Magnetic control of spacecraft

Abstract

A method of controlling a satellite using only magnetic forces, and a control system for implementing the method. The method involves: using magnetic force measurements to assess a current attitude of the satellite at a current time and a current location; setting a desired attitude of the satellite at a future time at a future location; developing a set of waypoints that provide attitudes of the satellite at a plurality of locations between the current location and the future location; and actuating a plurality of magnetic torquers to cause torques that cause the differences between the attitudes of the satellite between the waypoints to be as small as possible; and achieving the desired attitude at the future location, the magnetic torquers being the only means of causing rotation of the satellite to achieve the desired attitude.

Description

[0001] Related cross-references

[0002] This case claims priority to U.S. Patent Application No. SN 63 / 246,175, filed September 20, 2021, which is incorporated herein by reference. Technical Field

[0003] This invention relates to spacecraft such as satellites, and methods and apparatus for controlling satellites. Background Technology

[0004] Satellites requiring precise stability and pointing have historically demanded complex guidance and control systems, primarily relying on reaction wheels, control moment gyroscopes, or thrusters. Control systems based on reaction (or momentum) wheels (“RW”) and control moment gyroscopes (“CMG”) have a rotating mass (i.e., a flywheel) and rely on the conservation of angular momentum for reorientation of the satellite. Accelerating or reorienting the flywheel within the RW or CMG alters its angular momentum. This change in angular momentum induces rotation within the spacecraft, which counteracts the change in angular momentum generated by the RW or CMG. Three-axis control is achieved by actuating the RW / CMG on each axis. Larger and faster wheels can store more momentum, resulting in higher precision and rotational speeds.

[0005] Enhancements to these flywheel-based actuators are typically some form of magnetic control that relies on the Earth's magnetic field applying a coarse force to the satellite to support the primary system. Magnetic actuators—so-called "magnetic torquers"—consist of electromagnets that can be actuated or modulated at will, generating a controlled local magnetic field that attempts to align with the Earth's natural magnetic field, producing torque to cause the body to rotate. Magnetic torquers have not been used as primary pointing methods in communications or optical satellites that require precise control. Instead, they are used for secondary purposes, or only when very coarse pointing or detumbling is needed, such as tip-off detumbling (where precise final orientation is not required) or reaction wheel desaturation (unloading excess momentum from the RW into the Earth's magnetic field).

[0006] Although reaction wheels and control moment gyroscopes are effective, they are among the most prone to failure components in a satellite. They are complex electromechanical systems; the disks they contain rotate at speeds of up to approximately 10,000 rpm, and these disks must be kept lubricated in the vacuum of space. They contain microprocessors that are susceptible to radiation problems, and they include motors with moving parts such as bearings, which frequently fail in the vacuum and continuous temperature gradients of space.

[0007] Therefore, satellites typically include at least one additional reaction wheel, for a total of four reaction wheels, to provide a degree of redundancy. Even with redundancy, the inevitable failure of individual actuators will eventually reduce control, leading to satellite loss of control. Thrusters, often used in large systems with capacities dedicated to storing compressed gas, have lifespans limited by the rate of gas consumption. Therefore, these thrusters are unsuitable for prolonged continuous guidance and control operations.

[0008] In short, reaction wheels have the highest failure rate of all components on a satellite; they increase the satellite's mass, consume energy, and increase cost. Therefore, this technology will benefit from improvements in guidance and control. Summary of the Invention

[0009] Embodiments of the present invention provide a method for improving satellite pointing accuracy, which avoids some of the costs and disadvantages of existing technologies. According to some embodiments of the present invention, only magnetic force is used to accurately point the satellite.

[0010] The advantage of purely magnetic control for satellites is that it eliminates the need for moving components. Compared to the methods discussed above, it offers higher reliability, lighter weight, and lower cost. This removes constraints on satellite shape, allowing for optimized design to accommodate mission details rather than bulky reaction wheels.

[0011] In some embodiments, the present invention provides a method for controlling a first satellite using only magnetic force, the method comprising: (a) evaluating the current attitude of the first satellite at the current time and current position using magnetic measurements; (b) setting a desired attitude of the first satellite at a future position at a future time; (c) developing a group of waypoints for the first satellite, wherein the waypoints provide the attitude of the first satellite at multiple positions between the current position and the future position, wherein the waypoints are based on a model of the Earth's magnetic field, wherein the model provides the magnetic field state at each waypoint; and (d) actuating a plurality of magnetic torquers to induce torques that minimize the difference in attitude between the first satellites at the various waypoints; and achieving the desired attitude at the future position, wherein the magnetic torquers are the sole means of inducing rotation of the first satellite to achieve the desired attitude.

[0012] In some other embodiments, the present invention provides an apparatus including a control system for a satellite, wherein the control system uses only magnetic force to control the attitude of the satellite, wherein the control system includes: an actuator that actuates a plurality of magnetic torquers; a memory that stores triaxial magnetometer data and data based on the triaxial magnetometer data; and a processor, wherein the processor: (a) develops a group of waypoints for the satellite, wherein the waypoints provide the attitude of the satellite at a plurality of positions between the current position at the current time and the future position at a future time, wherein the waypoints are based on a model of the Earth's magnetic field and the ability to obtain the attitude at each of the plurality of positions using a plurality of magnetic torquers; and (b) transmits a signal that causes the actuator to actuate the plurality of magnetic torquers to induce torque during a time period beginning from the current time and ending at a future time when the desired attitude is obtained, wherein the magnetic torquers are the sole means of causing the satellite to rotate to obtain the desired attitude. Attached Figure Description

[0013] Figure 1A A diagram depicting the torque generated by the spacecraft's total magnetic torque (μ) on the Earth's magnetic field.

[0014] Figure 1B It depicts the per-axis contribution of the total magnetic torque (p) of (different types) magnetic torquers to form any desired vector from its contributing components (μx, μy, μz).

[0015] Figure 2 It describes the application of spacecraft magnetic torque to generate controllable torque within the Earth's magnetic field.

[0016] Figure 3 The text describes the collection of local orbital magnetospheric data from a leading satellite in a plane, and the transmission of such data to subsequent satellites, in accordance with this teaching.

[0017] Figure 4 An implementation of the magnetic control system according to this teaching is described.

[0018] Figure 5 An implementation of a method for precise attitude control using magnetic modeling and magnetic sensing, based on this teaching, is described.

[0019] Figure 6 Describing the use of with Figure 5 The optimization methods are combined with the methods used.

[0020] Figure 7 Describing the use of with Figure 6 The trajectory optimization method is combined with the magnetic model refinement method.

[0021] Figure 8A block diagram of an exemplary data processing system for use in conjunction with embodiments of the present invention is depicted. Detailed Implementation

[0022] The following description illustrates the principles of this disclosure. Therefore, it should be understood that those skilled in the art will be able to design various arrangements that, while not explicitly described or shown herein, embody the principles of this disclosure and are included within its spirit and scope. More specifically, although numerous specific details are set forth, it should be understood that embodiments of this disclosure may be practiced without these specific details, and in other instances, well-known circuits, structures, and techniques are not shown so as not to obscure the understanding of this disclosure.

[0023] Furthermore, all examples and conditional languages ​​listed herein are intended primarily for illustrative purposes only to help readers understand the principles of this disclosure and the concepts contributed by the inventors to advance the field, and all examples and conditional languages ​​described herein should be interpreted as not being limited to such specific examples and conditions listed.

[0024] Furthermore, all statements herein that describe the principles, aspects, and implementations of this disclosure and their specific examples are intended to cover their structural and functional equivalents. Moreover, such equivalents are intended to include both currently known equivalents and those developed in the future; that is, any elements developed that perform the same function, regardless of their structure.

[0025] Therefore, for example, those skilled in the art will understand that the figures herein represent conceptual views of exemplary structures that embody the principles of this disclosure.

[0026] Furthermore, those skilled in the art will understand that any flowchart, diagram, state transition diagram, pseudocode, etc., represents various processes that can be substantially represented in a computer-readable medium and thus executed by a computer or processor, whether or not such computer or processor is explicitly shown.

[0027] In the claims herein, any element referred to as means for performing the specified function is intended to cover any manner in which the function is performed, including, for example, a) a combination of circuit elements performing the function or b) any form of software, thus including firmware, microcode, etc., combined with appropriate circuitry for performing the software to perform the function. The invention defined by such claims lies in the combination and aggregation of functions provided by the various enumerated devices in the manner claimed in the claims. Therefore, the applicant considers any device capable of providing these functions to be equivalent to the device shown herein. Finally, unless expressly stated otherwise herein, the drawings are not drawn to scale.

[0028] Figure 1AA diagram is provided showing the torque T generated by the total magnetic torque μ of spacecraft 100 on the Earth's magnetic field. Figure 1B The components μ from the contributions of (different types) magnetic torquers 102A and 102B are depicted. x μ y μ z The contribution of the total magnetic torque μ to each axis of any desired vector formed in the vector.

[0029] Historically, achieving reasonable pointing accuracy using purely magnetic pointing systems has faced insurmountable challenges. In particular, among other things:

[0030] • The reference magnetic field model is low-resolution and predicts large local errors.

[0031] Due to the influence of the sun and the atmosphere, the magnetosphere itself is constantly and rapidly changing.

[0032] Satellites generate a lot of magnetic disturbances during operation, while the torque generated by magnetic force is relatively weak.

[0033] A magnetic torquer can only be applied to a plane orthogonal to the magnetic field at any given point, but may not cause rotation around the magnetic field vector.

[0034] Among other challenges, these drawbacks have prevented other systems from using purely magnetic actuation systems. Embodiments of the present invention combine the ability to model the satellite's magnetic environment, record its actual magnetic environment, and correct the model to account for these limitations and complexities in the magnetic control process.

[0035] Figure 2 It describes the application of spacecraft magnetic torque μ to generate controllable torque T within the space- and time-varying magnetic field 206 of the Earth.

[0036] Satellites such as Satellite 100 typically orbit Ring 204 within a "plane," in which multiple satellite planes exist within such a constellation. Multiple satellites within each plane are arranged around the Earth as the center of the ring and follow each other in orbit.

[0037] According to an exemplary implementation, and as Figure 3The local orbital magnetosphere data 310, as depicted, collected from the leading satellite (e.g., satellite 100-1, etc.) in the plane, is used to inform the control systems of satellites following the leading satellite (e.g., satellites 100-2, 100-3, and 100-4, etc.). More specifically, the acquired data is used to improve the magnetic model, and then the acquired data is used for trajectory planning and control systems in accordance with this teaching. When there are many satellites in the constellation, and when the satellites are designed with appropriately large and appropriately high-resolution magnetic induction mechanisms, measurements from the leading satellite can be used to develop a detailed and real-time (i.e., continuously updated) model of the magnetosphere. As the satellite moves along orbital direction 308, and the next satellite (i.e., satellite 100-2) becomes the leading satellite, the updated local orbital magnetosphere data 310 is collected from the then-leading satellite and then notified to the control systems of subsequent satellites.

[0038] Figure 4 An embodiment of a magnetic control system 400 according to this teaching is depicted. The magnetic control system 400 includes a basic (conventional) magnetic control system 412 well known in the art, as well as additional modules unique to embodiments of the present invention. The additional modules include an orbital spacecraft magnetic self-characterization module 414, a multi-satellite geomagnetic model module 416, and a trajectory optimization module 418.

[0039] The magnetic control system 400 includes a data processing system, which is not in Figure 4 It is clearly shown in the text; see Figure 8 Data processing system 800. The data processing system stores dedicated software and receives data (e.g., from airborne sensors, from other satellites, etc.) and processes the data using the dedicated software. In magnetic control system 400, modules 414, 416, and 418 are examples of such dedicated software, as are some modules of basic magnetic control system 412 such as attitude estimation 412-2 and magnetic attitude controller 412-3. Magnetic control system 400 also includes sensor 412-1 (i.e., for sensing the Earth's magnetic field) and actuator 412-4 for a magnetic torque actuator. The magnetic torque actuator includes both software (i.e., a driver) and an electromechanical actuation system. Basic magnetic control system 412 also includes a magnetic torque actuator (not shown). The design and operation of basic magnetic control system 412 are well known to those skilled in the art. Figures 5 to 7 A more detailed description of the magnetic control system 400 is provided.

[0040] Figure 5 An implementation of a method for precise attitude control using precise magnetic modeling and magnetic sensing, based on this teaching, is described. For example... Figure 5 The method described herein is a basic implementation of the technology; in view of this disclosure, any of the various optional modifications to the technology of the invention will be within the capabilities of those skilled in the art.

[0041] Now refer to Figure 5 The method, in mission S501, assesses the current attitude (i.e., the satellite's orientation and rotation rate). This can be achieved, for example, but not limited to, magnetic measurements (see...). Figure 4 The attitude estimation (412-2) is used to perform this.

[0042] In mission S502, the desired attitude of the satellite at a future point in time is set. The desired future attitude (i.e., the position the satellite will point to at the specified time) can be set by: (i) mission details, (ii) based on autonomous sensor readings, or (iii) manually by the operator. Full pointing authority (i.e., the ability to reorient the satellite at any time) can be achieved if there is sufficient time (and therefore sufficient magnetic field change) to circumvent the underactuated control limitations inherent in magnetic attitude control alone.

[0043] In this regard, considering that magnetic control alone cannot induce torque "around" the Earth's magnetic field at any given point—it can only induce torque against the Earth's magnetic field—conventional magnetic control can only cause pivoting around two axes orthogonal to the Earth's magnetic field, but not around a third axis aligned with the magnetic field. However, because the Earth's magnetic field constantly changes its orientation relative to the satellite, all axes can be used to induce torque over time. According to an exemplary implementation, the magnetic control system 400 operates within these limitations to achieve arbitrary rotations, which is necessary to achieve the desired future satellite attitude.

[0044] In mission S503, a trajectory planning optimization method implemented by trajectory optimization module 418 is applied to develop: (a) a set of waypoints between the current attitude and the final attitude (i.e., orientation + rotation rate at each time point), and (b) a control signal applied to the magnetic torquer to follow the waypoints. Furthermore, in mission S504, during the time period for calculating waypoints, the magnetic torquer of the basic magnetic control system 412 is actuated to induce a torque that minimizes the state increment (Δ) between the current attitude and the specified waypoints of the designed trajectory. In conjunction with this mission, closed-loop tracking control can be used to correct deviations from the planned trajectory when the satellite is on its way.

[0045] Various optimization models and methods can be used to achieve task S503. Figure 6 A non-limiting example of this method is described, which is performed via a trajectory optimization module (i.e., software) 418.

[0046] In mission S601, constraints are established, such as: (i) the satellite's initial state (i.e., current state) and (ii) the satellite's final state (the desired ultimate state) ("state" being the orientation of the spin components and their rate of change—the actual and desired limits throughout the process), and (iii) the satellite's orbital parameters. In mission S602, the satellite's geocentric inertial (ECI) position propagates between the initial and final times. As those skilled in the art will recognize, "ECI" is a way of describing a position independent of the Earth's current rotation (inertia). When combined with a specific time, the relative position above a point on the Earth's surface can be converted into this absolute position reference. Therefore, in mission S602, the progression of the ECI position from a given moment to its future position (from start to end) is simulated by applying a standard orbital dynamics model.

[0047] In mission S603, the state of the Earth's magnetic field is calculated for each ECI location in mission S602. This task is performed using data obtained from the multi-satellite Earth magnetic field modeling module 416 (via module 418). And in mission S604, an orientation trajectory is projected onto a time-varying magnetic environment to select an intermediate orientation, where this orientation is progressively attainable from the current (or previous) intermediate step via available underactuated magnetic control, such that the combination of intermediate steps (i.e., satellite orientations) makes the final desired state accessible. The intermediate orientation (at a specific time / location along the orbit) can be selected using brute-force analysis, an optimization engine, or an incremental heuristic. The analysis, optimization engine, or heuristic can each utilize heuristics to tune behavior to the operator's expectations for the specific system.

[0048] Figure 7 The document describes a non-limiting example of a magnetic model refinement method used during trajectory optimization. According to mission S701, triaxial magnetometer measurements are collected at regular intervals at any given satellite location in the satellite orbital plane, the interval being at least twice the frequency of the control signal to be updated.

[0049] In mission S702, magnetic field measurements from the magnetometer, along with measurements from any other available attitude sensors (e.g., coarse and fine solar sensors, Earth horizon / limb sensors, feedback from the payload, etc.), are used to estimate the current attitude and its covariance. In some implementations, each satellite acquiring magnetometer data performs this mission.

[0050] In mission S703, the "fit" of the magnetic measurements to the magnetic model of the receiving satellite is evaluated at the time and location of the collected measurements / corresponding attitude estimates (i.e., this task is performed by each satellite that acquires magnetometer data). Deviations from the local model of each measuring satellite are distributed to other satellites in the orbital plane via a network or link. In mission S704, the estimated deviations from the magnetic model and the corresponding covariance estimates (along the trajectory of the source satellite) are propagated to one or more satellites in the network.

[0051] According to mission S705, at any given receiving satellite, upon receiving estimates of magnetic field deviation (Δmagnetic field) and covariance from other satellites, the quality and correlation of these estimates are evaluated relative to the recent trajectory of the receiving satellite. Based on the quality / correlation evaluation, the estimates can be deweighted. For example, the deviation estimate can be deweighted based on the following considerations, as well as other factors:

[0052] • The estimated time period (i.e., the longer the estimate, the greater the deweighting);

[0053] • The distance between the fixed Earth data collection point and the fixed Earth point used to calibrate the local model (i.e., the greater the distance, the greater the deweighting).

[0054] • Based on the quality of the covariance it provides (i.e., the larger the covariance, the greater the deweighting);

[0055] • Understand the time variance of the magnetic field enhancement in a certain region (i.e., the larger the time variance, the greater the deweighting).

[0056] In mission S706, the satellite incorporates measurements from mission S705 into its local model, depending on the circumstances. This is done by subtracting an estimate of the magnetic field bias and a weighted time / position sequence from the current best local estimate of the magnetic field along the incoming trajectory of the receiving satellite. In cases where these bias estimates are received from multiple contemporary satellites, the local satellite can combine these estimates using a weighted linear two-dimensional regression mapped to the surface of the ellipsoid in which the orbit resides.

[0057] Finally, in mission S707, after the improvements to the local model implemented through missions S701 to S706, the biases observed locally are propagated according to this process, while the local model adjustment (relative to the baseline reference model) is parameterized. These measurements are considered as the "biases" that parameterize the local model adjustment. In this way, the propagated biases can be used effectively without the need for complete synchronization between the local models of the satellites or for them to reach agreement at any given point.

[0058] Figure 5 , Figure 6 and Figure 7The method shown can be executed by processing logic, which may include hardware (circuit, dedicated logic, etc.), software (such as running on a general-purpose computer system or a dedicated machine), or a combination of both. In some implementations, Figure 5 , Figure 6 and Figure 7 Some of the blocks depicted can be executed simultaneously, or in a different order than what is depicted. Furthermore, some processing may be performed by a ground-based processor.

[0059] Figure 8 A block diagram depicts an exemplary data processing system 800 operating according to various aspects and implementations of this disclosure. The data processing system 800 may be implemented in any form factor and includes a processor 802, a main memory 804, a storage device 806, and input / output (I / O) devices 808 interconnected as shown (e.g., via one or more buses, etc.).

[0060] Processor 802 represents one or more general-purpose processing devices, such as microprocessors, central processing units, etc. More specifically, processor 802 may be a Complex Instruction Set Computing (CISC) microprocessor, a Reduced Instruction Set Computing (RISC) microprocessor, a Very Long Instruction Word (VLIW) microprocessor, or a processor implementing other instruction sets or a combination of instruction sets. Processor 802 may also be one or more special-purpose processing devices, such as application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), network processors, etc. Processor 802 is capable of executing instructions stored in main memory 804 and storage device 806, including instructions corresponding to those described above. Figure 5 , Figure 6 and Figure 7 The instructions of the method described herein; the processor 802 is capable of reading data from the main memory 804 and the storage device 806 and writing data to the main memory 804 and the storage device 806; and the processor 802 is capable of receiving input signals and transmitting output signals to the input / output device 808. Although for simplicity... Figure 8 The document describes a single processor, but the data processing system 800 may include multiple processors.

[0061] Main memory 804 is capable of storing executable instructions and data, including those corresponding to the above. Figure 5 , Figure 6 and Figure 7The method includes instructions and data, and the main memory 804 may include volatile memory devices (e.g., random access memory [RAM]), non-volatile memory devices (e.g., flash memory) and / or other types of memory devices.

[0062] Storage device 806 is capable of persistently storing executable instructions and data, including those corresponding to the above. Figure 5 , Figure 6 and Figure 7 The method provides instructions and data, and the storage device 806 may include magnetic hard disks, Universal Serial Bus (USB) solid-state drives, Redundant Array of Independent Disks (RAID) systems, Network Attached Storage (NAS) arrays, etc. Although for simplicity... Figure 8 The image depicts a single storage device, but the data processing system 800 may include multiple storage devices.

[0063] I / O device 808 receives input signals, such as from other satellites, forwards the corresponding signals to processor 802, receives signals from processor 802, and transmits corresponding output signals that can be used to control devices such as magnetometers. In some embodiments, the I / O device may not be part of the data processing system 800 itself, but may be associated with other subsystems of the satellite or even a ground-based system. In some embodiments, the I / O device can establish a communication link between the satellite of interest and other satellites. In some embodiments, the I / O device can establish a communication link between multiple satellites (e.g., for transmitting data from a source to the satellite of interest). In some embodiments, the communication link can be relayed or established via a ground device, and / or some processing related to the communication link can be performed at a ground station. In an exemplary embodiment, the input mechanism of I / O device 808 is a transceiver. Although for simplicity... Figure 8 The diagram depicts a single I / O device, but the data processing system 800 may include multiple I / O devices.

[0064] Definitions. The following terms are used herein and in the appended claims:

[0065] • Magnetic torque generator. A magnetic torque generator is a solenoid device that generates a magnetic field, producing torque in the presence of an external magnetic field. Forms include, but are not limited to, solid magnetic torque generators and hollow coil magnetic torque generators.

Claims

1. A method for controlling a first satellite using only magnetic force, the method comprising: a) Use magnetometry to assess the current attitude of the first satellite at the current time and current location; b) Set the desired attitude of the first satellite at a future time and future location; c) Developing a group of waypoints for the first satellite, wherein the waypoints provide the attitude of the first satellite at multiple locations between the current location and the future location, wherein the waypoints are based on a model of the Earth's magnetic field, wherein the model provides the state of the magnetic field at each waypoint; and d) Actuating a plurality of magnetic torquers to generate torques that minimize the differences in attitude between the first satellite at various waypoints and to achieve the desired attitude at the future position, wherein the magnetic torquers are the only means of causing the first satellite to rotate to achieve the desired attitude.

2. The method according to claim 1, wherein, The group of waypoints developed includes: a) Estimate the position progression of the first satellite in its orbit, the progression defining the group of waypoints; b) Calculate the state of the Earth's magnetic field at each waypoint; and c) Define the orientation trajectory, which specifies an intermediate orientation of the first satellite that can be achieved solely through magnetically induced rotation, such that the desired attitude is achieved at a future time.

3. The method according to claim 2, wherein, Calculating the state of the Earth's magnetic field includes receiving data from an additional satellite that has the same orbital plane as the first satellite and is positioned ahead of the first satellite in its orbit.

4. The method according to claim 3, wherein, The data is from a triaxial magnetometer.

5. The method according to claim 4, wherein the method comprises: For each additional satellite from which data is obtained, the current attitude of each of the additional satellites is estimated based on the data, and the covariance of the estimated current attitude of each of the additional satellites is estimated.

6. The method according to claim 5, wherein the method comprises: The deviation between the magnetometer data and the model of the Earth's magnetic field at the time and location where the magnetometer data was collected is evaluated.

7. The method according to claim 6, wherein the method comprises: The deviation from the model of the magnetic field is propagated.

8. The method according to claim 7, wherein the method comprises: The correlation between the propagated deviation and the recent trajectory of the first satellite is assessed.

9. The method according to claim 8, wherein the method comprises: Taking into account the assessed correlation, the magnetometer data at the first satellite is incorporated into the magnetic field model of the first satellite.

10. An apparatus comprising a control system for a satellite, wherein, The control system uses only magnetic force to control the attitude of the satellite, wherein the control system includes: An actuator that actuates a plurality of magnetic torquers; A memory that stores triaxial magnetometer data and data based on the triaxial magnetometer data; Processor, wherein the processor: (a) Developing a group of waypoints for a satellite, wherein the waypoints provide the attitude of the satellite at multiple locations between its current position at a current time and its future position at a future time, wherein the waypoints are based on a model of the Earth's magnetic field and the ability to obtain the attitude at each of the multiple locations using multiple magnetic torquers; and (b) Sending a signal that causes the actuator to actuate a plurality of the magnetic torquers to induce torque during a time period beginning at the current time and ending at a future time when the desired attitude is obtained, wherein the magnetic torquers are the only means of inducing the rotation of the satellite to obtain the desired attitude.

11. The device according to claim 10, wherein, The resulting torque minimizes the differences in satellite attitude between waypoints.

12. The device according to claim 10, wherein, The device in question is a satellite.

13. The device according to claim 10, wherein, The triaxial magnetometer data and the data based on the triaxial magnetometer data are received from other satellites in the orbital plane of the satellite.

14. The device according to claim 13, wherein, The processor also uses the triaxial magnetometer data and data based on the triaxial magnetometer data to modify the model of the Earth's magnetic field on which the waypoints are based.

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