Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
I
SPACECRAFT CONTROL USING RESIDUAL DIPOLE
FIELD
.. [0001] The field generally relates to spacecraft attitude control, and more
particularly to a method and apparatus for unloading reaction wheel momentum
using a magnetic dipole of a spacecraft.
BACKGROUND
[0002] Spacecraft are often provided with reaction wheels which allow for
momentum to be transferred between the wheels and the spacecraft body.
Transferring momentum in this fashion can allow for precise control of the
spacecraft's attitude. However, excess momentum can build up in the reaction
wheels over time as they counter disturbance torques to maintain pointing at a
particular attitude. It is therefore necessary to regularly unload excess
momentum
building up in the reaction wheels to avoid saturation and maintain attitude
control.
[0003] There are different existing methods for unloading momentum of a
spacecraft. Such methods involve using some form of actuator to generate a
torque which can be used to counter the excess momentum. For spacecraft in
proximity to an ambient magnetic field (for example in Low Earth Orbit), a
common
method for unloading momentum involves the use of magnetorquers (also known
as magnetic torquers or torque rods) to interact with the ambient magnetic
field to
generate a desired torque. Unfortunately, complete or partial failure of the
magnetorquer subsystem can be a mission-killer, as absent a redundant
actuator,
it would no longer be possible to unload momentum, resulting in the eventual
saturation of the reaction wheels and loss of attitude control.
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SUMMARY
[0004] According to an aspect, a method for desaturating reaction wheels of a
spacecraft having a magnetic dipole is provided. The method includes the
processes of: a) orienting the spacecraft relative to an external magnetic
field to
apply a torque to the spacecraft via the magnetic dipole in a direction
opposing
momentum stored in the reaction wheels; and b) using the applied torque to
unload
at least some of the momentum stored in the reaction wheels.
[0005] In an embodiment, the method includes a preliminary process of
determining a magnetic dipole vector corresponding to a magnitude and
direction
of the magnetic dipole of the spacecraft; and process b) includes orienting
the
spacecraft to align the magnetic dipole vector relative to the external
magnetic field
to apply the torque in the direction opposing the momentum.
[0006] In an embodiment, determining the magnetic dipole includes: monitoring
a
change in momentum of the spacecraft over a trajectory of the spacecraft
relative
to a known or measurable external magnetic field, said change in momentum
being
caused by a torque applied to the spacecraft by the external magnetic field
via the
spacecraft's magnetic dipole; and using the monitored change in momentum and
known or measurable external magnetic field to solve for the magnetic dipole
vector.
[0007] In an embodiment, desaturating the reaction wheels using the applied
torque includes slowing down the reaction wheels to unload momentum in a
direction which opposes the applied torque.
[0008] In an embodiment, the method includes: determining a magnetic field
vector corresponding to a direction and magnitude of the external magnetic
field
relative to the spacecraft; determining a momentum vector corresponding to a
magnitude and direction of a total momentum of the spacecraft; determining a
target torque vector corresponding to a torque which opposes the momentum
vector; and orienting the spacecraft to align the magnetic dipole of the
spacecraft
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relative to the magnetic field vector to produce the torque in the direction
of the
target torque vector.
[0009] In an embodiment, the method further includes determining a target
dipole
vector corresponding to a cross product between the magnetic field vector and
the
momentum vector, and wherein orienting the spacecraft comprises adjusting an
attitude of the spacecraft to orient the magnetic dipole of the spacecraft in
alignment with the target dipole vector.
[0010] In an embodiment, the method further includes applying an additional
constraint to resolve a degree of freedom of the orientation of the spacecraft
while
the produced torque is in the direction of the target torque vector.
[0011] In an embodiment, the target torque vector is calculated continuously
throughout a trajectory of the spacecraft; and the spacecraft is continuously
reoriented to maintain the alignment of the magnetic dipole relative to the
external
magnetic field to produce the torque in the direction of the target torque
vector as
the magnetic field vector and momentum vector change throughout the
spacecraft's trajectory, thereby unloading momentum from the spacecraft.
[0012] In an embodiment, the method further includes, when the magnitude of
the
momentum vector is below a predetermined threshold, orienting the spacecraft
to
substantially align the magnetic dipole with the magnetic field vector to
attenuate
changes in the spacecraft's momentum.
[0013] In an embodiment, the spacecraft is orbiting the Earth and the external
magnetic field corresponds to Earth's magnetic field, and the magnetic field
vector
is determined by determining a current position and orientation of the
spacecraft
relative to the Earth, and using a stored model of Earth's magnetic field to
estimate
the magnitude and direction of Earth's magnetic field at the determined
current
position and orientation.
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[0014] In an embodiment, the method includes continuously determining an
instantaneous orientation of the spacecraft; and continuously adjusting the
orientation of the spacecraft to maintain an alignment of the magnetic dipole
relative to the external magnetic field to either produce a torque in the
direction
opposing the spacecraft momentum, or minimize torques and changes to the
spacecraft momentum.
[0015] In an embodiment, at least one of the reaction wheels is oversaturated
and
the spacecraft is in a tumbling state due to a lack of control authority, and
the
method includes: determining a desired orientation of the spacecraft relative
to the
external magnetic field which applies, via the magnetic dipole, the torque in
the
direction which opposes the excess momentum; during a period of the tumbling
in
which the spacecraft is rotating towards the desired orientation, operating
the
reaction wheels to decelerate the tumbling of the spacecraft; and during a
period
of the tumbling in which the spacecraft is rotating away from the desired
orientation, operating the reaction wheels to accelerate the tumbling of the
spacecraft.
[0016] In an embodiment, the method includes restoring attitude control by
desaturating the reaction wheels while the spacecraft is rotating towards the
desired orientation, continuously until the reaction wheels are no longer
oversaturated, and once attitude control is restored, performing steps a) and
b) to
unload remaining excess momentum.
[0017] In an embodiment, the reaction wheels are desaturated without the use
of
torque rods.
[0018] In an embodiment, orienting the spacecraft includes operating the
reaction
wheels to adjust an attitude of the spacecraft.
[0019] In an embodiment, the magnetic dipole is a permanent residual dipole of
the spacecraft.
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[0020] In an embodiment, the external magnetic field is produced by a
celestial
body.
[0021] According to an aspect, a method for operating a spacecraft is
provided.
The method includes transmitting instructions to a spacecraft, said
instructions
causing the spacecraft to desaturate its reactions wheels according to the
method
as described above.
[0022] According to an aspect, a spacecraft is provided. The spacecraft
includes:
a body; at least three reaction wheels supported by the body; electronic
components supported by the body and producing a magnetic dipole; an actuator
for adjusting an attitude of the spacecraft; and a controller in operative
communication with the reaction wheels and the actuator, said controller being
programmed with instructions to: adjust the attitude of the spacecraft
relative to an
external magnetic field to apply a torque to the spacecraft body via the
magnetic
dipole in a direction opposing momentum stored in the reaction wheels; and
operate the reaction wheels to unload at least some of the momentum stored in
the reaction wheels using the applied torque.
[0023] According to an aspect, a non-transitory computer-readable medium is
provided. The non-transitory computer-readable medium has instructions stored
thereon which, when executed by a processor of a control system onboard a
spacecraft having a magnetic dipole, cause the processor to carry out the
processes of: a) orienting the spacecraft relative to an external magnetic
field to
apply a torque to the spacecraft via the magnetic dipole in a direction
opposing
momentum stored in the reaction wheels; and b) using the applied torque to
unload
at least some of the momentum stored in the reaction wheels.
[0023a]According to an aspect, a method for unloading momentum from a
spacecraft having a magnetic dipole is provided. The method includes: a)
determining a momentum vector corresponding to a magnitude and direction of
momentum to be unloaded from the spacecraft; b) determining a target
orientation
Date Recue/Date Received 2022-09-14
5a
of the spacecraft relative to an external magnetic field, wherein in said
target
orientation the magnetic dipole interacts with the external magnetic field to
apply a
torque in a direction at least partially opposing the momentum vector; c)
operating
at least one actuator to move the spacecraft into the target orientation; and
d)
maintaining the spacecraft in the target orientation to unload at least some
of the
momentum using the applied torque.
[002313]According to an aspect, a spacecraft is provided. The spacecraft
includes:
a body; at least one actuator for adjusting an attitude of the spacecraft; and
a
controller in operative communication with the at least one actuator, said
controller
being programmed with instructions to: determine a momentum vector
corresponding to a magnitude and direction of momentum to be unloaded from the
spacecraft; determine a target orientation of the spacecraft relative to an
external
magnetic field, wherein in said target orientation the magnetic dipole of the
spacecraft interacts with the external magnetic field to apply a torque in a
direction
at least partially opposing the momentum vector; operate the at least one
actuator
to move the spacecraft into the target orientation; and maintain the
spacecraft in
the target orientation to unload at least some of the momentum using the
applied
torque.
BRIEF DESCRIPTION OF THE DRAWINGS
[0024] Figure 1 is a perspective view of a spacecraft, according to an
embodiment.
Date Recue/Date Received 2022-09-14
6
[0025] Figure 2 is a schematic showing components of the spacecraft of Figure
1.
[0026] Figure 3 is a schematic illustrating spacecraft and its interaction
with
Earth's magnetic field while in orbit.
[0027] Figure 4 is a schematic illustrating alignment of the spacecraft of
Figure 1
relative to an external magnetic field to produce a desired torque.
[0028] Figure 5 is a schematic illustrating the use of two vectors to provide
a triad
solution for a desired orientation of the spacecraft.
[0029] Figure 6 is a simulation graph illustrating momentum unloading of the
spacecraft while in a stumbling state.
[0030] Figure 7 is a simulation graph illustrating total spacecraft momentum
during desaturation and while parked.
[0031] Figure 8 is a simulation graph illustrating total spacecraft momentum
during detumbling, desaturation, and resaturation.
[0032] Figure 9 is a flowchart illustrating a method for desaturating a
spacecraft
using available control authority to orient the spacecraft, according to an
embodiment.
[0033] Figure 10 is a flowchart illustrating a method for dumping momentum
from
a spacecraft in the absence of control authority in the reaction wheels,
according
to an embodiment.
[0034] Figure 11 is a flowchart illustrating transitioning between
desaturation
methods and resaturation, according to an embodiment.
DETAILED DESCRIPTION
[0035] Various embodiments are described hereinafter with reference to the
figures. It should be noted that, for simplicity and clarity of illustration,
elements
shown in the figures have not necessarily been drawn to scale. For example,
the
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dimensions of some of the elements may be exaggerated relative to other
elements for clarity. Further, where considered appropriate, reference
numerals
may be repeated among the figures to indicate corresponding or analogous
elements. In addition, numerous specific details are set forth in order to
provide a
thorough understanding of the exemplary embodiments described herein.
However, it will be understood by those of ordinary skill in the art that the
embodiments described herein may be practiced without these specific details.
In
other instances, well-known methods, procedures and components have not been
described in detail so as not to obscure the embodiments described herein.
Furthermore, the description and figures are not to be considered as limiting
the
scope of the invention in any way, but rather as merely describing the
implementation of the various exemplary embodiments.
[0036] With reference to Figures 1 and 2, a spacecraft 100 is shown according
to
an embodiment. In the present embodiment, spacecraft 100 is an artificial
satellite
designed to operate in low Earth orbit, but it is appreciated that other types
of
spacecraft are also possible. For example, spacecraft can be a different type
of
artificial satellite and/or can be a different type of man-made device
designed to
operate in space.
[0037] The illustrated spacecraft 100 comprises a body 101 having a
substantially
cuboid shape. More specifically, body 101 comprises a housing having six faces
respectively facing in the +x, -x, +y, -y, +z and -z directions in a body
frame of
reference. It is appreciated, however, that different configurations and
shapes of
body 101 are also possible. Moreover, in the present embodiment, body 101 is
configured such that spacecraft 100 corresponds to a microsatellite (ex:
between
approx. 10 and 100 kg), but it is appreciated that other sizes are also
possible.
[0038] The spacecraft 100 can include a number of modules, allowing for
spacecraft 100 to be operated and/or controlled. For example, in the present
embodiment, the spacecraft 100 comprises a payload module 103, solar panel
module 105, a thermal control 107, battery module 109, reaction wheel module
111, magnetorquer module 113, magnetometer module 115, sun sensor module
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117, and a GPS module 119 among others. As can be appreciated, each module
can comprise a number of components secured relative to and/or forming part of
body 101, and each can be operated to perform a number of different functions
and/or form part of one or more subsystems relating to spacecraft 100
operation
and control. Although the modules are shown as distinct elements, it is
appreciated
that this is for illustrative purposes only, and that different modules can
share
components and/or that components of a given module can perform multiple
functions, including those of one or more other modules.
[0039] In more detail now, payload 103 can be secured relative to body 101 for
carrying out operations in space. In the present embodiment, payload 103 is a
scientific payload, and includes a telescope which can be used to detect
celestial
objects. It is appreciated that telescope can also function as a star tracker
and can,
for example, form part of a navigational or guidance subsystem, acting as an
attitude sensor to determine the spacecraft's orientation. Although in the
present
embodiment payload 103 comprises a telescope, it is appreciated that different
payloads are possible depending on the mission.
[0040] Solar panel module 105 can comprise one or more solar panels exposed
on an exterior of the spacecraft body 101. In the present embodiment, solar
panels
are mounted on each of the faces of body 101, but it is appreciated that in
other
embodiments, solar panels can be provided on only some faces and/or can be
spaced apart from the spacecraft body 101 for example via a support. As can be
appreciated, solar panel module 105 can serve to generate electricity to power
electrical components/modules of spacecraft 100. Solar panel module 105 can
also form part of the navigational or guidance subsystem, for example acting
as a
coarse sun sensor to estimate the attitude of spacecraft by measuring sun
exposure of the different faces of the spacecraft body 101.
[0041] Thermal control module 107 can be provided to maintain the
components/modules of the spacecraft 100 at acceptable temperatures during
operation. In the present embodiment, thermal control module 107 comprises one
or more radiators for dissipating excess heat from spacecraft body 101. It is
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appreciated that in other embodiments, other types of active and/or passive
thermal control elements can be provided, such as heaters, louvers, among
others.
[0042] Battery module 109 can comprise one or more batteries operatively
connected to solar panel module 105. As can be appreciated, battery module 109
can store energy which can be used to power the various components/modules of
the spacecraft 100. Battery module 109 can be charged by solar panels and/or
by
other energy generating means, and can be configured to supply energy as
needed, for example during periods when the energy generating means are not
supplying sufficient electricity to operate the spacecraft 100. In the present
embodiment, the battery module 109 comprises Li-ion batteries, but it is
appreciated that in other embodiments, other types of batteries are possible.
[0043] Reaction wheels module 111 can form part of the spacecraft's attitude
control subsystem and can comprise a plurality of reaction wheels (also
referred
to as momentum wheels) for storing/transferring momentum to control angular
movement of the spacecraft body 101. In the present embodiment, at least three
reaction wheels are secured relative to the spacecraft body 101 to allow for
three-
axis attitude control thereof. More specifically, each reaction wheel is
configured
to spin about one of three perpendicular axes, in the present embodiment
corresponding the x, y, and z axes of spacecraft body 101. It is appreciated,
however, that in other embodiments, more reaction wheels can be provided, for
example to provide redundancy in case of failure of one or more of the
reaction
wheels, and/or to increase capacity for momentum storage in one or more axes.
It
is also appreciated that the position and/or orientation of the reaction
wheels can
differ, so long as they allow for three-axis attitude control.
[0044] As is known to persons of skill in the art, reaction wheels can be used
to
control attitude of a spacecraft 100 by transferring angular momentum between
the spacecraft's body 101 and the reaction wheels. More specifically, each
reaction
wheel can be secured relative to the spacecraft body 101 and can comprise a
flywheel for storing rotational energy, and a motor or other actuator which
can be
operated to speed up or slow down the flywheel. Angular momentum can be
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transferred from the spacecraft's body 101 and stored in the reaction wheels
by
speeding up the flywheel. Similarly, angular momentum stored in the reaction
wheels can be transferred to the spacecraft's body 101 by slowing down the
flywheel. Transferring angular momentum to and from the spacecraft's body 101
in this fashion can allow for the angular movement of the spacecraft 100 to be
precisely controlled. Similarly, unwanted angular momentum building up in the
spacecraft's body 101, for example due to external forces or disturbance
torques,
can be absorbed by (i.e. transferred to) the reaction wheels, for example to
maintain the spacecraft in a desired pointing direction. The momentum stored
in
wheels can be measured, for example, using rate sensors to determine the speed
of the wheels.
[0045] As can be appreciated, in order to maintain attitude control of the
spacecraft 100, the reaction wheels must be capable of fully absorbing the
angular
momentum of the spacecraft's body 101 at any given moment. Over time, as the
is reaction wheels absorb unwanted momentum building up in the spacecraft
body
101, the reaction wheels may reach a state of "oversaturation" or "hyper
saturation"
in which they cannot absorb any more momentum (for example, due to the
flywheels spinning at a maximum speed). In such a state, the spacecraft can be
said to lose control authority, as the reaction wheels can no longer continue
to
absorb momentum required from the spacecraft body to maintain required stable
pointing. Consequently, the spacecraft 100 will start to tumble and become
uncontrollable. It is therefore necessary to be able to desaturate the
reaction
wheels (i.e. unload momentum from the spacecraft) to maintain attitude
control.
[0046] In some embodiments, spacecraft can be provided with a mechanism to
actively unload momentum. In the present embodiment, and by way of example,
magnetorquer module 113 is provided as part of the spacecraft's attitude
control
subsystem to unload (or "dump") momentum to an external body. Magnetorquer
module 113 comprises one or more magnetorquers or torque rods operable to
generate a magnetic dipole. The generated dipole can interact with an ambient
or
external magnetic field to generate a torque which can then be used reduce the
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spacecraft's momentum. In this fashion, the magnetorquers effectively allow
for
the spacecrafts momentum to be transferred or unloaded to the external body
generating the external or ambient magnetic field. Although magnetorquers are
described in the present embodiment, it is appreciated that other mechanisms
can
be provided to unload momentum, including other actuators, such as thrusters.
[0047] As can be appreciated, traditional methods for using a magnetorquer
module 113 to desaturate reaction wheels would require magnetorquer module
113 to be capable of generating torque along each of the three perpendicular
axes
about which the reaction wheels spin, in the present embodiment corresponding
the x, y, and z axes of spacecraft body 101. In other words, traditional
desaturation
techniques would require at least three torque rods (i.e. one torque rod per
reaction
wheel). It is appreciated, that in some embodiments, more torque rods can be
provided, for example for redundancy in case of failure. Although existing
techniques require at least three torque rods, it will be appreciated that
following
the novel methods described hereinbelow, it is possible to desaturate reaction
wheels using two or fewer torque rods, for example due to partial or total
failure of
magnetorquer module 113, in situations where it would not be desirable to
operate
magnetorquer modules 113 (for example to conserve energy), or in embodiments
where spacecraft 100 is not provided with a magnetorquer module 113 at all.
[0048] In order to interact with an ambient or external magnetic field to
produce a
desired torque, the characteristics of the external magnetic field should be
known
(such as the magnitude and direction of the magnetic field at the spacecraft's
current position at any given time). In the present embodiment, magnetometer
115
is provided to measure the magnetic field in the x, y, and z directions.
Although in
the present embodiment a magnetometer 115 is described, it is appreciated that
in other embodiments, different sensors can be provided for the purposes of
measuring and/or estimating an external magnetic field, for example in the
event
that magnetometer 115 fails or if spacecraft 100 is not provided with
magnetometer
115. For example, in some embodiments, the orientation and position of
spacecraft
100 relative to a celestial body can be used to estimate the magnitude and
direction
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of the external magnetic field, using an existing model of the external
magnetic
field. It is further appreciated that magnetometer 115 can be used as part of
the
spacecraft's navigational or guidance subsystem, for example to determine the
spacecraft's attitude by correlating the measured magnetic field with an
existing
model of the external magnetic field.
[0049] In the illustrated embodiment, sun sensor module 117 and GPS module
119 are also provided as part of the spacecraft's navigational or guidance
subsystem. Sun sensor module 117 comprises one or more sensors configured to
detect the position of the sun relative to the spacecraft 100. As can be
appreciated,
the sun sensor module 117 can comprise one or more dedicated photosensors,
although it is appreciated that other types of sensors are also possible.
Moreover,
as explained above, although sun sensor module 117 is illustrated separately
from
solar panel module 105, it is appreciated that the solar panels can be
configured
to act as a sun sensor module 117.
[0050] GPS module 119 can comprise one or more receivers configured to
receive and process GPS signals from nearby GPS satellites via one or more
antennae 121 positioned on different sides of the spacecraft body 101. As can
be
appreciated, measuring the GPS signals can allow for determining distances
between the spacecraft 100 and GPS satellites. Thus, processing the GPS
signals
can allow for determining a current position of the satellite relative to the
GPS
satellites. Moreover, given the known position of the GPS satellites,
processing the
GPS signals in this fashion can allow for determining the spacecraft's
position
relative to the Earth in addition to the spacecraft's attitude. Accordingly,
the GPS
module 119 can, in some embodiments, act as an attitude sensor, It can further
act in place of magnetometer module 115, for example by using a model of the
Earth's magnetic field to estimate the strength of the magnetic field at the
measured position and orientation of the spacecraft. Although a GPS module 119
is described, it is appreciated that attitude and/or position can be
determined using
other satellite-based navigation systems.
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[0051] Although in the present embodiment a sun sensor module 117 and GPS
module 119 are described, it is appreciated that in other embodiments, other
elements can form part of the spacecraft's navigational subsystem, including a
different types of attitude sensors such as a horizon sensor, an orbital
gyrocompass, an earth sensor, a star tracker, and a magnetometer, among
others.
[0052] The various modules described above, in addition to other modules
operating in the spacecraft 100, include materials and electrical components
which
are each susceptible to creating a magnetic field. The combined effect of
these
magnetic fields results in the spacecraft 100 having a net magnetic dipole 150
which can be characterized as a vector Fri having a given magnitude and
direction
relative to the spacecraft body 101. The magnetic dipole 150 can be referred
to as
a residual dipole in that it is a side effect of any current-carrying devices
in the
spacecraft 100 and/or its payload 103, and/or any materials provided in the
spacecraft 100 and/or its payload 103, including any magnetic materials or
metallic
structures (such as metallic frame of spacecraft body 101) having eddy
currents
produced therein. In some embodiments, the magnetic dipole 150 can be
substantially static, in that it will change very little (ex: < 10%) or not at
all over the
course of a mission. In other embodiments, the magnetic dipole 150 can be
variable, in that it can change over the course of a mission, for example when
some
electrical components are operated or powered on and/or when some components
are powered down. In some embodiments, the dipole 150 can be manipulated
purposely, for example by using specialized components such as a magnetorquer
module 113, if available.
[0053] As can be appreciated, the magnetic dipole 150 of the spacecraft 100
can
interact with an ambient or an external magnetic field in order to produce a
torque
on the spacecraft 100. For example, with reference to Figure 3, an exemplary
spacecraft 100 is shown in orbit around a celestial body 350 (in this case the
Earth)
producing an ambient magnetic field B. As shown in exemplary orbital position
300, the torque 74-; associated with the spacecraft's dipole rii against the
magnetic
field B is given by the cross product gm' = hi x 17 i . Following existing
methods for
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spacecraft control, torque g¨m can be considered as a disturbance torque
producing
excess momentum which would need to be absorbed by the reaction wheels.
However, it will be appreciated that in some control methods, this torque can
be
used in order to reduce momentum of the spacecraft 100. As can be appreciated,
this can be useful when traditional desaturating methods have failed or are
not
available, for example in the event of partial or total torque rod failure, or
if
spacecraft is not provided with torque rods.
[0054] Broadly described, a method for reducing momentum of a spacecraft 100
can comprise orienting the spacecraft 100 relative to an external or ambient
magnetic field to apply a torque to the spacecraft via the magnetic dipole 150
in a
direction opposing the momentum. The applied torque can subsequently be used
to reduce, discharge, or dump the momentum. As can be appreciated, the
momentum to be reduced can be defined as a vector H. In order to reduce the
momentum, the generated torque 47; should be in a direction which opposes
momentum vector ii. It should be appreciated that the momentum vector 11 can
correspond to any momentum which is desired to be discharged. For example, the
vector Ii can correspond to the momentum stored in the spacecraft's reaction
wheels 117, the momentum of the spacecraft's body 101, and/or a combination of
both. As can be appreciated, it is often required to reduce momentum to
maintain
attitude control of the spacecraft 100. Accordingly, momentum can be referred
to
as "excess" momentum, which can correspond to the total momentum of the
spacecraft 100 and/or a portion thereof.
[0055] Given a spacecraft momentum vector II, an ambient magnetic field vector
, and a spacecraft dipole vector hi, a target orientation or attitude of the
spacecraft 100 can be determined in order to produce a torque g¨m which
opposes
momentum vector I. In the present embodiment, and as illustrated in exemplary
orbital position 301 of Figure 3, a target inertial dipole vector M, can be
calculated
by taking the cross product of the magnetic field vector and the momentum
vector
x As shown in Figure 4, when the attitude of the spacecraft 100
is
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adjusted to bring the spacecraft dipole vector sifi, in alignment with the
target dipole
vector Mõ, the resulting torque :411,7, will be in a direction opposing
momentum vector
ri, effectively allowing the momentum of the spacecraft to be reduced.
Although in
the present embodiment a target dipole vector M, is used to determine a
desired
orientation of spacecraft 100, it is appreciated that other targets vectors
can be
used, and/or that other orientation algorithms can be applied, so long as the
torque
gni produced via dipole opposes the spacecraft momentum. For example, in some
embodiments, a target torque vector can be determined, and a desired
orientation
of the spacecraft can be determined in order to produce a torque g¨m aligned
with
the target torque vector.
[0056] As can be appreciated, in calculating a target inertial dipole vector
MI as
described above, a degree of freedom will remain, as the spacecraft 100 will
be
free to rotate about the M, vector while satisfying the condition that 712 and
M,
remain in alignment. Accordingly, in some embodiments, calculating a target
orientation can comprise a process of applying an additional constraint to
resolve
the remaining degree of freedom, and provide a unique solution for a desired
orientation of the spacecraft. For example, as illustrated in Figure 5, a Sun
vector
". can be applied as an additional constraint to resolve the degree of
freedom. In
the illustrated embodiment, the Sun vector S corresponds to an orientation of
the
spacecraft 100 (defined as a vector) which defines an optimal power and
thermal
body-frame direction, for example maximizing exposure of solar panels 105 to
the
Sun 500, while minimizing exposure of radiator 107 and/or batteries 109. It is
appreciated that this vector can vary according to the design of the
spacecraft 100
and/or mission-specific requirements. It is also appreciated that other
vectors or
constraints can be applied instead of Sun vector , such as an optimal antenna
pointing direction, or an optimal payload pointing direction, among others.
[0057] As shown in Figure 5, without applying an additional constraint, M,
provides a single body-frame-to-inertial-frame target which effectively allows
the
spacecraft 100 to orient itself in a plane 403 perpendicular to target dipole
vector
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Mi. The Sun vector ' provides a second body-frame-to-inertial-frame target
which
allows the spacecraft to orient itself in a plane 401 perpendicular to the Sun
vector
..s. Applying both the dipole vector Mt, and Sun vector S' body-frame-to-
inertial-frame
targets provides a triad solution which can give a single solution for a
desired
desaturation pointing attitude for the spacecraft. As illustrated in Figure 5,
this
essentially corresponds to the intersection between planes 401 and 403. As can
be appreciated, depending on the relative orientations of both body-frame-to-
inertial-frame targets, it may not be possible to fully respect both
constraints.
Therefore, in some embodiments, determining the desired desaturation pointing
attitude can comprise determining an orientation which corresponds to an exact
match to the body-to-inertial-frame spacecraft dipole vector /141, and a best-
fit
solution to the body-to-inertial-frame Sun vector S.
[0058] With reference now to Figure 9, a method 900 for reducing momentum of
a spacecraft is shown according to an embodiment. As will be appreciated, the
method 900 includes a number of processes which can be carried out by a
processor in a control system onboard the spacecraft. In some embodiments, the
method can be carried out autonomously by the processor, whereas in other
embodiments, the process can be commanded from the ground, for example
through the transmission of control signals to the satellite from a ground
control
station. In some embodiments, the control system can be programmed with
instructions to carry out the method 900 prior to launch, whereas in other
embodiments the spacecraft can be programmed with such instructions while in
space. Finally, it should be appreciated that although processes of method 900
are
described in a particular order, this is for exemplary purposes only, and some
processes can be carried out in a different order in other embodiments.
[0069] A first process 901 can comprise determining a magnetic dipole vector
Fri
describing a magnitude and direction of the magnetic dipole of the spacecraft.
In
some embodiments, the dipole of the spacecraft can be determined by measuring
the net dipole directly, for example on the ground prior to launch and/or
using a
duplicate model of the spacecraft, if available. In some embodiments, the
dipole
CA 3033612 2019-02-12
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can be determined while the spacecraft is in space and/or in orbit about a
celestial
body. As described above, as the spacecraft travels relative to an external or
ambient magnetic field, the external or ambient magnetic field will interact
with the
spacecraft's dipole to generate torque and impart momentum to the spacecraft.
Therefore, changes in the spacecraft's momentum can be monitored over a
trajectory, and these changes can be used to mathematically solve for the
spacecraft's momentum, provided the external or ambient magnetic field is
known
or measurable (ex: using a magnetometer, or a model of the magnetic field). It
is
appreciated, however, that other techniques for determining the spacecraft's
dipole
are also possible.
[0060] A second process 903 can comprise determining a momentum vector ii
describing the magnitude and direction of momentum stored in the spacecraft.
As
can be appreciated, the momentum can be measured using sensors onboard the
spacecraft, for example by measuring an angular rotation speed of each of the
reaction wheels, and by measuring an angular rotation speed of the
spacecraft's
body. In the present embodiment, the momentum vector ii is calculated as the
total momentum stored in the spacecraft, and therefore corresponds to the
total
momentum stored in both the reaction wheels and the spacecraft body. It is
appreciated that in other embodiments, the momentum vector H can be calculated
differently.
[0061] A third process 905 can comprise determining a target pointing vector,
describing an orientation of the spacecraft to produce a torque which opposes
ii.
As can be appreciated, the target pointing vector of the spacecraft is based
on a
desired interaction of dipole vector i with an ambient or external magnetic
field.
Accordingly, process 905 can comprise determining magnetic field vector
describing the magnitude and direction of the ambient or external magnetic
field
relative to the spacecraft. The magnetic field vector n can be measured using
a
magnetic field sensor onboard the spacecraft as described above, such as a
magnetometer and/or can be estimated using a position/orientation sensor in
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combination with a known model of the ambient or external magnetic field. As
can
be appreciated, the target pointing vector can be any vector which aligns the
spacecraft so as to produce the desired torque. In the present embodiment, the
target pointing vector corresponds to a target dipole vector M, defining a
desired
alignment of the spacecraft's dipole vector f ri when the spacecraft is
correctly
oriented. As described above, this can be calculated by taking a cross product
between the magnetic field vector -1-3 and the momentum vector II, and
resolving a
degree a freedom by applying a Sun vector S. It is appreciated that further
parameters can be taken into account when calculating the target orientation.
For
example, the target orientation can be limited to a predetermined amount
relative
to the spacecraft's current orientation. This can be useful, for example, to
avoid
changing the orientation of the spacecraft too rapidly and exceeding maximum
desired body rotation rates of the spacecraft. Accordingly, in this fashion,
the target
pointing direction can be said to be limited by a defined maximum body
rotation
rate of the spacecraft.
[00621 A fourth process 907 can comprise determining whether the spacecraft's
momentum is below a predetermined threshold. As can be appreciated, as the
spacecraft momentum is reduced to small levels, small perturbations in the
determined momentum vector ii caused by estimation error can have a
significant
impact on calculations to determine a target pointing vector of the
spacecraft.
Accordingly, corrective measures can be taken to avoid instabilities when the
spacecraft momentum is small. The threshold used for this purpose can vary in
different implementations and/or can be based on different parameters or
metrics
relating directly or indirectly to the momentum vector 11. For example, in the
present embodiment, determining whether the momentum vector ri is below a
predetermined threshold comprises calculating a metric /*actor corresponding
to
the ratio IFILI1/111111- If Mractor is not below a predetermined threshold,
the method
can continue normally. If m
¨factor is below the predetermined threshold, the control
objective can be no longer to dump momentum, but rather to avoid momentum
buildup. For this objective, a new target orientation can be used, aligning
the
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spacecraft dipole with the magnetic field to minimize the production of torque
and
maintain a low amplitude for the onboard momentum. As can be appreciated,
Mfactor will also be small when and ii are aligned, defining another
scenario
where the control objective can be to minimize momentum buildup to avoid
instabilities. Accordingly, the fourth process 907 can, in some embodiments,
comprise determining whether the magnetic field vector /3 and the momentum
vector if are substantially aligned.
[0063] By way of example, in the present embodiment, the control state of
avoiding momentum buildup comprises a fifth process 909 of orienting the
spacecraft to reduce the torque produced by the interaction between the
spacecraft's dipole and the external magnetic field. More specifically, this
can
involve orienting the spacecraft such that the spacecraft's dipole vector ill
is
substantially aligned with the magnetic field vector ri. In other words, in
the present
embodiment, this comprises setting the target dipole vector ivi, to be equal
to li .
When aligned in this fashion, the magnetic dipole and external magnetic field
should produce little or no torque on the spacecraft, thereby imparting no
further
substantial momentum to the spacecraft, and allowing the total momentum of the
spacecraft to remain at a minimal level. As can be appreciated, this allows
for the
spacecraft to be kept in a "parked" state indefinitely after the majority of
its
momentum has been unloaded. If sufficient momentum builds up again, the
method can continue as normal with the subsequent processes to unload the
excess momentum and return to a state where the momentum vector ii is at or
below the desired threshold. An exemplary simulation illustrating this process
of
parking the spacecraft is shown in Figure 7. During period 700, the spacecraft
is
desaturated as normal by orienting the spacecraft in a desaturation
orientation. In
period 701, once the momentum has been reduced below a predetermined
threshold, the spacecraft is oriented towards a parking orientation in which
the
momentum is maintained relatively constant, with only minor fluctuations.
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[0064] Although in the present embodiment a single threshold was described, it
is appreciated that two or more thresholds can be defined, for example to
define a
smoother transition between the targeted desaturating orientation and the
parking
orientation of the spacecraft and/or to allow for minor adjustments in the
spacecrafts orientation to prevent momentum from building up. For example, in
some embodiments, a first and second threshold can be defined. When the
momentum is below the first threshold, the spacecraft can be oriented in a
parking
orientation to reduce or eliminate torque created by interaction of the dipole
and
external magnetic field. When the momentum is above the second threshold, the
spacecraft can be oriented according to a desaturation orientation to produce
a
torque to oppose momentum in the spacecraft. When the momentum is between
the first and second thresholds, the target orientation of the spacecraft can
be set
somewhere between the parking and the desaturation orientation, depending on
how close the momentum is to the first or second threshold. In the present
embodiment, this can correspond to setting M, to ii when Mfactor is below the
first
threshold, keeping M, as is when factor .S m i
above the second threshold, and when
¨
Mfactor is between the first and second thresholds, rotating M, towards B
(i.e.
rotating M, in a plane defined by Mi A /4) as M, approaches the first
threshold. It is
appreciated, however, that other methods of transitioning between a parking
orientation and a desaturation orientation are also possible.
[0065] Once the target orientation of the spacecraft has been determined, a
subsequent process 911 can comprise positioning the spacecraft in the desired
orientation. This can be accomplished, for example, by operating the reaction
wheels (or other attitude adjustment actuators, such as thrusters,
magnetorquers,
etc.) to adjust the spacecraft's attitude as necessary. In this present
embodiment,
this comprises adjusting the attitude of the spacecraft such that dipole
vector in is
aligned with target dipole M,, in this case corresponding to an orientation
which
produces a torque opposing momentum vector ii. Once the spacecraft is
correctly
oriented, the produced torque will reduce the overall momentum of the
spacecraft.
Accordingly, the reaction wheels of the spacecraft can be desaturated in
process
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913, for example by slowing down the reaction wheels opposite the produced
torque.
[0066] As illustrated schematically in orbital positions 301 and 303 of Figure
3,
throughout the spacecraft's trajectory, for example in orbit around the Earth
350,
.. the external magnetic field vector 14 will change in the frame of reference
of the
body of spacecraft 100. Similarly, momentum vector ri will change as momentum
is unloaded. Accordingly, the processes of method 900 can be repeated
continuously and/or at regular intervals, to recalculate the target
orientation vector
of spacecraft (in the present embodiment NO as B and H change, and to reorient
the spacecraft as necessary, in order to maintain a desired alignment of the
spacecraft to produce a torque to reduce the momentum of the spacecraft and/or
maintain the spacecraft in a parked state with low momentum.
[0067] Although particular processes of method 900 were described above in
accordance with an exemplary embodiment, it is appreciated that in other
.. embodiments, some processes can be omitted, and that in other embodiments,
additional processes can be provided. For example, in some embodiments, in
addition to controlling the spacecraft orientation to produce a desired
torque, the
method can include processes for purposely manipulating the spacecraft's
dipole
to assist in producing the desired torque. This can apply, for example, when
one
or two torque rods are operable. Accordingly, in such methods, at least some
of
the spacecraft's momentum can be absorbed by a torque produced via the
spacecraft's residual dipole, while at least some of the remaining momentum
can
be absorbed via a controllable or variable dipole.
[0068] As can be appreciated, in the above-described method, it is assumed
that
the reaction wheels are able to fully absorb the spacecraft's momentum, such
that
they can be used to fully control the spacecraft's attitude and maintain a
desired
pointing direction. However, in some scenarios, the reaction wheels may be
oversaturated or hyper-saturated, and control authority of the spacecraft
would be
lost, such that it would not be possible to maintain the spacecraft in a
desired
CA 3033612 2019-02-12
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orientation. Accordingly, the spacecraft could be tumbling uncontrollably.
Accordingly, in some embodiments, a method can be provided to slowly
desaturate
the reaction wheels while tumbling (i.e. while control authority is lost)
until attitude
control can be regained, prior to performing the method 900.
[0069] An exemplary method 1000 for dumping momentum from a spacecraft in
the absence of control authority in the reaction wheels is shown in Figure 10.
In a
first process 1001, an optimal or desired orientation of the spacecraft can be
determined. In some embodiments, the optimal or desired orientation can
correspond to an orientation of the spacecraft which produces a torque which
at
least partially opposes the spacecraft's momentum. For example, the optimal
orientation can correspond to the target dipole vector M, as described above
in
method 900 and can be calculated in a similar fashion. It is appreciated,
however,
that the desired orientation can correspond to any orientation which produces
a
torque which can be useful in desaturating the reaction wheels of the
spacecraft.
[0070] Subsequent processes of method 1000 can involve using whatever control
measures are available in order to control the rate and/or direction of the
tumble (if
possible) to maximize the amount of time the spacecraft spends in an
orientation
in which the produced torque reduces the spacecraft's momentum (i.e. in a
favorable orientation) and minimize the amount of time the spacecraft spends
in
an orientation in which the produced torque increases the spacecraft's
momentum
(i.e. in an unfavorable orientation). For example, in the present embodiment,
this
can comprise a process 1003 of determining whether the spacecraft is rotating
towards the optimal orientation. In the negative, the tumbling of the
spacecraft can
be accelerated in process 1005, for example by slowing down the reaction
wheels
to transfer momentum to the body of spacecraft. In the affirmative, the
tumbling of
the spacecraft can be decelerated in process 1007, for example by speeding up
the reaction wheels to absorb momentum from the body of spacecraft. The
resulting effect, as illustrated in the simulation of Figure 6, is that the
spacecraft
will spend more time in a favorable orientation 600 (ex: angle between 00 and
90
relative to the optimal orientation) compared to an unfavorable orientation
601 (ex:
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angle between 900 and 180 relative to the optimal orientation), with a net
result of
the spacecraft's momentum being reduced over time. Although a particular
method
for controlling tumbling has been described, it is appreciated that other
methods
are possible, so long as the net effect is that the net torque applied is one
that
reduces the spacecraft's overall momentum. In processes 1009 and 1011, while
the spacecraft is in the favorable orientation 600, the reaction wheels can be
desaturated. The processes of method 1000 can be repeated until the reaction
wheels have been sufficiently desaturated to regain attitude control authority
and
use attitude control functionality to remove the spacecraft from the tumbling
state
by transferring momentum from the body into the reaction wheels.
[0071] As can be appreciated, the above-described methods can be used as
needed during different control states of spacecraft operation to desaturate
as
necessary. By way of example, a method 1100 for operating a spacecraft is
shown
in Figure 11. In the illustrated method, a first process 1101 can comprise
determining whether the reaction wheels have the control authority to absorb
the
spacecraft's total momentum. In the negative, the spacecraft can be operated
in a
state in which desaturation is performed in a tumbling state, for example
according
to the method 1000 described above. As shown in period 800 of the simulation
of
Figure 8, the spacecraft can remain in this state for an extended period of
time until
the total momentum of the spacecraft has been reduced to an acceptable amount.
Once attitude control has been restored, the spacecraft can be operated in a
more
optimal desaturation state, in which attitude control is leveraged to more
optimally
reduce total spacecraft momentum to near zero, for example according to the
method 900 described above. As shown in period 801 of the simulation of Figure
8, the spacecraft can remain in the desaturation state until total spacecraft
momentum is near zero. With total momentum at minimal levels, a subsequent
process 1103 can comprise operating the spacecraft normally, orienting the
spacecraft according to its nominal mission requirements. As can be
appreciated,
this can vary according to the function of spacecraft. For example, in the
present
embodiment, it can comprise operating the spacecraft in a fine pointing mode
to
point the spacecraft's telescope at a desired target in the context of a
scientific
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mission. As can be appreciated, and as illustrated in period 802 of Figure 8,
the
spacecraft momentum can fluctuate during this period, with an overall gain of
momentum absorbed by the reaction wheels, resulting in resaturation thereof.
Accordingly, in process 1105, it can be determined that the reaction wheels
are
approaching saturation levels, and the spacecraft can be transitioned back
into a
desaturation state 900. As illustrated in period 803 of Figure 8, this will
again
desaturate the reaction wheels and reduce overall spacecraft momentum to
minimal levels, eventually allowing the spacecraft to resume normal
operation 1103.
[0072] As can be appreciated, the above described methods and corresponding
systems can provide many advantages compared to methods and systems of the
prior art. For example, the methods and systems can allow for spacecraft
control
without the use of torque rods and/or with only partial use of torque rods.
This can
allow for spacecraft recovery in case of total or partial torque rod failure,
can allow
for more efficient spacecraft design by allowing for the omission of torque
rods,
and/or can provide means to control a spacecraft while avoiding the use of
energy-
demanding torque rods. Of course, many other advantages will be apparent to
one
skilled in the art upon reading the present disclosure.
[0073] While the above description provides examples of embodiments, it will
be
appreciated that some features and/or functions of the described embodiments
are
susceptible to modification without departing from the spirit and principles
of
operation of the described embodiments. Accordingly, what has been described
above has been intended to be illustrative and non-limiting and it will be
understood
by persons skilled in the art that other variants and modifications may be
made
without departing from the scope of the invention as defined in the claims
appended hereto.
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