195:
de-spin antennas or optical instruments that must be pointed at targets for science observations or communications with Earth. Three-axis controlled craft can point optical instruments and antennas without having to de-spin them, but they may have to carry out special rotating maneuvers to best utilize their fields and particle instruments. If thrusters are used for routine stabilization, optical observations such as imaging must be designed knowing that the spacecraft is always slowly rocking back and forth, and not always exactly predictably. Reaction wheels provide a much steadier spacecraft from which to make observations, but they add mass to the spacecraft, they have a limited mechanical lifetime, and they require frequent momentum desaturation maneuvers, which can perturb navigation solutions because of accelerations imparted by the use of thrusters.
364:
which allows for the unity constraint on the quaternion to be better handled. It is also common to use a technique known as dynamic model replacement, where the angular rate is not estimated directly, but rather the measured angular rate from the gyro is used directly to propagate the rotational dynamics forward in time. This is valid for most applications as gyros are typically far more precise than one's knowledge of disturbance torques acting on the system (which is required for precise estimation of the angular rate).
1298:
266:. A rotation matrix, on the other hand, provides a full description of the attitude at the expense of requiring nine values instead of three. The use of a rotation matrix can lead to increased computational expense and they can be more difficult to work with. Quaternions offer a decent compromise in that they do not suffer from gimbal lock and only require four values to fully describe the attitude.
270:
180:, must be occasionally removed from the system by applying controlled torque to the spacecraft to allowing the wheels to return to a desired speed under computer control. This is done during maneuvers called momentum desaturation or momentum unload maneuvers. Most spacecraft use a system of thrusters to apply the torque for desaturation maneuvers. A different approach was used by the
1544:. Conversely, by inducing a counter-current, using solar cell power, the orbit may be raised. Due to massive variability in Earth's magnetic field from an ideal radial field, control laws based on torques coupling to this field will be highly non-linear. Moreover, only two-axis control is available at any given time meaning that a vehicle reorient may be necessary to null all rates.
1591:
1577:
1383:(proportional to exhaust velocity) and the smallest torque impulse it can provide (which determines how often the thrusters must fire to provide precise control). Thrusters must be fired in one direction to start rotation, and again in the opposing direction if a new orientation is to be held. Thruster systems have been used on most crewed space vehicles, including
2128:
224:
can compute the proper direction to point the appendages. It logically falls to the same subsystem – the
Attitude and Articulation Control Subsystem (AACS), then, to manage both attitude and articulation. The name AACS may even be carried over to a spacecraft even if it has no appendages to articulate.
1115:
where a crystal cup shaped like a wine glass can be driven into oscillation just as a wine glass "sings" as a finger is rubbed around its rim. The orientation of the oscillation is fixed in inertial space, so measuring the orientation of the oscillation relative to the spacecraft can be used to sense
175:
back and forth between spacecraft and wheels. To rotate the vehicle on a given axis, the reaction wheel on that axis is accelerated in the opposite direction. To rotate the vehicle back, the wheel is slowed. Excess momentum that builds up in the system due to external torques from, for example, solar
1564:
technology demonstration. In low Earth orbit, the force due to drag is many orders of magnitude more dominant than the force imparted due to gravity gradients. When a satellite is utilizing aerodynamic passive attitude control, air molecules from the Earth's upper atmosphere strike the satellite in
223:
main engine nozzles were steerable. Knowing where to point a solar panel, or scan platform, or a nozzle — that is, how to articulate it — requires knowledge of the spacecraft's attitude. Because a single subsystem keeps track of the spacecraft's attitude, the Sun's location, and Earth's location, it
194:
There are advantages and disadvantages to both spin stabilization and three-axis stabilization. Spin-stabilized craft provide a continuous sweeping motion that is desirable for fields and particles instruments, as well as some optical scanning instruments, but they may require complicated systems to
88:
may be accurately pointed to Earth for communications, so that onboard experiments may accomplish precise pointing for accurate collection and subsequent interpretation of data, so that the heating and cooling effects of sunlight and shadow may be used intelligently for thermal control, and also for
1557:
hysteretic materials or a viscous damper. The viscous damper is a small can or tank of fluid mounted in the spacecraft, possibly with internal baffles to increase internal friction. Friction within the damper will gradually convert oscillation energy into heat dissipated within the viscous damper.
1466:
to provide attitude control. Although a CMG provides control about the two axes orthogonal to the gyro spin axis, triaxial control still requires two units. A CMG is a bit more expensive in terms of cost and mass, because gimbals and their drive motors must be provided. The maximum torque (but not
363:
could be used, and can provide benefits in cases where the initial estimate is poor). Multiple methods have been proposed, however the
Multiplicative Extended Kalman Filter (MEKF) is by far the most common approach. This approach utilizes the multiplicative formulation of the error quaternion,
114:
Spin stabilization is accomplished by setting the spacecraft spinning, using the gyroscopic action of the rotating spacecraft mass as the stabilizing mechanism. Propulsion system thrusters are fired only occasionally to make desired changes in spin rate, or in the spin-stabilized attitude. If
1552:
Three main types of passive attitude control exist for satellites. The first one uses gravity gradient, and it leads to four stable states with the long axis (axis with smallest moment of inertia) pointing towards Earth. As this system has four stable states, if the satellite has a preferred
1511:. The upper end of the vehicle feels less gravitational pull than the lower end. This provides a restoring torque whenever the long axis is not co-linear with the direction of gravity. Unless some means of damping is provided, the spacecraft will oscillate about the local vertical. Sometimes
1556:
The second passive system orients the satellite along Earth's magnetic field thanks to a magnet. These purely passive attitude control systems have limited pointing accuracy, because the spacecraft will oscillate around energy minima. This drawback is overcome by adding damper, which can be
1485:
Small solar sails (devices that produce thrust as a reaction force induced by reflecting incident light) may be used to make small attitude control and velocity adjustments. This application can save large amounts of fuel on a long-duration mission by producing control moments without fuel
1091:
Many sensors generate outputs that reflect the rate of change in attitude. These require a known initial attitude, or external information to use them to determine attitude. Many of this class of sensor have some noise, leading to inaccuracies if not corrected by absolute attitude sensors.
1565:
such a way that the center of pressure remains behind the center of mass, similar to how the feathers on an arrow stabilize the arrow. GASPACS utilized a 1 m inflatable 'AeroBoom', which extended behind the satellite, creating a stabilizing torque along the satellite's velocity vector.
213:, for example, were designed with scan platforms for pointing optical instruments at their targets largely independently of spacecraft orientation. Many spacecraft, such as Mars orbiters, have solar panels that must track the Sun so they can provide electrical power to the spacecraft.
945:
Another important and common control algorithm involves the concept of detumbling, which is attenuating the angular momentum of the spacecraft. The need to detumble the spacecraft arises from the uncontrollable state after release from the launch vehicle. Most spacecraft in
1432:
driven rotors made to spin in the direction opposite to that required to re-orient the vehicle. Because momentum wheels make up a small fraction of the spacecraft's mass and are computer controlled, they give precise control. Momentum wheels are generally suspended on
1506:
In orbit, a spacecraft with one axis much longer than the other two will spontaneously orient so that its long axis points at the planet's center of mass. This system has the virtue of needing no active control system or expenditure of fuel. The effect is caused by a
383:, to complex nonlinear estimators or many in-between types, depending on mission requirements. Typically, the attitude control algorithms are part of the software running on the computer hardware, which receives commands from the ground and formats vehicle data
566:
1467:
the maximum angular momentum change) exerted by a CMG is greater than for a momentum wheel, making it better suited to large spacecraft. A major drawback is the additional complexity, which increases the number of failure points. For this reason, the
1370:
are the most common actuators, as they may be used for station keeping as well. Thrusters must be organized as a system to provide stabilization about all three axes, and at least two thrusters are generally used in each axis to provide torque as a
242:
it occupies. Attitude and position fully describe how an object is placed in space. (For some applications such as in robotics and computer vision, it is customary to combine position and attitude together into a single description known as
319:
systems allows for precise position knowledge to be obtained easily. This problem becomes more complicated for deep space vehicles, or terrestrial vehicles operating in Global
Navigation Satellite System (GNSS) denied environments (see
298:) from a set of measurements (often using different sensors). This can be done either statically (calculating the attitude using only the measurements currently available), or through the use of a statistical filter (most commonly, the
1234:
uses a horizon sensor to sense the direction to Earth's center, and a gyro to sense rotation about an axis normal to the orbit plane. Thus, the horizon sensor provides pitch and roll measurements, and the gyro provides yaw. See
310:
For some sensors and applications (such as spacecraft using magnetometers) the precise location must also be known. While pose estimation can be employed, for spacecraft it is usually sufficient to estimate the position (via
71:
to command the actuators based on (1) sensor measurements of the current attitude and (2) specification of a desired attitude. The integrated field that studies the combination of sensors, actuators and algorithms is called
394:, most spacecraft make use of active control which exhibits a typical attitude control loop. The design of the control algorithm depends on the actuator to be used for the specific attitude maneuver although using a simple
937:
850:
763:
1214:. This sensor provides orientation with respect to Earth about two orthogonal axes. It tends to be less precise than sensors based on stellar observation. Sometimes referred to as an Earth sensor.
669:
408:
The appropriate commands to the actuators are obtained based on error signals described as the difference between the measured and desired attitude. The error signals are commonly measured as
390:
The attitude control algorithms are written and implemented based on requirement for a particular attitude maneuver. Asides the implementation of passive attitude control such as the
379:
that receive data from vehicle sensors and derive the appropriate commands to the actuators to rotate the vehicle to the desired attitude. The algorithms range from very simple, e.g.
1536:
exert a moment against the local magnetic field. This method works only where there is a magnetic field against which to react. One classic field "coil" is actually in the form of a
426:
262:. While Euler angles are oftentimes the most straightforward representation to visualize, they can cause problems for highly-maneuverable systems because of a phenomenon known as
1809:
294:
Before attitude control can be performed, the current attitude must be determined. Attitude cannot be measured directly by any single measurement, and so must be calculated (or
2009:
1004:
1515:
are used to connect two parts of a satellite, to increase the stabilizing torque. A problem with such tethers is that meteoroids as small as a grain of sand can part them.
1076:
1379:
to the vehicle. Their limitations are fuel usage, engine wear, and cycles of the control valves. The fuel efficiency of an attitude control system is determined by its
1341:
strength and, when used in a three-axis triad, magnetic field direction. As a spacecraft navigational aid, sensed field strength and direction is compared to a map of
596:
1444:
To maintain orientation in three dimensional space a minimum of three reaction wheels must be used, with additional units providing single failure protection. See
678:
making use of either momentum or reaction wheels as actuators. Based on the change in momentum of the wheels, the control law can be defined in 3-axes x, y, z as
1047:
1027:
616:
1410:
To minimize the fuel limitation on mission duration, auxiliary attitude control systems may be used to reduce vehicle rotation to lower levels, such as small
352:
302:) that statistically combine previous attitude estimates with current sensor measurements to obtain an optimal estimate of the current attitude.
141:
is an alternative method of spacecraft attitude control in which the spacecraft is held fixed in the desired orientation without any rotation.
1211:
1323:(s) or a camera. It uses magnitude of brightness and spectral type to identify and then calculate the relative position of stars around it.
2148:
2132:
1180:
351:
Kalman filtering can be used to sequentially estimate the attitude, as well as the angular rate. Because attitude dynamics (combination of
355:
and attitude kinematics) are non-linear, a linear Kalman filter is not sufficient. Because attitude dynamics is not very non-linear, the
1813:
84:
A spacecraft's attitude must typically be stabilized and controlled for a variety of reasons. It is often needed so that the spacecraft
1560:
A third form of passive attitude control is aerodynamic stabilization. This is achieved using a drag gradient, as demonstrated on the
1345:
stored in the memory of an on-board or ground-based guidance computer. If spacecraft position is known then attitude can be inferred.
858:
771:
684:
2016:
1742:
1112:
1107:
without reliance on the observation of external objects. Classically, a gyroscope consists of a spinning mass, but there are also "
1910:
73:
171:, also called momentum wheels, which are mounted on three orthogonal axes aboard the spacecraft. They provide a means to trade
2153:
1501:
391:
621:
2168:
2163:
1604:
1176:
1129:
315:) separate from the attitude estimation. For terrestrial vehicles and spacecraft operating near the Earth, the advent of
337:
1553:
orientation, e.g. a camera pointed at the planet, some way to flip the satellite and its tether end-for-end is needed.
1468:
1194:
This class of sensors sense the position or orientation of fields, objects or other phenomena outside the spacecraft.
49:
958:
or torque rods as control actuators. The control law is based on the measurement of the rate of change of body-fixed
1757:
Crassidis, John L.; Markley, F. Landis (May 23, 2012). "Unscented
Filtering for Spacecraft Attitude Estimation".
1342:
1230:
to sense local gravity and force its gyro into alignment with Earth's spin vector, and therefore point north, an
1151:
1125:
951:
1457:
35:
1540:
in a planetary magnetic field. Such a conductive tether can also generate electrical power, at the expense of
561:{\displaystyle T_{c}(t)=K_{\text{p}}e(t)+K_{\text{i}}\int _{0}^{t}e(\tau )\,d\tau +K_{\text{d}}{\dot {e}}(t),}
420:. The PID controller which is most common reacts to an error signal (deviation) based on attitude as follows
164:
employ this method, and have used up about three quarters of their 100 kg of propellant as of July 2015.
1838:
1614:
1362:
1104:
360:
149:
1376:
1302:
1210:
sensing is often used, which senses the comparative warmth of the atmosphere, compared to the much colder
1133:
356:
278:
244:
181:
1206:
is an optical instrument that detects light from the 'limb' of Earth's atmosphere, i.e., at the horizon.
148:
of allowed attitude error. Thrusters may also be referred to as mass-expulsion control (MEC) systems, or
1609:
1537:
1164:
2066:
1953:
1876:
1681:
1529:
1108:
380:
316:
209:
1784:
968:
214:
1396:
1384:
1146:
312:
233:
1634:
144:
One method is to use small thrusters to continually nudge the spacecraft back and forth within a
2084:
1941:
1892:
1596:
1400:
1372:
282:
110:
1414:
that accelerate ionized gases electrically to extreme velocities, using power from solar cells.
1052:
333:
1305:
2012, a high-altitude balloon-borne cosmology experiment launched from
Antarctica on 2012-12-29
1738:
1533:
1524:
1512:
1236:
295:
185:
184:, which had sensitive optics that could be contaminated by thruster exhaust, and instead used
85:
2074:
1961:
1884:
1766:
1730:
1434:
1380:
1367:
1297:
955:
413:
376:
177:
172:
53:
17:
1289:, but Earth sensors are still integrated in satellites for their low cost and reliability.
574:
2158:
2079:
2054:
1582:
1388:
1282:
1140:
947:
251:
239:
204:
31:
2040:
2070:
1957:
1880:
1725:
Markley, F. Landis; Crassidis, John L. (2014), "Static
Attitude Determination Methods",
1438:
1429:
1423:
1392:
1338:
1111:" utilizing coherent light reflected around a closed path. Another type of "gyro" is a
1032:
1012:
674:
A simple implementation of this can be the application of the proportional control for
601:
395:
168:
1918:
336:. Many solutions have been proposed, notably Davenport's q-method, QUEST, TRIAD, and
2142:
2088:
1896:
1541:
1404:
299:
167:
Another method for achieving three-axis stabilization is to use electrically powered
116:
97:
Attitude control of spacecraft is maintained using one of two principal approaches:
2102:
1445:
1411:
1333:
1311:
1286:
959:
409:
259:
250:
Attitude can be described using a variety of methods; however, the most common are
2055:"Studying the Effects of Disturbance Torques on a 2U CubeSat in Low Earth Orbits"
1734:
1508:
1223:
950:(LEO) makes use of magnetic detumbling concept which utilizes the effect of the
263:
1703:
1492:
adjusted its attitude using its solar cells and antennas as small solar sails.
1987:
1888:
1656:
1572:
1488:
1480:
1258:
1249:
417:
372:
321:
274:
255:
127:
121:
89:
guidance: short propulsive maneuvers must be executed in the right direction.
68:
45:
67:
to apply the torques needed to orient the vehicle to a desired attitude, and
1864:
1320:
1262:
1100:
384:
269:
160:
154:
131:
probes in the outer Solar System are examples of spin-stabilized spacecraft.
64:
359:
is usually sufficient (however
Crassidis and Markely demonstrated that the
2127:
2010:"Investigation of Pulsed Plasma Thrusters for Spacecraft Attitude Control"
1660:
1227:
1207:
412:(Φ, θ, Ψ), however an alternative to this could be described in terms of
145:
115:
desired, the spinning may be stopped through the use of thrusters or by
2041:
Attitude and
Determination Control Systems for the OUFTI nanosatellites
1561:
60:
1965:
343:
Crassidis, John L., and John L. Junkins.. Chapman and Hall/CRC, 2004.
238:
Attitude is part of the description of how an object is placed in the
1463:
1301:
The STARS real-time star tracking software operates on an image from
954:. The control algorithm is called the B-Dot controller and relies on
1029:
is the commanded magnetic dipole moment of the magnetic torquer and
1988:
Magnetically suspended momentum wheels for spacecraft stabilization
1770:
1353:
Attitude control can be obtained by several mechanisms, including:
1296:
1278:
1136:. They have applications outside the aeronautical field, such as:
675:
268:
30:"Attitude control" redirects here. For the use in psychology, see
1914:
1316:
932:{\displaystyle T_{c}z=-K_{\text{q3}}q_{3}+K_{\text{w3}}{w_{z}},}
845:{\displaystyle T_{c}y=-K_{\text{q2}}q_{2}+K_{\text{w2}}{w_{y}},}
758:{\displaystyle T_{c}x=-K_{\text{q1}}q_{1}+K_{\text{w1}}{w_{x}},}
1254:
2103:"GASPACS Get Away Special Passive Attitude Control Satellite"
1727:
Fundamentals of
Spacecraft Attitude Determination and Control
1562:
Get Away
Special Passive Attitude Control Satellite (GASPACS)
1437:
to avoid bearing friction and breakdown problems. Spacecraft
1116:
the motion of the spacecraft with respect to inertial space.
1986:
Henrikson, C.H.; Lyman, J.; Studer, P.A. (January 1, 1974).
1471:
uses a set of four CMGs to provide dual failure tolerance.
203:
Many spacecraft have components that require articulation.
1657:"Basics of Space Flight Section II. Space Flight Projects"
27:
Process of controlling orientation of an aerospace vehicle
1128:
with single- or multi-axis motion sensors. They utilize
1315:
is an optical device that measures the position(s) of
942:
This control algorithm also affects momentum dumping.
664:{\displaystyle K_{\text{p}},K_{\text{i}},K_{\text{d}}}
1706:. Basics of Spaceflight Section II (Report). NASA JPL
1285:; nowadays the main method to detect attitude is the
1078:
is the rate of change of the Earth's magnetic field.
1055:
1035:
1015:
971:
861:
774:
687:
624:
604:
577:
429:
1462:
These are rotors spun at constant speed, mounted on
332:
Static attitude estimation methods are solutions to
1157:
High speed craft motion control and damping systems
44:is the process of controlling the orientation of a
1070:
1041:
1021:
998:
931:
844:
757:
663:
610:
590:
560:
1132:. Some multi-axis MRUs are capable of measuring
1833:
1831:
1253:is a device that senses the direction to the
8:
397:proportional–integral–derivative controller
56:, certain fields, and nearby objects, etc.
48:(vehicle or satellite) with respect to an
2078:
1759:Journal of Guidance, Control and Dynamics
1277:is a device that senses the direction to
1261:and shades, or as complex as a steerable
1175:Orientation and attitude measurements on
1057:
1056:
1054:
1034:
1014:
985:
984:
970:
919:
914:
908:
895:
885:
866:
860:
832:
827:
821:
808:
798:
779:
773:
745:
740:
734:
721:
711:
692:
686:
655:
642:
629:
623:
603:
582:
576:
535:
534:
528:
514:
496:
491:
481:
456:
434:
428:
1865:"Gyrocompass for Orbital Space Vehicles"
34:. For attitude control of aircraft, see
1812:. Kongsberg Maritime AS. Archived from
1729:, Springer New York, pp. 183–233,
1626:
618:is the attitude deviation signal, and
1222:Similar to the way that a terrestrial
387:for transmission to a ground station.
59:Controlling vehicle attitude requires
2059:Journal of Physics: Conference Series
2043:. Vincent Francois-Lavet (2010-05-31)
2015:. Erps.spacegrant.org. Archived from
1704:"Chapter 11. Typical Onboard Systems"
1441:often use mechanical ball bearings.
1265:, depending on mission requirements.
1181:Remotely operated underwater vehicles
1143:motion compensation and stabilization
1124:Motion reference units are a kind of
7:
1172:Offshore structure motion monitoring
2053:Mohammad Nusrat Aman, Asma (2019).
1103:are devices that sense rotation in
671:are the PID controller parameters.
1163:Motion compensation of single and
328:Static attitude estimation methods
25:
1940:Acuña, Mario H. (November 2002).
2126:
1946:Review of Scientific Instruments
1839:Spacecraft Earth Horizon Sensors
1589:
1575:
1375:in order to prevent imparting a
1257:. This can be as simple as some
74:guidance, navigation and control
63:to measure vehicle orientation,
2080:10.1088/1742-6596/1152/1/012024
1785:"Hemispherical Resonator Gyros"
1532:or (on very small satellites)
1502:Gravity-gradient stabilization
1496:Gravity-gradient stabilization
1177:Autonomous underwater vehicles
999:{\displaystyle m=-K{\dot {B}}}
552:
546:
511:
505:
471:
465:
446:
440:
405:satisfies most control needs.
392:gravity-gradient stabilization
52:or another entity such as the
1:
1844:(Report). NASA. December 1969
1605:Longitudinal static stability
1049:is the proportional gain and
347:Sequential estimation methods
1113:hemispherical resonator gyro
338:singular value decomposition
18:3-axis stabilized spacecraft
2149:Spacecraft attitude control
2133:Spacecraft attitude control
1942:"Space-based magnetometers"
1735:10.1007/978-1-4939-0802-8_5
1469:International Space Station
368:Attitude control algorithms
188:for desaturation maneuvers.
50:inertial frame of reference
42:Spacecraft attitude control
2185:
1917:. May 2004. Archived from
1522:
1499:
1486:expenditure. For example,
1478:
1455:
1421:
1360:
1160:Hydro acoustic positioning
1134:roll, pitch, yaw and heave
1071:{\displaystyle {\dot {B}}}
273:Changing orientation of a
231:
108:
29:
1889:10.1134/S0010952521030011
1190:Absolute attitude sensors
1126:inertial measurement unit
1087:Relative attitude sensors
1682:"Voyager Weekly Reports"
1548:Passive attitude control
1458:Control moment gyroscope
1418:Reaction/momentum wheels
1337:is a device that senses
152:(RCS). The space probes
150:reaction control systems
137:Three-axis stabilization
36:Aircraft flight dynamics
1863:Abezyaev, I.N. (2021).
1615:Reaction control system
1363:Reaction control system
1169:Ocean wave measurements
1105:three-dimensional space
598:is the control torque,
361:Unscented Kalman filter
1637:. NASA. March 26, 2007
1635:"The Pioneer Missions"
1343:Earth's magnetic field
1306:
1185:Ship motion monitoring
1165:multibeam echosounders
1120:Motion reference units
1072:
1043:
1023:
1000:
952:Earth's magnetic field
933:
846:
759:
665:
612:
592:
562:
357:Extended Kalman filter
290:Attitude determination
286:
182:Hubble Space Telescope
93:Types of stabilization
2154:Aerospace engineering
1790:. Northropgrumman.com
1610:Directional stability
1300:
1073:
1044:
1024:
1001:
934:
847:
760:
666:
613:
593:
591:{\displaystyle T_{c}}
563:
272:
2169:Dynamics (mechanics)
2164:Spaceflight concepts
2135:at Wikimedia Commons
1452:Control moment gyros
1428:Momentum wheels are
1053:
1033:
1013:
969:
859:
772:
685:
622:
602:
575:
427:
381:proportional control
317:Satellite navigation
2071:2019JPhCS1152a2024N
1958:2002RScI...73.3717A
1881:2021CosRe..59..204A
1281:. It is usually an
1232:orbital gyrocompass
1218:Orbital gyrocompass
1147:Dynamic positioning
501:
353:rigid body dynamics
313:Orbit determination
234:Attitude (geometry)
176:photon pressure or
1810:"MRU Applications"
1597:Spaceflight portal
1307:
1154:of offshore cranes
1152:Heave compensation
1068:
1039:
1019:
996:
929:
842:
755:
661:
608:
588:
558:
487:
373:Control algorithms
287:
111:Spin stabilization
104:Spin stabilization
2131:Media related to
2022:on April 22, 2014
1966:10.1063/1.1510570
1952:(11): 3717–3736.
1538:conductive tether
1534:permanent magnets
1525:Magnetic torquers
1519:Magnetic torquers
1435:magnetic bearings
1368:Vernier thrusters
1237:Tait-Bryan angles
1212:cosmic background
1065:
1042:{\displaystyle K}
1022:{\displaystyle m}
993:
911:
888:
824:
801:
737:
714:
658:
645:
632:
611:{\displaystyle e}
543:
531:
484:
459:
377:computer programs
306:Position/location
252:Rotation matrices
186:magnetic torquers
178:gravity gradients
86:high-gain antenna
16:(Redirected from
2176:
2130:
2114:
2113:
2111:
2109:
2099:
2093:
2092:
2082:
2050:
2044:
2038:
2032:
2031:
2029:
2027:
2021:
2014:
2006:
2000:
1999:
1997:
1995:
1983:
1977:
1976:
1974:
1972:
1937:
1931:
1930:
1928:
1926:
1921:on July 21, 2011
1907:
1901:
1900:
1860:
1854:
1853:
1851:
1849:
1843:
1835:
1826:
1825:
1823:
1821:
1816:on April 2, 2016
1806:
1800:
1799:
1797:
1795:
1789:
1781:
1775:
1774:
1754:
1748:
1747:
1722:
1716:
1715:
1713:
1711:
1700:
1694:
1693:
1691:
1689:
1678:
1672:
1671:
1669:
1667:
1653:
1647:
1646:
1644:
1642:
1631:
1599:
1594:
1593:
1592:
1585:
1580:
1579:
1578:
1381:specific impulse
1208:Thermal infrared
1109:ring laser gyros
1077:
1075:
1074:
1069:
1067:
1066:
1058:
1048:
1046:
1045:
1040:
1028:
1026:
1025:
1020:
1005:
1003:
1002:
997:
995:
994:
986:
938:
936:
935:
930:
925:
924:
923:
913:
912:
909:
900:
899:
890:
889:
886:
871:
870:
851:
849:
848:
843:
838:
837:
836:
826:
825:
822:
813:
812:
803:
802:
799:
784:
783:
764:
762:
761:
756:
751:
750:
749:
739:
738:
735:
726:
725:
716:
715:
712:
697:
696:
670:
668:
667:
662:
660:
659:
656:
647:
646:
643:
634:
633:
630:
617:
615:
614:
609:
597:
595:
594:
589:
587:
586:
567:
565:
564:
559:
545:
544:
536:
533:
532:
529:
500:
495:
486:
485:
482:
461:
460:
457:
439:
438:
416:matrix or error
414:direction cosine
220:
173:angular momentum
139:
138:
106:
105:
54:celestial sphere
21:
2184:
2183:
2179:
2178:
2177:
2175:
2174:
2173:
2139:
2138:
2123:
2118:
2117:
2107:
2105:
2101:
2100:
2096:
2052:
2051:
2047:
2039:
2035:
2025:
2023:
2019:
2012:
2008:
2007:
2003:
1993:
1991:
1985:
1984:
1980:
1970:
1968:
1939:
1938:
1934:
1924:
1922:
1909:
1908:
1904:
1869:Cosmic Research
1862:
1861:
1857:
1847:
1845:
1841:
1837:
1836:
1829:
1819:
1817:
1808:
1807:
1803:
1793:
1791:
1787:
1783:
1782:
1778:
1756:
1755:
1751:
1745:
1724:
1723:
1719:
1709:
1707:
1702:
1701:
1697:
1687:
1685:
1680:
1679:
1675:
1665:
1663:
1655:
1654:
1650:
1640:
1638:
1633:
1632:
1628:
1623:
1595:
1590:
1588:
1583:Aviation portal
1581:
1576:
1574:
1571:
1550:
1527:
1521:
1504:
1498:
1483:
1477:
1460:
1454:
1439:Reaction wheels
1426:
1420:
1365:
1359:
1351:
1329:
1295:
1283:infrared camera
1271:
1245:
1220:
1200:
1192:
1130:MEMS gyroscopes
1122:
1098:
1089:
1084:
1051:
1050:
1031:
1030:
1011:
1010:
967:
966:
948:low Earth orbit
915:
904:
891:
881:
862:
857:
856:
828:
817:
804:
794:
775:
770:
769:
741:
730:
717:
707:
688:
683:
682:
651:
638:
625:
620:
619:
600:
599:
578:
573:
572:
524:
477:
452:
430:
425:
424:
370:
349:
334:Wahba's problem
330:
308:
292:
285:attached to it.
283:reference frame
277:is the same as
236:
230:
218:
201:
169:reaction wheels
136:
135:
113:
103:
102:
95:
82:
39:
32:Attitude change
28:
23:
22:
15:
12:
11:
5:
2182:
2180:
2172:
2171:
2166:
2161:
2156:
2151:
2141:
2140:
2137:
2136:
2122:
2121:External links
2119:
2116:
2115:
2094:
2045:
2033:
2001:
1990:(Report). NASA
1978:
1932:
1902:
1875:(3): 204–211.
1855:
1827:
1801:
1776:
1771:10.2514/2.5102
1765:(4): 536–542.
1749:
1743:
1717:
1695:
1673:
1648:
1625:
1624:
1622:
1619:
1618:
1617:
1612:
1607:
1601:
1600:
1586:
1570:
1567:
1549:
1546:
1523:Main article:
1520:
1517:
1500:Main article:
1497:
1494:
1479:Main article:
1476:
1473:
1456:Main article:
1453:
1450:
1430:electric motor
1424:Momentum wheel
1422:Main article:
1419:
1416:
1361:Main article:
1358:
1355:
1350:
1347:
1339:magnetic field
1328:
1325:
1294:
1291:
1270:
1267:
1244:
1241:
1219:
1216:
1204:horizon sensor
1199:
1198:Horizon sensor
1196:
1191:
1188:
1187:
1186:
1183:
1173:
1170:
1167:
1161:
1158:
1155:
1149:
1144:
1121:
1118:
1097:
1094:
1088:
1085:
1083:
1080:
1064:
1061:
1038:
1018:
1007:
1006:
992:
989:
983:
980:
977:
974:
956:magnetic coils
940:
939:
928:
922:
918:
907:
903:
898:
894:
884:
880:
877:
874:
869:
865:
853:
852:
841:
835:
831:
820:
816:
811:
807:
797:
793:
790:
787:
782:
778:
766:
765:
754:
748:
744:
733:
729:
724:
720:
710:
706:
703:
700:
695:
691:
676:nadir pointing
654:
650:
641:
637:
628:
607:
585:
581:
569:
568:
557:
554:
551:
548:
542:
539:
527:
523:
520:
517:
513:
510:
507:
504:
499:
494:
490:
480:
476:
473:
470:
467:
464:
455:
451:
448:
445:
442:
437:
433:
401:PID controller
369:
366:
348:
345:
329:
326:
307:
304:
291:
288:
281:the axes of a
232:Main article:
229:
226:
200:
197:
192:
191:
190:
189:
165:
132:
109:Main article:
94:
91:
81:
78:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2181:
2170:
2167:
2165:
2162:
2160:
2157:
2155:
2152:
2150:
2147:
2146:
2144:
2134:
2129:
2125:
2124:
2120:
2104:
2098:
2095:
2090:
2086:
2081:
2076:
2072:
2068:
2065:(1): 012024.
2064:
2060:
2056:
2049:
2046:
2042:
2037:
2034:
2018:
2011:
2005:
2002:
1989:
1982:
1979:
1967:
1963:
1959:
1955:
1951:
1947:
1943:
1936:
1933:
1920:
1916:
1912:
1911:"Star Camera"
1906:
1903:
1898:
1894:
1890:
1886:
1882:
1878:
1874:
1870:
1866:
1859:
1856:
1840:
1834:
1832:
1828:
1815:
1811:
1805:
1802:
1786:
1780:
1777:
1772:
1768:
1764:
1760:
1753:
1750:
1746:
1744:9781493908011
1740:
1736:
1732:
1728:
1721:
1718:
1705:
1699:
1696:
1683:
1677:
1674:
1662:
1658:
1652:
1649:
1636:
1630:
1627:
1620:
1616:
1613:
1611:
1608:
1606:
1603:
1602:
1598:
1587:
1584:
1573:
1568:
1566:
1563:
1558:
1554:
1547:
1545:
1543:
1542:orbital decay
1539:
1535:
1531:
1526:
1518:
1516:
1514:
1510:
1503:
1495:
1493:
1491:
1490:
1482:
1474:
1472:
1470:
1465:
1459:
1451:
1449:
1447:
1442:
1440:
1436:
1431:
1425:
1417:
1415:
1413:
1412:ion thrusters
1408:
1406:
1405:Space Shuttle
1402:
1398:
1394:
1390:
1386:
1382:
1378:
1374:
1369:
1364:
1356:
1354:
1348:
1346:
1344:
1340:
1336:
1335:
1326:
1324:
1322:
1318:
1314:
1313:
1304:
1299:
1292:
1290:
1288:
1284:
1280:
1276:
1268:
1266:
1264:
1260:
1256:
1252:
1251:
1242:
1240:
1238:
1233:
1229:
1225:
1217:
1215:
1213:
1209:
1205:
1197:
1195:
1189:
1184:
1182:
1178:
1174:
1171:
1168:
1166:
1162:
1159:
1156:
1153:
1150:
1148:
1145:
1142:
1139:
1138:
1137:
1135:
1131:
1127:
1119:
1117:
1114:
1110:
1106:
1102:
1095:
1093:
1086:
1081:
1079:
1062:
1059:
1036:
1016:
990:
987:
981:
978:
975:
972:
965:
964:
963:
961:
957:
953:
949:
943:
926:
920:
916:
905:
901:
896:
892:
882:
878:
875:
872:
867:
863:
855:
854:
839:
833:
829:
818:
814:
809:
805:
795:
791:
788:
785:
780:
776:
768:
767:
752:
746:
742:
731:
727:
722:
718:
708:
704:
701:
698:
693:
689:
681:
680:
679:
677:
672:
652:
648:
639:
635:
626:
605:
583:
579:
555:
549:
540:
537:
525:
521:
518:
515:
508:
502:
497:
492:
488:
478:
474:
468:
462:
453:
449:
443:
435:
431:
423:
422:
421:
419:
415:
411:
406:
404:
402:
398:
393:
388:
386:
382:
378:
374:
367:
365:
362:
358:
354:
346:
344:
341:
339:
335:
327:
325:
323:
318:
314:
305:
303:
301:
300:Kalman filter
297:
289:
284:
280:
276:
271:
267:
265:
261:
257:
253:
248:
246:
241:
235:
227:
225:
222:
217:
212:
211:
206:
198:
196:
187:
183:
179:
174:
170:
166:
163:
162:
157:
156:
151:
147:
143:
142:
140:
133:
130:
129:
124:
123:
118:
117:yo-yo de-spin
112:
107:
100:
99:
98:
92:
90:
87:
79:
77:
75:
70:
66:
62:
57:
55:
51:
47:
43:
37:
33:
19:
2106:. Retrieved
2097:
2062:
2058:
2048:
2036:
2026:September 9,
2024:. Retrieved
2017:the original
2004:
1994:December 30,
1992:. Retrieved
1981:
1971:December 30,
1969:. Retrieved
1949:
1945:
1935:
1923:. Retrieved
1919:the original
1905:
1872:
1868:
1858:
1846:. Retrieved
1818:. Retrieved
1814:the original
1804:
1794:September 9,
1792:. Retrieved
1779:
1762:
1758:
1752:
1726:
1720:
1708:. Retrieved
1698:
1686:. Retrieved
1676:
1664:. Retrieved
1651:
1639:. Retrieved
1629:
1559:
1555:
1551:
1528:
1505:
1487:
1484:
1461:
1446:Euler angles
1443:
1427:
1409:
1366:
1352:
1334:magnetometer
1332:
1330:
1327:Magnetometer
1312:star tracker
1310:
1308:
1293:Star tracker
1287:star tracker
1275:Earth sensor
1274:
1272:
1269:Earth sensor
1248:
1246:
1231:
1221:
1203:
1201:
1193:
1123:
1099:
1090:
1008:
960:magnetometer
944:
941:
673:
570:
410:euler angles
407:
400:
396:
389:
371:
350:
342:
331:
309:
293:
260:Euler angles
249:
237:
215:
208:
202:
199:Articulation
193:
159:
153:
134:
126:
120:
101:
96:
83:
58:
41:
40:
2108:November 3,
1820:January 29,
1509:tidal force
1475:Solar sails
1377:translation
1259:solar cells
1224:gyrocompass
418:quaternions
264:Gimbal lock
256:Quaternions
2143:Categories
1848:January 1,
1710:January 1,
1684:. Nasa.gov
1641:January 1,
1621:References
1489:Mariner 10
1481:Solar sail
1403:, and the
1319:(s) using
1250:Sun sensor
1243:Sun sensor
1101:Gyroscopes
1096:Gyroscopes
322:Navigation
275:rigid body
128:Pioneer 11
122:Pioneer 10
69:algorithms
46:spacecraft
2089:127003967
1897:254423773
1357:Thrusters
1349:Actuators
1321:photocell
1263:telescope
1063:˙
991:˙
979:−
962:signals.
879:−
792:−
705:−
541:˙
519:τ
509:τ
489:∫
385:telemetry
296:estimated
161:Voyager 2
155:Voyager 1
65:actuators
1688:July 15,
1666:July 15,
1661:Nasa.gov
1569:See also
1228:pendulum
279:rotating
228:Geometry
146:deadband
80:Overview
2067:Bibcode
1954:Bibcode
1925:May 25,
1877:Bibcode
1513:tethers
1464:gimbals
1389:Mercury
1226:uses a
1141:Antenna
1082:Sensors
216:Cassini
210:Galileo
205:Voyager
61:sensors
2159:Orbits
2087:
1895:
1741:
1397:Apollo
1393:Gemini
1385:Vostok
1373:couple
1009:where
571:where
258:, and
119:. The
2085:S2CID
2020:(PDF)
2013:(PDF)
1893:S2CID
1842:(PDF)
1788:(PDF)
1530:Coils
1401:Soyuz
1279:Earth
240:space
219:'
2110:2022
2063:1155
2028:2013
1996:2022
1973:2022
1927:2012
1915:NASA
1850:2023
1822:2015
1796:2013
1739:ISBN
1712:2023
1690:2015
1668:2015
1643:2023
1317:star
1303:EBEX
1179:and
375:are
245:Pose
207:and
158:and
125:and
2075:doi
1962:doi
1885:doi
1767:doi
1731:doi
1273:An
1255:Sun
324:).
247:.)
2145::
2083:.
2073:.
2061:.
2057:.
1960:.
1950:73
1948:.
1944:.
1913:.
1891:.
1883:.
1873:59
1871:.
1867:.
1830:^
1763:26
1761:.
1737:,
1659:.
1448:.
1407:.
1399:,
1395:,
1391:,
1387:,
1331:A
1309:A
1247:A
1239:.
1202:A
910:w3
887:q3
823:w2
800:q2
736:w1
713:q1
340:.
254:,
76:.
2112:.
2091:.
2077::
2069::
2030:.
1998:.
1975:.
1964::
1956::
1929:.
1899:.
1887::
1879::
1852:.
1824:.
1798:.
1773:.
1769::
1733::
1714:.
1692:.
1670:.
1645:.
1060:B
1037:K
1017:m
988:B
982:K
976:=
973:m
927:,
921:z
917:w
906:K
902:+
897:3
893:q
883:K
876:=
873:z
868:c
864:T
840:,
834:y
830:w
819:K
815:+
810:2
806:q
796:K
789:=
786:y
781:c
777:T
753:,
747:x
743:w
732:K
728:+
723:1
719:q
709:K
702:=
699:x
694:c
690:T
657:d
653:K
649:,
644:i
640:K
636:,
631:p
627:K
606:e
584:c
580:T
556:,
553:)
550:t
547:(
538:e
530:d
526:K
522:+
516:d
512:)
506:(
503:e
498:t
493:0
483:i
479:K
475:+
472:)
469:t
466:(
463:e
458:p
454:K
450:=
447:)
444:t
441:(
436:c
432:T
403:)
399:(
221:s
38:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.