THE ATTITUDE CONTROL SYSTEM OF THE WILKINSON MICROWAVE ANISOTROPY PROBE F. Landis Markley,* Stephen F. Andrews,? James R. O’Donnell, Jr.,** David K. Ward** NASA Goddard Space Flight Center ABSTRACT The Wilkinson Microwave Anisotropy Probe mission produces a map of the cosmic microwave background radiation over the entire celestial sphere by executing a fast spin and a slow precession of its spin axis about the Sun line to obtain a highly interconnected set of measurements. The spacecraft attitude is sensed and controlled using an inertial reference unit, two star trackers, a digital sun sensor, twelve coarse sun sensors, three reaction wheel assemblies, and a propulsion system. Sufficient attitude knowledge is provided to yield instrument pointing to a standard deviation (lo) of 1.3 arc-minutes per axis. In addition, the spacecraft acquires and holds the sunline at initial acquisition and in the event of a failure, and slews to the proper orbit adjust orientations and to the proper off-sunline attitude to start the compound spin. This paper presents an overview of the design of the attitude control system to carry out this mission and presents some early flight experience. INTRODUCTION The Wilkinson Microwave Anisotropy Probe (MAP). the second Medium-Class Explorer (MIDEX) mission, was launched on June 30, 2001 as a follow-on to the Cosmic Background Explorer (COBE), which made precise measurements of the cosmic microwave background * Aerospace Engineer, Fellow AIAA, Greenbelt, MD, 20771, USA ? Aerospace Engineer, Greenbelt, MD, 20771, USA ** Aerospace Engineer, Senior Member AIAA, Greenbelt, MD, 20771, USA 1 (CMB) that is believed to be a remnant of the Big Bang marking the birth of the universe.I4 WMAP has measured the CMB anisotropy with sensitivity 50 times that of the Differential Microwave Radiometer (DMR) instrument on COBE and angular resolution 30 times finer, specifically 20 microKelvin and 14 arc minutes, respectively, enabling scientists to determine the values of key cosmological parameters and to answer questions about the origin of structure in the early universe and the fate of the uni~erse.~’ Since the major error sources in the DMR data arose from COBE’s low Earth orbit, WMAP was placed in a Lissajous orbit around the Sun-Earth L, Lagrange point to minimize magnetic, thermal, and radiation disturbances from the Earth and Sun. WMAP attained its Lissajous orbit around L, in early October 2001, about 100 days after launch by a Delta 11 launch vehicle, using a lunar gravity assist following three phasing loops, as shown in Figure 1. The trajectory design and opeiatioiis x ed iscussed in detzil in Refs. 7-12 Figure 1: W W Tr ajectory to L2 2 The WMAP instrument includes radiometers at five frequencies, passively cooled to about 90"K, covering two fields of view (FOVs) 141" apart on the celestial sphere. The WMAP observatory executes a fast spin coupled with a slower precession of its spin axis at a constant angle of 22.5" from the Sun line to obtain a highly interconnected set of measurements over an annulus between 87" and 132" from the Sun. The rotation about the spin axis has to be at least an order of magnitude faster than the rate of precession of the spin axis; the rates chosen were 2.784 deg/s (0.464 rpm) for the spin rate and -0.1 de& (1 revolution per hour) for the precession rate. Figure 2 shows the scan pattern covered by one of the two FOVs in one complete spacecraft precession (1 hour), displayed in ecliptic coordinates in which the ecliptic equator runs horizontally across the map. The bold circle shows the path for a single spin (2.2 minutes). As the Earth revolves around the Sun, this annulus of coverage revolves about the ecliptic pole as shown in Figure 3. Thus the entire celestial sphere will be observed once every six months, or eight times in the planned mission life of f c iy eas. North Ecliptic Pok 93" 93" South Ecliptic Fob Figure 2: WMAP Scan Pattern 3 6E Figure 3: WMAP Spin-Scan Concept This paper gives an overview of the Attitude Control System (ACS) that acquires and maintains the spacecraft orbit, controls the spacecraft angular momentum, provides for safety in the event of an anomaly, and implements the spin-scan observing strategy while minimizing thermal and magnetic fluctuations, especially those synchronous with the spin period. More detail can be found in Refs. 13-19. ACS OVERVIEW WAF 'uses three right-handed, orthonormal coordinate systems. The Geocentric Inertial kame (GCI) is an Earth-centered frame with its XI axis pointing to the vernal equinox, its ZI axis pointing to the North Celestial Pole (parallel to the Earth's spin axis), and y~ = ZIx XI. The Rotating Sun Referenced frame (RSR) is a spacecraft-centered frame in which the axis points ZR from the WMAP spacecraft to the Sun, XR is a unit vector in the direction of ZR x 21, and 4 yR = ZR x xR. The RSR frame rotates at approximately 1" /day with respect to the GCI frame. The body frame is centered at the spacecraft center of mass with ZB axis parallel to the spacecraft centerline, directed from the instrument to the solar arrays, YB axis normal to the instrument radiator faces, and XB = YB x ZB, as shown in Figure 4. As a minimum, all the WMAP ACS control modes maintain the spacecraft ZB axis within 25" of the Sun, to satisfy thermal and power constraints. Instrument priraary mirrors \ 1 Sun shield' 1 % axis Figure 4: Spacecraft Layout The WMAP attitude is sensed by an Inertial Reference Unit (IRU), two Autonomous Star I Trackers (ASTs), a Digital Sun Sensor (DSS), and twelve Coarse Sun Sensors (CSSs); it is controlled by three Reaction Wheel Assemblies (RWAs) and a propulsion system. Figure 5 i~ illustrates the WMAP ACS architecture. More detail on the WMAP ACS hardware suite can be found in Refs. 16 and 19. 5 ACS PmeSsor C&DH , Sync. 4 ---- T ! 1773 Fiber- optic Bus I I ! ACE I. Attitude Conml Elecmnics Sak hold Pnxessor Figure 5: Attitude Control System Architecture The IRU comprises two Kearfott Two-Axis Rate Assemblies (TARAs), one with input axes aligned with the ZB and XB axes and the other with input axes aligned with the ZB and YB axes. This gives redundant rate inputs on the axis; the DSS outputs can be differentiated to provide ZB rates on the other axes in the event of an IRU failure. The boresights of the two Lockheed-Martin ASTs'* are in the ~ Y dBir ections. Each AST tracks up to 50 stars simultaneously in its 8.8" square FOV, matches them to stars in an internal star catalog, and computes its attitude as a GCI-referenced quaternion with accuracy of 21 arc- seconds (la) around its boresight axis and 2.3 arc-seconds (lo)i n the other two axes. 6 The Adcole two-axis DSS has two heads, each with 64" square FOV and an accuracy of 1 arc- minute (30). The centers of the FOVs of the two heads are in the XB-ZB plane at angles of f29.5" from the zB-axis. The CSSs are cosine eyes located in pairs looking outward from the edges of the six solar array panels, alternately pointing 36.9" up and 36.9" down from the plane. XB-YB The RWAs are Ithaco Type E wheels each with a momentum storage capacity of 70 Nms. The available reaction torque of each wheel is 0.35 Nm, but this is limited to 0.215 Nm by the WMAP software to satisfy power constraints. The reaction wheel rotation axes are tilted 60" from the -ZB axis and uniformly distributed 120" apart in azimuth about this axis. The wheels serve the dual function of counterbalancing the body's spin angular momentum to maintain the system momentum (i.e. body plus wheels) near zero while simultaneously applying control torques to provide the desired spacecraft attitude. The wheel axis orientations result in all wheel speeds being biased away from zero while the spin-scan observing motion is being executed, thus avoiding zero-speed crossings that would occur if the wheel spin axes were oriented along the spacecraft body frame coordinate axes. The propulsion system comprises eight monopropellant hydrazine Reaction Engine Modules (REMs) and associated hardware. Each REM generates a maximum thrust of 4.45 N. MOMENTUM MANAGEMENT STRATEGY The choice of an L2 orbit to minimize magnetic, thermal, and radiation disturbances precludes the use of magnetic sensing or torquing. Thus, the propulsion system provided for orbit maneuvers and stationkeeping is also used to unload accumulated system angular momentum after each orbit adjust. These occur several times in the phasing loops but no more than once every three months at Lz to minimize interruptions of science observations. The RWAs can store on the order of 70 Nms of angular momentum in non-spinning modes, and a significant fraction of this along the ZB axis while spinning about this axis. While executing the Observing Mode 7 spin-scan, however, the transverse momentum storage capacity (i.e. in the XB-YB plane) is limited to 3 Nms, the amount that can be cycled among the three RWAs at the fast spin rate without adversely affecting attitude control. Gravity-gradient, atmospheric drag, and outgassing torques are significant in the phasing loops, but the accumulated angular momentum of less than 1 Nms per orbit is easily stored until removal following orbit maneuvers at apogee or perigee. Solar radiation pressure torque is the only significant disturbance torque at L2, and the uniform rotation of the spin axis reduces its average along the XB and YB axes by more than two orders of magnitude compared to its instantaneous value. The only potentially troublesome component is a “pinwheel” torque along the axis, which might result from an imperfect deployment of the solar array panels. The ZB angular momentum is accumulated in inertial space, so it is clear from Figure 3 that the pinwheel torque at one point in the orbit leads to a transverse angular momentum one-quarter orbit, or 91 days, later. This means that any accumulation of angular momentum from the pinwheel torque of more than about 0.03 Nms per day would require momentum unloading more frequently than desired. Pre-flight estimates of the pinwheel torque gave angular momentum accumulation ranging from 0.0016 to 0.065 Nms per day, depending on the accuracy of deployment of the solar arrays and the resulting symmetry of the ~pacecraft.’T~h e worst-case estimate would reach the Observing Mode system angular momentum limit of 3 Nms in 46 days, which is highly undesirable. Flight data indicates an angular momentum accumulation of about 0.005 Nms per day, which easily meets the three-month requirement. In fact, since this is less than 0.03 Nms per day, Figure 3 shows that the pinwheel torque will begin to unload the accumulated angular momentum on the next quarter orbit, so no unloading by the REMs is required at all, in principle. The orbit perturbations at L2 have also been well within requirements, so it has been possible to perform stationkeeping and momentum unloading only once every four months, rather than every three months. 8 ACS OPERATIONAL MODES WMAP has six ACS modes. The Inertial, Observing, Delta V, Delta H, and Sun Acquisition modes are implemented in the main spacecraft (Mongoose V) processor, while the Safehold Mode resides in the Attitude Control Electronics Remote Services Node (ACE RSN). Figure 6 shows the modes and the transitions among them. Anomalous behavior can result in ACE Every mode autonomous transitions from any other mode to Sun Acquisition Mode or Safehold Mode, even though these transitions are not shown explicitly. Figure 6: ACS Mode Transitions Each of the modes of the WMAP ACS will be discussed below, including a discussion of the sensors, actuators, and control algorithms used in that mode. Examples of in-flight performance are also provided. ACS DESIGN AND PERFORMANCE Sun Acquisition Mode Sun Acquisition Mode uses the CSS, IRU, and RWAs to acquire and maintain the spacecraft ZB axis within 25" of the Sun, starting from any initial orientation and with any initial body momentum less than [13, 13, 551 Nms. 'l'his is a thermally safe and power-positive orientation before instrument power-on, and this is the mode entered after separation from the launch 9 vehicle. If the rates at entry to the RWA-based Sun Acquisition Mode exceed those that can be handled by this mode, the REM-based DeIta H Mode is entered to reduce the rates to an acceptable level, after which the spacecraft returns to Sun Acquisition Mode. Transition from Sun Acquisition Mode to Inertial Mode can be commanded after the Sun has been acquired. Transition to the Mongoose control modes from the ACE Safehold Mode is through Sun Acquisition Mode. Normal exit from Sun Acquisition Mode is to either Delta H or Inertial Mode, depending on the residual spacecraft spin rate. The attitude error signals in Sun Acquisition Mode are calculated by computing the cross product of theaun vector computed from CSS measurements with the desired sun vector. The nominal desired sun vector points the axis, the solar array normal, directly at the sun. The attitude +ZB error signals are limited and multiplied by the proportional control gain. The rate error signal is the body rate measured by the IRUs. The rate error vector is multiplied by the spacecraft inertia and then each axis is multiplied by a derivative control gain. The output of this proportional- derivative (PD) control algorithm is three torque commands in the body frame. A body-to-wheel reference frame transformation matrix is used to transform these commands to the reaction wheel frame. The wheel torque commands are scaled down by a common factor if the largest command exceeds the wheel torque capability, so that the torque direction is preserved while the largest command is the maximum reaction wheel torque command. In pre-launch analysis and testing, Sun Acquisition Mode was found to meet its performance requirements for all initial system mommtum magnitudes of 55 Nms or less. Because this level represented 20 separation rates from the Delta IT third stage, a contingency thruster momentum unload was unlikely, but would be possibly needed. In addition, there were a few degenerate cases (e.g., 180 degrees off of the sun with zero rates) that did not satisfy the requirements, but these were deemed too unrealistic to be of concern. 10