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Cassini Spacecraft Attitude Control System Flight Performance
Dr. Allan Y. Lee1 and Gene Hanover Jet Propulsion Laboratory, California Institute of Technology
Cassini is the largest and most sophisticated interplanetary spacecraft humanshave ever built. It was launched on 15 October 1997 by a Titan 4B launchvehicle. After an interplanetary cruise of almost seven years, it arrived at Saturnon June 30, 2004. The Huygens Probe, developed by the European Space Agency,was successfully released on December 24, 2004. On January 14, 2005, the Probeentered the atmosphere of Titan and transmitted back to Earth, via the spacecraft,more than four hours of Titan science data. The Cassini Attitude and ArticulationControl Subsystem is perhaps the spacecraft subsystem that must satisfy the mostscience and mission requirements. An overview of the design and flightperformance of the Cassini Attitude Control System, from October 1997 to thespring of 2005, is described in this paper.
AcronymsAACS = Attitude and Articulation Control SubsystemACC = AccelerometerADC = Analog to Digital ConverterAFC = AACS Flight ComputerAGC = Automatic Gain ControlAPWA = Adaptive Pulse Width AdjusterARPC = Ascending Ring Plane CrossingARWA = Articulatable Reaction Wheel AssemblyA.U. = Astronomical Unit (mean Earth-Sun distance)BOB = Bang-Off-Bang (Controller)BVT = Body Vector TableBW = BandwidthCAIP = Constraint Avoidance In ProgressCAPS = Cassini Plasma SpectrometerCCD = Charge Coupled DeviceCDA = Cosmic Dust AnalyzerCHWM = Clear High Water MarkCIRS = Composite Infrared Spectrometerc.m. = Center of MassCMT = Constraint Monitorc.p. = Center of PressureCRAF = Comet Rendezvous/Asteroid FlybyCSI = Control Structure InteractionsDB = Dead-BanddBm = Signal Strength Expressed in dB Relative to the 1-milliwatt StrengthDF = Describing Function (of a Nonlinear Element)DOY = Day Of the YearDRPC = Descending Ring Plane CrossingDSM = Deep Space ManeuverDSP = Digital Signal ProcessingECA = Earth Closest ApproachEGA = Engine Gimbaled ActuatorEHD = Elasto-Hydro-Dynamics (Lubrication Film)EKB = Extended Kalman-Bucy Filter (Attitude Estimator)
1Project Element Manager, Attitude and Articulation Control System, Cassini Spacecraft Operations Office.Mail Stop 230-104, Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, California 91109-8099, [email protected]
AIAA Guidance, Navigation, and Control Conference and Exhibit15 - 18 August 2005, San Francisco, California
NomenclatureB = IRU Bias Vector (rad/s)bi = Per-axis HGA Bore-sight Angular Offsets (radians) (i= X and Y-axis)c = Speed of Light (≈ 2.997925×108 m/s)
= Viscous Coefficient of Reaction Wheel Bearing (Nms/rad)CDiffuse = Coefficient of Diffuse Reflection of the HGA Reflector (or Magnetometer Boom) (-)CD = Drag Coefficient associated With the Free Molecular Flow of Titan atmospheric constituents (-)DHGA = Depth of the HGA Parabolic Reflector (m)Erf(x) = Error Function = (2/√π)∫exp(-u2)du, Integration from u = 0 to u = xF = Main Engine Thrust (N)fRPWS = Correction Factor for Solar Radiation Force on the Magnetometer Boom Due to RPWS Antennas (-)GSC(s) = Transfer Function of the Spacecraft, from Engine Gimbal Angle γ to spacecraft attitude θGTVC(s) = Transfer Function of the Thrust Vector ControllerGega(s) = Transfer Function of the Engine Gimbal ActuatorH = HGA transmission signal strength (dBm)HRWA = Angular Momentum Vector of the Reaction Wheels (Nms)HTotal = Total Angular Momentum Vector of the Spacecraft System (Nms)I0 = Solar constant at 1 A.U. (≈1353±20 W/m2)I0(x) = Bessel Function of the First Kind, Order = 0, and with Argument xI1(x) = Bessel Function of the First Kind, Order = 1, and with Argument xIRWA = Inertia Tensor of the Reaction Wheels (kg-m2)Isc = Inertia Tensor of the Spacecraft (kg-m2)j = √-1 (unit of Imaginary Number)k = HGA Transmission Pattern Shape Parameter (dBm/rad2)L = Distance from Engine Gimbal Pivot to Spacecraft’s Center of Mass (m)LMAG = Exposed Length of the Magnetometer Boom (m)P = Coordinate Transformation Matrix, Inertial Frame to the Spacecraft Axes (-)qi = Euler’s Parameters, Quaternion (i = 1-4)RHGA = Radius of the High Gain Antenna Parabolic Reflector (m)RMAG = Radius of the Magnetometer Boom (m)s = Laplace Variable (rad/s)T = Coordinate Transformation Matrix, Reaction Wheel Axes to Spacecraft Axes (-)TDahl = Reaction Wheel Bearing Dahl Friction Torque (Nm)TNongra = Non-gravitational Torque Imparted on Spacecraft (Nm)U = Reaction Wheel 4 Orientation Vector (-)ρ = Reaction Wheel Spin Rate Vector (rad/s)ρTitan = Density of Titan Atmospheric Constituents (kg/m3)ω = Spacecraft Angular Rate Vector (rad/s)ω Boom = Fundamental Frequency of the Magnetometer Boom (rad/s)∆V = Change in Spacecraft’s Velocity Vector (m/s)µ = Gravitational Parameter (m3/s2 or km3/s2)µTitan = Gravitational parameter for Titan (≈8.9782×103 km3/s2)µrad = Microradian (≈5.729578e-5 degrees)ε = Scale Factor Error Vector of an Inertial Reference Unit (-)θ = Misalignments of an Inertial Reference Unit (radians)γ = Engine Gimbal Angle (radians)Ω = Spacecraft Inertial Rate Vector (rad/s)
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Table of ContentsSection Page Acronyms................................................................................................................................... 1Nomenclature .............................................................................................................................. 3
I. Cassini/Huygens Mission to Saturn and Titan................................................................................... 5A The Names Behind the Orbiter and the Probe .............................................................................. 6B The Organization of This Paper................................................................................................. 6
II. Spacecraft Configuration................................................................................................................ 7A Flexibility of the Cassini Spacecraft .......................................................................................... 8B Slewing the Spacecraft ............................................................................................................ 8C Science Instruments ................................................................................................................ 9D Use of Reaction Wheels to Achieve Good Pointing Stability........................................................ 10
III. Cassini Attitude and Articulation Control System............................................................................ 11A Attitude Estimation Function................................................................................................. 13B Attitude Control Functions Performed by Thrusters.................................................................... 14C Attitude Control Functions Performed by Reaction Wheels.......................................................... 15D Propulsive Maneuvers Performed by A Rocket Engine................................................................ 16E Propulsive Maneuvers Performed by Thrusters........................................................................... 16F Cassini Pointing System and Inertial Vector Propagator .............................................................. 16G Attitude Control Fault Protection Design ................................................................................. 19H Flight Rules........................................................................................................................ 20
IV. Flight Performance of the Cassini Attitude Control System............................................................... 23A1 Reaction Wheel Attitude Control System Performance................................................................ 23A2 Attitude Control Performance During Gravitational Wave Search .................................................. 24A3 In-Flight Estimation of the Spacecraft’s Inertia Tensor ................................................................ 24A4 Articulation of the Backup Reaction Wheel Platform .................................................................. 26A5 Reaction Wheel Bias Optimization Tool .................................................................................. 28B1 Performance of the Reaction Control System ............................................................................ 29B2 Selections of Thruster Controller Dead-bands for Various Flight Scenarios ..................................... 31B3 Tuning of RCS Controller Pulse Width Adjuster Parameters........................................................ 32B4 Performance of the RCS Detumbling Controller Design after Probe Release.................................... 34C1 Performance of the Thrust Vector Controller during Main Engine Burns......................................... 36C2 Stable Limit Cycle Observed in Spacecraft “Dynamics” Telemetry during Main Engine Burns .......... 38C3 Observed High-g Bi-propellant Fuel Sloshing Frequencies during SOI........................................... 41C4 Performance of Propulsive Maneuvers Using Four Z-facing Thrusters ............................................ 42D1 Performance of the Spacecraft Attitude Estimator ....................................................................... 43D2 Performance of the Attitude Estimator with Star Identification Suspended ...................................... 44E1 In-Flight Calibrations of the Accelerometer’s Bias...................................................................... 46E2 In-Flight Calibrations of the Inertial Reference Units .................................................................. 46E3 In-Flight Characterization of the Reaction Wheel Drag Torque...................................................... 49E4 In-Flight Calibrations of the Stellar Reference Units ................................................................... 52E5 In-Flight Calibrations of the Narrow Angle Camera Bore-sight Vector ........................................... 54E6 In-Flight Calibration of the High Gain Antenna Electrical Bore-sight Vectors.................................. 54E7 In-Flight Confirmation of Sun Sensor Performance .................................................................... 55E8 In-Flight Calibration of Thrusters’ Magnitudes.......................................................................... 56E9 In-Flight Estimation of Main Engine Thrust ............................................................................. 59F1 In-Flight Monitoring of the High Water Marks of AACS Error Monitors ....................................... 60F2 In-Flight Adjustments of Selected AACS Error Monitors’ Thresholds and Persistence Limits ............ 61G1 Performance of the Dynamic Constraint Monitor........................................................................ 62G2 Performance of the Geometric Constraint Monitor ...................................................................... 62H Tracking of AACS Consumables ............................................................................................ 66I Impact of Radiation on AACS Sensors .................................................................................... 69J Estimation of Titan Atmospheric Density ................................................................................. 72K AACS Equipment Operating Temperatures ............................................................................... 75L In-Flight Estimation of Non-gravitational Torque....................................................................... 76
V. Summary and Conclusions .......................................................................................................... 78References................................................................................................................................. 81
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I. Cassini/Huygens Mission to Saturn and TitanThe Cassini spacecraft was launched on 15 October 1997 by a Titan 4B launch vehicle. After an interplanetary
cruise of almost seven years, it has arrived at Saturn on June 30, 2004. To save propellant, Cassini made severalgravity-assist flybys: two at Venus and one each at Earth and Jupiter. Figure 1 shows the interplanetary trajectorydesign of the Cassini mission.
Figure 1. Cassini Interplanetary Trajectory
In the late 1970’s, a proposed mission to Saturn and Titan was named Saturn Orbiter Dual Probe (SOP2).1
The scheduled launch date for SOP2 was March 1989. Similar to the interplanetary trajectory depicted in Figure 1,the 10-year mission of the 3000-kg SOP2 was to consist of a seven-year flight to Saturn and a three-year primemission in Saturn orbit. In 1987-88, NASA worked on the Mariner Mark 2 spacecraft and the missions designed touse it: Cassini/Huygens to Saturn and Titan, and the Comet Rendezvous/Asteroid Flyby (CRAF). In 1991-92,CRAF was canceled, and the original design of the Cassini spacecraft was greatly simplified. A 2-dof high-precision gimbaled platform and a turntable (that would rotate continuously), originally designed to carry most ofthe Cassini science instruments, were removed. All science instruments (except for the dual techniquemagnetometer instruments) are now mounted on the base-body of the spacecraft (see Figure 2). With the newdesign, the entire spacecraft must be slewed from one to another inertial attitude in order to point a remote sensinginstrument. Also, to observe fields, particles, and plasma waves, the entire spacecraft must be spun about its “axisof symmetry”.
Unlike Voyagers 1 and 2, which only flew by Saturn, Cassini achieved orbit at Saturn and is scheduled tooperate there for at least four years. Major science objectives of the Cassini mission include investigations of theconfiguration and dynamics of Saturn’s magnetosphere, the structure and composition of the rings, thecharacterization of several of Saturn’s icy satellites, and Titan’s atmosphere constituent abundance. The radarmapper will perform surface imaging and altimetry during many Titan flybys. Doppler tracking experiments usingthe Earth and the Cassini spacecraft as separated test masses have also been conducted for gravitational wavesearches. The performance of the Doppler phase shift during the first Gravitational Wave Experiment (GWE) (inDecember 2001) is described in Section IV.A2.
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En route to Saturn, the Cassini spacecraft encountered Jupiter on December 30, 2000. The Cassini Jupiterflyby was slow and nearly equatorial. Data collection for the “Jupiter campaign” began on October 1, 2000. ByJanuary 15, 2001, the spacecraft was on an asymptotic trajectory out of the Jovian system. Cassini’s closestapproach distance to Jupiter’s cloud tops was 9.72 million km. During the encounter, the Cassini Imaging Sciencesystem, the highest resolution two-dimensional imager on the orbiter collected about 26,000 images of Jupiter.2
During the Jupiter campaign, Cassini, together with the Galileo spacecraft (which was orbiting Jupiter) and theHubble Space Telescope (which was orbiting Earth) also participated in a so-called “millennium” observation of theJovian system. The Jupiter encounter also provided the Cassini spacecraft operations team and the investigationscientists an opportunity to practice their skills as well as to exercise and calibrate the capabilities of the spacecraftbefore the Saturn encounter three and a half years later.
After an interplanetary cruise that lasted almost seven years, the Cassini spacecraft arrived at Saturn in June2004. On June 30, 2004, Cassini fired one of its two rocket engines for about 96 minutes in order to slow downthe spacecraft’s velocity (by about 626.17 m/s) and allowed it to be captured by the gravity field of Saturn. Thiswas the most critical engineering event of the entire mission and was executed faultlessly. After the completion ofthe Saturn Orbit Insertion (SOI), cameras onboard the spacecraft were used to image Saturn and its rings. Onboardscience instruments were also used to study the structure and composition of the rings during both the ascendingand descending ring-plane crossings that happened before and after the Saturn Orbit Insertion.
The Huygens Probe, developed by the European Space Agency (ESA), was successfully released on December24, 2004. At separation, the spin ejection device located on the orbiter imparted on the Probe a spin rate of about8.1 rpm and a relative velocity of about 0.39 m/s. Details of the Probe separation event are given in SectionIV.B4. The Probe was dormant from separation until it reached a Titan-relative altitude of 1270 km, on January14, 2005. The Probe accelerometers and a radio transmitter were then turned on for measurements during entry. TheProbe was first aerodynamically decelerated to Mach 1.5 (approximately 400 m/s) at an altitude of 150-180 km.The heat shield and covers were then jettisoned, and a parachute was deployed. Data were collected over thedescent phase of the Probe mission, which lasted about 2 hours and 27 minutes. Data transmission from the Probewhile it was on the surface of Titan lasted another 1 hour and 12 minutes.
Titan is Saturn's largest moon. It is the second largest moon in the Solar System. Only Jupiter's moonGanymede is larger. At 5150 kilometers in diameter, Titan is larger than either of the planets Mercury or Pluto.Titan orbits Saturn at a distance of 1,222,000 kilometers, taking 15.9 days to complete one revolution. Titan is ofgreat interest to scientists because it is the only known moon in the Solar System with a “major” atmosphere.Titan's atmosphere is 10 times thicker than Earth's. Except for some clouds, Earth's surface is visible from space.But on Titan, a thick haze extending up to 3,000 kilometers above the surface obscures the entire surface fromoptical observations. Through ongoing observations from Earth as well as data collected by the Pioneer 11 andVoyager 1 and 2 spacecraft, scientists now know that Titan's atmosphere is composed primarily of nitrogen. Infact, over 95% of its atmosphere is composed of nitrogen, while only 5% is composed of methane, cyanide, andother hydrocarbons. The Cassini-Huygens Mission seeks to study Titan via 45 close flybys during its four-yeartour of Saturn.
I.A The Names Behind the Orbiter and the ProbeThe orbiter for the mission to Saturn and Titan is named after Jean Dominique Cassini (1625-1712), a famous
French-Italian astronomer. The Titan probe developed by ESA is named after the Dutch philosopher ChristiaanHuygens (1629-1695). Both were highly accomplished scientists, astronomers, and mathematicians.
Huygens invented the pendulum clock in 1656.31 He discovered the rings of Saturn in 1655-1656 and thelargest moon of Saturn, Titan, in 1655. In his studies of mechanics, he introduced the important concepts of“moment of inertia” (1673) and “centrifugal force.” He also made the first accurate determination of the value ofacceleration due to gravity and showed that it varied with latitude. Cassini discovered four Saturnian moons(Iapetus in 1671, Rhea in 1672, Dione in 1684, and Tethys also in 1684). Cassini’s most important workconcerned the size of the Solar System. His published value of the Astronomical Unit (A.U.), the mean distancebetween the Sun and the Earth was 140 million km. This value is just a few percent lower than today best estimateof 149.598 million km.
I.B The Organization of this PaperThe organization of this paper is as follows. Section II provides a brief description of the Cassini spacecraft
configuration. Section III describes the Attitude and Articulation Control System (AACS) design. The flightperformance of AACS is given in Section IV. Summary and conclusions are given in Section V.
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II. Spacecraft Configuration4
Cassini is perhaps the largest and most sophisticated interplanetary spacecraft humans have ever built andlaunched. The orbiter is about 6.8 m in height with a “diameter” of 4 meters. The total mass of the spacecraft atlaunch was approximately 5574 kg, which includes about 3000 kg of bi-propellant (1869 kg of Nitrogen Tetroxide,and 1131 kg of mono-methyl hydrazine), 132 kg of high purity hydrazine, and 2442 kg of “dry” mass (includingthe 320-kg Huygens Probe and 9 kg of helium mass). Fig. 2 depicts the Cassini spacecraft.
Figure 2. Cassini Cruise Configuration
The base body of the orbiter is a stack consisting of a lower equipment module, a propellant module, an upperequipment module, and a 4-m High Gain Antenna (HGA). The axis of the stack is the Z-axis of the spacecraft.Attached to the stack are the Remote Sensing Pallet and the Fields and Particles Pallet with their scientificinstruments. Until separation, the Huygens probe was attached to the base body with its axis of symmetry pointedparallel to the negative X-axis of the spacecraft. The orbiter’s 12-bay electronics bus is part of the upper equipmentmodule. An 11-m magnetometer boom is mounted to the upper equipment module. At launch, the boom wasstowed inside a canister. The magnetometer boom was deployed on August 16, 1999, two days before the Earthswing-by on August 18, 1999.
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The 4-m parabolic HGA and two Low Gain Antennas (LGAs) are the main communication antennas of thespacecraft. An X-band feed is used for both uplink and downlink communications. The maximum engineering datatelecommunication rate is 1896 bps. An S-band feed was used for communications with the Probe during itsdescent through the Titan atmosphere. A Ka-band feed is provided for Radio Science. Five Ku-band feeds supplyfive beams for radar mapping at Titan. For communications, AACS must point the X-band radio-frequency bore-sight of HGA to Earth. At other times, especially while the spacecraft is in the inner Solar System, AACS mustpoint the HGA axis of symmetry to the Sun so that the antenna will shade most of the spacecraft. During certainhazardous Saturn ring-plane crossings, the HGA axis is pointed parallel to the velocity vector of the orbiter(relative to the ring particles) in order to protect most of spacecraft instruments from the incoming energetic ringparticles.II.A Flexibility of the Cassini Spacecraft
Cassini is a flexible spacecraft containing four structural appendages and three propellant tanks. The fourbooms are the 11-meter long magnetometer boom and three similar Radio and Plasma Wave Science (RPWS)antennas. The fundamental frequency of the magnetometer boom is 0.7 Hz, and its damping ratio is between 0.2and 1%. Its second mode frequency is 4 Hz. The RPWS antennas have a fundamental frequency of 0.13 Hz and adamping ratio of 0.2%. Its second mode frequency is 0.86 Hz. The propulsion module houses two cylindricaltanks with hemispherical end domes. These tanks each contain an eight-panel Propellant Management Device(PMD) of the surface tension type. These PMDs are used to control the orientation of the propellant in the low-genvironment via surface tension forces. The monopropellant (hydrazine) is kept in a spherical tank that is locatedoff the Z-axis. The tank contains an elastomeric diaphragm for bubble-free expulsion of hydrazine in micro-gcondition. The total mass of the hydrazine at launch was about 132 kg.
When the spacecraft experiences “high” acceleration due to the firing of a rocket engine (with a nominal thrustof 445 N), the sloshing motions of the bipropellant in the tanks are in a so-called “high-g” mode. In this mode, theacceleration force is large enough that surface tension forces do not significantly affect the propellant motion. Atthe time of launch, the spacecraft mass was 5574 kg. Therefore, the acceleration of the spacecraft during rocketengine burns during early Cruise was about 0.08 m/s2. The estimated damping ratio of the fuel sloshing motionwas about 35%. To be conservative, a damping ratio of 10% was used instead in the design of thrust vector controlalgorithms (see also Section IV.C1). During a main engine burn with the tanks at about 50% fill fractioncondition, the fuel-sloshing frequency is estimated to be 0.05-0.14 Hz. A confirmation of these estimated fuel-sloshing frequencies is given in Section IV.C3.
When the spacecraft attitude is controlled by a set of three reaction wheels or eight thrusters, the bipropellant isin a so-called “low-g” sloshing mode. In this mode, surface tension forces control the motion of the propellantinside the tanks. During a thruster-based burn, the acceleration of the spacecraft is about 0.000723 m/s2. Again, at a50% fill fraction condition, the monomethyl hydrazine/nitrogen tetroxide (MMH/NTO) fuel sloshing frequenciesare estimated to be between 2 and 4 mHz.4,6,7 At a fill fraction of 10%, the estimated frequencies are 4 to 7 mHz.However, the estimation uncertainties associated with these frequency estimates are likely to be large. The dampingratio of the fuel sloshing motion in the ‘low-g” mode is estimated to be 10%.
II.B Slewing the SpacecraftDuring early Cruise, Cassini used a set of eight thrusters to control the spacecraft’s attitude. Figure 3 (from
Reference 5) shows the locations of the four thruster pods that are mounted on a structure that is attached to thelower equipment module. On each one of these pods are mounted two primary thrusters and their “backups.”Pointing controls about the S/C’s X and Y-axis are performed using four Z-facing thrusters. Controls about the Z-axis are performed using four Y-facing thrusters. Cassini’s thrusters have rich heritage from the Voyager program.
Y
X
Z
Z1
Z2
Z4
Z3Y1
Y2
Y4
Y3c.m.
Figure 3. Cassini Thruster Pod Location
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With reference to Figure 3, we see that to slew about the positive Z-axis of the spacecraft, one must fire boththe Y2 and Y4 thrusters simultaneously. Thrusts generated by these firings will almost cancel each other, and the∆V imparted on the spacecraft will be quite small. Similarly, to slew about the negative Z-axis of the spacecraft,one must fire both the Y1 and Y3 thrusters simultaneously. Again, the ∆V imparted on the spacecraft will besmall. On the other hand, a slew about either the ±X-axis or ±Y-axis will involve firings of the Z-facing thrusters.Since these Z-facing thrusters all point in the same direction, slewing the spacecraft about either the X or Y-axiswill generate unwanted ∆V on the spacecraft that must be predicted and incorporated into the designs of thespacecraft trajectory maneuvers.
During Tour, the spacecraft was slewed using three reaction wheels. To this end, one must assure that both theslew rate and acceleration are consistent with the control authority, power allocation, and the angular momentumcapacity of the wheels. The obvious merits of using reaction wheels over thrusters are the absence of unwanted ∆Vimparted on the spacecraft and the conservation of hydrazine.
II.C Science InstrumentsCassini carries twelve scientific instruments. Six of the instruments measure properties of objects remote from
the spacecraft. These remote sensing instruments are:(1) Imaging Science Subsystem (ISS),(2) Visible and Infrared Mapping Spectrometer (VIMS),(3) Composite Infrared Spectrometer (CIRS),(4) Ultraviolet Imaging Spectrograph (UVIS),(5) Cassini Radar (RADAR), and(6) Radio Science Subsystem (RSS).The first four of these instruments are mounted and co-aligned on the remote sensing pallet, which in turn is
mounted on the upper equipment module (see Figure 2). Also mounted on the remote sensing pallet are tworedundant stellar reference units (star trackers). The ISS consists of two cameras: Narrow Angle Camera (NAC) andthe Wide Angle Camera (WAC). The Field of View (FOV) of the NAC is 6.1×6.1 mrad. That of WAC is61.2×61.2 mrad. The FOV of CIRS is φ3.9 mrad (for Focal Plane-1, FP1). Its FOV for FP3 and FP4 is 0.3×2.9mrad. The FOV of UVIS (narrow) is 0.75×61 mrad. The FOV of UVIS (wide) is 8×61 mrad. The FOV of VIMSis 32×32 mrad. With fields of view that are on the order of a few mrad, the inertial pointing control requirementfor science observations made using these remote sensing instruments is 2 mrad (radial 99%). See Table 1 inSection III for details. Typically, these observations are made with the spacecraft controlled by reaction wheels.
RADAR is designed for observation of the surface of Titan during close flybys of the satellite. It operates atKu-band. The five operating “states” of RADAR are: High-resolution synthetic aperture imaging, low-resolutionsynthetic aperture imaging, altimetry, scatterometry, and radiometry. Radio science measurements will provide dataon the atmospheres and ionospheres of Saturn and Titan, on the rings, and on the gravity field of Saturn. Duringcruise, RSS instruments were be used to search for gravitational waves (see also section IV.A2).
In addition to the remote sensing instruments, Cassini also carries six instruments that observe fields,particles, and plasma waves. These instruments are:
(1) Dual technique magnetometer (MAG),(2) Radio and Plasma Wave Science (RPWS),(3) Cassini Plasma Spectrometer (CAPS),(4) Magnetospheric Imaging Instrument (MIMI),(5) Cosmic Dust Analyzer (CDA), and(6) Ion and Neutral Mass spectrometer (INMS).These instruments are located on various parts of the orbiter as indicated in Figure 2. The dual technique
magnetometer instruments are mounted on the magnetometer boom (see also Section II.A). The RPWS instrumenthas measured AC electric and magnetic fields in the plasma of the interplanetary medium as well as Saturn’smagnetosphere. Sensors used include an electric antenna, a magnetic search coil, and a Langmuir Probe. Theantenna consists of three elements arranged as a dipole and a monopole. The antennas are mounted on the upperequipment module.
The Cassini plasma spectrometer measures the composition, density, flow velocity, and temperature of ionsand electrons in Saturn’s magnetosphere. The MIMI is providing images of the plasma surrounding Saturn anddetermining ion charge and composition. The cosmic dust analyzer measures flux, velocity, charge, mass, andcomposition of dust and ice particles in the mass range of 10-16 to 10-6 grams. It has two types of sensors: high ratedetectors and a dust analyzer. An articulation mechanism permits these sensors to be rotated to several positions
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relative to the orbiter. The INMS is determining the chemical, elemental, and isotopic composition of the gaseousand volatile components of the neutral particles and the low-energy ions in Titan’s atmosphere and ionosphere.
The Huygens probe carried six science instruments. The Aerosol Collector Pyrolyzer was designed to performin-situ study of clouds and aerosols in the Titan atmosphere. The Descent Imager and Spectral Radiometer wasdesigned to measure aerosol and cloud optical properties and to perform spectroscopy measurements of Titan’satmosphere and surface. The Doppler Wind Experiment was designed to study winds from the effect it had on theProbe during Titan descent. The Gas Chromatograph and Mass Spectrometer was designed to perform in-situmeasurements of the chemical composition of gases and aerosols in Titan’s atmosphere. The Huygens AtmosphericStructure Instrument was designed to perform in-situ study of Titan atmosphere physical and electrical properties.Lastly, the Surface Science Package was designed to measure the physical properties of Titan’s surface and relatedatmosphere properties. Detailed descriptions of both the remote sensing and field science instruments carriedonboard the Cassini spacecraft, as well as the six science instrument packages carried onboard the Huygens Probe,are given in Ref. 3.II.D Use of Reaction Wheels to Achieve Good Pointing Stability
A high level of spacecraft pointing stability is needed during imaging operations of high-resolution scienceinstruments such as the Narrow Angle Camera (NAC). Typically, the required level of pointing stability is notachievable with the orbiter controlled by thrusters. Instead, one must employ three Reaction Wheel Assemblies.
Cassini carries a set of three “strap-down” reaction wheels that are mounted on the lower equipment module.They are oriented “equal distance” from the spacecraft’s Z-axis. That is, the angle between any of these threeRWA’s angular momentum vector and the spacecraft’s Z-axis is cos-1(1/√3) = 54.7356°. The first use of thereaction wheel control was on March 16, 2000, several months ahead of the Jupiter science campaign that began onOctober 1, 2000. The flight performance of the reaction wheel control system is given in Section IV.A1.
A backup reaction wheel is mounted on top of an articulatable platform. At Launch, the backup reaction wheelis mounted parallel to reaction wheel 1. On July 11, 2003, the platform was articulated in order to align the backupreaction wheel with reaction wheel 3. See Section IV.A4 for details of this event. Figure 4 depicts the orientationsof the four reaction wheels relative to the spacecraft’s coordinate frame at Launch.
Figure 4. Cassini Reaction Wheel Locations and Orientations
11
xB
x B
yB
yB
45 3 26 12 12 113
123
4
5
6 7 8
9
10
12
RWA-4
RWA-3RWA-1
RWA-2
RWA-1
RWA-4RWA-3
xB
ZBZB
Magnetometer Boom
RWA-1
RWA-4
RWA-3
30˚
30˚
tan-1 2 tan-1 12
tan-1 2
1
2
3
=
0 23
13
−12 −
16
13
12 −
16
13
xB
yB
zB
1
2
3
4
1 3
4
4
At Launch,
RWA Direction Cosines
RWA4 is Redundant, Articulable
y B
BB
can be aligned with 1 or 2 or 3ˆ ˆ4 &1 are aligned
10/26/95
Torque on spacecraft opposestorque on flyhwheel.
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III. Attitude and Articulation Control SystemPerhaps no other spacecraft subsystem must satisfy as many science and mission requirements as the Attitude
and Articulation Control Subsystem (AACS). The Cassini AACS estimates and controls the attitude of the three-axis stabilized Cassini spacecraft. It responds to ground-commanded pointing goals for the spacecraft’s scienceinstruments and communication antennas with respect to targets of interest. To this end, the AACS uses eitherthrusters or reaction wheels to slew the spacecraft. The AACS also executes ground-commanded spacecraft velocitychanges. To this end, AACS uses either a rocket engine or a set of Z-facing thrusters to effect a velocity change.Table 1 lists the major accuracy requirements for the Cassini spacecraft.8
Table 1. Major Cassini Accuracy Requirements
Accuracy Requirements Requirements
HGA pointing control requirement (radial 99%)
X-band (Telecommunications)
Ka-band (Radio Science)
Ku-band (Radar Mapping of Titan)
S-band (Huygens Probe Relay)
3.2 mrad
2.0 mrad
4.6 mrad
6.0 mrad
LGA X-band pointing control requirement (radial 99%) 4.0 degrees
Science pointing stability requirements (2σ per axis) for time windows of:9
0.5 s
1 s
5 s
22 s
100 s
900 s
1200 s
1 hour
4 µrad
8 µrad
36 µrad
100 µrad
160 µrad
200 µrad
220 µrad
280 µrad
Main engine ∆V burns (1σ):
Fixed Magnitude
Fixed Pointing
Proportional Magnitude
Proportional Pointing
10 mm/s
17.5 mm/s
0.2 %
3.5 mrad
Thruster ∆V burns (1σ):
Fixed Magnitude
Fixed Pointing
Proportional Magnitude
Proportional Pointing
3.5 mm/s
3.5 mm/s
2 %
12 mrad
12American Institute of Aeronautics and Astronautics
To achieve a high degree of maneuverability, and to facilitate high-resolution camera imaging, Cassini isdesigned as a three-axis stabilized spacecraft. A list of equipment use by Cassini AACS is given in Table 2.AACS sensors and actuators used by four other interplanetary missions are also given in Table 2 for comparison.The locations of the Cassini AACS equipment are depicted in Figure 5. How this set of equipment is used toperform various AACS functions (attitude estimation, attitude control, etc.) are described in the followingsubsections. The AACS flight software (FSW) that was used at Launch was named A6.3.5. Consistent with theplan made at Launch, the AACS FSW was updated with new versions on the following dates during the longcruise and early Tour: A7.7.6 on March 7, 2000, A8.6.5 on February 16, 2003, A8.6.7 on April 27, 2004, A8.7.1on October 2, 2004, and A8.7.2 on May 26, 2005.
Table 2. A Summary of Attitude Control Sensors and Actuators Used by Five Planetary Spacecraft
Missions Planets Attitude Estimation Sensors Attitude Control ActuatorsVoyagerI and II (1977)
JupiterSaturnUranusNeptune
1-dof Canopus star trackers (2)2-dof SSA (2)2-dof dry-tuned gyroscopes (3)
Mars Mars horizon sensor assembly (1)Celestial sensor assembly (1)Sun sensor assemblies (2)(each with five detectors and one sensorelectronics)Inertial Measurement Unit (1)(with four 1-dof gyroscopes and fouraccelerometers)
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III.A Attitude Estimation FunctionThe spacecraft’s attitude in a celestial frame is estimated using a Stellar Reference Unit (SRU, sometimes
called a star tracker) and an Inertial Reference Unit (IRU, each with four gyroscopes). Both the SRU and the IRUhave an identical backup unit. The star trackers are co-aligned, and their bore-sight vectors are nominally parallel tothe spacecraft’s X-axis. The optical Field of View (FOV) of these trackers is a square: ±7.5° by ±7.5°. The stray-light FOV of the SRU is circular with a radius of 30°. In flight, both star trackers are calibrated annually (seeSection IV.E4). Each IRU contains four Hemispheric Resonator Gyroscopes (HRGs). Three of the four HRGs areused as prime inertial sensors while the fourth gyroscope is used as a “parity checker.” The HRG inertial sensor isunique in its use of the resonant vibrations of an axis-symmetric shell to accurately sense rotational motion. Thereis a very small amount of energy and mechanical stress imparted to the shell while operating. This allows forreliable long-duration operation for the Cassini mission.11 The Cassini gyroscope has a resolution of 0.25 µrad. In-flight, various IRU parameters (such as its scale factor errors, biases, misalignments, etc.) are calibrated. Results ofthese calibrations are given in Section IV.E2.
Figure 5. Attitude Control Equipments
Spacecraft attitude estimation is initialized using knowledge of the Sun position. To this end, the celestial andinertial attitude sensors are augmented with a two-axis Sun sensor (and its backup unit). The bore-sight vector ofthe SSA is aligned with the minus Z-axis of the spacecraft. The FOV of these SSAs is a square: ±32° by ±32°.The stray-light FOV of the Sun sensor is a rectangle: ±35° by ±65°. The AACS acquires stellar reference by firstlocating the Sun, and then Sun-pointing the HGA using data from the SSA. A Star IDentification algorithm (SID)then uses star data captured by the star tracker to acquire a three-axis stellar reference. The front-end of the Cassiniattitude estimator is a pre-filter that combines multiple star updates into one “composite” star update. Thesecomposite star updates are then sent to the attitude estimator (which is an Extended Kalman-Bucy filter, EKBfilter) every 1-5 seconds. In between star updates, the S/C’s attitude is propagated using the IRU data. Onceattitude is initialized, the AACS maintains knowledge of the spacecraft attitude in a celestial coordinate frame that
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is called “J2000 frame.” It is a coordinate frame that is defined by the Earth Mean Equator and Equinox at the year2000 epoch. The performance of the attitude estimator design is described in Sections IV.D1 and IV.D2.
III.B Attitude Control Functions Performed by ThrustersDuring early Cruise, Cassini used a set of eight thrusters to maintain three-axis attitude control of the
spacecraft. Pointing controls about the Spacecraft’s X and Y-axis are performed using four Z-facing thrusters.Controls about the Z-axis are performed using four Y-facing thrusters. Thrusters have been and/or are also used toperform the following unique functions:
[a] Detumble the spacecraft after it was separated from the launch vehicle and after the Huygens probe wasreleased from the spacecraft.
[b] Perform a spiral search for the Sun. Unless the Sun has already been captured inside the SSA’s FOV, thisSun search maneuver must be performed as the first step in the establishment of the spacecraft’s three-axisattitude knowledge.
[c] Control the spacecraft’s attitude during low-altitude Titan flybys. Titan is the largest moon of Saturn, andit is covered with an atmosphere. Titan atmosphere density is a function of altitude. During low-altitudeTitan flyby, the atmospheric torque imparted on the spacecraft is higher than that the reaction wheels canhandle. Hence, during these low-altitude Titan flybys, Cassini is controlled by reaction control thrusters.
[d] Biasing the reaction wheels’ angular momentum vectors. A representative reaction wheel biasing is carriedout as follows. The spacecraft is Earth-pointed and is on thruster control, with dead-bands of [2, 2, 2]mrad. After being powered on, the reaction wheels are spun up to attain a set of pre-selected spin rates. Inso doing, the D.C. motors of the RWAs impart equal and opposite torque on the S/C. Thrusters are thenfired to maintain the S/C’s attitude in the presence of these disturbance torques. In the worst case, areaction wheel biasing will take less than 20 minutes to complete.
[e] Trajectory correction maneuvers could be achieved by firing four Z-facing thrusters. In flight, thrusterswere used to impart ∆V as small as 15.9 mm/s on the spacecraft. The largest ∆V imparted on thespacecraft by the thrusters was 368 mm/s. See also Section IV.C4.
The monopropellant propulsion system for Cassini is of the blow-down type. With this system, the hydrazinetank pressure will decay slowly with time as hydrazine is depleted through thruster firings. At launch (October 15,1997), the thrust magnitude is about 0.97 N. By the time of Saturn Orbit Insertion (June 30, 2004), the thrustmagnitude had decayed to 0.75 N. By the time of Probe relay (January 14, 2005), the thrust magnitude was 0.69N. The monopropellant tank will be “recharged” only once, which is planned in May/June 2006.
A conventional Bang-Off-Bang (BOB) thruster control algorithm is used by Cassini AACS. The BOBalgorithm uses error signals that are the weighted sums of per-axis attitude errors and attitude rate errors to controlthruster firings. But such a control algorithm can result in “two-sided” limit cycles that waste both hydrazine andthruster on/off cycle. To counter these drawbacks, the Cassini’s BOB incorporated a “self-learning” feature toproduce, as much as possible, “one-sided” limit cycles in the presence of small environmental torque. In thisscheme, an “optimal” thruster pulse is fired to send the spacecraft attitude control error signal towards the otherside of the dead-band. The pulse is adaptively adjusted so that it will get close to the dead-band space but without“touching” it. The resultant “one-sided” limit cycles save both hydrazine and thruster on/off cycle. The flightperformance of the RCS attitude controller is described in Sections IV.B1 to IV.B3.
A second feature that was incorporated in BOB is the so-called “walking” dead-band. It was added to avoid anundesirable phenomenon called “double pulsing” (which also wastes both hydrazine and thruster on/off cycle). Theneed arose during most of the Cruise phase when the environmental torque imparted on the spacecraft was so smallthat the resulting limit cycle rate was smaller than the rate noises generated by the attitude estimator. As a result,the rate noise could easily trigger an extra thruster firing when the attitude error was hovering near either end of thedead-band space. The “walking dead-band” feature is activated whenever dead-band crossing occurs. The “dead-band” is “stretched” to a value that is larger than that commanded by the ground operators by one or more smallsteps. Representative walking dead-band “step” size is 200 µrad, and a maximum of five steps are allowed. Thesewalking dead-band parameters could be changed via an AACS command. The commanded dead-band is restored toits original nominal value whenever the attitude control error has decreased to within 80% of the nominal dead-band value. The flight performance of this design feature is described in Section IV.B2.
Another important design consideration of the Cassini RCS controller is related to the possible Control-Structure Interactions (CSI) between thruster firings and the 0.7-Hz magnetometer boom especially during a low-altitude Titan flyby. To avoid these undesirable interactions, 2nd order notch filters (with a notch frequency of 0.7Hz) are used to filter both the attitude and attitude rate control error signals. The filtered signals are then combinedto form the error signal for the RCS controller. The bandwidth of the RCS attitude controller is selected to be 0.15Hz, which is significantly higher than the low-g bi-propellant slosh appendage modes (2-4 mHz at 50% tank fill
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fraction). The gain and phase margins of the RCS controller are 18 dB and 25°, respectively. Flight performance ofBOB is given in Section IV.B1.
III.C Attitude Control Functions Performed by Reaction Wheels16
The Reaction Wheel Assemblies (RWAs) are used primarily for attitude control when precise and stablepointing of a science instrument (such as NAC) is required during the prime mission phase. To this end, RWAsare used to slew the spacecraft from one attitude to another, rest to rest. Once it has arrived at the targeted attitude,the NAC “stares” at the target for a period of time during which the spacecraft attitude must be stable. As arequirement, the Reaction Wheel Attitude Control System (RWAC) must control the spacecraft with per-axisattitude control errors that are smaller than 40 µrad. Additionally, while under reaction wheel control, the spacecraftpointing stability must be better than those specified in Table 1. However, these pointing stability requirements areapplicable only when the spacecraft is in a quiescent state (with all per-axis spacecraft rates under 0.01 °/s) and onlyafter a 20-second settling time has elapsed after the last spacecraft rate change.
If many rest-to-rest slews are stacked together, they form a mosaic or strip. In so doing, an extended target thatis larger than the FOV of the imaging instrument can be studied. The flight performance of the RWAC is describedin Section IV.A1. The RWAC was also used during three 40-day gravitational wave experiments (GWEs) duringouter Solar cruise. The performance of the RWAC during these GWEs is given in Section IV.A2. Figure 6 (fromRef. 16) is an illustration of the RWAC design.
Kd
+rateerrorKp
+poserror
Inertia
ratecmd
acccmd
torqcmd Inertia-1 1/s 1/s
rate pos
S/C + Wheels Model
Torq = I ωdot + ω x (I ω + Hwhls)
ω x (I ω + Hwhls)
Gyroscopic TorqueEstimate
++
ratelimiter
acclimiter
4thorderLowPass
Wheel MomentumEstimate (Hwhls)
AttitudeEstimator
Gyros
StarCamera
rateestimate
filteredrate
estimate
posestimate
(quaternion)
-
disturbancetorques
-
pos profile(quaternion)
rate profile
accelerationprofile
++
RLi RLo ALi ALo
Figure 6. Block Diagram of the Reaction Wheel Attitude Control System
Because the spacecraft’s principle axes are very closely aligned with the spacecraft’s mechanical axes, the basicstructure of the RWAC is a decoupled, three-axis, Proportional and Derivative (PD) controller. As indicated inFigure 6, the control torque vector is determined using the equation: ISCdω/dt+ω×(ISCω+HRWA). Here, dω/dt is thespacecraft’s acceleration and ω is the spacecraft rate vector (both vectors are expressed in a body-fixed coordinateframe). The second term in the equation represents the gyroscopic torque vector. The HRWA in the last component ofthe equation represents the total angular momentum vector of the three prime RWA expressed in the spacecraft’sbody-fixed frame.
An important design feature that is depicted in Figure 6 is the addition of the rate and acceleration feed-forwardcommands. These feed-forward commands generate immediate control action instead of “waiting” for theaccumulation of error signals via the feedback loops. As such, the RWAC responses quickly to these profiled slewcommands (rather than one without the feed forward signals). The feed-forward command is generated by theAttitude Commander. It derives these signals using commands sent by the spacecraft control team.
Due to the presence of bearing frictional torque in the reaction wheels, an RWAC with the “PD” controlarchitecture will not be able to drive the spacecraft attitude control error to zero unless an integral term is added tothe PD controller. This difficulty was overcome by the addition of a Proportional and Integral (PI) estimator of thereaction wheel frictional torque in the reaction wheel “Hardware Manager.” In effect, integral control action is added“locally” to remove any steady-state spacecraft’s attitude control errors. The RWAC design has a bandwidth of
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0.0299 Hz. The gain and phase margins of RWAC are 10 dB and 30°, respectively. Flight performance of theRWAC is given in Section IV.A1.
III.D Propulsive Maneuvers Performed by A Rocket Engine15
The Cassini interplanetary mission requires both large and small trajectory correction maneuvers for navigationpurposes. Trajectory corrections before Saturn Orbit Insertion (SOI) on June 30, 2004 are called TrajectoryCorrection Maneuvers (TCMs). Corrections after SOI are called Orbit Trim Maneuvers (OTMs). Most thespacecraft’s velocity changes were produced by one of the two rocket engines (with a nominal thrust of 445 N).Smaller ∆V’s were generated using the four Z-facing thrusters.
During the early phase of Cruise, thrusters were used to roll and yaw the spacecraft attitude so as to align thepre-aimed rocket engine with the target ∆V vector. “Settling” times on the order of 5 minutes were “inserted” inbetween the roll and yaw turns, and in between the end of the yaw turn and the start of the burn. Once a burn wascompleted, the spacecraft would “un-yaw” and “un-roll” back to its initial attitude. Again, settling times wereinserted between these “unwind” turns. These thruster-based slewings imparted unwanted ∆V on the spacecraft.Even though the magnitudes of these ∆V could be predicted, they still, in a small way, affected the accuracy of theburn. As such, beginning with TCM-18 (see Table 7), both the roll and un-roll turns were executed using a set ofreaction wheels. These RWA-based slews did not produce unwanted ∆V. The ∆V produced by thruster-based yawand un-yaw slews was considered in the design of each target ∆V vector.
Three-axis stabilized orbiters such as the Viking Mars Orbiter had used two-axis engine gimbal actuatorautopilot for Thrust Vector Control (TVC). Cassini uses a similar design. Experiences gained from past missionshad been incorporated into the Cassini TVC design. For example, the Cassini TVC design considered the effects ofpropellant line stiffness, and propellant sloshing, as well as the spacecraft structural characteristics. As waspracticed on Viking, pre-aim of the gimbal through the predicted spacecraft c.m. was commanded to minimizeattitude disturbances at ignition. During the burn, the X- and Y-axes of the spacecraft’s attitude were controlled bythe EGA using a TVC algorithm.15 At the same time, four Y-facing thrusters were used to control the spacecraft’sZ-axis motion (with a dead-band of ±1°). See also Section IV.C2.
The ∆V imparted on the spacecraft is measured by an accelerometer (ACC) that is mounted parallel to thespacecraft’s Z-axis. The scale factor of the ACC data was estimated pre-launch to be 2.02033 mm/s per datanumber. Its bias was estimated to be 2.7 mm/s2 (see Table 9). However, since the ACC’s bias changes slightlyfrom burn to burn, a one-minute calibration is always performed before the start of the burn to determine the actualACC’s bias (The stability of the ACC’s bias over time is given in Section IV.E1). The flight software then usesthe calibrated ACC to accurately determine the magnitude of the ∆V imparted on the spacecraft. The burn isterminated once the commanded ∆V is achieved.
The bandwidth of the TVC algorithm is selected to be 0.23 Hz. It is higher than the high-g fuel sloshingfrequency (≈ 0.05-0.14 Hz at 50% tank fill fraction). As such, the TVC algorithm could control the considerableenergy contained in the fuel sloshing motion. On the other hand, since the TVC bandwidth is lower than themagnetometer boom frequency (0.7 Hz), energy in the boom vibration must be gain-stabilized using a 2nd orderroll-off filter for which the frequency is 0.3 Hz and the damping ratio is 0.5. The gain and phase margins of theTVC algorithm are 9 dB and 30°, respectively. From Launch in 1997 until the end of January 2005, the smallestand largest ∆V’s performed using a main engine were 0.407 m/s (OTM-6) and 626.17 m/s (SOI), respectively.Flight performance of the TVC control algorithm is given in Section IV.C1.
III.E Propulsive Maneuvers Using ThrustersCassini sometimes uses the four Z-facing thrusters to impart a small ∆V on the spacecraft. This is called an
RCS burn. During an RCS burn, the Z-facing thrusters are used to achieve the targeted ∆V as well as to controlboth the X and Y-axis of the spacecraft during the burn. The X and Y-axis dead-bands of the RCS controller areboth ±0.5°. At the same time, four Y-facing thrusters are used to control the spacecraft’s Z-axis motion. The Z-axisdead-band of the RCS controller is ±1°. The bandwidth of the RCS ∆V controller is selected to be 0.07 Hz. Thegain and phase margins of the RCS ∆V controller are 15 dB and 35°, respectively. From Launch in 1997 until theend of January 2005, the smallest and largest ∆V’s performed using thrusters were 15.9 (OTM-9) and 368 (OTM-4)mm/s, respectively. Flight performance of a representative RCS burn is given in Section IV.C4.
III.F Cassini Pointing System and Inertial Vector Propagator13,14
All spacecraft pointing needs could be stated as follows: “align a body vector with an inertial vector.” ForCassini AACS, we call the two vectors involved the “primary” body vector and “primary” inertial vector. This isthe fundamental requirement of a pointing goal. However, to uniquely define the spacecraft inertial attitude, thepointing of a second pair of vectors (called secondary body vector and secondary inertial vector) must also be
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specified. The spacecraft pointing control system will align the secondary vectors as close as possible, subject tothe constraint imposed by the primary vector pair. An example is the pointing of the NAC at Saturn’s moon Titan.In this example, the primary body vector is the bore-sight vector of the camera, which is “fixed” on the spacecraft’sbase body. The primary inertial vector is a vector from the spacecraft to Titan, which varies slowly with time. Thesecondary body and inertial vectors could be the star tracker’s bore-sight vector and the Z-axis of the J2000 frame(which is fixed in an inertial frame), respectively. Obviously, the selection of the secondary vector pair is non-unique.
The Cassini pointing system is a software engine consisting of several inter-connected software “objects”working together to achieve the pointing goal. Some of these software objects are collections of algorithms that runperiodically. Others are tables with associated algorithms that run when changes to the tables are commanded.Table 3 and Figure 7 (both adapted from Reference 13) capture the principal components of the Cassini pointingsystem design.
Table 3. Principal Components of the Cassini Pointing System Model
Inertial Vector Table A commandable list of time-varying inertial vectors that are related to one another ina tree topology
Inertial Vector Propagator Evaluates time histories of the active members of the Inertial Vector Table
Target Table A list of paths through the inertial vector tree that are currently needed for targetpointing
Target Table Propagator Evaluates the time histories of member vectors in the Target Table
Body Vector Table A commandable list of vectors that are fixed on the S/C
Base Attitude Generator Evaluates the base attitude for the commanded target
Offset Profile Generator Evaluates commanded pointing profiles, which are offsets relative to the baseattitude
Constraint Table A commandable list of pointing geometric constraints (e.g., “Do not point the camerabore sight vector too close to the Sun”)
Constraint Monitor Detects and corrects violations of constraints by the commanded attitude
Inertial VectorPropagator
Inertial Vector Table
Constraint Table
Offset Profile Generator
Base Attitude Generator
Body Vector TableTarget Table
Target Table Propagator
Constraint Monitor
Autonomous Entries
Time (All Components)
Commands
Figure 7. Cassini Pointing System Model13
Consider the scenario of pointing the narrow angle camera at Titan. This pointing could be achieved if we haveknowledge of the spacecraft-to-Titan vector in an inertial coordinate frame. This inertial vector could be computed
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onboard if we have knowledge of the spacecraft and Titan positions. Hence, we need, in some form, knowledge ofthe spacecraft trajectory, ephemeredes of Saturn and Titan. To locate a target object such as Titan from thespacecraft, it is (some times) convenient to follow a path through two or more vectors. In our example, Titan isusually found by following a vector path through two tree “branches”: spacecraft to Saturn, and Saturn to Titan.This path is depicted in Fig. 8. Once the path to a target is known, the vectors along the path are added (with theappropriate sign) to produce the target location.
With reference to Table 3 and using the “Point NAC at Titan” example, the NAC bore-sight vector is stored inthe Body Vector Table. The Sun-to-Cassini, Saturn-to-Titan, Sun-to-Saturn, and Sun-to-Earth vectors are stored inthe Inertial Vector Table. The Cassini-to-Titan vector, which is formed by the vector sum of the Cassini-to-Saturnand Saturn-to-Titan vectors, is kept in the Target Table. The flight software object named Constraint Monitor(CMT) is placed in between the attitude commander and the attitude controller.13 Two aspects of attitudecommands generated by the attitude commander are checked by the CMT. Brief descriptions of these checks aregiven below.
First, the per-axis slew rates and accelerations are checked against a set of rate and acceleration limits thatrepresents the capability of the thrusters (or a set of reaction wheels). Any per-axis rates or accelerations that ishigher than its CMT limits will be “truncated” by the CMT. Only the truncated slew command is sent to theattitude controller. CMT also checks to make sure that the angle between a specific body vector and an inertialvector (usually the Sun-line vector) is larger than a pre-selected threshold. For example, the bore-sight vector of thenarrow angle camera must NOT be closer than 12° relative to the Sun-line vector (actually, any part of the Sun).This and other geometric constraints are stored in the Constraint Table. The commanded S/C attitude will bealtered by the CMT if a geometric constraint violation is anticipated by the CMT. Flight performance of the CMTdesign is described in Sections IV.G1 and IV.G2.
The Inertial Vector Propagator (IVP) object is described in greater details in the following. Readers who areinterested in the details associated with other components of the Cassini pointing system model (depicted inFigure 7) should consult References 4 and 13.
Most vectors (the arrows in the Fig. 8) could be modeled accurately as Conics (conic section). By conics we
mean the relative motion that satisfies the differential equation: r ˙ r = −µr r / r r 3
. Here, r r is the inertial position
vector of the orbiting body relative to the dominant central body, and µ is a gravitational parameter (product of theuniversal gravitational constant G and the sum of the masses of the orbiting and the central bodies). Vectors fromthe Sun to the planets and vectors from the planets to their moons are all well described by conics for long periodsof time. This is so because the spacecraft is far from the intersection between spheres of influence of two celestialbodies. Only seven parameters (and time) are necessary to define conics.
Figure 8. A Representative IVP Vector “Tree” (from Ref. 13)
Because conics do not always suffice, polynomial vectors are also used by the IVP. Polynomials with themost attractive fitting characteristics are the Chebyshev polynomials. Chebyshev polynomials of up to 12th orderare used by the Cassini AACS. Propagation via polynomial vectors is not only more expensive (in terms ofcomputational resources), but polynomials also tend not to fit accurately over as long a time interval as do conics.
Saturn
Sun
Earth
Titan
Cassini Spacecraft
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Polynomials are used mainly to cover transitional periods in the spacecraft’s trajectory as gravitational dominanceshifts from one body to another. Titan flyby is a frequent example.
Parameters that define the Conic vectors and polynomial vectors are determined using ground software tools.The software tools accept as inputs the time histories of the position and velocity vectors of one object (such asEarth) relative to another object (such as the Sun). One must also specify a requirement on an acceptable level ofIVP modeling error. The IVP modeling error requirement is typically selected to be 40 µrad per axis. The timesegment over which the conic (or polynomial) vector could approximate the actual trajectory with errors that arebounded by the specified modeling error requirement can then be determined. In this way, the position vector fromthe spacecraft to a target such as Titan at any given time can be determined and used for pointing the camera.Inertial vectors (Conics or polynomial) must be “updated” from time to time before they “expire.” Similarly, bodyvectors (such as the optical bore-sight vector of the narrow angle camera and the electrical bore-sight vector of theHGA) must be updated from time to time when updated vectors are available via in-flight calibrations. SeeSections IV.E5 and IV.E6.
III.G Attitude Control Fault Protection Design21
There are two fundamental AACS Fault Protection (FP) requirements. Firstly, during all mission phases, thespacecraft must be able to Fail Safe by autonomously locating and isolating any single failure, recovering to athermally safe and commandable attitude, and then waiting for further instructions from the ground operators.Secondly, during a few time-critical events (including Launch, SOI, and Probe relay), the spacecraft cannot affordto simply isolate a failure and wait for ground instruction. In these “time-critical” events, the spacecraft must beFail Operational by autonomously recovering a much larger set of its capabilities and then proceeding with apreviously uplinked “critical” command sequence.
Figure 9 (from Reference 21) illustrates the architecture of the AFC-resident flight software algorithms thatperform autonomous detection, isolation, and recovery from failures of AACS equipment and AACS-controlledpropulsion elements. The components of this architecture are Error monitors, Activation rules, and Responsescripts. Error monitors test the performance of AACS sensors, actuators, or functions (e.g., attitude control,attitude estimation, etc.) against expectations. Deviations between the actual and expected performance are gaugedagainst a pre-selected set of “thresholds.” An error monitor is “triggered” if its threshold is exceeded for a timeduration that is longer than a persistence limit. Pre-launch, both the thresholds and persistence limits of all theerror monitors were carefully selected by a team of FP engineers. Pre-launch, some of the selected parameters weresubsequently adjusted to comply with the ground-based test results. Flight experience indicated that most of theseparameters were well selected but some thresholds and persistence limits were found to be inappropriate. They werechanged in-flight. Details of some of these changes are described in Section IV.F2.
Mode Commander,Hardware Configuration Manager,Hardware Interface Managers, etc.
Alert Messages to SFP
AACS Commands
Commanded States,Calculated States
Current Hardware Usage,Current Software Goals
Commanded Mask States
AACSCommand Handler
Commanded Mask States
OutputColors
A
Safing in Progress to SFP
Current Hardware Usage,Current Software Goals
Repair Managers
E 12
3•
AACS Commands
Repair Manager States
Repair Operation Requests
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Activation rules evaluate the outputs of error monitors in the context of the subsystem’s current hardwareconfiguration and activity goals. They provide a diagnosis of the most likely causes of any anomalous behaviors.They then activate one or more appropriate response scripts in attempting to rectify the detected anomalousbehaviors. Response scripts isolate failed equipment and recover a desired level of subsystem functionality. Theydo so by issuing commands directly to the subsystem. Commands generated by the FP software are captured in aso-called “Fault Protection Event Log” which could aid the ground operators in understanding what has happenedon board the spacecraft. Readers with an interest on the Cassini AACS FP design should consult Reference 21.
III.H Attitude Control Flight RulesPre-launch, many engineers worked on the designs and testing of various AACS functions, hardware, and
software. Knowledge on the limitations associated with these AACS functions had to be passed from the designteams to the Operations team to ensure safe operations. One efficient way to transfer the knowledge was for thedesign teams to write sets of “rules” (called flight rules) and to ask the Operations team to follow them when they“fly” the spacecraft. To this end, members from the design teams must write these rules clearly and concisely. Therationales behind the needs to enforce these rules must be clearly stated. Once approved, each flight rule will beenforced either via ground software checking, manual inspection, or by other means. A flight rule is waived only ifthere is a strong motivation for so doing. In any case, the original author of the to-be-waived flight rule must beconsulted before the waiver is approved. Flight rules must be enforced until they are no longer applicable. Forexample, flight rules applicable to the launch sequence were “retired” after Launch. On the other hand, new flightrules might have to be written in order to incorporate lessons learned from mistakes made in flying the spacecraft.
The following is an incomplete list of flight rules that are used to guide AACS flight operations.(a) Minimum warm-up times of AACS equipment:
1. The accelerometer must be powered on at least 1 hour prior to its use.2. The inertial reference unit must be powered on at least 2 hours prior to its use.3. The stellar reference unit must be powered on at least 1 hour prior to its use.4. The Sun sensor must be powered on at least 1 minute prior to its use.5. The reaction wheels must be powered on at least 10 seconds prior to their use.6. The main engine pre-aim vector must not be sent unless the EGA driver has been powered on for
at least 10 seconds.(b) Minimum post-slew settling times:
1. The settling time between the end-time of the roll turn and the start-time of the yaw turn to themain engine burn attitude must be at least 5 minutes.
2. The settling time between the end-time of the roll turn and the start-time of the yaw turn to thethruster burn attitude must be at least 5 minutes.
3. The settling time between the end-time of the yaw turn and the ignition of the main engine mustbe at least 5 minutes.
4. The settling time between the end-time of the yaw turn and the start-time of the thruster burnmust be at least 5 minutes.
5. The settling time between the end-time of the engine (or thruster) burn and the start-time of the“un-yaw” turn must be at least 5 minutes.
(c) Thruster controller dead-band settings (see also Table 5):1. All per-axis attitude control dead-band must not exceed 2 mrad prior to a main engine burn.2. Both the Y- and Z-axis dead-band must not exceed 2 mrad prior to the release of the Huygens
Probe.3. Both the X- and Y-axis dead-band must not exceed 2 mrad during X-band HGA downlink.4. Both the X- and Y-axis dead-band must not exceed 20 mrad during X-band LGA-1 downlink.5. All per-axis dead-band must not exceed 2 mrad prior to a thruster to reaction wheel attitude
control mode transition.(d) Parameter update restrictions:
1. Thruster-related FSW parameters must be updated when the spacecraft is on reaction wheelcontrol.
2 . Reaction wheel-related FSW parameters must be updated when the spacecraft is on thrustercontrol.
3. Spacecraft inertia tensor must be updated when the spacecraft is on thruster control.4 . Spacecraft inertia tensor must be updated after the following discrete events: Deep space
maneuver in 1998, Deployment of the magnetometer boom in 1999, Saturn orbit insertion in
21American Institute of Aeronautics and Astronautics
2004, and the release of the Huygens probe in late 2004. It must be updated while the spacecraftis on thruster control.
5 . Parameters associated with the “Excessive Thruster Commanding” error monitor (that wasimplemented to detect the presence of a thruster leakage) must be managed before and after thefollowing events: Venus flybys (in 1998 and 1999), Earth swing-by (in 1999), Saturn orbitinsertion (in 2004), and all thruster-based Titan flybys (during Tour, in 2004-2008).
6. Flight software knowledge of the thruster magnitudes must be updated, while the spacecraft is onreaction wheel control, before the recharge of the monopropellant tank.
(e) SID suspend-related restrictions:1. SID must be suspended if the edge of the un-occulted Sun is inside the SRU’s B/S ±30° for
longer than 6 minutes. (B/S denotes Bore-sight vector).2. SID must be suspended if the S/C’s rate is “fast” such that |ωY| + 0.131 × |ωX| >9.6 mrad/s.3. SID must be suspended if the S/C’s rate is “fast” such that |ωZ| + 0.131 × |ωX| >9.6 mrad/s.4. SID must be suspended if any part of an object with a diameter >0.5° is inside the SRU’s B/S
±12°.5. SID must be suspended if any part of an object with a diameter >1.7° is inside the SRU’s B/S
±18°.6. SID must be suspended if any part of an object with a diameter >2.0° is inside the SRU’s B/S
±30°.7. At the start and end times of an “SID suspend” event, the spacecraft must be quiescent with all
three per-axis rates below 0.01 °/s.8. The duration of a “SID suspend event” must not exceed 5 hours.
(f) Frequency of in-flight calibrations and characterizations of AACS equipment:1. Engine gimbal actuators must be exercised every 90 ± 10 days.2. Reaction wheel assemblies must be exercised every 90 ± 10 days.3. Stellar reference units must be calibrated every year (±90 days).4. Inertial reference units must be calibrated at least twice a year.5. Reaction wheel bearing drag torque must be characterized every 180 ± 21 days.
(g) Use appropriate slew profile limits:1 . Thruster-based profile limits must be commanded before a reaction-wheel-to-thruster control
mode transition has occurred. 2 . Reaction wheel-based profile limits must be commanded before a thruster-to-reaction-wheel
control mode transition has occurred. 3 . Reaction wheel-based slew profile limits must be selected consistent with the RWA power
allocation.(h) Other slew restrictions:
1. A turn (with a small slew rate and a large slew angle) that takes >1 year to complete must not becommanded.
(i) Restrictions that are related to ∆V burns:1. Upon the completion of a main engine (or thruster) burn, AACS FSW autonomously makes a
transition from the “main engine ∆V” state (or “RCS ∆V” state) to the “Home Base” state.Thereafter, the flight team must send a command to block a transition to the “Main engine ∆V”(or “RCS ∆V” state).
2. The flight team must send a command to “unblock” an AACS mode transition from the HomeBase state to the “main engine ∆V” state (or “RCS ∆V” state) before a ∆V burn is initiated.
3. Each time the engine gimbal actuator is powered on, the first positional command after closingthe servo loops must be an extension of at least 2 mm.
(j) Restrictions that are related to the operations of reaction wheels:1. Reaction wheels shall not be powered off until after their spin rates are all within ±5 rpm.
(k) Restrictions that are related to the maintenance of the IVT and BVT:1. Active IVP vectors must be updated before they expired.2. A body vector should not be updated while it is being used.3. No more than 15 vectors should be “connected” to form a vector “tree.”4. An IVP vector must not be deleted until after (at least) 10 seconds after its last use.5. A non-existence body or inertial vectors must not be deleted.6. The “head” and “base” objects of all vectors must be different.7. There cannot be parallel paths for a given head-base IVP pair.
22American Institute of Aeronautics and Astronautics
(l) Geometric constraints during Tour:1. The angle between a vector from the spacecraft to any part of the un-occulted Sun and the
positive X-axis of the spacecraft must exceed 83°. This constraint is named “POSX_SUN”constraint.
2 . The angle between a vector from the spacecraft to any part of the un-occulted Sun and thenegative Y-axis of the spacecraft must exceed 12°. This constraint is named “NEGY_SUN”constraint.
(m) Maximum number of commands per unit time:1. No more than three commands per second may be sent to the AACS command handler from all
planned non-critical command sources (background sequences, mini-sequences, etc.).2. No more than four commands per second may be sent to the AACS command handler from a
critical sequence.
23American Institute of Aeronautics and Astronautics
IV. Flight Performance of the Cassini Attitude Control SystemThe performance of the Cassini AACS is described in the following sub-sections. Flight experience associated
with the reaction wheel control system is described in Sections IV.A1 to IV.A5. The performance of the reactioncontrol system is described in Section IV.B1 to IV.B4. The performance of propulsive maneuvers executed with arocket engine or a set of thrusters is described in Sections IV.C1 to IV.C4. The performance of the attitudeestimator design is described in Sections IV.D1 and IV.D2. Flight calibrations and characterizations of AACSsensors and actuators, as well as the determinations of NAC and HGA bore-sight vectors are described in SectionsIV.E1 to IV.E9. Flight experiences related to the AACS Fault Protection Design are described in Sections IV.F1and IV.F2. Flight experiences related to the CMT design are described in Sections IV.G1 and IV.G2. Tracking ofAACS “consumables” is given in Section IV.H. The impact of the space radiation environment on AACSperformance is given in Section IV.I. The operational temperatures of AACS equipment are given in Section IV.K.Flight determinations of non-gravitational torques imparted on the spacecraft are described in Section IV.L.Summary and conclusions are given in Section V.
IV.A1 Reaction Wheel Attitude Control System Performance16
The RWAC was first used on March 16, 2000, several months ahead of the start of the Jupiter campaign.Reaction wheels 1, 2, and 3 were used as the prime RWA set for controlling the spacecraft’s attitude from March16, 2000 to July 11, 2003. In late 2002, AACS observed anomalous frictional torque in the bearing(s) of reactionwheel 3. A decision was made in mid-2003 to articulate the ARWA platform so as to align the backup RWA(reaction wheel 4) with reaction wheel 3. After July 11, 2003, the prime reaction wheel set became RWA-1, RWA-2, and RWA-4. Details of the articulation of reaction wheel 4 are given in Section IV.A4.
During the Jupiter campaign, the Approach Science (January to June, 2004), and at the start of the primemission, the following per-axis slew rates and accelerations were used to slew the spacecraft using the reactionwheels: [1.65, 1.78, 3.08] mrad/s and [9, 10, 17] µrad/s2 about the spacecraft’s X, Y, and Z-axis, respectively.These slew profile limits were selected to be consistent with the capabilities of the reaction wheel torque andmomentum storage capacity. They were also selected assuming at least 90 W of power is allocated for the threereaction wheels. In flight, the actual power allocation is 110 W (with a 20-W power margin). The Huygens Probewas successfully released on December 24, 2004. There was a corresponding drop in the moments of inertia ofspacecraft after the Probe release. As such, the slew profile limits were raised in early 2005 to [1.92, 2.30, 3.90]mrad/s and [10, 13, 22] µrad/s2 about the spacecraft’s X, Y, and Z-axis, respectively.
Flight experience indicated that the RWAC is well designed. Representative per-axis attitude control errorswhile the spacecraft is in a quiescent state are always bounded by ±40 µrad about all the spacecraft axes (this is therequirement specified in Reference 8). The pointing stability performance of the spacecraft is summarized in Table4. Obviously, the achieved spacecraft pointing stability is better than the requirements specified in Table 1 by atleast a factor of 3. The high quality of images returned by the high-resolution cameras provides ample evidence tothis claim.
24American Institute of Aeronautics and Astronautics
IV.A2 Attitude Control Performance During Gravitational Wave Search10
Doppler tracking experiments using the Earth and the spacecraft as test masses were conducted by Cassini forgravitational wave searches in the low frequency range (10-4 to 10-3 Hz). For 40 days centered about its solaropposition in December 2001, the spacecraft was tracked continuously (in Ka-band, approximately 32 GHz) in thefirst search for gravitational waves (11/26/01-1/5/02) that were predicted by Einstein’s general relativity theory.During this 40-day period, the Doppler tracking system continuously measured the Earth-spacecraft normalizedrelative velocity, ∆v/c. Here, ∆v is the relative velocity and c is the speed of light. A gravitational wavepropagating through the radio link was expected to cause small perturbations in the Doppler time series ∆v/c.These perturbations would be replicated three times in the tracking signal with a certain characteristic pattern thatcould be detected. The second gravitational wave search also lasted 40 days and was conducted over 12/6/02-1/14/03. The third and last search was only two weeks long and was conducted over 12/15/03-1/04/04.
Because of the stringent requirements on the pointing of the spacecraft antenna for Ka-band observations, theCassini spacecraft was controlled using three reaction wheels (instead of reaction control thrusters) during theDoppler experiments. In these 40-day periods, other experiments on board the spacecraft were requested not toarticulate their instruments or cause unnecessary fluctuations in the power load. The GWE requirement on thespacecraft contribution to the Allan variance of the noise (fractional frequency stability) was <10-15 for 103-104
seconds integration time. The Allan variance achieved by the spacecraft (during the first gravity wave searchexperiment) was on the order of 2.3 × 10-16, which is better than the requirement. The performance of the RWACfor the second and third GWE was equally good.
Beside spacecraft pointing stability, the initial spin rates of the reaction wheels must also be carefully selectedahead of the experiments. This is important because the spin rates of the reaction wheels will “drift” slowly overthe 40-day span of the experiment due to the presence of small environmental torque (solar radiation torque andradiation torque due to the power generators) imparted on the spacecraft. At the time of the first GWE, theapproximate magnitudes of these disturbance torques were [+2, -1, +2] µNm, with respect to the spacecraft’s X toZ-axis, respectively. Using predicted values of these disturbance torques, the AACS team biased reaction wheels 1,2, and 3 to -1028, -900, and -1330 rpm, respectively, at the start of the first GWE. At the end of the GWE (40days later), the reaction wheels spin rates were -869, -963, and -702 rpm. These wheel rates were all well below thesaturation rate of the reaction wheels (which is about 2029 rpm). At the same time, their magnitudes were higherthan 700 rpm to ensure the presence of elasto-hydrodynamic lubrication films in the bearings of the reactionwheels. The initial RWA spin rates for the other two GWE were similarly selected.
IV.A3 In-Flight Estimation of the Spacecraft’s Inertia Tensor17
Several attitude control algorithms on board the Cassini spacecraft use knowledge of the spacecraft’s inertiatensor. It is used in the RWAC, TVC, several fault protection error monitor designs, and the attitude estimatoralgorithms. As such, it is important to have an accurate estimate of the spacecraft’s inertia tensor. Before launch,the inertia tensor was estimated by adding together the moments of inertia of the individual components of thespacecraft. The moments of inertia of individual components were computed with respect to the predicted center ofmass of the overall spacecraft before being summed. After launch, the onboard inertia matrix is updatedperiodically using estimates of how much propellant (both mono and bi-propellant) has been used to date, as wellas two discrete events: The deployment of the magnetometer boom and the release of the Huygens Probe. Thespacecraft inertia matrix, on March 15, 2000, estimated using the “sum-of-components” method, is:
This estimate of the spacecraft’s inertia tensor had not been confirmed in-flight until the “conservation ofangular momentum” approach that was proposed in References 3 and 4.
The underlying principle of the “conservation of angular momentum” approach is explained as follows. Whena spacecraft is slewed using the RWAs, the total angular momentum vector of the spacecraft expressed in an inertialcoordinate frame is conserved. This conservation occurs because the addition of angular momentum on thespacecraft due to external torque, such as solar radiation torque, is typically very small over the duration of theslew. On March 15, 2000, the largest per-axis external torque due to all sources was about the spacecraft’s X-axiswas less than 15 µNm. The conservation of angular momentum allows the total angular momentum evaluated justprior to the beginning of the slew to be set equal to the total angular momentum evaluated throughout the slew.This equality gives an equation for each sample time step throughout the slew with only one unknown, ISC, that
25American Institute of Aeronautics and Astronautics
can then be estimated via a least-squares approach. Note that ISC contains the moments of inertia of the threestationary reaction wheels.
During a spacecraft slew, good estimates of the following quantities are available, either from directmeasurement prior to launch or from the telemetry data:
(1) Spacecraft angular rates (ωx, ω y, and ωz),(2) RWA spin rates with respect to its spin axis (ρ1, ρ2, and ρ3),(3) Spacecraft Euler parameters (q1, q2, q3, and q4),(4) Inertia matrix of the three RWAs (IRWA), and(5) Transformation matrix, from the RWA spin axes to the XYZ body coordinate frame (T).The total angular momentum vector of the spacecraft, expressed in the spacecraft body frame, has two
components:
r H Total =
r H SC +
r H RWA . The component due to the spacecraft rates is:
r H SC = ISC
r ω where
v ω =
[ωx, ω y, ω z]T. To determine the angular momentum of the RWAs, we first define
r ρ = [ρ1, ρ2, ρ3]
T, where ρi is the
spin rate of the ith RWA about its spin axis. To find
r H RWA, we simply multiply
r ρ first by the inertia matrix for
the RWAs, and then multiply by the transformation matrix T. Note that the component of
r H RWAdue to spacecraft
rates has already been accounted for in
r H SC .
r H RWA = TIRWA
r ρ (2)
The conservation of angular momentum is only valid in an inertial coordinate system. As such, a transformationmatrix, P, defined here from the J2000 inertial frame to the body coordinate frame, must be defined. It is computedusing the four Euler parameters (qi, i =1-4). Multiplying the total angular momentum of the spacecraft in bodycoordinates by the inverse of the transformation matrix P gives the total angular momentum vector in the inertialcoordinate frame. The resultant vector, given below, is approximately conserved over a spacecraft slew.
r H Total (t) = P −1(t)ISC
r ω (t) + P −1(t)TI RWA
r ρ (t) (3)
The spacecraft is quiescent just prior to the slew, with all angular rates approximately zero. As such, theinitial angular momentum vector is given by:
r H Total 0( ) = P−1(0)TIRWA
r ρ (0) (4)
Invoking the conservation of angular momentum, one gets:
P(t)−1 ISC
r ω (t) + P(t)−1TIRWA
r ρ (t) ≈ P(0)−1TIRWA
r ρ (0) (5)
Now, for the sake of simplicity, consider the special case in which the spacecraft slews about one axis at atime. In this case, the rate components about the other two axes go to zero. For example, for a slew about the X-axis, Eq. (5) becomes:
€
ISC
ωx (t)00
= P(t)P−1(0)TIRWAr ρ (0) − TIRWA
r ρ (t) ≡
r Q (t) (6)
Denote the right hand side of Eq. (6) by a new vector. r Q (t) = [Qx(t), Qy(t), Qz(t)]
T. Using this notation, the firstcomponent of the vector-matrix Eq. (6) is:
€
IXXωx (t) =QX(t) . In Eq. (6), both ω x(t) and Qx(t) will take on anew value for each sample instance, t, throughout the slew, producing a new equality for each sample instance. If
r ϖ X and
r Q X represent NS × 1 column vectors of data points from all sample instances (NS is the total number of
samples), a least-squares approach can be used to find the best estimate of IXX:
€
ˆ I XX = [ r ϖ X
T r ϖ X ]−1 r
ϖ XT
r Q X (7)
This process can be repeated for IYX and IZX using the pairs of vectors [r ϖ X
r Q Y] and [
r ϖ X
r Q Z ], respectively.
The entire process can then be repeated for slews about the Y and Z-axis as well. This process will give oneestimate for each of the moments of inertia and two estimates for each one of the products of inertia (POI). Thetwo POI estimates have been averaged together to obtain the best estimate. The results obtained are:
26American Institute of Aeronautics and Astronautics
This estimate of the spacecraft inertia matrix is close to that determined pre-launch. The estimates for the threemoments of inertia are consistently lower than their pre-launch counterparts by nearly 3%. This offset could pointto a bias in the estimate of the spacecraft inertia matrix prior to launch. A bias in the pre-launch estimate ispossible because the knowledge requirement for the MOI of the “dry” spacecraft is quite large: ±10%. Also, thePOI estimates are within 40 kg-m2 of their pre-launch counterparts. The magnitudes of the POI estimates are alllarger than their pre-launch counterparts, which again could be evidence of a bias. Pre-launch, the knowledgerequirement for the POI of the “dry” spacecraft was ±75 kg-m2.
IV.A4 Articulation of the Backup Reaction Wheel PlatformA backup reaction wheel (RWA-4) is mounted on an articulatable platform. At Launch, it was aligned parallel
with reaction wheel 1. If the need arises, the RWA platform could be articulated to align RWA-4 with either RWA-2 or RWA-3. Figure 4 depicts the orientations of the four reaction wheels relative to the spacecraft’s coordinateframe at the time of Launch.
On July 11, 2003, the platform was articulated to align the backup reaction wheel with reaction wheel 3. Thiswas necessary because, since late 2002, the bearing(s) of reaction wheel 3 had developed occasional excessivefrictional torque. The articulation of reaction wheel 4 and the related in-flight testing were carried out as follows.
Before the articulation of the RWA platform, the RWAC performance with reaction wheels 2, 3, and 4 wasfirst evaluated. To this end, the spacecraft was commanded to slew about the X-axis (+180°), Y-axis (±90°), Z-axis(±90° and +180°), and a multi-axis (+30°, +30°, +30°). Results from these tests were compared with thoseobtained when identical slews were made using reaction wheels 1, 2, and 3. These comparisons confirmed that theperformance of RWAC with reaction wheels 2/3/4 are comparable to that with reaction wheels 1/2/3. It alsoconfirmed that RWA-4 performance is comparable to that of RWA-1.
Next, with the spacecraft in an Earth-pointed attitude and under thruster control, the articulatable platform wasarticulated 120° in order to align reaction wheel 4 with reaction wheel 3. The platform articulation was carried outwith all reaction wheels powered off. The next step was to calibrate the orientation of reaction wheel 4 (relative tothe spacecraft) in its new position. To this end, the Earth-pointed spacecraft was transitioned back from thrustercontrol to reaction wheel control (using reaction wheel 1, 2, and 3). While in an “RWA rate control” mode,reaction wheel 4 was commanded to change its spin rate to track a series of spin rate commands depicted in Figure10. Due to conservation of total angular momentum of the spacecraft, there were corresponding changes in the spinrates of reaction wheels 1, 2, and 3. Using the spin rate telemetry, we could determine the orientation of reactionwheel 4.
The total angular momentum vector of the spacecraft system in an inertial frame is:
€
r H Total(t) = P−1(t){ISC
r ω (t) + TIRWA
r ρ (t) +UIRWA4ρRWA4 (t)} (9)
The symbols used in this equation were defined in Section IV.A3. The 3×1 vector U gives the orientation ofreaction wheel 4 in the spacecraft coordinate frame. Equation (9) is simplified if we invoke the following twoapproximations. Firstly, since the spacecraft is quiescent throughout the calibration, P(t) ≈ constant and ω(t) ≈ 0.Secondly, the spin rate of reaction wheel 4 at the start of the test is zero. The simplified equation is:
€
UIRWA4ρRWA4 (t) = TIRWA{r ρ (0) - r
ρ (t)} (10)The last equation could be denoted compactly by:
€
UX
UY
UZ
R(t) =
QX(t)QY(t)QZ(t)
(11)
Here, R(t) denotes IRWA4ρ RWA4(t), and Qi(t) is the ith component of TIRWA{ρ(0) - ρ(t)}. If ΦX = [QX(1),…, QX(N)],ΦY = [QY(1),…, QY(N)], ΦZ = [QZ(1),…, QZ(N)], and Σ = [R(1),…, R(N)] (where N = Total number of datapoint), the reaction wheel 4 orientation vector U (=[UX,UY,UZ]T) could be determined using the following least-square expressions:
€
UX = [ΣTΣ]-1ΣTΦX
UY = [ΣTΣ]-1ΣTΦY
UZ = [ΣTΣ]-1ΣTΦZ
(12)
The process of getting these least-square estimates might cause [UX, UY, UZ]T not to be a unit vector. If this is thecase, there might be a need to re-normalized this vector.
27American Institute of Aeronautics and Astronautics
Figure 10. Calibration of the Reaction Wheel 4 Angular Momentum Vector
The targeted orientation of reaction wheel 4, in spacecraft coordinate frame, is [0.707107, -0.408248, 0.577350]T.The calibrated orientation of reaction wheel 4 is U = [0.713318, -0.402252, 0.573909]T. The misalignment is onlyabout 0.53°, which is better than the 2-degree requirement.
Upon completion of the articulation of the RWA platform, the RWAC performance with reaction wheels 1, 2,and 4 was evaluated. To this end, the spacecraft was commanded to slew about various axes with rate profilesidentical to those used for testing the performance of RWAC with reaction wheels 2, 3, and 4. Results from thesetests were compared with those obtained with reaction wheels 1/2/3 and 2/3/4. These test results confirmed that theperformance of RWAC with reaction wheels 1/2/4 is comparable to that with reaction wheels 1/2/3 and 2/3/4. Withthe successful completions of the platform articulation, alignment calibration, and performance checkout, Cassinibegan using the RWAC with reaction wheels 1/2/4 on July 13, 2003. To date, its performance has been excellent.
28American Institute of Aeronautics and Astronautics
IV.A5 Reaction Wheel Bias Optimization Tool (RBOT)During the tour, a high level of spacecraft pointing stability is needed during imaging operations of cameras
and other science data collect activities. The needed level of spacecraft stability could only be met using reactionwheel control. However, the use of reaction wheels is subjected to three physical constraints. Firstly, at no timeshould we allow the spin rates of any of the three reaction wheels to exceed the angular momentum capacity limit(about ±2000 rpm) of the wheels. In fact, the AACS fault protection design will initiate an autonomous reaction-wheel-to-thruster transition when a “high rpm” condition is detected. Secondly, the total number of revolutions ofthe three prime wheels that is incurred as a result of science slews must be kept as low as possible. Officially, theuseful “life” of each reaction wheel is 4 billion revolutions (see also Table 15). These two constraints bothdiscourage high-speed wheel operations. Thirdly, the operational hours the wheels spent inside a “low-rpm” region(±300 rpm) must also be minimized. The requirement is to limit the low-rpm dwell time (of each wheel) to be lessthan 12,000 hours for the four-year prime mission. This need is explained as follows.
Each Cassini reaction wheel uses two R10-size ball bearings that are spring preloaded (a common practiceamong reaction-wheel manufacturers). The bearings contain a crimped stainless steel ribbon cage, and they arelubricated with 25-30 mg of light ester oil (trade name is Windsor Lube L245X), containing 5% tricresylphosphate (TCP) as an anti-wear additive. The bearings each have metal shields to help prevent oil loss. The wheelunits were shielded with a 1.5-psia (about 10 kPa) atmosphere of helium gas to retard oil evaporation within thehousing. The estimated vapor pressure of the lubricant is 2.6×10-8 Torr (1 Torr ≈ 133.322 N/m2) at 25 °C. Coupledwith the helium atmosphere, evaporative loss of lubricant is likely at a minimum.
The bearing spin rate that is required to achieve the Elasto-Hydro-Dynamic (EHD) lubrication condition forthese bearings with the Windsor Lube is estimated to be 300-550 rpm. This is a speed range below which thethickness of the lubrication film (between the balls and the races) is smaller than the root-mean-square value of thesurface roughness of the bearing balls and the races. As such, operating the bearings at spin rates below this range,there will be metal-to-metal contact between the balls and the races. This is highly undesirable.
However, it is very difficult to completely avoid operating the wheels inside the “low-rpm” region. This is sobecause, as explained above, there is a “competing” requirement of avoiding high-rpm operations too. As such, thebest one can do is to operate the wheel in such a way to minimize the time the wheels spent inside the ±300-rpmlimit.
To operate the RWAs within these three constraints, since early 2001, the Cassini AACS team developed andused a ground software tool named Reaction Wheel Bias Optimization Tool (RBOT). Given the time histories ofthe spacecraft’s science slew attitude and rate, from one RWA biasing to the next, RBOT will select a set of“optimal” reaction wheel biasing rates in such a way as to minimize a cost functional J. In a simplified form, thecost functional J defined as follows:
€
J = W (ω i)Start
End
∫ ω idti=1
3
∑ (13)
Here, ωi (i= RWA-1, RWA-2, and RWA-3) denote the time histories of the three prime reaction wheels (which areassumed to be RWA 1/2/3). Given the time histories of the spacecraft’s science slew attitude and rate, and anestimate of the environment torque vector, the reaction wheel rates ω i could be easily be computed via theconservation of the total angular momentum vector of the spacecraft in an inertial frame. The weighting function Wis a function of the reaction wheel spin rate ω. It is constructed to reflect the three operational constraints describedabove. It is large when the RWA spin rate is inside the low-rpm region (it becomes very large when the spin rate isvery close to zero rpm). Outside the low-rpm region, W has a small value when the spin rate is at 300 rpm. Itsvalue then increases slowly with the magnitude of the wheel spin rate so as to discourage operations at high spinrate. The weighting function is made very large once the spin rate exceeds 1850 rpm. This will strongly“discourage” the reaction wheels from operations with spin rates that are too close to the momentum limit of ≈2000 rpm. A fault-protection error monitor will be triggered if the rate limit is exceeded. The monitor will initiatea reaction-wheel-to-thruster transition but without calling Safing. This is highly undesirable because all scienceslews will now be executed using thrusters, consuming a large amount of hydrazine and a large number ofthrusters’ on/off cycles. The spacecraft will also experience a large ∆V.
The formulated nonlinear optimization problem is solved numerically using the Nelder-Mead simplex method.Other details of the RBOT ground software are given in Reference 20.
29American Institute of Aeronautics and Astronautics
IV.B1 Performance of the Reaction Control System (RCS)During early Cruise, Cassini used a set of eight thrusters to control the spacecraft attitude. Figure 3 shows the
locations of the four thruster pods. All rest-to-rest slews are profiled using a pre-selected set of per-axis “coast”rates and a set of per-axis accelerations. Hence, the time history of the rate command is either “trapezoidal” or“triangular” in shape. Let us denote the acceleration, coast rate, and slew angle of a slew by α , ω , and θ,respectively. If the slew angle θ is smaller than ω 2/α , then the rate profile is triangular, and the time it takes tocomplete the slew is 2√(θ/α). On the other hand, if θ ≥ ω 2/α , then the rate profile is trapezoidal, and the time ittakes to complete the slew is (θ/ω+ω/α). If θ = ω2/α, then either expression gives a slew time of 2ω/α.
During cruise, all spacecraft slews were profiled with rate limits of [4.54, 4.54, 4.54] mrad/s and accelerationlimits of [98, 81, 201] µrad/s2 (about the spacecraft’s X, Y, and Z-axis, respectively). These slew profile limitswere selected to be consistent with the capabilities of the thruster force magnitude, the moment arms, and themoments of inertia of the spacecraft. Using this set of slew profile limits, representative spacecraft per-axis ratecontrol errors were bounded by ±0.1 mrad/s during the “Coast” phase of the slew. During both the “acceleration”and “deceleration” phases of the slew, the per-axis rate control errors are larger but are still bounded by ±1 mrad/s.
During the long outer Solar cruise, several special-purpose slew profiles had also been used. In 2002, certainspacecraft slews were performed using a set of “slow” slew profile limits: [1.1, 1.1, 1.1] mrad/s and [25, 20, 50]µrad/s2 about the spacecraft’s X, Y, and Z-axis, respectively. The slower slew profile was used to save bothhydrazine and thrusters’ on/off cycles. On March 2, 2003, the performance of high-rate spacecraft slew was checkedout. To this end, we used a set of “fast” slew rate limits of [8.73, 8.73, 8.73] mrad/s, about the spacecraft’s X, Y,and Z-axis, respectively. The acceleration limits were unchanged. The faster slew rate of 8.73 mrad/s (about 0.50°/s) was selected to be comparable to the target motion compensation rate of icy moon flybys during Tour.
The Spacecraft’s attitude control errors while on thruster control are “commandable” via a “7DEADBAND”command. The three arguments of this command provide the FSW with the magnitudes of the one-sided dead-bandabout the spacecraft’s X, Y, and Z-axis. During the early phase of the outer Solar cruise with the HGA pointed atEarth for X-band communication, dead-band of [2, 2, 20] mrad was used to assure that the inertial pointing controlrequirement for X-band downlink (see Table 1) was met. At times when accurate pointing was not needed, AACSused dead-band of [20, 20, 20] mrad in order to save both hydrazine and thruster on/off cycle. On the other hand,the attitude control dead-band was tightened to [0.5, 2, 0.5] mrad during the Titan-B flyby (December 6, 2004).This smaller dead-band was used to enable the precision pointing of a science instrument UVIS (for which thebore-sight vector is parallel to the spacecraft’s minus Y-axis and it has a small FOV of 0.75×61 mrad). Other dead-band settings are described in Section IV.B2. See also Table 5.
The performance of the RCS control system during probe relay tracking is described in the following. TheHuygens Probe, developed by the European Space Agency, was successfully released on December 24, 2004. TheProbe was dormant from separation until it reached a Titan-relative altitude of 1270 km, on January 14, 2005.During its descent through the Titan atmosphere, six science packages onboard the Probe sampled the atmosphereand transmitted back to the spacecraft the collected science data. Data collected over the descent phase of the Probemission lasted about 2 hours and 27 minutes. Data transmission from the Probe while it was on the surface ofTitan lasted another 1 hour and 12 minutes. To ensure that spacecraft received all the transmitted Science data, thepointing of the spacecraft HGA vector had to meet a pointing control requirement of 6 mrad (radial 99%, see alsoTable 1).
The commanded dead-band for the Probe relay critical event was [2, 2, 2] mrad. The walking dead-band stepsize selected for this event was 120 µrad. A maximum of three steps was also specified. Other details related to the“walking dead-band” are given in Section IV.B3. The time histories of the X- and Y-axis attitude control errorsobserved during Probe relay tracking are depicted in Figure 11. In these figures, both the X- and Y-axis attitudecontrol errors were controlled to within ±2 mrad 99% of time. There were occasional excursions outside either endof the dead-band. Larger dead-bands, from 2.12 to 2.24 mrad were observed. The X-axis attitude control errorbefore the start of the critical relay tracking was ≈ 3.3 mrad. This was due to the slewing of the spacecraft from anEarth-pointed attitude to the initial condition of the Probe tracking attitude. Also, due to this spacecraft slew, theRCS controller was in a “high rate” mode with relatively frequent thruster firings. Thereafter, it settled down to a“low rate” mode with only occasional thruster firings. Other details of the Huygens probe relay sequence are givenin Reference 44.
30American Institute of Aeronautics and Astronautics
Figure 11. X- and Y-axis Attitude Control Time Histories During Probe Relay in 2005(Unit of the vertical axis is milli-radians)
31American Institute of Aeronautics and Astronautics
IV.B2 Selections of RCS Dead-bands for Various Flight ScenariosThe sizes of the three RCS controller per-axis dead-bands used influence the consumptions of both hydrazine
and thrusters’ on/off cycle. As such, they are selected to be as large as possible while still meeting all theapplicable pointing control requirements. Table 5 is a list of dead-bands that were used over the past eight years tosupport various control functions. A comparison of the tightest one-sided dead-band for five JPL interplanetarymissions is given in Table 6. Clearly, Cassini has the tightest RCS controller dead-band.
RWA Rate Biasing 2 2 Typically, the S/C is Earth-pointed.RWA run-down tests(drag characterization)
2 2 For RWA drag characterizationperformed on thruster control.
Before transition fromthruster to RWA Control
2 2 To ensure a smooth thruster to RWAtransition.
Science Observations afterthe SOI burn
2 2 When the spacecraft was very close toSaturn and its rings.
Probe relay in-flight testperformed in 2003
0.5, 1, and 2 2 Pre 2003, Probe relay required [X,Y,Z]dead-band of [0.5, 0.5, 2] mrads.
Spacecraft slew on thrusters 2 2 These are representative values.Before/after a main engine∆V burn
2 2 These are representative values.
During a main engine ∆Vburn
- 17.5 Not commandable but FSW patchable.The [X,Y] attitudes are controlled bygimbal actuators.
Before/after a thruster ∆V 2 2 These are representative values.Thruster ∆V burns 8.75 17.5 Not commandable but FSW patchable.Before Probe release 2 2 To assure accurate Probe release
pointing. On December 24, 2004.LGA Downlink Pointing 20 20 Used during inner-Solar Cruise.HGA Downlink Pointing 2 20 Used during outer-Solar Cruise.Titan-A Flyby 2 2 1174 km altitude, October 15, 2004.Titan-B Flyby 0.5 (X), 2 (Y) 0.5 1194 km altitude, December 4, 2004.Titan-5 Flyby 20 (X), 5 (Y) 5 1025 km altitude, April 16, 2005.Sun Search 9 9 Not commandable but FSW patchable.Center Sun mode 9 9 Not commandable but FSW patchable.NAC observations of Spicaand Masursky
2 2 For NAC bore-sight vector calibrations.Fomalhaut was observed with RWAs.
Magnetometer boomdeployment
20 20 On August 16, 1999. Two days beforethe Earth swing-by.
32American Institute of Aeronautics and Astronautics
IV.B3 Tuning of RCS Controller Pulse Width Adjuster ParametersAfter crossing 2.5 A.U., communication with the Cassini spacecraft was switched to the HGA rather than the
LGA, which had been used during the inner Solar cruise phase. This required lowering the controller dead-bandfrom the previous [20, 20, 20] mrad to [2, 2, 20] mrad about the X, Y, and Z-axis respectively. This new dead-band significantly increased the number of thruster pulses and mass of hydrazine propellant that were beingconsumed per day. Following the completion of the inner Solar cruise phase, the AACS team analyzed theperformance of the RCS controller relative to some of its parameters. The analysis was under taken to improvelimit cycle behavior during the long outer Solar cruise phase, with the desire to reduce multiple thruster pulsingand hydrazine propellant usage. Some of the RCS controller parameters were hard to select pre-launch viasimulations. As such, the designers of the RCS controller recommended in-flight tuning of these controllerparameters.
During periods when fast changes in S/C attitude are not required, the RCS controller reverts from theconventional BOB thruster control algorithm (high rate mode) discussed in Section III.B to the Adaptive PulseWidth Adjuster mode (APWA, also known as “low rate mode”). The APWA adjusts the thruster “on-time” tosomewhere between a minimum value of 7 ms and a maximum value of 125 ms. The on-time selection depends onthe magnitude of the small environmental torque imparted on the spacecraft. The APWA logic is quite simple: thenext thruster “on-time” is the last thruster “on-time” multiplied by a multiplication factor. That factor is a functionof the magnitude of the external torque imparted on the spacecraft about the axis of interest. This environmentaltorque could be estimated by the angular excursion that the spacecraft transverses before the external torque stopsand reverses the spacecraft limit cycle motion.
For a small environmental torque that is not “strong” enough to “stop” the rate resulting from the last thrusterpulse, the dead-band is crossed (two sided limit cycle). In this case, we select a multiplication factor of 0.6 tolower the control impulse. In addition to reducing the opposing thruster “on-time” by a factor of 0.6, the dead-bandis also increased slightly by a magnitude that is specified by the FSW parameter named “Walking Dead-band Step”(WDS). This parameter increases the size of the dead-band by the step amount each time a thruster is fired near thedead-band for up to 5 steps. The WDS was set at 120 µrad at launch. The selected step size and step number cancause a worst case widening of the dead-band of up to 0.6 mrad. The widened dead-band is reset to its commandedvalue after 80% of the commanded dead-band has been traversed.
With a large environmental torque that causes one-sided limit cycle motion, the multiplication factor isdetermined by the following formula:12 Factor = [√L2+√L3]/[√L1+√L2], where L1 and L2 are the “normalized”spacecraft angular excursions transverse by two previous one-sided limit cycle excursions as shown in Figure 12.The normalization is made with respect to the two-sided dead-band.
- DeadBand
+ DeadBand
EnvironmentalTorque
L1L2
Figure 12. Adaptive Pulse Width Adjuster
L3 is the next desired limit cycle excursion. The parameter Factor is that factor that the previous thruster pulsewidth must increase in this thruster pulsing in order to get to L3. As can be seen from the Factor formula, if L1 issmaller than L3, then Factor is larger than one and the next pulse width is increased. Only if L1 is larger than L3
will the parameter Factor be less than one. The size of L3 was selected to cause maximum angular excursionwithout “touching” the other side of the dead-band “space.” But it must also be selected to be robust againstthrusters’ pulse-to-pulse variation. It was observed in-flight that the “Factor Next Limit Cycle” (FNLC) value of√0.75 (value of L3 at launch) was causing a significant amount of double-sided limit cycle motion, particularlywith small environmental torque. The RCS controller parameters selected for change were WDS and FNLC.
33American Institute of Aeronautics and Astronautics
The expected effect of the changing WDS was to reduce the number of multiple pulses during double-sidedlimit cycle motion. The desire to reduce the number of multiple pulses is driven by the maximum allowablenumber of 273,000 thruster cycles allocated per thruster (see also Table 14 in Section IV.H). The expected effect ofchanging FNLC was to reduce the amount of double-sided limit cycle motion under conditions of small externaltorques and thereby reduce the average hydrazine consumption.
Two in-flight tests were performed to test new values for the WDS and FNLC. The first test was performedfrom 2001-140T16:33:03 to 2001-144T12:22:54 when the WDS was changed from 120 to 200 µrad for theduration of the test. The second test was performed from 2001-203T16:03:30 to 2001-206T15:52:10 when theFNLC was changed from √0.75 to √0.5 for the duration of the test. AACS analysis of the test results indicatedthat there was a 6% decrease in multiple pulsing observed during the first test and a 26% reduction in the averagethruster “on-time” in the second test.
Independently, the Cassini propulsion team also analyzed the results of these tests. Their analysis of data fromthe first test indicated a 19.3% reduction in the total number of thruster valve cycles and a corresponding 2.5%reduction in hydrazine consumption. They also determined, for the second test, a 41% reduction in the hydrazineconsumption. See Reference 25. Based on these positive test results, these new parameter values were madepermanent in the AACS Flight Software build A7.7.6. These values have been continued in all subsequent FSWbuilds.
Further improvements in the RCS controller performance would be difficult to achieve, particularly in the X-axis and Y-axis that have very low environmental torques and that use small dead-bands (2 mrad). In fact,beginning the summer of 2001, these external torques were low enough such that even a 7-ms thruster pulse hasproduced rates that are too high to produce one-sided limit cycle motion with a 2-mrad dead-band.
An additional RCS controller parameter that is a good candidate for change and may be very effective inreducing limit cycle rates about the X and Y-axis is the minimum pulse width parameter “PMS Pulse Min.” In theLaunch flight software, it is 7 ms. During Cassini flight acceptance hot-fire tests of the 0.9-N thrusters, thethrusters were tested down to 4 ms pulse widths but the manufacturer recommended against any use of pulsessmaller than 5 ms (due to their concern about its poor repeatability performance). Based on the IBIT (impulse bit,in units of Ns) versus pulse width formula derived from the test data, there would be a 35-percent reduction inIBIT (and limit cycle rate) by reducing the minimum pulse width from 7 to 5 ms. Two possible adverseconsequences of reducing the minimum pulse width below 7 ms are a possible decrease in pulse-to-pulserepeatability and an increase in the amount of multiple pulsing. The 7-ms minimum pulse width implemented inthe flight software was selected to meet the pulse-to-pulse repeatability requirement of ±20%. The IBIT was notlowered below 7 ms in-flight due to these concerns.
Thrusters used by Cassini have rich heritage from the Voyager program. During the prime mission ofVoyagers, thruster valve on-times smaller than 20 ms were never used. However, during the extended mission, theflight team throttled back the size of the pulses, ultimately reaching 4 ms. The thrusters worked fine with the 4-mson time. The Cassini flight team might want to do something similar during the extended mission.
34American Institute of Aeronautics and Astronautics
IV.B4 Performance of the RCS Detumbling Controller Design after Probe ReleaseThe Huygens Probe, developed by the European Space Agency, was successfully released on December 24,
2004. A brief description of the performance of the thrusters in detumbling the S/C after the Probe was released isgiven below. Other details of the Probe release sequence design are given in Reference 18.
In the initial condition of the Probe release sequence, the spacecraft was Earth-pointed under thruster controlwith dead-band of [2, 2, 20] mrad about the spacecraft’s X to Z-axis, respectively. Because subsequent spacecraftslew (from the Earth-pointed attitude to the Probe release attitude) would place the Sun inside the stray-light FOVof the star tracker, the star identification algorithm had to be “suspended.” The SID suspend event started before theS/C was slewed away from the Earth-pointed attitude, and lasted about 37 minutes. Also, commands were sent tochange the “state” of the two geometric constraints from “AVOID” to “DETECT.” This was done in order toprevent the constraint monitor from issuing commands that interfere with those issued by the attitude commanderduring spacecraft slews and detumbling. These CMT-related commands were also sent while the spacecraft was inthe Earth-pointed attitude. The geometric constraints were re-established after the detumbled S/C was back in anEarth-pointed attitude.
A set of slew commands was then sent to align the axis of symmetry of the Probe with a pre-selected “ProbeRelease” inertial attitude. At the predicted end time of the slew, the attitude controller dead-band was tightened to[2, 2, 2] mrad. Probe ejection occurred about 6 minutes after the slew had ended. The 6-minute “settling time”allowed all fuel sloshing motion to subside so that the spacecraft’s per-axis rates at the time of Probe release wereall lower than 0.004 °/s.
The release of the probe involved the firing of a set of pyrotechnics to enable the Spin Ejection Device (SED).Separation was achieved via both a linear and an angular impulse between the orbiter and the Probe. Impulsesexperienced by the spacecraft caused it to tumble. After the expiration of a 5-minute control inhibition time (whichwas intentionally designed in the sequence), the thrusters began to “detumble” the spacecraft. The 5-minute “nothruster firing” time (as measured from the time of Probe ejection) was implemented to prevent any potentialcollision between the tumbling orbiter (with an 11-m magnetometer boom) and the departing Probe. It was alsoimplemented to use the sloshing motion of the fuel in the tanks to damp out some of the separation-inducedspacecraft tumbling rates. With reference to Figure 13, we see that the Y-axis rate of the spacecraft dropped fromabout 8 to 2 mrad/s during this “no thruster firing” time.
“Detumbling” was completed when both the X- and Y-axis rates of the spacecraft fell below 0.01 °/s, but withthe spacecraft spinning about its Z-axis at rate of -3.666 mrad/s. This is the so-called “bore-sight protection spin”which was built into the “detumbling” control algorithm. This spin assures that the bore-sight of the imaginginstruments such as NAC, will not stay stationary in inertial space for too long a time (for it might be pointedvery close to the Sunline vector). Thereafter, the Y-facing thrusters nulled the Z-axis rates, and the spacecraft wasslewed back to an Earth-pointed attitude. As measured from the time of Probe release, ground telecommunicationlink with the spacecraft was re-established in about 16 minutes.
The estimated magnitudes of linear and angular impulses imparted on the spacecraft were 126.1 Ns and 108.6Nms, respectively.18 Uncertainties associated with these estimates are ±20% and ±30%, respectively. Theseimpulses caused the spacecraft to tumble with peak per-axis rates of at least 0.83, 0.44, and 0.106 °/s about the X-,Y-, and Z-axis, respectively. The magnitude of the separation rate is about 0.95 °/s. Figure 13 depicts the timehistories of the spacecraft X and Y-axis rates. However, the probe release event is very “impulsive,” and the lowfrequency of the S/C rate telemetry (one data point every 2 seconds) might fail to capture the “peak” rates. Theangular impulse also caused the departing Probe to spin at a rate of about 8.1 rpm. The linear impulse imparted a∆V of about 0.39 m/s on the Probe.
At launch, the spacecraft was released from the Centaur upper stage on 1997-288/09:26:00. The separationevent imparted a rate vector of [-0.109, -0.74, -0.01] °/s (about the S/C’s X-, Y-, and Z-axis, respectively) on thespacecraft. The magnitude of the separation rate is about 0.75 °/s, which was smaller than that caused by the Probeejection. The spacecraft was detumbled by the same detumble controller design in less than 3 minutes. Overall,the performance of the RCS detumble control algorithm was excellent for both separation events.
35American Institute of Aeronautics and Astronautics
Figure 13. X- and Y-axis Attitude Control Error Time Histories During Probe Release in 2004
36American Institute of Aeronautics and Astronautics
IV.C1 Performance of the Thrust Vector Controller during Propulsive Maneuvers with a Rocket Engine
A list of all propulsive maneuvers (∆V) performed using main engine A, from Launch until early 2005, isgiven in Table 7.
Table 7. Performance of Engine-based Propulsive Maneuvers
Engine
Maneuver
Date Commanded
∆V [m/s]
Magnitude
Error [%]
Pointing
Error [mrad]
TCM-1
TCM-5
TCM-6
TCM-9
TCM-10
TCM-11
TCM-12
TCM-13
TCM-14
TCM-17
TCM-18
TCM-19
TCM-19b
TCM-20
TCM-21
SOI
OTM-2
OTM-3
OTM-5
OTM-6
OTM-8
OTM-10
OTM-11
OTM-12
OTM-14
11/9/97
12/2/98
2/4/99
7/6/99
7/19/99
8/2/99
8/11/99
8/31/99
6/14/00
2/28/01
4/3/02
5/1/03
10/1/03
5/27/04
6/16/04
6/30/04
8/23/04
9/7/04
10/29/04
11/22/04
12/18/04
12/29/04
1/16/05
1/27/05
2/18/05
2.73
449.96
11.53
43.54
5.13
36.3
12.26
6.70
0.5546
0.4905
0.8907
1.595
2.00
34.7228
3.6956
626.17
392.9416
0.4954
0.6387
0.4074
11.9027
23.759
21.583
18.66
0.683
0.8
0.065
0.011
0.007
0.10
0.01
0.045
0.044
0.92
4.5
1.35
0.12
-
0.01
0.2
-
0.13
3.5
1.3
4.1
0.07
0.02
0.11
0.07
1.3
5.2
1.4
0.8
0.76
1.4
0.3
0.94
1.52
11.1
5.3
2.1
1.64
-
0.44
0.32
-
0.06
3.6
1.5
1.8
0.4
0.8
0.5
0.2
1.4
In this table, all burns are “blow-down” except TCM-5, TCM-13, TCM-20, SOI, and OTM-2, which are“regulated.” The performance of the TVC algorithm is gauged by comparing the execution errors of these
maneuvers with the error requirements given in Table 1. Let
€
r V C and
€
r V A denote the commanded and achieved ∆V
vectors in J2000 frame, and
€
r v C denotes the unit vector of
€
r V C . The magnitude error and pointing error of the ∆V
burn are then given by the following expressions:
37American Institute of Aeronautics and Astronautics
€
r e Magnitude =r V C − (
r V A • r v C)r v C
r e Pointing =r V A − (
r V A • r v C)r v C
(14)
These two error vectors represent the maneuver execution errors that are parallel and perpendicular to the
commanded ∆V vector,
€
r V C . Small ∆V errors due to the slewing of the spacecraft to and from the
€
r V C attitude by
thrusters are book kept elsewhere. The magnitudes of the two error vectors,
€
r e Magnitude and
€
r e Pointing should be
compared with their respective 1σ requirements given in Table 1: 1σ magnitude error requirement = 0.01 + 0.002
× |
€
r V C | m/s, and 1σ pointing error requirement = 0.0175 + 0.0035 × |
€
r V C | m/s. For simplicity , the magnitude and
pointing errors given in Table 7 are determined by dividing |
€
r e Magnitude | and |
€
r e Pointing | by |
€
r V C |.
The very first TCM of the Cassini mission, TCM-1 (2.73 m/s) was performed using the main engine onNovember 9, 1997. The magnitude error of TCM-1 was relatively large because of an error in the FSW knowledgeof the accelerometer’s scale factor (about -1%). This FSW error was corrected after TCM-1 via a flight softwarepatch. The pointing error of TCM-1 was also relatively large because of a 0.5-0.75 degree main engine pre-aimerror. At the end of this burn, the engine thrust vector almost pointed through the spacecraft center of mass. Assuch, the telemetry of the engine gimbal angles were used to pre-aim the rocket engine for the next main engineburn (TCM-3, since TCM-2 was a thruster-based ∆V burn).
With reference to Table 7, the mean value of the magnitude errors for all ∆V with magnitudes that are largerthan 3 m/s is 0.064%. The smallest ∆V performed using the main engine is OTM-6 (with a magnitude of 0.4074m/s). The magnitude error of OTM-6 given in Table 7 is 4.08% which looks significantly larger than the 0.6%requirement. In reality, the size of the magnitude error for OTM-6 was 16.6 mm/s. The 1σ magnitude errorrequirement for OTM-6 is 10 + 0.002 × 407.4 ≈ 10.81 mm/s. That is, the magnitude error is only 16.6/10.81 =1.53σ, which is less than 3σ. Overall, the performance of the TVC ∆V control algorithm is excellent. Other detailson the performance of the ∆V burns executed using a rocket engine are given in Reference 22.
TCM-19b and SOI were “special” burns in that they did not aim to achieve a target ∆V vector. Instead of atarget ∆V, they had a target ∆E (Energy). The merits of the ∆E approach over the traditional ∆V approach arebriefly described below (details are given in References 19 and 41). The SOI algorithm must be robust relative tomany “off-nominal” burn scenarios: (1) a late start of the SOI burn (for whatever reason), (2) a prematuretermination of the ∆V burn due to a fault followed by a engine restart (using the backup engine and after a enginecool-down time), and (3) a burn with two or more engine restarts. As an example, consider the case of a late startof the SOI burn. If pre-burn FP activities caused the burn to start 21 minutes late (an example), the required SOI∆V magnitude for this “late start” scenario is 610 m/s (instead of the nominal ∆V value of 626.17 m/s).41 Hence,the traditional ∆V approach will result in an “over-burn” scenario. The over-burn must then be corrected via asubsequent orbit trim maneuver. In contrast, the new ∆E approach will “adapt” itself automatically to the delay anda smaller burn will be made. In this sense, the ∆E approach is robust relative to various ∆V fault scenarios.However, none of these fault scenarios occurred during the actual SOI burn.
TCM-19b was the very first energy-based ∆V burn performed by a JPL-built interplanetary spacecraft (onOctober 1, 2003). It was executed to check out the energy-based ∆V algorithm coded in the AACS FSW A8.6.5(that was uploaded to the spacecraft in the spring of 2003). The successfully executed TCM-19b provided theCassini flight team with additional confidence for the Saturn Orbit Insertion burn.
The Saturn Orbit Insertion (SOI) burn was the most critical engineering event for the entire Cassini mission.The burn started on 2004-DOY-183/01:12:00 and lasted about 5780.5 s. The spacecraft mass at the start of SOIwas estimated to be 4522 kg. At the end of SOI, the spacecraft mass was estimated to be about 3673.7 kg. That is,the SOI burn depleted about 848.3 kg of bi-propellant. Post-burn, the AACS team used the accelerometer toestimate the mean value of the engine thrust. The estimate ranges from 441.9 to 445.1 N (see also Section IV.E9).
Unlike all other main engine burns with a burn attitude that is fixed relative to the inertial frame, the burnattitude of SOI rotated slowly (“steering”) with a rate of about 0.14 mrad/s. Over the course of the burn, thespacecraft attitude rotated 46.37°. Nevertheless, the TVC control algorithm performed well even in the presence ofthis “steering” turn. The SOI burn caused the spacecraft velocity to be lowered by about 626.17 m/s, allowing it tobe captured by the gravity field of Saturn. The targeted change in the specific energy of the spacecraft was 17.830km2/s2. The achieved change in specific energy was 17.831 km2/s2. The execution accuracy of the SOI burn wasexcellent. The superb accuracy of the SOI burn led to the cancellation of OTM-1, the very first orbit trim maneuverof Tour.
38American Institute of Aeronautics and Astronautics
IV.C2 Stable Limit Cycle Observed in Spacecraft “Dynamics” Telemetry During Main Engine Burns
Stable limit cycles with frequencies of about 0.03-0.04 Hz were observed in all “dynamics”-related telemetry(for example, spacecraft’s per-axis rates, engine gimbal angles, etc.) of all “long” burns performed with a rocketengine. These limit cycles were first observed in the telemetry of the Deep Space Maneuver (DSM, TCM-5, ≈1.46hours) performed in 1998. They were also observed during the long Saturn Orbit Insertion burn (≈1.61 hours)executed in 2004. Figure 14 depicts the time history of the spacecraft’s X-axis rate (near the end of the SOI burn).A 0.033-Hz stable limit cycle could be clearly observed in this telemetry.
Figure 14. Time History of the Spacecraft’s X-axis Rate Near the End of SOI (2004).[Note the presence of a 0.033-Hz limit cycle]
The frequencies of these limit cycles were about 0.05 Hz near the start of the DSM burn (in 1998), but theydecreased slowly to 0.036 Hz just before the termination of the DSM burn. The frequency observed near the end ofthe SOI burn (which is depicted in Figure 14) was 0.033 Hz. The frequency of these limit cycle oscillations tendsto drop with the reducing inertia of the spacecraft. The observed limit cycle frequency is quite close to thefundamental frequency of the high-g bi-propellant sloshing motion mentioned in Section II.A, which is about0.05-0.06 Hz. However, fuel sloshing motion modeled by a second-order system with a natural frequency of 0.05Hz and a damping ratio of 0.12 should settle down in about 4/(2% × 0.05 × 0.12) < 2 min. after burn ignition.This prediction disagrees with the fact that the observed oscillations continued for more than an hour. Hence, whatwe observed is not due to fuel sloshing motion.
The source of the observed sustained oscillation in the S/C’s rates comes from a stable interaction betweennonlinear elements in both the engine gimbal actuators and the rocket engine, the thrust vector control algorithm,and the flexible dynamics of the spacecraft base-body, as illustrated in Figure 15.
39American Institute of Aeronautics and Astronautics
γGSC(s)GTVC(s) GGuidance(s)
Stable Sustained Oscillations
θθCommand γ Com
man
d
Gega(s)Compliances of
“Soft” mount and Fuel flexlines, etc.+ -
Figure 15. A Simplified Representation of the Cassini Thrust Vector Control System
In Figure 15, the spacecraft’s equation of motion, from the engine gimbal angle γ to the base-body inertialangle θ, is represented by GSC(s). Here, s demotes the Laplace variable. GSC(s) captures the effect due to the 0.7-Hzmagnetometer boom as well as the fuel sloshing motions that occurred in both the MMH and NTO tanks. TheTVC compensator design is denoted by GTVC(s). The guidance loop design is represented by the transfer functionGGuidance(s). The compensated errors from the output of GTVC(s) are multiplied by the loop gain, resulting in whatare effectively the angular acceleration commands. These commands are then multiplied by the upper 2×2 of the3×3 “transformed” spacecraft inertia tensor. The transformed inertia tensor is simply that defined with respect to theTVC control coordinate frame. If the computed torque is divided by the product of engine thrust and moment arm,one obtains the required engine gimbal angle γ C. The gimbal angle commands are sent to the engine gimbalactuators. Other details of the guidance loop, such as the guidance filter, anti-windup limiters, etc., are described inReference 15.
The engine gimbal actuator (EGA) is a ball-screw assembly driven by a brushed DC motor. It is mounted tothe thrust plate via a universal joint. The output shaft of the gimbal actuator is connected via a pin joint to therocket engine above the gimbal plane. In this way, an extension or retraction of the actuator causes the engine torotate in its gimbal system. For small gimbal motions about the “null” position, the gimbal angle displacementsare proportional to the shaft displacements.
The dynamic of the EGA system is represented by Gega(s). The response of the EGA is fast enough to bealmost transparent to the TVC algorithm. As an approximation, Gega(s) is represented by a first-order lag with atime constant of about 0.036 second. Gega(s) = 1/(1+Tas). The transfer function from the linear actuator motion(after it has been converted to an equivalent rocket engine rotation, γC) to the rotational motion of the rocket enginecontains several nonlinearities. It contains the compliance and backlash (free-play) of the soft mount. Thecompliance and hysteretic element of the propellant flex line must also be considered. Finally, there is also thereaction flexing of the soft mount against the propellant line forces. These nonlinear elements could be representedby a composite “describing function” N(γC). The representation of a nonlinear control element by a “describingfunction” is explained in, for example, Reference 30.
For ease of notation, let C(jω) denote the overall control transfer function of the TVC algorithm, the guidanceloop, and the engine gimbal actuator, C(jω)=GTVC(jω)•GGuidance(jω)•Gega(jω). Let G(jω) denotes GSC(jω ), andN(γC) denotes the describing function of all the nonlinear elements mentioned above. Note that the describingfunction N(γC) is a function of the magnitude of its input signal γC. A sustained oscillation is observed in theoutput of the TVC control loop whenever the following condition is satisfied:
G(jωC)C(jωC) = -1/N(γC) (15)The frequency of the oscillation ωC and the amplitude of the oscillation γ C could be determined as follows.
Figure 16 is the polar plot of the transfer function GC(jω). The polar plot is often called the Nyquist plot.Superimposed on this plot is the negated reciprocal of the describing function N(γC). The interceptions of GC(jω)and -1/N(γC) are operating points that satisfy the condition specified in Equation (15). They represent either astable or unstable oscillation. In Figure 16, the interception that is denoted “stable oscillation” is stable because ifthe amplitude of the oscillations diverges, the operating point will move to the left of the -1/N(γC) curve. Theshifted operating point is now not encircled by GC(jω), and the overall system is stable (Nyquist condition). Thiswill cause the amplitude of the oscillations to decrease (and the operating point is shifted back to the originalinterception point). Conversely, if the amplitude of the oscillation decreases, the operating point will shift to theright of the -1/N(γC) curve. The shifted operating point is now encircled by GC(jω) and the overall system isunstable (Nyquist condition). This will cause the amplitude of the oscillation to increase (and the operating pointis shifted back to the original interception point). Hence, a sustained oscillation with an (almost) constant
40American Institute of Aeronautics and Astronautics
frequency ωC and an (almost) constant amplitude γ C will be observed. The frequency of the oscillation ωC isdetermined from GC(jω) at the operating point. Similarly, the amplitude of the oscillation γC is determined from -1/N(γC) at the operating point. For the SOI scenario, ωC is about 0.033 Hz, and γ C fluctuated between ±0.03 and±0.04 mm (see Figures 14 and 17).
Real 0
•
Imag
iner
y
Stable Oscillations
Unstable Oscillations GC(jω)
-1/N(γC)
•
increasing ω
increasing γC
Figure 16. Stable and Unstable Oscillations in a Control System with Nonlinear Elements
Figure 17. Time History of the EGA LVDT Q-Axis Motion (Near the End of SOI)
41American Institute of Aeronautics and Astronautics
IV.C3 Observed High-g Bi-propellant Fuel Sloshing Frequencies during SOIThe power spectral density of the spacecraft’s X-axis rate during SOI is depicted in Fig. 18. The spacecraft’s
mass at the start of SOI was 4522 kg (the “wet” mass is 2121 kg). At the end of the burn, the spacecraft’s mass is3674 kg (the “wet” mass is 1273 kg). This long burn depleted about 848 kg of fuel.
Figure 18. Power Spectral Density of the Spacecraft’s X-axis Rate During SOI
With reference to Figure 18, the following “peaks” are clearly visible. The frequency of the first peak is about0.033 Hz. It corresponds to the frequency of the limit cycle resulting from the stable interactions between thenonlinear elements in the EGA and the REA, and the TVC controller discussed in Section IV.C2. The frequency ofthe second peak is about 0.074 Hz (together with another two smaller peaks with frequencies of 0.058 and 0.065Hz). This set of frequencies is close to the estimated value of the first high-g bi-propellant fuel sloshing frequency,0.05-0.14 Hz (see Section II.A). The third peak frequency is close to the 0.13-Hz frequency of the RPWS antennas.The last peak, observed near 0.18 Hz, is close to the estimated value of the second high-g bi-propellant sloshingfrequency. The damping ratios of the fuel sloshing motions are hard to estimate with any accuracy from these PSDdata.
42American Institute of Aeronautics and Astronautics
IV.C4 Performance of Propulsive Maneuvers Using Four Z-facing thrustersA list of all propulsive maneuvers (∆V) performed using the Z-facing thrusters, from Launch until early 2005,
is given in Table 8.
Table 8. Performance of Thruster-based Propulsive Maneuvers
Thruster
Maneuver
Date
Commanded
∆V
[mm/s]
Magnitude
Error
[%]
Pointing
Error
[mrad]
Mean
Z Thrusters
Duty Cycle
[%]
TCM-2
TCM-7
TCM-19a
OTM-4
OTM-9
OTM-10a
OTM-13
2/25/98
5/18/99
9/10/03
10/23/04
12/23/04
1/3/05
2/11/05
185
240
120
368
15.9
134.7
202.8
3.24
0.042
0.35
0.18
2.33
0.16
0.21
23.95
9.84
7.93
12.42
67.9
6.83
6.0
91.4
91.5
92.2
91.6
100.0
92.6
92.4
The magnitudes of the two error vectors,
€
r e Magnitude and
€
r e Pointing , computed using equation (14), should be
compared with their respective 1σ requirements given in Table 1: 1σ magnitude error requirement is 0.0035 + 0.02
× |
€
r V C | m/s, and 1σ pointing error requirement is 0.0035 + 0.012 × |
€
r V C | m/s. For simplicity , the magnitude and
pointing errors given in Table 8 are determined by dividing |
€
r e Magnitude | and |
€
r e Pointing | by |
€
r V C |. With reference to
Table 8, all RCS thruster ∆V magnitude errors were better than 6% (the 3σ proportional magnitude errorrequirement). Also, the pointing errors of all RCS ∆V burns (except for the very small OTM-9) were better than 36mrad (the 3σ proportional pointing error requirement). However, in reality, the magnitude of
€
r e Magnitude for OTM-9
was only 0.37 mm/s. The 1σ magnitude error requirement for OTM-9 is 3.5 + 0.02 × 15.9 ≈ 3.818 mm/s. That is,the magnitude error was only 0.37/3.818 ≈ 0.1σ. Also, the magnitude of
€
r e Pointingfor OTM-9 was 1.08 mm/s. The
1σ pointing error requirement for OTM-9 is 3.5 + 0.012 × 15.9 ≈ 3.69 mm/s. That is, the pointing error was only1.08/3.69 ≈ 0.3σ. As such, the performance of the RCS controller, even for OTM-9, was excellent.
During an RCS burn, the four Z-facing thrusters are commanded on except when off-pulsing is required for X-and Y-axis attitude stabilization. The primary “disturbances” in the X/Y-axes are self-induced, arising mainly fromthe offset of the S/C’s c.m. from the origin of the spacecraft mechanical frame. To a lesser extent, the structuralmisalignments of these Z-facing thrusters, and the thruster-to-thruster performance variation also contributed tothese off-pulsing. Accordingly, one should expect the mean duty cycle of the four Z-facing thrusters to be less than100%. The mean duty cycle of the four Z-facing thrusters for seven RCS burns are listed in Table 8. The dutycycle for OTM-9 was 100% because the burn was very short. Off-pulsing was never necessary for this burn becauseof the short burn duration. The overall average duty cycle is 93.1%. The “efficiency” of the RCS burn is quitegood indeed.
43American Institute of Aeronautics and Astronautics
IV.D1 Performance of the Spacecraft Attitude Estimator (ATE)AACS acquires stellar reference by first locating the Sun, and then Sun-pointing the HGA using data from the
SSA. A SID algorithm then uses star data captured by the star tracker to acquire a three-axis stellar reference. Thefront-end of the Cassini attitude estimator is a pre-filter that combines multiple star updates into one composite starupdate. These composite star updates are then sent to the attitude estimator every 1-5 seconds. In between starupdates, the S/C attitude is propagated using the IRU data. Once attitude is initialized, AACS maintainsknowledge of the spacecraft attitude in a celestial coordinate frame that is called the “J2000 frame.”
The performance of the ATE is quantified by the magnitudes of the three per-axis attitude estimationuncertainties (σi, i = X to Z-axis). The star tracker B/S vector is aligned with the positive X-axis of the spacecraft.As such, typically, σX is larger than σY and σZ. Representative values of σX, σY, and σZ are 12, 3, and 3 µrad,respectively, when the spacecraft is quiescent. The “number of stars” used by SID in a quiescent state is typically 4or 5 stars. These attitude estimation uncertainties are higher when the spacecraft is spinning (usually about the Z-axis). Representative values of σX, σY, and σZ in a scenario when the Z-axis spin rate is 3.89 mrad/s are 120, 30,and 30 µrad, respectively. The time history of σZ when the spacecraft is spinning about its Z-axis (at a rate of 3.89mrad/s) on 2005-DOY-60 is depicted in Figure 19. As the time neared 2005-DOY-060T07:00:00, the spinningmotion of the spacecraft was halted. Thereafter, the value of σZ was improved (lowered) from 30 µrad to 5 µrad.
44American Institute of Aeronautics and Astronautics
IV.D2 Performance of the Attitude Estimator with the Star Identification Algorithm “Suspended”During Tour, Saturn, its rings, and its satellites sometime enter the tracker’s FOV. The presence of one or
more of these bright objects might affect the nominal operation of the SID algorithm. As such, the SID operationhas to be temporarily “suspended” via an AACS command named “7SID_SUSPEND.” While SID is suspended,the S/C attitude is propagated using the gyroscopes. In-flight, the AACS team suspends the SID operationwhenever any one of the following conditions is true.
[a] The edge of the un-occulted Sun is inside the SRU’s B/S±30° for longer than 6 minutes.[b] If the S/C’s rate is “fast” such that |ωY| + 0.131 × |ωX| > 9.6 mrad/s.[c] If the S/C’s rate is “fast” such that |ωZ| + 0.131 × |ωX| > 9.6 mrad/s.[d] Any part of an object (such as Titan) with a diameter >0.5° is inside the SRU’s B/S ± 12°.[e] Any part of an object with a diameter >1.7° is inside the SRU’s B/S ± 18°.[f] Any part of an object with a diameter >2.0° is inside the SRU’s B/S ± 30°.At the start and end times of an SID “suspend” event, the spacecraft must be quiescent with all per-axis rates
below 0.01 °/s. The requirement at the start time is important in order to assure that the per-axis ATE uncertaintiesat the start of the SID suspend event are as small as possible (see Section IV.D1). The requirement at the end timeis important in order to ensure that the SID algorithm can seamlessly transition from the “Suspend” state to the“Track” state without having to perform either a “mini-acquisition” or “reacquisition.” In-flight, we also restrict theduration of the SID “Suspend” event to be less than 5 hours.
When SID is suspended, the S/C’s attitude is propagated using the gyroscopes. If the S/C’s attitude estimate ispropagated by gyro over a time duration T (in seconds) during which its ith-axis is slewed through an angle θ (inradians), then the ith-axis attitude estimation variance is approximately given by the sum of the following errorvariances:
ATE error at the start of the propagation: Vstart = σ2start
In these expressions, Nwalk is the IRU angle random walk PSD, Nstability is the IRU bias stability PSD, and σstart
is the attitude estimation error at the start of the SID “Suspend” event when the spacecraft attitude was estimatedusing both the star tracker and gyroscopes. A representative value of σstart is 0.012 mrad (about the worst axis).(See Section IV.D1). The gyroscope biases determined just before the start of a SID “suspended” event will be usedby the FSW in subsequent attitude propagation when SID is suspended. The estimation error of the gyro bias isσBiasError whose representative value is 0.1 µrad/s. Subsequent propagated attitude will contain an error term whosevariance is proportional to σ2
BiasError×T2. Scale factor errors (σSFE) of the gyroscopes typically make the largestcontribution to the error of the propagated attitude (when SID is suspended) of a spinning spacecraft. Arepresentative value of σSFE about the S/C’s Z-axis is 0.05-0.06%. If SID is suspended for 5 hours, during whichthe spacecraft is spinning about the Z-axis at a rate of 3.9 mrad/s, then one can expect an error of about 5 × 3600 ×3.9 × 0.05 × 0.01 = 35.1 mrad (about 2°) about the Z-axis at the end of the SID suspend event.
The alignment of the gyroscopes with respect to the AACS coordinate frame is calibrated during all IRUcalibrations (see Section IV.E2). The calibrated results are incorporated in the FSW via the introduction of amodified coordinate transformation matrix. As such, the contribution to the error of the propagated attitude due toerror in gyro misalignment knowledge errors (σMisalign) is typically small. A representative value of σMisalign is 0.15mrad. However, one can expect a 1-to-2 mapping.
Representative time histories of the Y-axis and Z-axis attitude control errors when the spacecraft is spinningabout its Z-axis (at a coast rate of 3.89 mrad/s on 2005-074) for an angle of 56548.7 mrad (about 9 revolutions)over a time duration of 4.483 hours and with the SID suspended are given in Figures 20 and 21, respectively. Notethat the magnitude of the Y-axis error is very small. This is because there was not any angular rotation about theY-axis of the spacecraft. As such, the error due to the gyroscope scale factor errors about this axis is insignificant.Only the sinusoidal contribution of the gyroscope misalignment is visible in Figure 20. However, near the end ofthe SID suspend event, the attitude estimation error about the Z-axis is quite large. Figure 21 depicts a 35-mrad Z-axis attitude control error at the end time of the SID suspend event. Note that 35/56548.7 ≈ 0.061%.
45American Institute of Aeronautics and Astronautics
Figure 20. Y-axis Attitude Control Error (Spinning Spacecraft, SID Suspended)
Figure 21. Z-axis Attitude Control Error (Spinning Spacecraft, SID Suspended)
46American Institute of Aeronautics and Astronautics
IV.E1 In-Flight Calibrations of the Accelerometer’s BiasThe accelerometer’s bias is calibrated before each and every main engine-based maneuver. To this end, the
ACC is powered on 1 hour before the start of the bias calibration. The ACC’s output data number (NACC)accumulated over a one-minute time span is then sent to the FSW. The ACC’s bias is estimated using theequation: Bias = NACC × 2.02033/60 mm/s2. Results are tabulated in Table 9. The stability of the ACC’s bias overtime is excellent and is significantly better than the long-term ACC bias stability requirement of 180 µg (about1.766 mm/s2). Also, note that the Probe was ejected on 12/24/04, in between OTM-8 and OTM-10. Theaccelerometer bias was not changed by the ejection impulses.
Table 9. Flight Calibrated Accelerometer Bias
Maneuver Date Bias (mm/s2)
TCM-1
TCM-5
TCM-6
TCM-9
TCM-10
TCM-11
TCM-12
TCM-13
TCM-14
TCM-17
TCM-18
TCM-19
TCM-19b
TCM-20
TCM-21
SOI
OTM-2
OTM-3
OTM-5
OTM-6
OTM-8
OTM-10
OTM-11
OTM-12
OTM-14
11/9/97
12/2/98
2/4/99
7/6/99
7/19/99
8/2/99
8/11/99
8/31/99
6/14/00
2/28/01
4/3/02
5/1/03
10/1/03
5/27/04
6/16/04
6/30/04
8/23/04
9/7/04
10/29/04
11/22/04
12/18/04
12/29/04
1/16/05
1/27/05
2/18/05
2.800
3.064
3.064
3.030
3.031
3.031
3.030
3.030
2.997
2.930
2.862
2.828
2.862
2.829
2.829
2.795
2.795
2.795
2.795
2.795
2.795
2.795
2.795
2.795
2.795
IV.E2 In-Flight Calibrations of the Inertial Reference Unit A and BIRU-A has been used by Cassini AACS as the prime inertial sensor since launch except during a brief period
of time in 2003 during which IRU-B was powered on and made prime in order to check out its performance. Afterthe first in-flight calibration of IRU-A in 2002, the calibrated values of the scale factor errors of the gyroscopes andtheir misalignments with respect to the AACS frame were incorporated in the AACS FSW version A8.6.5 (which
47American Institute of Aeronautics and Astronautics
was uploaded in the Spring of 2003). Similarly, from the in-flight calibration of IRU-B in 2003, we determinedvalues of the scale factor errors of the IRU-B gyroscopes and their misalignments. The calibrated values wereincorporated in the AACS FSW version A8.6.7 (which was uploaded in late Spring, 2004). After theincorporations of results from these two “first-time” IRU calibrations in the FSW, subsequent in-flight calibrationsestimated small deviations from these implemented FSW values. The calibrated values of the gyroscope biases arenot incorporated in the FSW. This is because in the day-to-day operation of the attitude estimator, biases of the“virtual” axes are always estimated in conjunction with the spacecraft attitude.
In a typical gyroscope calibration, reaction wheels were used to slew the spacecraft first about its Z-axis (inboth the clockwise and anti-clockwise directions, ±3000 mrad). Thereafter, the spacecraft was slewed about the Y-axis (±1500 mrad), and finally about the X-axis (±3000 mrad). The slew angles were designed to be as large aspossible subjected to the need to avoid any geometric constraint violation. As an example, the spacecraft slew ratesfor the 2002 IRU-A calibration are depicted in Figure 22.
Figure 22. X- and Z-axis Spacecraft Slew Rates during an IRU Calibration Performed in 2002
48American Institute of Aeronautics and Astronautics
In addition to “formal” IRU calibrations scheduled by the AACS team, the team also took advantage of themany RWA-based spacecraft slews performed for the purpose of “optical navigation” to calibrate the gyroscopes.However, unlike the large and multi-axis calibration slews performed during “formal” gyro calibrations, many ofthese optical navigation slews are small (≈1000 mrad). Moreover, often times, the spacecraft only slewed about twoof the three axes. Nevertheless, results obtained from these optical navigation slews could be used to confirmresults obtained from the “formal” IRU calibrations.
Cassini AACS models the “imperfections” associated with an IRU by the following expression:
€
r Ω gyro =
1+ εX 0 00 1+ εY 00 0 1+ εZ
r Ω true +
0 θxy θxz
θyx 0 θyz
θzx θzy 0
r Ω true +
r B +
r N (17)
Since neither the A1A2A3 gyroscopes (of IRU-A) nor B1B2B3 gyroscopes (of IRU-B) are aligned with thespacecraft mechanical frame, the gyro imperfections given in equation (17) are associated with three “virtual” gyroaxes. In equation (17), the IRU bias and the zero-mean “angle random walk” vectors are denoted by B and N,respectively. Gyro scale factor errors are denoted by ε i (i = X, Y, and Z-axis). The IRU misalignment is denotedby θ (which has six independent components). Calibrated biases and scale factor errors are tabulated in Table 10.The calibrated values of the biases of the IRU-A’s gyroscopes are within its requirement of 4.848 µrad/s (1 °/h).However, we note that the biases of both A2 and A3 increase slowly with time with rates of about 0.0009 µrad/sper day (for A3). If this trend continues, at the end of the prime mission (July 1, 2008), the bias of A3 will beabout -4.93 µrad/s. It will slightly exceed its requirement (4.848 µrad/s). But this will not be a problem becausethe EKB filter routinely estimates both the spacecraft’s attitude vector and the IRU’s bias vector (except when theSID is suspended). Spacecraft attitude estimates include compensation for the IRU biases.
The calibrated values of the scale factors of IRU-A’s gyroscopes A2 and A3 are well within the requirement of0.25%. That of gyroscope A1 is just within the requirement. However, the scale factor error of both IRU-A andIRU-B are compensated in the FSW. Residual errors are on the order of only 0.05-0.06% (see Section IV.D2). Forbrevity, the calibrated values of the IRU-A misalignments are not given here but they are all bounded by 1.75mrad, which are better than both the IRU alignment control requirement (5 mrad, 3σ per axis) and alignmentknowledge requirement (2.5 mrad, 3σ per axis).
Only one IRU-B calibration was performed in-flight (in 2003). Calibrated gyroscope biases and scale factorerrors for IRU-B are also given in Table 10. The calibrated biases, scale factors, and misalignments are all betterthan their respective requirements given in Reference 8.
Table 10. Flight Calibrated Gyroscopes’ Biases and Scale Factor Errors
49American Institute of Aeronautics and Astronautics
IV.E3 In-Flight Characterization of the Reaction Wheel Drag TorqueAs part of the Cassini RWA acceptance testing, the RWA vendor had characterized the drag torque of all the
reaction wheels using coast-down tests (sometime called “run-down” tests). In these tests, conducted at a roomtemperature of 25 °C, the reaction wheels were first commanded to a particular initial spin rate and were allowed to“coast” down under the action of only bearing drag torque. More than 100 initial reaction wheel spin rates, evenlyspaced over the entire speed range of the RWA (±2000 rpm), were used in these coast-down tests. Coast down testdata were next fitted with a linear drag torque model of the form:Tdrag = -c × ω - TDahl × Sgn(ω). Here, c (in Nms/rad) is the viscous coefficient of the reaction wheel bearings, ω isthe angular rate of the wheel (in rad/s), Sgn(ω) is the Signum function, and TDahl is the Dahl friction. Dahl frictionis similar to Coulomb friction. However, reaction wheel bearings do not exhibit the classical stick/slip phenomenaof Coulomb friction. Rather, they ramp up to the steady-state Coulomb level exponentially with an “angle”constant of a few degrees of the wheel rotation. Ground test results yielded viscous coefficients of 11.7, 10.8, 10.0,and 9.5 ×10-5 Nms/rad for RWA-1 to RWA-4, respectively. Results of TDahl are 3.4, 6.7, 3.0, 4.8 × 10-4 Nm forRWA-1 to RWA-4, respectively. They represent mean values for both clockwise and counter-clockwise wheelrotations.
In-flight, the reaction wheel friction is calibrated every six months via similar “coast-down” tests. Typically,these in-flight coast-down tests involved commanding the reaction wheels to speeds of +Ω 0, +Ω 0, -Ω0, and -Ω0,for RWA-1 to RWA-4, respectively. (A typical value of +Ω0 is 900 rpm). The speeds of RWA-1 and RWA-2 areidentical and are clockwise. Those for RWA-3 and RWA-4 are also identical but are counter-clockwise. In this way,the reaction torques imparted on the spacecraft due to the frictional torques will approximately cancel each other(however, this is an inexact cancellation). The resultant ∆V due to thruster firing generated by the RWA frictioncharacterization is thus kept to a minimum. Thereafter, the reaction wheels were commanded to -Ω0, -Ω 0, +Ω 0,and +Ω0 (for RWA-1 to RWA-4, respectively) in order to determine the wheel friction characteristics when they arespun in the opposite direction.
The torque applied by the RWA D.C. motor on the RWA spun mass is zero during these run-down tests. Assuch, the RWA spin rate decays due only to the drag torques:
IRWA ˙ ω = -c×ω -TDahl × Sgn(ω) (18)Here, IRWA is the moment of inertia of the RWA about its spin axis. If ω = +Ω 0 at time t = 0, the solution of thisdifferential equation is:
ω(t) = - TDahl/c × Sgn(ω) + [Ω0 + TDahl/c × Sgn(ω)]×e-t/τ (19)Here, the time constant of the RWA speed decay, τ , is given by IRWA/c. Given the time histories of the reactionwheel spin rates, Cassini AACS team uses a nonlinear parameter optimization algorithm (which is based on theNelder-Mead simplex method) to determine both the viscous coefficient and the Dahl friction that best fit the timehistory the reaction wheel spin rate ω(t). Results obtained for the mean viscous coefficient of RWA-2, in the yearsfrom 2000 to 2004, are given in Figure 23. In reviewing data given in Figure 23, one should note that fact the pre-launch viscous coefficient of RWA-2 was 1.08 × 10-4 Nms/rad.
Figure 23. Trend of RWA-2’s Viscous Coefficient Since First Day of 2000
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 200 400 600 800 1000 1200 1400 1600
Days Since 2000 DOY-001
Vis
cous
Coef
fici
ent
[1.0
e-4 N
m/(
rad/s
)]
50American Institute of Aeronautics and Astronautics
The long-term trend of the viscous coefficient of RWA-3 since 2000-DOY-001 is given in Figure 24. In reviewingthe data given in Figure 24, one should note that the pre-launch viscous coefficient of RWA-3 was 1.00 × 10-4
Nms/rad.
Figure 24. Trend of RWA-3’s Viscous Coefficient Since First Day of 2000
Since late 2002, the bearing(s) of RWA-3 had developed a bearing cage instability condition that appeared (anddisappeared) spontaneously and unpredictably. Cage (sometimes called a retainer or a pocket) instability is anuncontrolled high frequency vibration of the bearing cage that can produce high-impact forces internal to thebearing that will cause intermittent torque transients. In many cases, cage instability caused sudden torque changesand has an adverse effect on the performance of the mechanism in which the bearing is situated.46 However, forCassini, the effects of this anomalous drag condition is greatly alleviated by the “drag torque compensator”function implemented in a flight software object named RWA Manager.16
As described in Reference 16, RWA bearing drag torque is estimated using the RWA tachometer data. Theestimated drag torque is used as follows. First, its magnitude is compared with a pre-selected drag level to assurethat the estimated drag torque is not excessive. A caution error monitor will be triggered if a Drag torque is toohigh condition is found. Second, the control torque computed by the RWAC is augmented with the estimated dragtorque to form the total torque. The RWA D.C. motor is commanded to deliver the total torque, which, uponsubtracting the drag torque, will generate the needed control torque. But, even with this drag torque compensationtechnique, the bearing cage instability condition still threatens the long-term safe operations of RWA-3. Due tothis concern, on July 11, 2003 (day 1286 in Figure 24), RWA-3 was replaced by RWA-4 as one of the three primereaction wheels.
Another RWA friction-related metric that is monitored and trended by the AACS team is the duration of the“drag torque spikes” that we observed in the RWA friction torque telemetry. A set of representative friction spikesof RWA-4 is depicted in Figure 25. Each data number in this figure represents 10-5 Nm. In this particular case, theRWA-4 spin rate was constant and was about 270 rpm. The nominal value of the frictional torque at this rpm isabout 2.8 to 3.1×10-3 Nm. This is the horizontal straight line we see in Figure 25. Superimposed on this nominalfrictional torque level are “spikes” of various sizes and durations. Their sizes are bounded by 1.5×10-3 Nm. Theroot cause of these spikes is not well understood, but it might be due to the fact that the wheel was operatinginside the “low-rpm” region. The presence of these spikes is one reason why the “low-rpm” region should beavoided as much as practical (see Section IV.A5). However, frictional spikes were also observed when the wheelswere operated outside the “low-rpm” region.
To monitor and trend these RWA drag spikes, the AACS team uses a ground software tool to estimate thetime durations of the spikes. As an illustration, the long-term trend of the RWA-2 drag friction spike durations,from the year 2000 to 2004, is depicted in Figure 26. This figure reveals not long-term growth in the duration ofthese drag spikes.
0.0
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n V
isco
us
Coef
fici
ent
[1.0
e-4
Nm
/(ra
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)]
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Figure 25. Unexpected RWA Frictional “Spikes”(Scale factor of vertical axis is 10-5 Nm)
0
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0 365 730 1095 1460 1825
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Figure 26. Trend of RWA-2’s Drag Torque Spike Duration Since First Day of 2000
52American Institute of Aeronautics and Astronautics
IV.E4 In-Flight Calibrations of the Stellar Reference UnitsSRU-A was used by AACS as the prime celestial sensor for the first 5 months after launch. Thereafter, SRU-
B has been used as the prime sensor. Both SRUs have been calibrated annually since launch. To date, there havebeen eight SRU calibrations of both star trackers. However, the SRU calibration performed in December 1998 wasunsuccessful due to a radiation-induced Solid State Power Switch (SSPS) problem on SRU-A (the backup SRU).Radiation caused SRU-A SSPS to trip. As a result, the power-on command in the calibration sequence did notpower on SRU-A. A subsequent calibration command named “7SID_SPOT_LIST” caused the SID algorithm tohang up, and it had to be reset by ground commands.
Star tracker calibrations are performed using a “7SID_SPOT_LIST” command. This command is typicallyissued four times (to each tracker) to collect redundant sets of star data (three times in 1997 and four timesthereafter). The star tracking process is temporarily interrupted by the calibration. Once the calibration iscompleted (in less than one minute), SID automatically resumes star tracking. The calibration command resultedin the collection of both the centroid and intensity data of 25 stars. The process is designed to capture a maximumof 32 stars but only the top 25 brightest stars are sent to the ground.
The ground calibration processing uses the known calibration parameters (provided by vendor of the startrackers) to mimic the on-board process. It involves the conversion of the star centroid data to SRU frame vectors,identification of the stars, and compensations for optic geometric distortion effects, star color, and opticstemperature. It ends with the generations of “arrow plots.” The predicted positions (based on the J2000 starcatalog) of the 25 identified stars are plotted in the figures with arrows drawn next to them. Each arrow size isproportional to the position error of that star and is in the direction of the error. Figure 27 shows tworepresentative arrow plots, one for the SRU-A and the other for SRU-B. As can be seen in these figures, mostposition errors are sub-pixel in magnitude or less than 100 µrad (The SRU CCD FOV is comprised of 1024 ×1024 pixels with 255.6-µrad per pixel resolution). Position errors of around 100 µrad or less have not changedsince the first calibration.
In addition to measuring star position errors, the calibrations also estimate the focal length errors of thetrackers. The nominal focal length of the tracker is a nonlinear function of radial distance from the center of theFOV. It varies from 43.6 mm at the edge of the FOV to 45.7 mm near the center of the FOV. Calibrated focallength errors never exceed 9 microns (this is smaller than the 12-micron pixel size of the CCD). The magnitudesof the star trackers’ focal lengths in the FSW have not been changed since the first calibration.
Stars’ brightness magnitudes are also measured by the calibrations. Initially, all measured star brightnessmagnitudes averaged about 1.5 times the star catalog magnitudes. As such, a SID-related FSW parameter waschanged in March 2000 (in the AACS FSW build A7.7.6) to bring the measured star magnitudes closer to the starcatalog magnitudes. Subsequent SRU calibrations yielded star magnitudes that are within expectations except fora few B type stars (stars with temperatures that range from 10,000 to 30,000 K) that measured significantlybrighter than their catalog values. No further update to the star magnitudes has been made after the AACS FSWbuild A7.7.6. Other details of the Cassini SRU calibration process are given in Reference 23.
53American Institute of Aeronautics and Astronautics
Figure 27. Star Tracker Calibrations in 2001-DOY-258 (by Jim Alexander)
54American Institute of Aeronautics and Astronautics
IV.E5 In-Flight Calibrations of the Narrow Angle Camera Bore-Sight VectorThe NAC boresight vector is nominally aligned with the minus Y-axis of the spacecraft. Calibration of the
NAC vector was a joint undertaking between the Cassini AACS team and the ISS Imaging team. The Cassiniimaging team used two instrument calibrations and one science observation to calibrate the NAC bore-sightvector. The first instrument calibration was made with the star Spica (on January 16, 1999) and the second wasmade with the star Fomalhaut (on September 18, 2000). Spica is the α star in the Virgo constellation. Itsdiameter is eight times that of the Sun. Fomalhaut is the α star in the Piscis Austrinus constellation. It is a blue-white star with a diameter that is 1.4 times that of the Sun. The Spica observation was made while the spacecraftwas on thruster control. The Fomalhaut observation was made with the spacecraft controlled by three RWAs. Assuch, the most accurate calibration was made with Fomalhaut.
The science observation was made with the asteroid Masursky 2685 on January 23, 2000. It was observedwhile the spacecraft was on thruster control. Using the array of images taken during each observation, the imagingteam found the location of the object in the images. They then used the estimated spacecraft attitude and the SRU-to-body transformation matrix (furnished by the AACS team) to determined the NAC bore-sight vector in bodycoordinates. Results are given in Table 11. From this Table, we note that the nominal value of the NAC B/Smisalignment is on the order of 0.60-0.64 mrad (Masursky data were not used for reason given below).
Table 11. Narrow Angle Camera Calibrated Bore-sight Vectors
ObservationsAACS Body Axes Spica (1999) Masursky (2000) Fomalhaut (2000)
X +0.0006260±1.1e-5 +0.0006447±1.8e-5 +0.0005760±1.8e-6Y -0.99999979±1.0e-8 -0.99999960±2.0e-8 -0.99999982±1.0e-8Z +0.0001341±6.0e-6 -0.0005469±2.4e-6 -0.0001710±1.6e-6
The NAC bore-sight vector in the AACS FSW was first updated to the Spica-determined value prior to theFomalhaut observation. It was later updated to the Fomalhaut-determined value. The value obtained from theMasursky observation was never used due to fact that the asteroid was not a point source and that the Masurskyobservation was made with substantial ephemeris errors. The NAC bore-sight vector determined by the Fomalhautobservation has been adequate for science observation during Saturn tour.
IV.E6 In-Flight Calibrations of the High Gain Antenna Electrical Bore-sight VectorsThe Cassini HGA electrical bore-sight vector has been calibrated twelve times in-flight between March 2000
and September 2004. The X-band frequency (8.425 GHz) is used for communication and Radio Science, and itsbore-sight vector was determined during all twelve calibrations. The Ka-band frequency (2.298 GHz) is used forRadio Science, and its bore-sight vector was determined during the last eleven calibrations. The -3 dB Half PowerBeam Widths, HPBW (receiving) of X-band and Ka-band are about 11.34 and 4.01 mrad (0.65° and 0.23°),respectively. For transmission, the -3 dB HPBW of X-band and Ka-band are about 9.77 and 3.32 mrad (0.56° and0.19°), respectively.
The HGA is co-aligned with the spacecraft negative Z-axis (see Fig. 2). The spacecraft’s HGA is pointed atEarth at the start of the calibration. Calibration is performed by slewing the spacecraft using the reaction wheelsabout the X and Y-axis in a cross (“”) pattern. The “size” of the cross pattern is ±0.5°. That is, the end-to-endtravel of the calibration “cross” pattern is about 1.5 times the size of the X-band HPBW. In these calibrations, thesignal strength (H), expressed in dB relative to the one milliwatt strength (dBm) is recorded as a function of theangular offsets of the spacecraft relative to its initial attitude (θX, θY). Typical transmission signal strength isexpressed in terms of decibels relative to one watt (dBW). But for a weak signal, decibels relative to one milliwatt(dBm) is used instead. Hence, 0 dBm = -30 dBW. The misalignment of the HGA bore-sight vector (bX, bY) isthen determined based on the following signal strength model:
H(θX, θY) = -k{(θX-bX)2 +(θY-bY)2}+P (20)In this equation, k is the pattern shape parameter in dBm/rad2. [bX, bY] represent the X and Y components of thenormalized HGA electrical bore-sight vector in radians, and P is the peak power of the transmission in dBm. Thegeneral approach that is used to determine the HGA bore-sight vector is sketched as follows. First, the fourunknown parameters are stacked together to form an unknown parameter vector U = [P, bX, bY, k]. Let us denotethe value of this parameter vector at iteration step J by UJ = [P, bX, bY, k]J. A better U that minimizes thedifference (R) between the left and right hand sides of Equation (20) could be found by a “steepest descent” orgradient method. The residual R is given by:
55American Institute of Aeronautics and Astronautics
= UJ - KSTEP × [-1, -2k(θX - bX), -2k(θY - bY), +{(θX - bX)2 + (θY - bY)2}]J (21)In the last equation, ∂R/∂U denotes the gradient vector, and KSTEP is a positive scalar constant. The iteration isstopped whenever the H2 norm of the gradient vector ∂R/∂U is smaller than a pre-selected threshold. Table 12shows the [bX, bY] results of the calibrations.
Not all planned calibrations yielded useful data. Some failed due to loss of data during one or more legs ofthe calibration “cross” pattern. The calibration in April 2000 was performed twice back-to-back and analyzedseparately. In addition to the AACS team, the Radio Science (RSS) team also performed an independent analysisof the calibration data. The AACS team used the closed-loop Automatic Gain Control (AGC) data while the RSSteam used the more accurate open-loop AGC data. For this reason, results from the RSS team analysis were usedto update the HGA body vector in the Body Vector Table (see Figure 7) of the flight software. Results computedby the AACS team were only used to check the results from the RSS team. Since the X-band and Ka-band bore-sight vectors are very close but the Ka-band pointing requires a better pointing accuracy, the calibrated Ka-bandelectrical bore-sight vector has been used for both X-band and Ka-band pointing purposes. From Table 12, onenotes that the angular misalignment of the HGA X-band bore-sight vector is on the order of 0.46-1.1 mrad(0.0264-0.0630°). That for the Ka-band frequency is on the order of 0.36-0.74 mrad (0.0206-0.0424°). Thesemisalignments are very small when compared with the -3 dB HPBW. Nevertheless, the calibrated Ka-band bore-sight vector is always used to point the HGA at Earth during both X-band and Ka-band operations.
Table 12. Calibrated HGA Bore-sight Vectors
X-band Bore-sight Unit Vector Ka-band Bore-sight Unit VectorCalibrationDate X-axis Y-axis Z-axis X-axis Y-axis Z-axis
10/27/01 0.0004618 0.0000634 -0.9999999 Bad data5/7/02 0.0005294 0.0005147 -0.9999997 Bad data1/21/03 0.0005072 0.0003943 -0.9999998 Bad data9/25/03 0.0004698 0.0010180 -0.9999994 0.0004507 0.0009902 -0.99999943/16/04 0.0004934 0.0003405 -0.9999998 0.0006171 0.0004018 -0.99999979/18/04 0.0004570 0.0005075 -0.9999998 Bad data
IV.E7 In flight Confirmations of Sun Sensor Performance The unit vector of the Sun line (spacecraft-to-Sun vector), expressed in the spacecraft frame, is estimated on-
board via three independent sources. If the Sun is inside the ±32° by ±32° FOV of the prime SSA (usually SSA-A), the two-axis SSA measurements could be used to determine the unit vector. Typically, the backup SSA is notpowered on and could not provide information on the Sun position. But, before several hazardous ring-planecrossings (for example, those that occurred on 2005-DOY-047 and 2005-DOY-068), the AACS team powered onthe backup SSA (SSA-B). As such, the two-axis SSA-B measurements could also be used to determine the Sunline vector. Finally, the Sun-to-spacecraft vector is being continuously propagated by IVP (in the J2000 frame).Estimates of the Sun line vector made using SSA-A, SSA-B, and the IVP were compared (in the spacecraft frame)immediately after the two ring-plane crossings that happened near the SOI. Two similar comparisons were alsomade after the hazardous ring-plane crossings that happened on February 16, 2005 (2005-DOY-047) and March 9,2005 (2005-DOY-068). Possible performance degradation in either Sun sensor could then be detected.
The per-axis accuracy and resolution error of the Sun sensor are 1° and 0.5°, respectively. The bit transitionerror and random noise of the SSA are 0.3° and 0.15°, respectively. The mechanical misalignment of the SSArelative to the S/C mechanical frame is about 1°. As such, in comparing data between SSA-A and SSA-B, adiscrepancy as large as 3-4° is considered acceptable.
56American Institute of Aeronautics and Astronautics
A comparison between data from SSA-A and SSA-B made after the February 16, 2005 ring-plane crossing isdepicted in Figure 28. (The actual ring-plane crossing happened on 2005-047T23:38:00.) The comparison is madein the [U1, U2] coordinate frame of the Sun sensors. Note that [U1, U2]
T = [-1/√2, -1/√2; -1/√2, +1/√2][X, Y]T.Sun sensor data, from about 6 hours before the crossing to 9 hours after the crossing, are depicted in Figure 28. Inthis time window, the Sun is not inside the SSA’s FOV all the time (which explained why the data pointsdepicted in this figure are discontinuous). Only valid SSA data are compared in this figure. The largest discrepancybetween the U1 data of the Sun sensors is 1.0°. The largest discrepancy between the U2 data of the Sun sensors is1.05°. Comparisons between SSA-A data and IVP, and between SSA-B data and IVP were also made.Discrepancies from these comparisons were also found to be well below the 4° pass/fail criterion.
Figure 28. A Comparison Between SSA-A Data and SSA-B Data (by Cliff Lee)
IV.E8 In-Flight Calibration of the Thrusters’ MagnitudesThrusters are used to perform many AACS functions listed in Section III.B. The monopropellant propulsion
system for Cassini is of the blow-down type. With this system, the hydrazine tank pressure, which was about 2635kPa at Launch, will decay slowly with time as hydrazine is depleted through thruster firings. At launch (October15, 1997), the thrust magnitude was about 0.97 N. By the time of Saturn Orbit Insertion (June 30, 2004), thethrust magnitude had decayed to 0.75 N. During Probe relay tracking (January 14, 2005), the thrust magnitude was0.69 N. The monopropellant tank will be “recharged” only once, which is currently planned in May/June 2006.
The time-varying magnitudes of eight A-branch and another eight B-branch thrusters are estimated by thePropulsion team. The magnitudes of the eight thrusters on the A-branch are represented by one mean value in theAACS flight software. Those for the B-branch thrusters are represented by another value. These thruster magnitudesare updated from time to time to reflect the decaying thrust. Cassini RCS thrusters are characterized during flightacceptance testing. One set of test results is captured by an equation that relates the nominal steady state RCSthrust to the pressure of the hydrazine tank. The uncertainty associated with this thrust equation is on the order of±5%.8 Thruster magnitude estimated via this equation is further verified in flight by the Propulsion team. Detailsof this in-flight calibration are given in Reference 25.
There is an AACS-centric approach that could also be used to independently determine the RCS thrusters’magnitudes. The underlying principle of the AACS approach is the Euler’s equation. In-flight, in two sets ofspecial events (RWA drag torque run-down test and RWA biasing), the reaction wheels are powered on while thequiescent spacecraft attitude is maintained by eight thrusters. Changes in the reaction wheels’ rates (during RWAbiasing or drag torque run-down test) produce reaction torque on the spacecraft and hence thruster firings. RWA
-40 -30 -20 -10 0 10 20 30 40-40
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10
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30
40SUN in SSA-A/B FOV U1/U2 sensor head frame
U1 (deg)
U2 (deg)
SSA-ASSA-B2005-047T18:17:10 to 2005-048T08:15:02
57American Institute of Aeronautics and Astronautics
spin rate data collected from these events could be used to calibrate the thrusters. Details associated with the RWAbiasing event are given below to illustrate the underlying principle. The effectiveness of the approach is currentlybeing assessed using flight data. No estimates of thruster magnitudes have yet been made via application of thismethodology.
A representative reaction wheel biasing is carried out as follows. The spacecraft is Earth-pointed and is onthruster control, with dead-bands of [2, 2, 2] mrad. After being powered on, the reaction wheels are spun up toattain a set of pre-selected spin rates. In so doing, the D.C. motors of the RWAs impart equal and opposite torqueon the S/C. Thrusters are then fired to maintain the S/C’s attitude in the presence of these reaction torques. Therotational motion of the spacecraft during a RWA biasing event is governed by the Euler equation:
€
ISCr ˙ ω +
r ω × (ISC
r ω +
r H RWA) +
r ˙ H RWA =r T PMS (22)
In Eq. (22), ISC is the S/C’s inertia tensor. The spacecraft rate vector, ω, is estimated by the attitude estimator.The total angular momentum vector of the three reaction wheels, in spacecraft frame, HRWA, is available from theRWA “manager.” Torque vector exerted on the spacecraft due to thruster firing, TPMS, is available from thepropulsion “manager.” Taking the time integration of the Equation (22) from time = 0 to time = ti, we have:
€
ISC{ r ω (ti) −
r ω (0)} + {
r H RWA(ti) −
r H RWA(0)} +
r ω × (ISC
r ω +
r H RWA)dt
0
ti∫ ≈
r T PMSdt
0
ti∫ (23)
This is an approximate equation because the small angular momentum accumulated due to the non-gravitational torque has been neglected. Let us simplify this equation using the following notations. Let ∆ω(ti) =ω(ti) - ω(0), ∆HRWA(ti) = HRWA(ti) - HRWA(0), ∆G(ti) = ∫ω × (ISCω + HRWA) dt, where the integration is from t = 0to ti. The per-axis angular impulses imparted on the spacecraft due to thruster firings are determined as follows.The coordinates of eight A-branch thrusters, Z1, Z2, Z3, Z4, Y1, Y2, Y3, and Y4 are given by: [+LX, +LY, +LZZ], [-LX, +LY, +LZZ], [-LX, -LY, +LZZ], [+LX, -LY, +LZZ], [+LX, +LY, +LZY], [-LX, +LY, +LZY], [-LX, -LY, +LZY], and[+LX, -LY, +LZY]. Let [eX, eY, eZ] denotes the coordinates of the S/C’s center of mass, and Q (3×8) denotes themoment matrix from the eight thrusters Z1, Z2, Z3, Z4, Y1, Y2, Y3, and Y4 (with magnitudes of F1, F2, F3, F4, F5,F6, F7, and F8, respectively) to the three S/C’s coordinate axes:
Using these notations, we have ∫TPMS dt = Q•[F1∆τ1(ti),…,F8∆τ8(ti)]T, where ∆τ1(ti) denotes the Z1 thruster’s
incremental on-time from t = 0 to t = ti, and ∆τ8(ti) denotes the Y4 thruster’s incremental on-time from t = 0 to t =ti. Equation (23) is now denoted compactly by the following expression:
€
ISCΔω(t i ) + ΔHRWA(t i ) + ΔG(t i ) = Q • [F1Δτ1(t i ), ..., F8Δτ8 (t i )]T
(25)If we assume that the Z-facing thrusters are mounted exactly parallel to the S/C’s Z-axis, and the Y-facing
thrusters are mounted exactly parallel to the Y-axis, then equation (25) could be decoupled into two “components.”This is because the Z-facing thrusters’ firings only impart torque about the S/C’s X and Y-axis, and Y-facingthrusters’ firings (in pair) only impart torque about the S/C’s Z-axis. The [X, Y] rows of equation (25), for time ti
Here, PZ = [F1, F2, F3, F4]T, is the unknown Z-facing thruster magnitude vector. Equations similar to (26)
could be written for time steps t2,…,tN where N is the total number of time steps. All these equations could bestacked together to form the following “composite” matrices:
MQ11Δτ1 ( t N ) Q12Δτ 2 (t N ) Q13Δτ 3 (t N ) Q14Δτ 4 ( t N )Q21Δτ1 ( t N ) Q22Δτ 2 (t N ) Q23Δτ 3 (t N ) Q24Δτ 4 ( t N )
(27)
58American Institute of Aeronautics and Astronautics
Note that VXY is a 2N × 1 matrix and UXY is a 2N × 4 matrix. The least-square solution of PZ is then given byPZ = {UT
XYUXY}-1UTXYVXY. See also equation (7).
Similarly, the Z-axis row of equation (25), for time t = t1,…,tN, could be denoted by UZ•PY=VZ. Here, PY =[F5, F6, F7, F8]
T, is the unknown Y-facing thruster magnitude vector, VZ is a N×1 matrix, and UZ is a N×4 matrix:
€
VZ =
{ISCΔω( t1 )+ΔHRWA(t1 )+ΔG(t1 )}ZM
{ISCΔω( t N )+ΔHRWA(t N )+ΔG(t N )}Z
, UZ =
Q35Δτ 5 (t1 ) Q36Δτ 6 ( t1 ) Q37Δτ 7 ( t1 ) Q38Δτ 8 (t1 )M M M M
Q35Δτ 5 (t N ) Q36Δτ 6 ( t N ) Q37Δτ 7 ( t N ) Q38Δτ 8 (t N )
(28)
However, the determination of PY using equation (28) will encounter the following difficulty. With referenceto the third row of equation (24), since eX is typically very small compared to LX, the (3,5) element of Q is almostequal to the (3,7) element. Similarly, the (3,6) and (3,8) elements of Q are almost identical. As such, one mightnot be able to estimate the individual magnitudes of the four Y-facing thrusters via the least-square fit: PY ={UT
ZUZ}-1UTZVZ. This is the case because {Y1 and Y3} and {Y2 and Y4} are always fired in pairs. Hence, the rank
of the matrix UZ is 2 instead of 4. To overcome this difficulty, let us define the following new vector and matrix:PYY (2×1) = [(F5 + F7)/2, (F6 + F8)/2]T, and UZZ is an N × 2 matrix:
Q35Δτ 5 ( t N )+Q37Δτ 7 (t N ) Q36Δτ 6 (t N )+Q38Δτ 8 ( t N )
The least square fit result is: PZZ = {UTZZUZZ}-1UT
ZZVZ. The estimated magnitudes of the Y-facing thrusters are: F5
= F7 = PZZ(1,1), and F6 = F8 = PZZ(2,1). Finally, we might want to just estimate the mean value of the four Y-facing thrusters. Again, let us define the following new vector and matrix: PYYY (1×1) = (F5 + F6 + F7 + F8)/4, andUZZZ is an N × 1 matrix:
Q35Δτ 5 ( t N )+Q36Δτ 6 ( t N )+Q37Δτ 7 (t N )+Q38Δτ 8 (t N )
The least square fit result is: PZZZ = {UTZZZUZZZ}-1UT
ZZZVZ. The magnitudes of the Y-facing thrusters are: F5 = F6 =F7 = F8 = PZZZ(1,1).
In flight, the AACS and PMS teams typically generate only one thruster magnitude estimate for the eight A-branch thrusters and another one estimate for the eight B-branch thrusters. This single estimate could be estimatedusing the following matrices: VXYZ (3N×1) and UXYZ (3N×1). The mean magnitude of the eight thrusters are thengiven by: F1 = F2 = F3 = F4 = F5 = F6 = F7 = F8 = {UT
MQ11Δτ1 ( t N )+Q12Δτ 2 ( t N )+Q13Δτ 3 (t N )+Q14Δτ 4 (t N )+Q15Δτ 5 ( t N )+Q16Δτ 6 ( t N )+Q17Δτ 7 (t N )+Q18Δτ 8 (t N ) Q21Δτ1 ( t N )+Q22Δτ 2 ( t N )+Q23Δτ 3 (t N )+Q24Δτ 4 (t N ) Q35Δτ 5 ( t N )+Q36Δτ 6 ( t N )+Q37Δτ 7 (t N )+Q38Δτ 8 (t N )
Use of Accelerometer Data to Calibrate the Z-facing Thrusters’ MagnitudeThere is yet one more way to estimate the mean magnitude of the four Z-facing thrusters that has never been
practiced in flight. This method uses the thrusters’ on-time data collected from a thruster-based ∆V burn as well as
59American Institute of Aeronautics and Astronautics
∆V estimate made using an accelerometer (effects due to the ACC’s bias has been accounted for). The accelerometeris typically not powered on during a thruster-based ∆V burn. But, if the ACC is powered on and calibrated, it willprovide accurate estimate of the ∆V imparted on the spacecraft due to the firing of the Z-facing thrusters. Let Tzi (inseconds) be the “on-time” of thruster Zi (i=1-4) for a particular RCS ∆V burn, ∆V (in m/s) be the magnitude of thespacecraft’s velocity change as estimated by the accelerometer, and MSC is the spacecraft mass. Accordingly, themean magnitude of the four Z-facing thruster could be estimated via:
F1 = F2 = F3 = F4 = MSC×∆V/(∆τZ1+∆τZ2+∆τZ3+∆τZ4).The last equation was written assuming that both the Z-facing thrusters and the accelerometer are mounted
parallel to the spacecraft’s Z-axis. The misalignment of the accelerometer’s sensing axis relative to the Z-axis isbounded by about 0.1°. That of the Z-facing thrusters’ thrust is on the order of 1°. Since cos(0.1°) ≈ cos(1°) ≈ 1,the errors introduced by the misalignments in the last equation are quite small.
IV.E9 In-Flight Estimation of the Main Engine ThrustDuring the preparation phase of each main engine burn, the Cassini Propulsion team has made and will make a
prediction of the mean value of the main engine thrust for the upcoming ∆V burn. The prediction is used toestimate the nominal burn duration. A “maximum” burn time (Tmax) must also be specified by the flight team foreach burn to guard against the unlikely event of a “faulty” accelerometer failing to cut off the burn at the time whenthe targeted ∆V has already been achieved. The maximum burn time is typically selected to be 5% higher than thepredicted burn duration. The main engine thrust magnitude is also used in the AACS FSW. For example, thethrust vector control algorithm that is used to control the spacecraft’s attitude about the [X, Y] axes during a mainengine burn uses the FSW knowledge of the thrust. Additionally, an AACS error monitor named BurnAcceleration Error also uses the FSW knowledge of the thrust magnitude. As such, it is important for the AACSteam to compare the PMS-predicted main engine thrust with the current FSW knowledge of the thrust. If thediscrepancy is larger than 1%, a command will be sent to update the FSW value to the latest ground-predictedvalue.
A main engine burn imparts a linear acceleration on the spacecraft that is sensed by an accelerometer. Theaccelerometer’s sensitive axis is parallel to the S/C’s Z-axis. On the other hand, the main engine thrust is parallelto a vector from the prime engine pivot to the spacecraft’s center of mass. As such, the thrust vector typicallymakes a small angle of a few degrees relative to the S/C’s Z-axis. Upon the completion of a main engine ∆V burn,the AACS team routinely used the following expression to estimate the mean engine thrust:
aMean(Z-axis) = FMean × cos(θMean)/{M0 - FMean × T/2ISP} (29)In Equation (29), M0 is the estimated mass of the spacecraft at the start of the burn, T is the actual burn time, andISP denotes the specific impulse of the bi-propellant, in Ns/kg. Hence,{M0 - FMean × T/2ISP} represents the spacecraftmass at the “mid-time” of the burn. The symbol aMean represents the mean acceleration sensed by the accelerometer.It is determined as follows. The time history of the ACC raw data count is least-square fitted to estimate a “mean”slope. The mean acceleration is the product of that slope and the known ACC scale factor, plus the ACC’s biasthat was calibrated just before the ∆V burn. Since the time constant (rise time) of the main engine thrust is on theorder of 0.03 s, the first 0.1-0.2 s of accelerometer data are excluded from our determination of aMean. Finally, θMean
represents the small angle made by the engine thrust relative to the S/C’s minus Z-axis. It is estimated fromtelemetry data. Given these data, the only unknown in Equation (29), FMean, the mean engine thrust, could bedetermined.
For the Saturn Orbit Insertion burn, aMean (Z-axis) ≈ 0.108 m/s2, θMean ≈ 6.88°, M0 ≈ 4522 kg, T ≈ 5780.5seconds, and ISP = 2987.1 Ns/kg. Accordingly, the reconstructed main engine thrust is about 445.1 N.
The accuracy of this estimation technique is related to the number of available ACC data points. Theapplication of this technique on short burns might produce questionable result. An alternative way to estimate themain engine thrust is via the “rocket” equation:
{FMean × T}/{M0 × ISP} = 1 - exp{-∆V/ISP} (30)For the Saturn Orbit Insertion burn, M0 ≈ 4522 kg, T ≈ 5780.5 seconds, ∆V = 626.17 m/s, and ISP = 2987.1Ns/kg. Accordingly, the main engine thrust FMean reconstructed via the rocket engine is about 441.9 N. The actualmean SOI thrust is likely to lie somewhere between 441.9 and 445.1 N.
60American Institute of Aeronautics and Astronautics
IV.F1 In-Flight Monitoring of the High Water Marks of AACS Error MonitorsThe Cassini AACS FP design contains more than four hundred error monitors. Not all error monitors are
active during a particular spacecraft activity, but a large number of them are. The performance of these active errormonitors must be monitored even if none of them are triggered. This is because one or more “un-triggered” errormonitors might be a “hair line” away from being triggered. To monitor the performance of these error monitors, the“High Water Marks” (HWM) of the error monitors are computed by the FSW and sent down as telemetry. TheHWM of a time-varying quantity (that is related to an error monitor design) represents the largest value thatvariable has attained since the last “Clear High Water Mark” (CHWM) command was sent. As an example,consider the error monitor named Excessive RWA-1 Rate. This monitor is triggered if the RWA-1 spin rateexceeded the allowable rate limit of 2029 rpm. The time-varying variable of this error monitor is simply themagnitude (absolute value) of the spin rate of RWA-1. Its HWM is the largest RWA-1 spin rate achieved since thelast CHWM command. All HWMs should not be allowed to be too close to their respective thresholds.
To efficiently monitor the performance of these error monitor designs, we first convert the HWM telemetryinto percents of their respective thresholds. Computed values of these “Percent of Threshold” quantities are thendisplaced graphically (see Figure 29). One glance at this plot will provide the AACS FP engineer with a quickassessment of the FP performance. For example, from Figure 29, we see that the threshold of the error monitornamed “IRU Parity Violation” error monitor has been violated (more details are given in Section IV.F2). Also, ifthe threshold of an error monitor was poorly selected pre-launch, one can see that the value of “Percent ofThreshold” quantity will always hover very close to the 100% “ceiling.” A revision of the threshold might then benecessary. Examples are given in Section IV.F2.
Figure 29. In-Flight Monitoring of the AACS Error Monitor Performance
61American Institute of Aeronautics and Astronautics
IV.F2 In-Flight Adjustments of Selected AACS Error Monitors’ Thresholds and Persistence LimitsCassini AACS FP design relies on more than four hundred error monitors to detect the presence of any
anomalous performance of AACS sensors, actuators, attitude control, and attitude estimation functions, etc.Typically, the magnitude of a measured or estimated quantity is compared with a “threshold” that is pre-selectedand implemented in the AACS FSW. If the magnitude of the quantity involved exceeds its threshold, a persistencecounter will begin to increment. If the duration of the “higher than threshold” condition exceeds another pre-selected persistence limit (which is another parameter implemented in the FSW), that particular error monitor istriggered. See also Reference 21.
Selections of error monitors’ threshold and persistence limits involved compromises. If the error monitor’sthreshold is selected to be too low, the monitor will be triggered even when there is no problem. This is a “FalseAlarm” scenario. On the other hand, if the threshold is selected to be too high, an abnormality might escapedetection when a FP response is warranted. This is a “Missed Detection” scenario. In flight, the AACS FP teamuses the graphical tool described in the last section to gauge the “goodness’ of the error monitors’ thresholds andpersistence limits selected pre-launch. Inappropriately selected thresholds or persistence limits are corrected viaFSW “patching.”
An example of an in-flight modification of an error monitor’s persistence limit is described below. It isrelated to an error monitor named “IRU Parity Violation” (IPV) monitor. In the flight software, the IRU hardware“manager” computes pulse rates (PR) based on the changes in gyro angles and the changes in the time tags betweenthese gyro data reads. The four pulse rates from the prime gyro foursome (three sensing axes and one parity axis)are combined to form a "parity" relationship.
€
Parity= KiPRii=1
4∑ (31)
For the A1A2A3A4 prime gyro foursome, the values of Ki are [1/√3, 1/√3, 1/√3, 1] for i = A1 to A4,respectively. This is so because the mutually orthogonal A1 to A3 axes each make an angle of cos-1(1/√3) with theminus A4 axis. Nominally, the sum Parity should be very close to zero. If the IRU hardware manager detects aparity sum that is larger than a threshold for a time duration that is longer than a persistence limit, a fault isassumed to have affected at least one of the four axes. However, the identity of the faulty gyro(s) could not bedetermined without additional information.
The threshold of the IPV monitor is “dynamic.” It is a function of Ki, PRi, as well as several IRU hardwareparameters (gyro quantization, rate “white” noise, scale factor errors, misalignments, and others). On the otherhand, the persistence limit is a constant, selected to be 1 second (8 RTI) in the launch FSW build. That is, it willtake 8 consecutive violations of the threshold to trigger the IPV monitor. This selection allows for one or more“spiky” rate noises to go through without accidentally triggering a fault response. That is, this error monitor is nothair-triggered.
In August 2000, the persistence limit was increased from 1 to 1.5 s (from 8 to 12 RTI) in order to providemargin against false alarms due to the occasional occurrences of gyro “spikes.” In the summer of 2000, weobserved that high-energy ions and/or protons deposited in the front end of the HRG buffer led to spikes in theangle pulses. As a result, the IPV threshold was exceeded, but the “threshold is exceeded” condition did not lastlonger than 1 s (8 RTI) and the monitor was not triggered. Analyses and discussions with the HRG manufacturerindicates that the behavior is a result of Single Event Transient (SET).
The impact of these SETs on the attitude estimation and control functions are negligible because gyro data areedited and filtered by the flight software. Indeed, whenever the IPV threshold is exceeded, data from that particulargyro reads are “edited” out and are replaced by the last good gyro data. Estimated spacecraft rates are further filteredby digital filters before being fed to the RCS/RWA controller. However, the IPV monitor might be falselytriggered if the SET lasted longer than the persistence limit of the IPV monitor.
The gyro manufacturer provided simulation data showing that all trace of a SET-induced transient disappearedwithin 750 ms. This time is rather close to the persistence limit of 1 s. As such, we increased the value of thepersistence limit to twice the value shown by the manufacturer's data, to 1.5 s. This selection is further supportedby telemetry that showed, over the past 7 years (since launch), all SET-induced transient falls to less than theparity threshold in less than 375 ms (3 RTI). That is, the new persistence limit is a factor of 4 larger than theworst-case flight experience. The new value of the persistence limit was permanently implemented in flightsoftware builds of A7.7.6, A8.6.5, A8.6.7, A8.7.1, and A8.7.2.
These types of “tuning” of fault protection parameters occurred several times in flight. Some of these changesare permanent, others are “temporary.” For example, the threshold of an error monitor named “No Star In Inertial”was intentionally tightened from a large number to a smaller number before the Probe relay tracking. The changewas motivated by the need to be more responsive to star tracker problems that might occur during the Probe relaysequence (in reality, none has occurred). With the change, the AACS FP will replace the prime star tracker (which
62American Institute of Aeronautics and Astronautics
might have detected a problem) by its backup quickly. In this way, data outage during the Probe relay sequencewould have been minimized. After the Probe relay sequence was successfully executed, the threshold was “un-patched” to its original value. There are other permanent changes in monitors’ thresholds. Examples are thethresholds of the “Illegitimate RWA Tachometer Error” and “RWA Unexpectedly High Current” error monitors.The reasonableness of the revised thresholds and persistence limits is confirmed by the long-term monitoring ofthe performance of these monitors. They passed the “test of time.”
IV.G1 Performance of the Dynamics Constraint MonitorDynamic constraints are used to ensure that commanded S/C rates and accelerations are within the physical
capability of the thrusters (or reaction wheels), with margin. The physical capability of the thrusters leads to oneset of three per-axis “coast” rate limits and another set of three per-axis acceleration limits. Another two sets areused when the spacecraft is controlled by reaction wheels. These slew profile limits are changed (via an AACScommand) from time to time as the inertia properties of the spacecraft or the thruster magnitudes vary. Based onthese rate and acceleration limits, rate and acceleration “ellipsoids” could be defined.
The commanded per-axis rates and accelerations must not lie outside their respective ellipsoids. To detectimminent rate violations, the per-axis rate commands at 1 RTI into the future are computed and checked against therate ellipsoid. To this end, the “future” rates are computed by assuming the current S/C accelerations. This “future”rate command must also stay within the rate ellipsoid. A “dynamic” violation is declared whenever any of thesethree ellipsoidal checks has failed.
When a “dynamic” constraint violation is detected, CMT exits the “Detect” mode and enters the “Avoid”mode. Next, the acceleration command is “scaled” back so that the S/C’s commanded acceleration is at most lyingon the surface of the acceleration ellipsoid. Based upon the scaled back acceleration command and the current S/C’srate command, the S/C’s rate projected to the next RTI is computed. If it violates the rate constraint ellipsoid, theS/C’s commanded rate is also scaled back. Ultimately, both the truncated rate and acceleration commands satisfyall the applicable constraint ellipsoids. Only these slew commands are sent to the attitude controller.
In flight, the commanded rate and acceleration profiles that are used to slew the spacecraft are selected by theAACS team. They are then checked by a ground software tool against their CMT-based counterparts. As a result,no actual ellipsoidal constraint violations have ever occurred in flight.
In addition to the “size” checks on the rate and acceleration commands, the “smoothness” of both thecommanded attitude and rate are also checked by CMT. “Large and sudden” change in either the attitude or ratecommand is unacceptable. Across one RTI (125 ms), if the commanded attitude “delta” exceeds more than 1% ofthe CMT rate limit (for the spacecraft axis in question), a dynamic constraint violation will be reported by CMT.Similarly, if the commanded rate “delta” exceeds more than 1% of the CMT acceleration limit (for the spacecraftaxis in question), a dynamic constraint violation will also be reported. In flight, there were five “false alarms” insmoothness checks that occurred during early outer Solar cruise due to inappropriately selected CMT parametersused in the Launch flight software build. These false alarms are described as follows.
“Smoothness” violations occurred five times in-flight (on 2000-340T14:24:00, 2000-348T05:45:00, 2001-128T09:28:00, 2001-179T05:15:00, and 2001-181T14:59:00). One reason the 1% “delta angle” criterion wasviolated is because, in early AACS flight software builds, the attitude commander algorithm used 32-bit variablesin its generation of attitude and rate commands. This caused numerical “noise” to be generated. This “noise”increased the risk of triggering smoothness checks during long slews. This “hair-trigger” condition was removed insubsequent flight software builds both by increasing the “delta angle” criterion from 1 to 10%, and by changing allattitude commander variables from 32-bit to 48-bit variables. With these changes, there had not been any dynamicconstraint violations detected in-flight.
Once the attitude, rate, and acceleration commands passed the five “dynamics” checks described above, theymust still be checked against potential geometric constraint violation. This is described next.
IV.G2 Performance of the Geometric Constraint Monitor (CMT) Geometric constraint checks protect against overexposure of specific body-fixed vectors to “dangerous” objects
(e.g., the Sun). Geometric constraint definitions reside in a Constraint Table (see Table 3 and Fig. 7). Groundoperators can add new constraints to the table or remove constraints from the table that are no longer needed. CMTwill initiate evasive slews if a constraint violation is anticipated. But to take evasive action when the spacecraft ismoments away from a violation is usually too late. As such, CMT anticipates (via on board computations) allfuture geometric constraint violations and reacts to them while there is still time. The main reason that we needCMT on board the spacecraft is to protect against operators’ mistakes that escaped detection by the groundsoftware. Details of the Cassini CMT design are documented in Reference 24.
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Since launch, two geometric constraints have been enforced by the constraint monitor design in the AACSFSW. The first constraint is used to avoid having the Sun line vector too close to the S/C’s positive X-axis. Thisconstraint is called a “POSX_SUN” constraint, and it protects both the AACS star trackers as well as scienceinstrument radiators used for thermal control from Sun heating. During tour, the minimum allowable anglebetween the Sun line vector and the positive X-axis is 83°. The second constraint is used to avoid having the Sunline vector too close to the S/C’s minus Y-axis. This constraint is called “NEGY_SUN” constraint. This constraintprotects the narrow angle camera and other Science instruments mounted on the Remote Sensing Pallet (RSP).During Tour, the minimum allowable angle between the Sun line vector and the minus Y-axis is 12°.
In addition to the enforcement of “non-timed” celestial constraints, Cassini CMT can also enforce “timed”celestial constraints. A “timed” constraint may be described as follows: The angular separation between a bodyvector and a celestial vector shall never be smaller than θ for a time duration that is longer than T. In addition tothe two Tour phase constraints POSX_SUN and NEGY_SUN mentioned above, there was another timed constraintnamed NEGX_SUN that was enforced during early Cruise when the spacecraft was <5 A.U. For brevity, flightexperience associated with timed constraint is not given here.
On 2000-321T01:01:27.625, an error monitor named “CONSTRAINT_AVOIDANCE_IN_PROGRESS”(CAIP) was triggered for the first time. The geometric constraint involved was the POSX_SUN constraint (whosehalf-cone angle at that time was 87.5º). In reality, the “angular distance” between the Sun line and the positive X-axis was 110.4º (which is larger than 87.5º) at the time CAIP was triggered. It looked as if the CMT monitor wastriggered 22.9º ahead of entering the constraint cone. Another eleven similar geometric constraint violations werealso detected on subsequent days in 2000: DOY-326, 331, 336, 343, 344 (twice), 345, 348, 349, 361, and 363.Six of these violations were related to the POSX_SUN constraint. The rest were related to the NEGY_SUNconstraint. All twelve violations involved spacecraft slews that were about the Z-axis. This is not a coincidence!
The observed CMT behavior was actually consistent with the CMT design in the Launch flight software build.At any moment, CMT asks the question: Given the current spacecraft deceleration capability, could thespacecraft be stopped using the remaining distance (to the constraint cone) without causing a constraintviolation? It answers this question by computing a “stopping distance”: ∆θstop = 0.5 × ω2/αWorst + ω × rti. Here, ωis the current spacecraft rate, αWorst is the deceleration capability of the spacecraft about the worst axis, and rti =0.125 seconds. In the 2000-DOY-321incident, the S/C RWA-based slew was about an axis that is close to the Z-axis with ω ≈ 2.93 mrad/s. The angular deceleration capability of the spacecraft about the Z-axis was 19 µrad/s2
but the smallest deceleration among the three axes ([10, 11, 19] µrad/s2 about [X, Y, Z] axes, respectively) wasαWorst = 10 µrad/s2. Hence, ∆θstop = 0.5 × 2.932/0.01 + 2.93 × 0.125 = 24.6°. The event on the spacecraft wastriggered at a “stopping” distance of 22.9°, which is quite close to the computed ∆θstop. Therefore, what happenedis consistent with the design. As a result, “evasive” slew commands were sent by CMT to avoid violating thePOSX_SUN constraint. Figure 30 depicts the time history of the S/C’s Z-axis rate near the time CMT was inaction (near 2000-321T01:00:00). In this figure, each data number on the vertical axis represents 5e-6 rad/s.
The lesson learned from the year 2000 constraint violation events is that the “stopping” distance computedusing the formula ∆θstop = 0.5 × ω2/αWorst + ω × rti is unnecessarily conservative. This formula was modified byreplacing αWorst with a more representative deceleration capability of the spacecraft about the “escape” axis. Thismodification was made in the FSW build A8.6.7 that was uploaded on the spacecraft in the spring of 2003. Afterthe FSW A8.6.7 was uploaded, three “imminent” constraint violation events observed in 2000 were intentionallyflight-tested using the new CMT design. No constraint violations were detected by the CMT using the new“stopping distance” formula. In fact, there was not another “false alarm” from the CMT until day 73 of 2004 whena real geometric constraint violation was detected by CMT.
During the design phase of a set of science observations, the AACS engineer involved uses a ground softwaretool to check for any geometric constraint violations. Detected geometric constraint violations are “removed” eithervia a redesign of the science observation sequence or by a “relaxation” of the geometric constraint angle (e.g., atemporary drop in the angle of the POSX_SUN constraint from 83° to 45°). However, the relaxation of a constraintmust be done with great care in order to assure that the instruments involved will not be irreversibly damaged bythe exposure. With these ground checks, Science observation sequences that are sent to spacecraft are always “freeof constraint violation.”
64American Institute of Aeronautics and Astronautics
Figure 30. Time History of S/C’s Z-axis Rate Due to CMT-Initiated Evasive Maneuver (2000-DOY-321)(Scale factor of the vertical axis is 5e-6 rad/s)
On day 73 of 2004, the spacecraft was commanded to execute a series of slews in order to calibrate the primeIRU. These calibration turns were checked by the same ground software tool and were declared to be “constraintviolation free” before being sent to the spacecraft. In reality, one of the calibration slews tried to put the Sun intothe “POSX_SUN” constraint region. The ground check failed because that particular slew is an exact 180° slew. Inthe ground software check, the S/C was slewed in one direction (which did not violate any constraint). In-flight,the flight software slewed the spacecraft in the other direction (which violated the “POSX_SUN” constraint).However, the failure of the ground check did not cause any actual problem because the violation was anticipated byCMT and “evasive” slews were commanded by the CMT. There was no adverse effect on the spacecraft or the IRUcalibration. Lessons learned from this incident led us to check and modify all “almost 180°” slews in the future.
Figure 31 depicts the time histories of cosine of the angle between the Sun-line vector and the positive X-axisof the spacecraft. In this figure, each data point on the vertical axis represents 3.051851e-5 units. Since that anglemust always be larger than 83°, the cosine of that angle must be <0.1218693 (3993.3 units). With reference toFigure 31, the constraint angle 83° is about to be violated at 2004-73T18:22:00. Before the occurrence of theviolation, CMT was triggered at about 2004-73T18:21:12.97. Evasive slew commands were issued by CMT thatsuperseded those issued by the attitude commander. These evasive commands avoided a constraint violation, andthe cosine of the POSX_SUN angle was always smaller than 0.1218693.
Figure 32 depicts the time history of the spacecraft’s X-axis rate. In this figure, each data point on the verticalaxis represents 5.0e-6 rad/s. To avoid geometric constraint violations, CMT generates a path that will leave theconstraint region as quickly as possible while trying to maintain goal attitude. As such, the commanded X-axisrate of spacecraft, which was originally zero, became that depicted in Figure 32. Note that, the X-axis rate does notresemble either a “triangular” or “trapezoidal” profile. In this scenario, CMT succeeded in avoiding the constraint,and all CMT actions ended near 2004-073T18:59:53.
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Figure 31. Time History of the Cosine of the POSX_SUN Angle on 2004-DOY-073(Scale factor of the vertical axis is 3.051851e-5)
Figure 32. Time History of the Spacecraft X-axis Rate on 2004-DOY-073(Scale factor of the vertical axis is 5.0e-6 rad/s)
66American Institute of Aeronautics and Astronautics
IV.H Tracking of AACS “Consumables”Many AACS-related consumables are being tracked via AACS telemetry. The main reason for performing this
tracking is to assure that the consumption rates of these consumables are such that none of these consumables willexceed their respective limits at the end of the prime mission. Tables 13, 14, and 15 give snapshots of all theAACS-related consumables on 2005-DOY-46.
Table 13. 2005-DOY-046 Status of Various AACS Equipment On/Off Cycle Consumables
Consumables Values on 2005-046 Requirements
Power On-off Cycle
ACC
ECECU-A
EGECU-B
RWA-1
RWA-2
RWA-3
RWA-4
IRU-A
IRU-B
SSA-A
SSA-B
SRU-A
SRU-B
28
61
32
71
71
51
61
1
8
1
2
9
1
550
1,000
1,000
300
300
300
300
500
500
300
300
None
None
Thruster On/Off cycles
Z1A
Z2A
Z3A
Z4A
Y1A
Y2A
Y3A
Y4A
62,287†
59,365
49,411
53,501
21,014
14,160
20,984
14,135
273,000
273,000
273,000
273,000
273,000
273,000
273,000
273,000
†Thruster Z1A is the thruster that is most used. Thruster Y4A is theone that is least used. Pre-launch, the estimates of thruster on/offcycles, from Launch to SOI, for (each) Z-facing and Y-facingthrusters were about 173,000 and 56,000 cycles, respectively. Theactual on/off cycles listed above, from Launch to early 2005, aresignificantly smaller. Part of “saving” came from the RCS controlparameter adjustments made in flight as detailed in Section IV.B3.
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Table 14. 2005-DOY-046 Status of Various AACS Equipment On-Time Consumables
Consumables Values on 2005-046 Requirements Units
Equipment On time
ACC
ECECU-A
EGECU-B
RWA-1
RWA-2
RWA-3
RWA-4
IRU-A
IRU-B
SSA-A
SSA-B
SRU-A
SRU-B
MEV-A
MEV-B
359
63
17
26,924
26,938
16,059
10,969
64,306
147
64,306
42
3,839
60,604
16398.75
60.0
15,000
150
150
†
†
†
†
30,000*
30,000*
105,120
105,120
105,120
105,120
None
None
hours
hours
hours
hours
hours
hours
hours
hours
hours
hours
hours
hours
hours
sec
sec
Thruster On Times
Z1A
Z2A
Z3A
Z4A
Y1A
Y2A
Y3A
Y4A
6626.337
6789.774
6611.072
6347.471
2181.993
2120.514
2181.261
2118.312
††
††
††
††
††
††
††
††
sec
sec
sec
sec
sec
sec
sec
sec
† There is no RWA “on time” requirement. Instead, the requirement is on the totalnumber of wheel revolution and the time the wheel spent inside the “low-rpm” region.See Table 15.
* The IRU on-time requirement is intentionally set low at 30,000 hours so that AACScould consider the use of mechanical gyroscopes during the design phase of Cassini.This requirement is being reviewed by the Project. A candidate requirement is 105,120hours (12 years. Launch to end of the prime mission is about 12 years minus 3months).
†† The throughput requirement of each thruster is 25 kg. The estimated value of thehydrazine’s specific impulse is 1979 Ns/kg. The thruster magnitude is <0.97 N.Hence, the “pseudo” thruster on-time requirement is at least 25 ×1979/0.97≈51,005 s.
68American Institute of Aeronautics and Astronautics
Table 15. 2005-DOY-046 Status of Various RWA Consumables
Consumables Values on 2005-046 Requirements Units
RWA Revolutions
RWA-1
RWA-2
RWA-3
RWA-4
868.573
858.135
515.615
442.306
4,000
4,000
4,000
4,000
Millions
Of
Revolutions
RWA Low-rpm Time
RWA-1
RWA-2
RWA-3
RWA-4
4.619
5.040
3.313
1.518
12.0
12.0
12.0
12.0
Thousands
of
Hours
With reference to Table 15, we note that both RWA-1 and RWA-2 have accumulated large numbers ofrevolutions as well as “low-rpm” hours. This is to be expected because both wheels have been used since March2000 to control the spacecraft’s attitude whereas RWA-3 was “retired” in early July 2003. It was replaced by RWA-4 at that time. As such, we have to pay special attention to the consumables associated with these two wheels.
Using data given in Table 15, we note that the 4-billion revolutions specification of RWA-1 will be exceededat the end of the prime mission (July 1, 2008) if the average daily consumption rate of RWA-1 is higher than2.542 millions of revolutions per day. The corresponding number for RWA-2 is 2.550 millions of revolutions perday. Similarly, the 12,000-hour low-rpm specification of RWA-1 will be exceeded at the end of the prime missionif the average daily consumption rate of RWA-1 is higher than 5.99 hours per day. The corresponding number forRWA-2 is 5.65 hours per day. If we are to consider a 2-year extended mission, then, the “acceptable” dailyrevolution consumption rates for RWA-1 and RWA-2 are 1.596 and 1.601 millions of revolutions per day,respectively. The corresponding “acceptable” daily low-rpm time consumption rates for RWA-1 and RWA-2 are3.76 and 3.55 hours per day, respectively.
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IV.I Impact of Radiation on AACS SensorsWhen high-energy ions and/or protons are deposited on the front end of the Cassini HRG buffer circuitry,
spikes are generated in the angle pulses. These events are called Single Event Transients (SETs). The gyroscopebuffer design has high impedance, and the deposited charge is drained to zero only after tenths of milli-seconds(instead of microseconds). Four gyro readout channels are followed immediately by high-gain circuitry that issaturated by these transients. The saturation condition temporarily “blinded” the analog demodulation circuit, theADC inputs, and the DSP (Digital Signal Processing), causing the effect to be magnified.
Cassini made swing-bys of Earth in 1999 and Jupiter in 2000. The Earth and Jupiter closest approacheshappened on 1999-230T03:28:00 and 2000-365T10:04:43, respectively. The longitude, latitude, and altitude of theEarth swing-bys were -132°, -23°, and 1188 kilometers, respectively. The longitude, latitude, and altitude of theJupiter swing-bys were +20°, 0°, and 9.723 million kilometers, respectively. The radiation environment of theEarth produced noticeable impact to the output of the HRG during Earth closest approach ±10 minutes. Gyro-basedSETs led to “spikes” in the estimated per-axis spacecraft rates. Figure 33 depicts the time history of the Y-axisspacecraft rate control error. At least 14 spikes were observed in the time window of ECA±10 minutes. The largestrate control error spike observed was 0.25 mrad/s. It lasted for about 3 RTI, and produced a persistence high watermark of 3 RTI on the “IRU Parity Violation” error monitor (see Section IV.F2). The radiation environment of theEarth also produced noticeable impact to the outputs of the star tracker. Figure 34 depicts the time history of theratio of the measured star brightness (for star-2, one of the five stars used by SID) to the catalogued brightnessvalue. These ratios typically fluctuated between 1.0 and 1.5, but a star brightness ratio as high as 3.3 was observednear ECA. Other than these “anomalies,” the impact of these SETs on both the attitude estimation and controlfunctions have been minimal. The worst-case per-axis attitude estimation error was 0.2 mrad.
Figure 33. Time History of the Spacecraft Y-Axis Rate Near Earth Closest Approach(Earth closest approach was on 1999-230/03:28:00)
70American Institute of Aeronautics and Astronautics
Figure 34. Time History of the Star Brightness Ratio (Star 2) Near Earth Closest Approach(Earth closest approach was on 1999-230/03:28:00)
The radiation environment of the Jupiter also impacted the performance of the HRG. But because the Jupiterclosest approach distance was almost 9.72 millions km, the impact was minimal. The Jupiter radiationenvironment produced a persistence high water mark of only 1 RTI on the “IRU Parity Violation” error monitor.
After an interplanetary cruise that lasted almost 7 years, the Cassini spacecraft arrived at Saturn on June 30,2004. On that day, after crossing a gap between the F and G rings of Saturn, Cassini fired one of its two rocketengines for about 96.4 minutes to slow down the spacecraft’s velocity (by about 626.17 m/s), and allowed itself tobe captured by the gravity field of Saturn. This event, named Saturn Orbit Insertion (SOI), was the most criticalengineering event of the entire mission and was executed faultlessly.
About 25 minutes before the start of the SOI burn (which was from 2004-183/01:12:00 to 02:48:00), thespacecraft crossed the Saturn ring from below at 2004-183/00:46:34. This is the so-called Ascending Ring-PlaneCrossing (ARPC). About 105 minutes after the completion of the SOI burn, the spacecraft crossed the ring-planefrom above at 2004-183/04:33:00. The second crossing is called a Descending Ring Plane Crossing (DRPC). Thetime histories of the spacecraft X- and Y-axis rates near the time of ARPC are depicted in Figure 35. One observesrate spikes in these time histories due to the radiation environment near the ring plane of Saturn. For example, near2004-183/00:48:10, [X, Y, Z] rate spikes of [-0.105, +0.31, 0+] mrad/s were observed. A 0.25-mrad/s SET-inducedspike in the A1 gyro will generate [-0.105, +0.23, 0+] mrad/s spikes about the [X, Y, Z] axes, respectively. This isclose to what we observed near 2004-183T00:48:10. Similarly, near 2004-183T00:32:00, [X, Y, Z] rate spikes of[+0.06, -0.15, 0+] mrad/s were observed. This could be due to a 0.143 mrad/s spike in the A1 gyro. Rate spikeswere also observed in the time vicinity of the DRPC. Again, the impact of these SETs on both the attitudeestimation and control functions have been minimal.
71American Institute of Aeronautics and Astronautics
Figure 35. Time History of the S/C’s X- and Y-Axis Rates Near Ascending Ring Plane Crossing(ARPC was on 2004-183/00:46:34)
72American Institute of Aeronautics and Astronautics
IV.J Estimation of Titan Atmospheric Density Using AACS DataTitan is the largest moon of Saturn. It was discovered by Huygens in 1655. It is of great interest to scientists
because it is the only known moon in the Solar system with a “major” atmosphere. Titan's atmosphere is ten times“denser” than Earth's. Except for some clouds, Earth's surface is visible from space. But on Titan, a thick hazeextending up to 3,000 kilometers above the surface obscures the entire moon from optical observations. Throughongoing observations from Earth as well as data collected by the Pioneer 11 and Voyager 1 and 2 spacecraft,scientists now know that Titan's atmosphere is composed primarily of nitrogen. In fact, over 95% of itsatmosphere is composed of nitrogen, while only 5% is composed of methane, cyanide, and other hydrocarbons.See also Reference 26. One of the major science objectives of the Cassini mission is an investigation of Titan’satmosphere constituent abundance. To this end, the instrument named Ion and Neutral Mass Spectrometer (INMS)is playing an important role. The INMS is determining the chemical, elemental, and isotopic composition of thegaseous and volatile components of the neutral particles and the low-energy ions in Titan’s atmosphere andionosphere. Additionally, the Huygens Atmospheric Structure Instrument (HASI), mounted on the Huygens probe,sampled and determined the Titan’s atmosphere density during the Probe’s 2.5-hour descent through the Titan’satmosphere on January 14, 2005.
Cassini is controlled by thrusters during low-altitude Titan flybys. The thrusters are fired to overcome theatmospheric torque imparted on the spacecraft due to the Titan atmosphere as well as to slew the spacecraft ininertial space to meet the pointing needs of science instruments such as INMS. The adequacy of the thrusters inproviding control torque about all three spacecraft axes is analyzed in Reference 45. Obviously, the denser Titan’satmosphere is, the more thruster firings will be needed. In other words, thruster firing telemetry data gathered bythe AACS flight software could be used to estimate the three per-axis torque imparted on the spacecraft due to theTitan atmosphere. Moreover, since there is a well-defined relation between the atmospheric torque imparted on thespacecraft and the Titan atmospheric density (see Equation (34)), one can use it to “reconstruct” the Titanatmospheric density.
To this end, we first note that the rotational motion of the spacecraft during a Titan flyby is governed by thefollowing Euler equation (as expressed in a body-fixed spacecraft coordinate frame):
€
ISCr ˙ ω +
r ω × (ISC
r ω +
r H RWA) =
r T PMS +
r T ATMO +
r ε (32)
In Eq. (32), ISC is the S/C’s inertia tensor, the spacecraft angular rate vector is r ω , and the spacecraft’s angular
acceleration vector is r ˙ ω . The inertia tensor is estimated by a ground software tool. It is sent to the AACS flight
software via a command (see also Section IV.A3). The on-board attitude estimator provides estimates of thespacecraft rate at 125 ms time intervals. The total angular momentum vector of the three reaction wheels is denotedby HRWA (which is zero if the reaction wheels are powered off). Torque exerted on the spacecraft due to thruster
firing,
r T PMS , is not available directly from the flight software. Instead, the on-board propulsion “manager”
estimates the force impulse due to all thruster firings. Using the estimated thruster moment arms, these force
impulses are converted into three per-axis torque impulses. In effect, what the FSW has estimated is ∫
r T PMS(t) dt.
Again, these data are available at time intervals of 125 ms. Torque exerted on the spacecraft due to the Titan
atmospheric density is denoted by
€
r T ATMO . This is the unknown quantity that we wish to estimate. Environmental
torque due to Titan’s gravity gradient, solar radiation, magnetic field, etc. are captured in the “ε” term. These non-gravitational torque are typically very small and are neglected to first order (see below).
The torque imparted on the spacecraft due to the Titan atmospheric density could be estimated as follows. Letus define the following angular momentum vector:
€
r R (t) = {
r T ATMO + r
ε }dτ 0
t∫
= {ISCr ˙ ω +
r ω × (ISC
r ω +
r H RWA) -
r T PMS}dτ
0
t
∫(33)
In this equation, r R denotes the angular momentum vector accumulated due to the Titan atmospheric torque
imparted on the spacecraft. This is the case because r ε contains zero-mean random fluctuations, which integrated
approximately to zero. The time derivative of the vector r R denotes the per-axis atmospheric torque imparted on the
spacecraft. In the flight software, these time derivatives are implemented via a lead-lag filter to minimize errorassociated with the “differentiation” of noisy signals. Results are available as AACS telemetry data. Thecomputational steps involved in the reconstruction of the per-axis atmospheric torque were coded in the AACSFSW build A7.7.6 that was uploaded to the spacecraft in the spring of 1999.
73American Institute of Aeronautics and Astronautics
The Titan atmospheric density is related to the torque imparted the spacecraft by the following approximateequation:
€
r T ATMO(t) ≈ 1
2CDρTitan (t)V(t)2 AProjected (t) r u V(t)× [r r CP(t)− r r CM] (34)
In Equation (34), ρTitan is the Titan atmospheric density in kg/m3. During a Titan flyby, the altitude of thespacecraft relative to the Titan surface first decreased and then increased with time. Since Titan atmospheric densityis a strong function of the Titan-relative altitude, ρTitan is a time-varying quantity. The spacecraft velocity relativeto Titan is denoted by V(t) (in m/s). Typically, the magnitude of V is on the order of 6 km/s. The orientation ofthe velocity vector as expressed in the S/C’s coordinate frame is denoted by the unit vector uV. The area of thespacecraft projected onto a surface that is perpendicular to the vector uV is denoted by AProjected (in m2). Thedisplacement vectors, from the origin of the spacecraft coordinate frame to the spacecraft’s center of mass and centerof pressure (in meters) are denoted by rCM and rCP, respectively. Note that rCM is a constant vector while the rCP is atime-varying vector. Both vectors are estimated by ground software. Finally, the dimensionless quantity CD is thedrag coefficient associated with the free molecular flow of Titan atmospheric constituents passed the body of theCassini spacecraft.
The drag coefficient CD can be estimated using formulae given in References 27, 28, and 29. The spacecraftmay be modeled either as a cylinder or a sphere. The drag coefficients of these objects in a “free molecular flow”field are given by the following expressions:
€
CDCylinder =
πSe−S2
2 {(S2 +32)I0(
S2
2) +(S2 +
12)I1(S2
2)} + π
32
4STMLIT∞
≈ 2.07
CDSphere =
2πSe−S2
2 (1+12S2
) +2(1+1S2
−14S4
)erf(S) + 2 π3S
TMLIT∞
≈ 2.06
(35)
In these expressions, S is the molecular speed ratio, which is about 19.89. I0(•) is the Bessel function of thefirst kind, order 0, and I1(•) is the Bessel function of the first kind, order 1. Erf(•) is the error function. T∝ is theTitan atmosphere temperature (which is assumed to be 175 K) and TMLI is the multi-layer insulation skintemperature (about 160 K). The error introduced by the assumed Titan atmosphere temperature is insignificantbecause the magnitudes of the last terms in these expressions are small (≈0.062-0.073). In our work, we use CD =2.1 ±0.1.
To reconstruct the Titan atmospheric density, the AACS team used two different approaches. The underlyingprinciple of these approaches is identical. In the first approach, we simply query the three per-axis atmospherictorques from the AACS telemetry after a Titan flyby. Equation (34) is then used to estimate the Titan atmosphericdensity as a function of time (or as a function of the Titan-relative altitude). In the second approach, the vector
R(t) is reconstructed on the ground using telemetry data of ω(t), ∫
r T PMS(t) dt, etc. (which are only available at time
intervals of once per 2 seconds or once per second). However, the advantage of the second approach is thatsophisticated techniques can be used on the ground to estimate the time derivatives of the three components of theR(t) vector. The Cassini attitude control team used both approaches for cross checking.
At the time this paper was being prepared, there were only three low-altitude Titan flybys: Titan-A (1174 km)happened on October 26, 2004; Titan-B (1194 km) happened on December 14, 2004; and Titan-5 (1027 km)happened on April 16, 2005. For brevity, only results collected using the first approach for the Titan-5 flyby aregiven here. Figure 36 depicts the estimated Titan atmospheric density (estimated using the first approach) as afunction of the Titan-relative altitude. At the Titan Closest Approach (TCA) of 1027 km, the estimated density is6.8×10-10 kg/m3. The density estimated via the second approach is 5.7×10-10 kg/m3. These AACS-centric resultsagreed quite well with unpublished results from an instrument carried on the Huygens Probe, but they deviatedsignificantly from that estimated by another science instrument on the spacecraft. The discrepancy might camefrom the knowledge uncertainties associated with the employed values of drag coefficient, projected area, center ofpressure location, etc. Data from 21 low-altitude Titan flybys in 2006-2008 will help to resolve thesediscrepancies. Results given here are preliminary in nature.
74American Institute of Aeronautics and Astronautics
0.0E+00
1.0E-10
2.0E-10
3.0E-10
4.0E-10
5.0E-10
6.0E-10
7.0E-10
8.0E-10
1000 1050 1100 1150 1200
Altitude [km]
Den
sity
[kg
/m
3]
Figure 36. Titan Atmospheric Density Estimate As a Function of Titan-Relative Altitude (Preliminary)
Other non-gravitational torque imparted on the spacecraft during a low-altitude Titan flyby includes Titangravity gradient torque and magnetic torque. The magnitude of gravity gradient torque is a function of bothspacecraft attitude and its distance from Titan. With a worst-case spacecraft attitude, this torque could be estimatedusing the following expression:
€
TGravity−Gradient =32
µTitan(IMax − IMin )(RTitan + h)3
(36)
Here, µTitan is the product of the universal gravitational constant and the mass of Titan (≈ 8.9782×103 km3/s2),RTitan is the radius of Titan (≈ 2575 km), h is the spacecraft’s Titan-relative altitude at Titan closest approach (1027km for the Titan-A flyby), and IMax and IMin are the maximum and minimum moments of inertia of the spacecraft,respectively. For the Titan-A flyby, IMax = IXX ≈ 7400 kg-m2, and IMin = IZZ ≈ 3720 kg-m2. The worst-casemagnitude of TGravity-Graident is only about 0.00106 Nm. It is small when compared with the atmospheric torque(which is larger than 0.4 Nm at the TCA).
Magnetic disturbance torque on the spacecraft results from the interaction between the spacecraft’s residualmagnetic field and the magnetic field of Saturn. With a worst-case spacecraft’s attitude, the magnetic disturbancetorque, TMagnetic, could be estimated using the following expression:
€
TMagnetic =Marm ×BSaturnrps3 (37)
Here, Marm is the spacecraft magnetic moment arm, estimated to be 1.4 Amp-m2. BSaturn is the magnetic fluxdensity on the surface of Saturn, estimated to be about 8.3e-5 Tesla (kg-s-2-A-1), and rps is the distance betweenSaturn and the spacecraft in planet radii. Near the Titan closest approach of a low-altitude Titan flyby (such asTitan-5), rps is about 20.3. Accordingly, the estimated worst-case magnitude of TMagnetic is 1.39e-8 Nm. Like thegravity gradient torque, the magnetic disturbance torque is small when compared with the atmospheric torque.Finally, as estimated in Section IV.L, the magnitudes of the direct solar radiation torque and the radiation torquedue to the power generator are on the order of micro-Nm. This being the case, the atmospheric torque imparted onthe spacecraft could be determined using the time derivatives of the vector R given by Equation (33).
75American Institute of Aeronautics and Astronautics
IV.K AACS Equipment Operating TemperaturesMany items of AACS equipment must operate within specified temperature ranges. Otherwise, the
performance requirements of these items of equipment (which are specified in Reference 8) might not be met. Table16 gives a snapshot of the temperatures of various AACS equipment on 2005-DOY-11. Note that thesetemperatures are all within the allowable flight temperature ranges.
Table 16. Temperatures of Selected AACS Equipment on 2005-DOY-11
AACS Equipment Temperature(°C)
Allowable Flight TemperatureRange (°C)
Powered on Equipment
RWA-1
RWA-2
RWA-4
SSA-A
SRU-B (Optical Barrel)
SRU-B (CCD)
IRU-A
23.2
19.4
22.1
-77.9
-1.1
-32.4
29.4
0, +40
0, +40
0, +40
-90, +80
-10, +30
-40, -30-5, +45
Powered Off Equipment
RWA-3
SSA-B
SRU-A (Optical Barrel)
SRU-A (CCD)
IRU-B
EGA-A
EGA-B
ACC
22.4
-77.8
-4.9
-18.7
15.1
26.0
25.5
23.4
-10, +50
-90, +80-20, +40
-50, +40
-20, +45
+5, +85
+5, +85
-40, +70
76American Institute of Aeronautics and Astronautics
IV.L In-Flight Estimation of Non-gravitational TorquePre-launch, the magnitudes of six sources of non-gravitational torque acting on the spacecraft were estimated:
direct solar radiation, reflected solar radiation, planet radiation, radiation due to the power generators (radioisotopethermoelectric generators, RTG), gravity gradient torque (due to planets and satellites), and magnetic field torque.Magnitudes of these non-gravitational torques were estimated for six mission phases. The Titan atmospheric torqueis book-kept elsewhere. In flight, whenever the spacecraft is in a quiescent Earth-pointed condition, controlled bythree reaction wheels, the AACS team used these opportunities to estimate the total non-gravitational torqueimparted on the spacecraft. Three such opportunities were provided by the three Gravitational Wave Experiments(GWEs) performed during outer Solar cruise. The process of using RWA data to estimate non-gravitational torqueis illustrated using one of these GWE.
The GWEs were conducted on 11/26/01-1/5/02 (40 days), 12/6/02-1/14/03 (40 days), and 11/10/03-11/30/03(20 days). During these GWE periods, the spacecraft maintained an HGA-to-Earth attitude using three reactionwheels. Non-gravitational torques that were significant during these experiments include only the body-fixed RTGtorque and the direct solar radiation torque. The presence of these non-gravitational torque on the spacecraft causedthe spin rates of the reaction wheels to “drift” slowly with time. For example, in GWE-1, the spin rates of reactionwheel 1, 2, and 3 drifted from their initial rates of [-1028, -900, -1330] rpm to their final rates of [-869, -963, -702] rpm. The ∆ωRWA was [+159, -63, +628]T rpm. Since the spacecraft was quiescent throughout the experiment,the estimated non-gravitational torque Tnongra can be estimated by:
€
r T nongra ≈
0 −12
+12
23
−16
−16
+13
+13
+13
(Δr ω RWA • 2π
60) • 0.16
40 • 24 • 3600Nm (37)
In this expression, we have used a mean moment of inertia of 0.16 kg-m2 for each RWA. The coordinatetransformation matrix, from the RWA to the spacecraft mechanical frame, is given in Figure 4. The estimatedvalue of Tnongra over the period 11/26/01-1/5/02 is [2.37. -0.49, 2.03]T µNm.
During the early part of the outer Solar cruise phase of the mission, from March 6 to September 30, 2000,the spacecraft was located far away from the planets Earth and Jupiter (see Figure 1). During this time period, theonly significant non-gravitational torque imparted on the spacecraft was the solar radiation torque and the RTGtorque. This is so because gravity gradient torque due to the planets, magnetic torque due to planets’ magneticfields, and planet thermal radiation torque were all very small. Within this time window, the spacecraft wassometime controlled by three reaction wheels. Hence, we can use the RWA rate data to estimate the magnitudes ofthe total non-gravitational torque (using the approach just described above). Result obtained for the X-axiscomponent of the total non-gravitational torque is given in Figure 37.
Figure 37. Variation of X-axis Non-gravitational Torque with 1/AU2
0
2
4
6
8
10
12
14
16
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11
Reciprocal of Squared A.U. Distance
X-a
xis
Non-g
ravi
tational
Torq
ue
(mic
ro-N
m)
77American Institute of Aeronautics and Astronautics
In Figure 37, we plotted the X-axis torque versus the inverse squared A.U. distance. The least-square fit forthis set of data is given by:
€
TXTotal ≈
158.4A.U.2
−1.71 µNm (38)
The first term in this equation represents X-axis torque due to direct solar radiation and the second term isthat due to the RTG torque. At a distance of 1 A.U., the solar forces on the HGA reflector and the magnetometerboom, as estimated theoretically using Equations (39) and (40) given below, are 55.3 and 26.7 µN, respectively.These forces generate a net solar torque about the S/C’s X-axis with a magnitude of 171.7 µNm (at 1 A.U.). Notethat this theoretical prediction is quite close to that given in Equation (38), which is158.4 µNm.
Theoretical predictions of solar radiation forces imparted on the magnetometer boom and HGA reflector couldbe made using the following simplified analyses. When the spacecraft is in an HGA-to-Earth attitude, both the Xand Y-axis components of the solar radiation force are very small. This is so because the angle formed by theSun-line and Earth-line vectors is very small. For the three GWE, that angle was below 4.5°. Between March 13and September 30, 2000, the angle was bounded by12°. The cosine of 12° is 0.978 and the following analysesrepresent good approximations.
The solar radiation force components (along the Z-axis) imparted on the HGA parabolic reflector and on themagnetometer boom could be estimated using formulae given in References 32 and 33.
€
FHGASolar =
I0cAU2 πRHGA
2 {12
+4CHGA
Diffuse cosΩ3(1+ cosΩ)
} (39)
In Equation (38),
€
FHGASolar is the solar radiation force imparted on the HGA, c is the speed of light (about
2.997925×108 m/s), I0 is the solar constant at 1 A.U. (about 1353±20 W/m2), RHGA and DHGA are the radius andthe depth of the HGA reflector, respectively. The angle Ω is tan-1(2DHGA/RHGA), and
€
CHGADiffuse is the coefficient of
diffuse reflection of the HGA surface. Equation (39) is a simplified expression of the solar force made with theassumption that the coefficient of specular reflection of the HGA surface is zero.
The solar radiation force imparted on the cylindrical magnetometer boom could be estimated similarly.32
€
FMAGSolar =
I0cAU2
6 + π − (π − 2)CMAGDiffuse
3RMAGLMAG × (1+ fRPWS) (40)
In Equation (40),
€
FMAGSolar is the solar radiation force imparted on the magnetometer boom, RMAG and LMAG are
the radius and the “exposed” length of the cylindrical magnetometer boom, respectively, and
€
CMAGDiffuse is the
coefficient of diffuse reflection of the multi-layer insulation. Again, we made the assumption that the coefficientof specular reflection of the boom surface is zero. The factor fRPWS is a small correction factor that is used toaccount for the effects of the two cylindrical RPWS dipole antennas that are exposed to the Sun in an HGA-to-Sun orientation. It is given by fRPWS ≈ 2 × cos(19°) × 0.076 ≈ 0.144. Here, 0.076 is the ratio of the radius of theRPWS antenna to the radius of the magnetometer boom. The approximate angle between the normal to the surfaceof the RPWS antenna and the Sun-line vector is 19°.
The Probe was ejected on December 24, 2004 (9.055 A.U.). This event affected the non-gravitational torqueestimate in two ways. First, the S/C’s c.m. shifted significantly. Second, the pre-release estimate of the RTG Y-axis torque changed significantly. Estimated total non-gravitational torques imparted on the spacecraft, withoutthe Probe, in an HGA-to-Earth attitude, and at about 9.055 A.U., are given in Table 17. Again, the “total” torquecomponents were estimated using RWA data. The solar radiation torque is estimated using the new S/C’s c.m.location and the theoretical expressions for solar radiation forces (see Equations (39) and (40)) at 9.055 A.U.Looking at Table 17, we note that, contrary to popular belief, the magnitude of the solar radiation torque (X-axis)is not small relative to the magnitudes of the RTG torque components. That is, the total radiation torquemagnitude is a function of the spacecraft’s attitude (because the solar radiation torque is a function of the S/C’sattitude).Table 17. Estimated Non-gravitational Torque During Tour With an Earth-Pointed Attitude (9.055 A.U.)
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V. Summary and Conclusions
Perhaps no other spacecraft subsystem must satisfy as many science and mission requirements as the Attitudeand Articulation Control Subsystem. Moreover, most of these requirements must be met under severe constraints.For example, the highly challenging spacecraft pointing stability requirements had to be met during Tour withlightly damped appendages on the spacecraft, and when the rings or satellites of Saturn might fall inside the FOVof the star tracker. Likewise, the TVC algorithm must achieve challenging maneuver execution accuracy with highor low liquid fill fractions in the fuel and oxidizer tanks. With outstanding technical innovation and skill, the pre-launch AACS design team overcame all these challenges. The Cassini AACS design this team produced is themost complex and most capable among all interplanetary spacecraft ever flown.
Since its launch on October 15, 1997, the performance of the Cassini AACS design has been superb. All keymission and science requirements have been met with margins. For example, the Allan variance requirement for thegravity wave experiment was met by a factor of more than 4. The mean accuracy (magnitude) of all rocket enginemaneuvers (with ∆V magnitudes larger than 3 m/s) is better than the pre-launch requirement by a factor of 10. Theactual total number of on/off cycles consumed by the eight thrusters, from Launch to SOI, was a factor of at least2.5 lower than the pre-launch estimate. A significant part of “saving” came from the RCS controller parameteradjustments made in flight (see Section IV.B3). The pointing stability requirements of the spacecraft base-bodyhave been met by a factor of at least 3. In fact, in an email sent to the AACS team, the principal investigator of theImaging Science team stated that “From all I have seen, the AACS guys have a lot to be proud of. You have givenus a remarkable platform from which to take pictures.”
The foundation of high quality science pictures is a set of three healthy reaction wheels. Therefore, a commongoal for both the Cassini science and engineering teams is to protect the reaction wheels against any undesirableoperations (such as a prolonged operation inside the low-rpm region of the reaction wheel bearings). Operating thereaction wheels inside the low-rpm region is highly undesirable because the lubrication film will not be adequate toprevent metal-to-metal contacts between the bearing balls and the inner/outer races of the bearings. But, because theangular momentum storage capacity of each reaction wheel is only 34 Nms (that corresponds to a reaction wheelspin rate of about 2029 rpm), to support science slew, it is impossible to avoid operating these wheels inside thelow-rpm region (see Section IV.E3). In flight, we had observed occasional occurrences of RWA bearing cageinstability, drag torque “spikes”, and other drag torque “surprises.” However, the effects of these anomalous dragconditions are greatly alleviated by the “drag torque compensator” function implemented in a flight software objectnamed RWA Manager. Nevertheless, these anomalous bearing drag conditions threaten the long-term safeoperations of the reaction wheels.
The AACS team responded to this threat with the creation of a ground software tool named RBOT (seeSection IV.A5). Since early 2001, RBOT has been used by AACS to select optimal sets of reaction wheel biasingrates for all RWA biasing events. An optimal set of RWA spin rates is one that minimizes the total time the threewheels spent inside the low-rpm region (from the current to the next reaction wheel biasing). Also, the optimalRWA bias rate set was selected in such a way that the upper bounds of the wheels’ spin rates, 2029 rpm, will notbe violated. Disciplined and long-term use of RBOT leads to significant reduction in the daily consumption rate ofthe RWA low-rpm dwell time (hours spent inside the low-rpm region per day). Additionally, the AACS teamconstantly looks up for opportunities that can further reduce low-rpm RWA usage. Techniques include the additionof an un-scheduled RWA biasing and the modifications of the science slew designs (e.g., instead of spinning thespacecraft about its X-axis, spins it about an axis that is 30° away from the X-axis). Continuous monitoring of theRWA bearing drag condition and the careful management of reaction wheel spin rates are key foci of the AACSteam for the remainder of the Cassini-Huygens mission.
The Cruise phase of the Cassini/Huygens mission was about 6.7 years long. The Cassini flight operationsteam took advantage of this long cruise duration to “update” the AACS FSW five times (see Section III). TheseAACS flight software updates were planned and scheduled at the time of Launch. The timings of these softwareuploads were selected strategically so as to avoid interfering with preparation activities for the critical events(Saturn orbit insertion, Probe release, and the Probe relay sequences). Changes incorporated in these FSW buildsinclude AACS capabilities whose development was intentionally postponed due to pre-launch schedule pressure.Changes also included lessons learned from early Cruise. In between these scheduled FSW uploads, when a needarises, AACS commands are sent to effect immediate changes in the magnitudes of certain parameters (instead ofwaiting for the next FSW upload). Subsequently, these temporary changes are made permanent in the next FSWbuild. Overall, smooth and efficient operations of the AACS could be attributed to the flexibility permitted by thepatchability of the flight software. This was the same lesson learned from the Voyager 1 and 2 missions. 34
On November 13, 1980, the Voyager 1 spacecraft encountered Saturn and sent to Earth high-resolution imagesof Saturn, its rings, and six of its satellites. To accomplish this goal, the Voyager AACS team had to overcome
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two difficulties. The first was related to the need to avoid placing Saturn (and its rings) inside the stray-light fieldsof view of both the Canopus star tracker (that provided spacecraft’s roll-axis attitude estimate) and the Sun sensor(that provided spacecraft’s pitch and yaw-axis attitude estimates). After a careful star search, the Voyager AACSteam solved the “stray-light” interference problem by a change in the “lock star” from Vega to Alhena. The seconddifficulty was related to the need to perform Target Motion Compensation (TMC) during these high-speed satelliteflybys. To solve this problem, the Voyager team studied the possibility of slewing the entire science platform totrack the target. Unfortunately, this entailed slewing the platform in two axes simultaneously, which could not bedone with the available software. The challenge was finally met by FSW modifications of the gyroscope driftcompensation logic. Pre-computed three-axis TMC rate data were “injected” into the gyroscope drift compensationlogic to slew the entire spacecraft. With these technical innovations, all science goals of the Saturn encounter wereflawlessly met.34
For Cassini, similar challenges must also be met but they are now met effortlessly. For example, the TMCneeded for the continuous tracking of Titan during a fast flyby is autonomously taken care of by the IVP pointingengine. If a “stray-light” interference problem is anticipated, the star identification algorithm can be “suspended”via a single command. Other built-in autonomous capabilities are the calibration of the inertial reference unit, thedetection and avoidance of a geometric constraint, the “suspension” of attitude control, and others. Because of thesebuilt-in capabilities, the AACS flight team did not find it difficult to “fly” this highly capable spacecraft. In avery significant way, these built-in autonomous capabilities have contributed to the high productivity of theCassini science campaigns.35-39 Not surprisingly, modified versions of the Cassini IVP pointing engine had alsobeen adopted by other interplanetary missions such as the Mars Exploration Rovers missions.40
A large number of AACS “flight rules” (see Section III.H) are generated and enforced to assure the safeoperations of the spacecraft. Sequences to be uploaded to the spacecraft must be checked against possible violationof any of these flight rules. To this end, ground software tools are designed, coded, tested, and missioned toperform these checking. For example, given the time history of the spacecraft’s attitude, one of these groundsoftware tools could flag a warning whenever the angle between the Sun-line vector and the bore-sight vector ofNAC is smaller than a selected threshold. Automated ground software-based checking of uplink sequences is aneffective and efficient way to detect possible mistakes made by the flight team or for whatever other reasons.Ground software tools are indispensable for smooth and efficient flight operations but there is no substitute foradherence to two basic engineering practices: Pay attention to the details, and triple checks your results! Here isthe reason why.
In flight operations, new things were learned everyday. As detailed in Section IV.G2, on day 73 of 2004, thespacecraft was commanded to execute a series of slews in order to calibrate the prime IRU. These calibration turnswere checked by the ground software tool and were declared to be free of any “constraint violation.” In reality, oneof the calibration slews tried to put the Sun into the “POSX_SUN” constraint region. The ground check failedbecause that particular slew is an “exact” 180° slew. In the ground software check, the S/C was slewed in onedirection (which did not violate any constraint). In flight, the flight software slewed the spacecraft in the otherdirection (which violated the “POSX_SUN” constraint). However, the failure of the ground check did not cause anyactual problem on the spacecraft. This is so because upon detecting the potential constraint violation, the onboardconstraint monitor issued “evasive” slew commands to avoid any actual violation. There was no adverse effect onthe spacecraft or the IRU calibration. This is one scenario that testifies to the usefulness of having an onboardconstraint monitor capability to guard against all You do not know what you do not know scenarios. The need toavoid making a 180° spacecraft slew was not known before this incidence!
Other than the RWA bearing drag problem reported in Section IV.E3, the performance of all AACSequipments, including the Sun sensors, accelerometer, stellar reference units, inertial reference units, valve driveelectronics, engine gimbal electronics and actuators, and AACS flight computers, has been virtually problem-free.The performance of algorithms that were designed to perform the following key AACS functions have been superb:attitude commander, inertial vector propagator, reaction-wheel attitude and rate controls, RCS thruster control,attitude estimation, star identification, thrust vector control, RCS ∆V control, command handler, and telemetry. Aparameter tweak was carried out during the inner solar cruise phase to fine-tune the RCS thruster controller that ledto savings in both hydrazine and thruster on/off cycles. Flight experience gained from the Jupiter campaign led usto improve both the dynamics and geometric constraint monitor designs in the AACS FSW A8.6.5 build (seeSection IV.G1 and IV.G2). As a result, to date, there has not been any CMT-related anomaly found during theTour phase of the mission.
The AACS fault protection designs for the SOI and probe relay critical sequences were substantially modified,reviewed, coded, and tested during the long outer Solar cruise phase of the mission. The modified FP designs forthe SOI and Probe relay critical events were implemented in the A8.6.7 and A8.7.1 FSW builds, respectively. The“energy-cutoff” algorithm that performed superbly for the SOI critical sequence was also implemented in the
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A8.6.7 FSW. The redesigns of these complex fault protection algorithms for the critical events and the design ofthe energy-cutoff algorithm for SOI could not have been done without two key test beds. These test beds are theFlight Software Development System (FSDS)43 and the Integrated Test Laboratory (ITL).42
The FSDS is an “all software” closed-loop, workstation-based, faster than real-time test bed. It was theprimary testing environment used by flight software engineers to develop and validate AACS flight software. Keyfeatures of FSDS are the high-fidelity modeling of attitude control actuators, sensors, spacecraft dynamics(including structural flexibilities and those due to fuel sloshing), AACS bus models, fault injection, starsimulation, injection of a time-varying Titan atmospheric torque, Command and Data Subsystem (CDS)emulation, and many other features. The ITL is a hardware-in-the-loop simulation test bed for both the AACS andCDS. Star tracker, inertial reference unit, Sun sensor, AACS flight computer, one (of three) reaction wheel, andother hardware are all used in ITL simulation tests. Both test beds are used to perform regression testing (guidanceand control, fault protection, FSW timing, etc.) of AACS flight software builds, to develop and fine-tune twocritical sequence designs,44,48 to develop and fine-tune science sequences with first-time events, as well as toinvestigate flight anomalies. The importance of these test beds could not be more emphasized. Of course, a goodtest bed is a necessary but not sufficient condition for good testing. Other necessary conditions include the designsof the test cases (with attentions given to initial conditions of the spacecraft and the AACS configuration, thepresence of non-gravitational torque, etc.), independent analyses and reviews of the test results, pre-testestablishment of well-defined Pass/Fail criteria, and the tracking/closure of failed test cases.49 Indeed, both theCassini AACS and ITL teams reviewed results of hundreds of test cases that are related to the Saturn OrbitInsertion as well as the Probe relay critical sequences.44, 47,48
It has been said that in making scientific advances, each generation of scientists stands on the shoulders of theprevious generation. Before Cassini, Saturn was visited and studied by Pioneer 11 (1979), Voyager 1 (1980), andVoyager 2 (1981). Similarly, in designing the Cassini attitude and articulation control subsystem, the pre-launchAACS design team incorporated lessons learned from the flight operations of these past missions in the design.With outstanding technical innovation and skill, the team produced the most capable and yet easy-to-flyinterplanetary spacecraft launched to date. Post-launch, many members of the design team continue to support theflight operations of Cassini. What the AACS flight team has accomplished over the past eight years (since launch)gives us confidence that we will be able to support the Cassini Science operations for the remainder of primemission, and any follow-on operations that may be authorized.
Acknowledgements
The work described in this paper was carried out by Jet Propulsion Laboratory, California Institute ofTechnology, under a contract with the National Aeronautics and Space Administration. Since its launch on October15, 1997, the following engineers have made contributions to the AACS operations of the Cassini spacecraft:Shadan Ardalan, Eric Arlington, Kevin Barltrop, David Bates, Rozita Belenky (who is now affiliated with theBoeing Corporation), Jay Brown (lead AACS FSW engineer for both the A8.7.1 and A8.7.2 flight softwarebuilds), Tom Burk (Cassini AACS uplink team lead), Larry Chang, David Faulkner, Martin Gilbert, AntonetteFeldman (who generated Figure 36), Kenneth Friberg, David Herman, Danny Lam (lead AACS FSW engineer forboth the A8.6.5 and A8.6.7 flight software builds), Cliff Lee (who generated Figure 28), Dr. Randy Lin, AudreyMark, John McNew, Peter Meakin, David M. Myers, Michael Pellegrin, Siamak Sarani, Dr. Kuei Shen, BrettSmith, Marek Tuszynksi (lead AACS FSW engineer for the A7.7.6 flight software build), Thi Vu, Eric Wang, andLisa Won (who is now affiliated with the Boeing Corporation). We are also grateful to Nelson Alhambra, DavidAllestad, Kareem Badaruddin, Todd Barber, Dr. Charles Bell, Randy Blue, Brian Bone, Daniel Cervantes, Dr.Alan Chamberlin, Richard Cowley, Dr. Fred Hadaegh, Juan Hernandez, Shin Huh, Edward Konefat, Mary Lam,Margaret Middleton, Jerry Millard, Leticia Montanez (Cassini ITL lead engineer), Tracy Nelson, Dr. RobertNorton, Duane Roth, Miguel San Martin, David Seal, Katalin Sherwood, David Skulsky, Dr. Claudio Sollazzo(Huygens Probe Operations Manager, European Space Agency), Shaun Standley, Fred Tomey, Dr. SamuelThurman, W. John Walker, Julie L. Webster (Cassini Spacecraft Operations Office manager), Dr. Edward C.Wong, and Elaine Zamani, our colleagues at Jet Propulsion Laboratory, for helpful assistance over the past years.The first author is especially grateful to the technical support of the following esteemed colleagues: Jim Alexander(who generated Figure 27), Dr. Doug Bernard, William Breckenridge, G. Mark Brown, Janis Chodas, AllanEisenman, Dr. Tooraj Kia, Dr. Edward H. Kopf, Jr., Edward Litty, Glenn Macala, Dr. Earl Maize, Scott Peer, Dr.Robert Rasmussen, Dr. Joseph Savino, Dr. Gurkirpal Singh, and John South. We are also indebted to followingCassini scientists for helpful discussions: Dr. Yanhua Anderson, Dr. John Armstrong, Dr. Candice Hansen, Prof.Essam Marouf (who is affiliated with the San Jose State University), Trina Ray, Dr. Nicole Rapapport, Dr. MarciaSequra, Dr. Linda Spilker (deputy Cassini project scientist), Prof. Hunter Waite (who is affiliated with the
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University of Michigan), and Prof. Roger Yelle (who is affiliated with the University of Arizona). Erin Maneri andJulie Wertz (both of whom are affiliated with the Massachusetts Institute of Technology), Sean Augenstein (who isaffiliated with Stanford University), Dr. Peter P. Frantz and Dr. Stephen V. Didziulis (both of whom are affiliatedwith the Aerospace Corporation), Dr. Daniel Santos-Costa, and Dr. Bradford Shogrin (who is affiliated with theBall Aerospace Corporation) have also made invaluable contributions. Many attitude control requirements werementioned in various sections of this paper. In case of conflict between requirements mentioned in this paper andthose given in official Cassini documents, requirements given in the official Cassini documents shall be used. Theground software named RBOT described in Section IV.A5, on the optimal selection of reaction wheel bias rates,has been reported to the Patent Counsel Office of the Jet Propulsion Laboratory for potential patent application.Mr. William Breckenridge, a senior member of the Guidance, Navigation, and Control Section, improved thetechnical accuracy of this paper through his careful reading. Any remaining errors of fact or interpretation are ofcourse our responsibility.
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