plane EFGH. Similarly, a magnetic dipole vector μa3 is defined originating from the center C3 of coil 12a3 and pointing in the direction normal to the plane ADHE. Similarly, a magnetic dipole vector μa4 is defined originating from the center C4 of coil 12a4 and pointing in the direction normal to the plane BCGF. Similarly, a magnetic dipole vector μa5 is defined originating from the center C5 of coil 12a5 and pointing in the direction normal to the plane ABFE. Similarly, a magnetic dipole vector μa6 is defined that points in the direction normal to the plane DCGH, starting from the center C6 of coil 12a6.

[0084] Based on the above-mentioned equation (5), the magnetic force vectors Pa1, Pa2, Pa3, Pa4, Pa5, and Pa6 are defined, respectively, based on the magnetic dipole vectors μa1, μa2, μa3, μa4, μa5, and μa6. The magnetic force vectors Pa1, Pa2, Pa3, Pa4, Pa5, and Pa6 are arranged so as not to pass through the centroid O of the approximately cubic 20. Furthermore, in the element satellite 10 in the configuration shown in Figure 3, condition (a): "At least three magnetic force vectors do not lie on the same plane" is satisfied. With this arrangement, it becomes possible to control the translational motion of the element satellite 10 with respect to three independent degrees of freedom in three-dimensional space. In the example shown in Figure 5, all of the magnetic field vectors Pa1, Pa2, Pa3, Pa4, Pa5, and Pa6 are positioned so that they do not pass through the centroid O of the roughly cubic 20. However, it is sufficient if at least three of these six magnetic field vectors are positioned so that they do not pass through the centroid O of the roughly cubic 20.

[0085] Based on the above-mentioned equation (11), the torque vectors Ta1, Ta2, Ta3, Ta4, Ta5, and Ta6 are defined, respectively, based on the magnetic dipole vectors μa1, μa2, μa3, μa4, μa5, and μa6. In the element satellite 10 with the coils arranged in the manner shown in Figure 3, condition (b): "At least three torque vectors do not lie on the same plane" is satisfied. This arrangement makes it possible to control the rotational motion of the element satellite 10 with respect to three independent degrees of freedom in three-dimensional space.

[0086] Furthermore, as long as conditions (a) and (b) are met, the element satellite 10 according to this embodiment may not include some of the six coils 12a1, 12a2, 12a3, 12a4, 12a5, and 12a6 shown in the figure. Also, as long as conditions (a) and (b) are met, the element satellite 10 according to this embodiment may include coils other than the six coils 12a1, 12a2, 12a3, 12a4, 12a5, and 12a6 shown in the figure.

[0087] (5-2)Specific Example 2 Figures 4A and 4B illustrate another example of the arrangement of coils 12 in the element satellite 10 according to this embodiment. The element satellite 10 comprises six coils 12b1, 12b2, 12b3, 12b4, 12b5, and 12b6. Figures 4A and 4B show a hypothetical approximately regular tetrahedron 30 with the six coils 12b1 to 12b6 arranged in it, viewed from different directions. As shown in Figures 4A and 4B, the vertices of the approximately regular tetrahedron 30 are A, B, C, and D, and the centroid of the approximately regular tetrahedron 30 is O. The shape of the hypothetical approximately regular tetrahedron 30 may be the same as or approximate to a geometrically exact regular tetrahedron.

[0088] The element satellite 10 may have a shape that encloses a hypothetical, roughly regular tetrahedron 30 in which six coils 12b1 to 12b6 are arranged. For example, the element satellite 10 itself may have the shape of the roughly regular tetrahedron 30, or the roughly regular tetrahedron 30 may be enclosed inside the element satellite 10 which has any arbitrary shape. In particular, the roughly regular tetrahedron 30 may be placed inside the element satellite 10 such that the center of gravity of the roughly regular tetrahedron 30 coincides with the center of gravity of the element satellite 10.

[0089] As shown in Figures 4A and 4B, the six coils 12b1, 12b2, 12b3, 12b4, 12b5, and 12b6 may be arranged in each of the six planes defined by the centroid of the substantially regular tetrahedron 30 and any two vertices of the substantially regular tetrahedron 30. Specifically, as shown in Figures 4A and 4B, coil 12b1 may be arranged on plane OAB, coil 12b2 on plane OAC, coil 12b3 on plane OAD, coil 12b4 on plane OBC, coil 12b5 on plane OCD, and coil 12b6 on plane ODB. Here, each coil 12b1 to 12b6 may be fixed within the element satellite 10 in any manner. Here, each coil 12b1 to 12b6 arranged in this manner may be fixed within the element satellite 10 in any manner. In other words, each coil 12b1 to 12b6 may be attached to a support frame or holder formed on the inner wall of the housing of the element satellite 10. Note that the illustration is just an example, and the arrangement of the coils is not limited to these.

[0090] When current flows through coil 12b1, a magnetic field is generated from coil 12b1. As shown in Figure 4A, a magnetic dipole vector μb1 is defined, pointing in the direction normal to plane OAB, starting from the center C1 of coil 12b1. Similarly, a magnetic dipole vector μb2 is defined, pointing in the direction normal to plane OAC, starting from the center C2 of coil 12b2. Similarly, a magnetic dipole vector μb3 is defined, pointing in the direction normal to plane OAD, starting from the center C3 of coil 12b3. Similarly, a magnetic dipole vector μb4 is defined, pointing in the direction normal to plane OBC, starting from the center C4 of coil 12b4. Similarly, a magnetic dipole vector μb5 is defined, pointing in the direction normal to plane OCD, starting from the center C5 of coil 12b5. Similarly, a magnetic dipole vector μb6 is defined, pointing in the direction normal to plane ODB, starting from the center C6 of coil 12b6.

[0091] Based on the above-mentioned equation (5), the magnetic force vectors Pb1, Pb2, Pb3, Pb4, Pb5, and Pb6 are defined, respectively, based on the magnetic dipole vectors μb1, μb2, μb3, μb4, μb5, and μb6. In the element satellite 10 with the coils arranged in the manner shown in Figures 4A and 4B, condition (a): "At least three magnetic force vectors do not lie on the same plane" is satisfied. With this arrangement, it becomes possible to control the translational motion of the element satellite 10 with respect to three independent degrees of freedom in three-dimensional space.

[0092] Based on the above-mentioned equation (11), the torque vectors Tb1, Tb2, Tb3, Tb4, Tb5, and Tb6 are defined, respectively, based on the magnetic dipole vectors μb1, μb2, μb3, μb4, μb5, and μb6, respectively. In the element satellite 10 with the coils arranged in the manner shown in Figures 4A and 4B, condition (b): "At least three torque vectors do not lie on the same plane" is satisfied. This arrangement makes it possible to control the rotational motion of the element satellite 10 with respect to three independent degrees of freedom in three-dimensional space.

[0093] Furthermore, as long as conditions (a) and (b) are met, the element satellite 10 according to this embodiment may not include some of the six coils 12b1, 12b2, 12b3, 12b4, 12b5, and 12b6 shown in the figure. Also, as long as conditions (a) and (b) are met, the element satellite 10 according to this embodiment may include coils other than the six coils 12b1, 12b2, 12b3, 12b4, 12b5, and 12b6 shown in the figure.

[0094] (5-3)Specific Example 3 Figure 5 is a diagram illustrating yet another example of the arrangement of coils 12 in the element satellite 10 according to this embodiment. The element satellite 10 comprises six coils 12c1, 12c2, 12c3, 12c4, 12c5, and 12c6. Figure 5 shows a hypothetical approximate sphere 40 in which the six coils 12c1 to 12c6 are arranged, circumscribing the hypothetical approximate tetrahedron 30 shown in Figures 4A and 4B. Figure 5 shows the vertices A, B, C, and D of the approximate tetrahedron 30 and the centroid O of the approximate tetrahedron 30. The vertices A, B, C, and D of the approximate tetrahedron 30 are included in the outer surface of the approximate sphere 40. The centroid O of the approximate sphere 40 coincides with the centroid O of the approximate tetrahedron 30. The shape of the approximate sphere 40 may be identical to or approximate to a geometrically exact sphere. Figure 5A shows six sectors OAB, OAC, OAD, OBC, OCD, and ODB centered on the centroid O of the approximately spherical sphere 40. That is, sectors OAB, OAC, OAD, OBC, OCD, and ODB are sectors centered on the centroid O of the approximately spherical sphere 40, with a portion of the outer surface of the approximately spherical sphere 40 forming an arc.

[0095] The element satellite 10 may have a shape that encloses a hypothetical approximately spherical 40 on which six coils 12c1 to 12c6 are arranged. For example, the element satellite 10 itself may have the shape of the approximately spherical 40, or the approximately spherical 40 may be enclosed inside the element satellite 10 which has any shape. In particular, the approximately spherical 40 may be positioned inside the element satellite 10 such that the center of gravity of the approximately spherical 40 coincides with the center of gravity of the element satellite 10.

[0096] The coils may be arranged in each of the six planes defined by the centroid of the roughly regular tetrahedron 30 and any two vertices of the roughly regular tetrahedron 30. In particular, as shown in Figure 5, the six coils 12c1, 12c2, 12c3, 12c4, 12c5, and 12c6 may be arranged in each of the six sectors formed by the centroid O of the roughly sphere 40 and any two vertices of the roughly regular tetrahedron 30 inscribed in the roughly sphere 40. Specifically, as shown in Figure 5A, coil 12c1 may be arranged in sector OAB, coil 12c2 in sector OAC, coil 12c3 in sector OAD, coil 12c4 in sector OBC, coil 12c5 in sector OCD, and coil 12c6 in sector ODB. Here, each coil 12c1 to 12c6 may be fixed within the element satellite 10 in any manner. Here, each coil 12c1 to 12c6 arranged in this manner may be fixed within the element satellite 10 in any manner. That is, each coil 12c1 to 12c6 may be attached to a support frame or holder formed on the inner wall of the housing of the element satellite 10. Note that the illustration is just an example, and the arrangement of the coils is not limited to these.

[0097] When current flows through coil 12c1, a magnetic dipole is generated from coil 12c1. As shown in Figure 5, a magnetic dipole vector μc1 is defined as the vector representing this magnetic dipole, pointing in the direction normal to the sector OAB, starting from the center C1 of coil 12c1. Similarly, a magnetic dipole vector μc2 is defined, pointing in the direction normal to the sector OAC, starting from the center C2 of coil 12c2. Similarly, a magnetic dipole vector μc3 is defined, pointing in the direction normal to the sector OAD, starting from the center C3 of coil 12c3. Similarly, a magnetic dipole vector μc4 is defined, pointing in the direction normal to the sector OBC, starting from the center C4 of coil 12c4. Similarly, a magnetic dipole vector μc5 is defined, pointing in the direction normal to the sector OCD, starting from the center C5 of coil 12c5. Similarly, a magnetic dipole vector μc6 is defined that points in the direction normal to the sector ODB, starting from the center C6 of coil 12c6.

[0098] Based on the above-mentioned equation (5), the magnetic force vectors Pc1, Pc2, Pc3, Pc4, Pc5, and Pc6 are defined, respectively, based on the magnetic dipole vectors μc1, μc2, μc3, μc4, μc5, and μc6. In the element satellite 10 with the coils arranged in the manner shown in Figure 5, condition (a): "At least three magnetic force vectors do not lie on the same plane" is satisfied. With such an arrangement, it becomes possible to control the translational motion of the element satellite 10 with respect to three independent degrees of freedom in three-dimensional space.

[0099] Based on the above-mentioned equation (11), the torque vectors Tc1, Tc2, Tc3, Tc4, Tc5, and Tc6 are defined, respectively, based on the magnetic dipole vectors μc1, μc2, μc3, μc4, μc5, and μc6. In the element satellite 10 with the coils arranged in the manner shown in Figure 5, condition (b): "At least three torque vectors do not lie on the same plane" is satisfied. This arrangement makes it possible to control the rotational motion of the element satellite 10 with respect to three independent degrees of freedom in three-dimensional space.

[0100] Furthermore, as long as conditions (a) and (b) are met, the element satellite 10 according to this embodiment may not include some of the six coils 12c1, 12c2, 12c3, 12c4, 12c5, and 12c6 shown in the figure. Also, as long as conditions (a) and (b) are met, the element satellite 10 according to this embodiment may include coils other than the six coils 12c1, 12c2, 12c3, 12c4, 12c5, and 12c6 shown in the figure.

[0101] (Note 1) A satellite system comprising N element satellites (where N is a natural number greater than or equal to 2) that perform formation flight, Each element satellite included in the aforementioned N element satellites is equipped with n coils (where n is a natural number greater than or equal to 4), Each of the n element satellites included in the N element satellites has the n coils, Of the magnetic field vectors generated by each of the n coils, at least three do not lie on the same plane, and The n coils are arranged such that at least three of the torque vectors generated by each coil do not lie on the same plane. N represents the degrees of freedom of translational and rotational motion of the aforementioned N element satellites. S And N represents the controllable degrees of freedom based on the n coils. C In relation to N S ≤N C Satisfying the conditions, The aforementioned N S It is defined as 6N-6 when N is 2 or greater, The aforementioned N C This is a satellite system defined as nN-1 when N is 2, and nN when N is 3 or greater. (Note 2) The satellite system as described in Appendix 1, wherein n is 6 or greater. (Note 3) The satellite system as described in Appendix 1, wherein n is 5 and N is 6 or less. (Note 4) The satellite system according to Appendix 1, wherein n is 4 and N is 2 or 3. (Note 5) The aforementioned n is 6, Each of the aforementioned element satellites has a shape that encloses a hypothetical approximate cube, The center of gravity of the aforementioned roughly cubic object coincides with the center of gravity of each of the element satellites. The satellite system as described in Appendix 1, wherein each of the six coils provided in each element satellite is positioned on each of the six faces of the substantially cube such that the direction of the magnetic force vector generated from the coil does not pass through the center of gravity of the substantially cube. (Note 6) The element satellite system described in Appendix 5, wherein the shape of each element satellite corresponds to the approximate cube. (Note 7) The aforementioned n is 6, Each of the aforementioned element satellites has a shape that encloses a hypothetical, roughly regular tetrahedron, The centroid of the aforementioned roughly regular tetrahedron coincides with the centroid of each of the element satellites, The satellite system as described in Appendix 1, wherein each of the six coils provided in each of the element satellites is positioned at each of the six approximate triangles whose vertices are the centroid of the approximate tetrahedron and any two vertices of the approximate tetrahedron. (Note 8) The satellite system described in Appendix 7, wherein the shape of each element satellite corresponds to the substantially regular tetrahedron. (Note 9) The satellite system described in Appendix 7, wherein the shape of each element satellite corresponds to a sphere circumscribing the substantially regular tetrahedron.

[0102] The embodiments described above are provided to facilitate understanding of the present invention and are not intended to limit its interpretation. The elements, arrangement, materials, conditions, shapes, and sizes of the embodiments are not limited to those exemplified and can be modified as appropriate. Furthermore, configurations shown in different embodiments can be partially substituted or combined. [Explanation of Symbols]

[0103] 1...Satellite system, 10...Element satellite, 11...Control device, 111...Processor, 112...Memory device, 12, 12a1~12a6, 12b1~12b6, 12c1~12c6...Coil, 13...Antenna, 14...Antenna, 15...Transmit / receive circuit, 20...Approximate cube, 30...Approximate tetrahedron, 40...Approximate sphere

Claims

1. A satellite system comprising N element satellites (where N is a natural number greater than or equal to 2) that perform formation flight, Each element satellite included in the N element satellites is equipped with at least six coils, Each of the N element satellites has at least six coils, Of the magnetic force vectors generated by each of the six coils, at least three do not lie on the same plane, and A satellite system in which the displacement vectors representing the difference between the center of gravity of each element satellite and the center of each of the at least six coils are distributed spatially independently in three dimensions, so that at least three of the torque vectors generated by each of the at least six coils do not lie on the same plane.

2. Each element satellite has a shape that encloses a virtual approximate cube, The center of gravity of the aforementioned roughly cubic object coincides with the center of gravity of each of the element satellites. The satellite system according to claim 1, wherein each of the six coils included in the at least six coils provided in each element satellite is arranged on each of the six faces of the substantially cube such that the direction of the magnetic force vectors generated from at least three of the six coils does not pass through the center of gravity of the substantially cube.

3. The satellite system according to claim 2, wherein the shape of each element satellite corresponds to the substantially cube.

4. Each element satellite has a shape that encloses a hypothetical approximately regular tetrahedron, The centroid of the aforementioned roughly regular tetrahedron coincides with the centroid of each of the element satellites, The satellite system according to claim 1, wherein each of the six coils included in the at least six coils provided in each element satellite is positioned at each of the six substantially triangles whose vertices are the centroid of the substantially regular tetrahedron and any two vertices of the substantially regular tetrahedron.

5. The satellite system according to claim 4, wherein the shape of each element satellite corresponds to the substantially regular tetrahedron.

6. The satellite system according to claim 4, wherein the shape of each element satellite corresponds to a substantially sphere circumscribing the substantially regular tetrahedron.

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