Frank H. Bauer

Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs

Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.

An Anomalous Force on the Map Spacecraft

The Microwave Anisotropy Probe (MAP) orbits the second Earth-Sun libration point (L 2)—about 1.5 million kilometers outside Earth’s orbit—mapping cosmic microwave background radiation. To achieve orbit near L2 on a small fuel budget, the MAP spacecraft needed to swing past the Moon for a gravity assist. Timing the lunar swing-by required MAP to travel in three high-eccentricity phasing loops with critical maneuvers at a minimum of two, but nominally all three, of the perigee passes. On the approach to the first perigee maneuver, MAP telemetry showed a considerable change in system angular momentum that threatened to cause on-board Failure Detection and Correction (FDC) to abort the critical maneuver. Fortunately, the system momentum did not reach the FDC limit; however, the MAP team did develop a contingency strategy should a stronger anomaly occur before or during subsequent perigee maneuvers. Simultaneously, members of the MAP team developed and tested various hypotheses for the cause of the anomalous force. The final hypothesis was that water was outgassing from the thermal blanketing and freezing to the cold side of the solar shield. As radiation from Earth warmed the cold side of the spacecraft, the uneven sublimation of frozen water created a torque on the spacecraft.

The Maneuver Planning Process for the Microwave Anisotropy Probe (MAP) Mission

The Microwave Anisotropy Probe (MAP) was successfully launched from Kennedy Space Centers Eastern Range on June 30, 2001. MAP will measure the cosmic microwave background as a follow up to NASAs Cosmic Background Explorer (COBE) mission from the early 1990s. MAP will take advantage of its mission orbit about the Sun-Earth/Moon L2 Lagrangian point to produce results with higher resolution, sensitivity, and accuracy than COBE. A strategy comprising highly eccentric phasing loops with a lunar gravity assist was utilized to provide a zero-cost insertion into a lissajous orbit about L2. Maneuvers were executed at the phasing loop perigees to correct for launch vehicle errors and to target the lunar gravity assist so that a suitable orbit at L2 was achieved. This paper will discuss the maneuver planning process for designing, verifying, and executing MAPs maneuvers. A discussion of the tools and how they interacted will also be included. The maneuver planning process was iterative and crossed several disciplines, including trajectory design, attitude control, propulsion, power, thermal, communications, and ground planning. Several commercial, off-the-shelf (COTS) packages were used to design the maneuvers. STK/Astrogator was used as the trajectory design tool. All maneuvers were designed in Astrogator to ensure that the Moon was met at the correct time and orientation to provide the energy needed to achieve an orbit about L2. The Mathworks Matlab product was used to develop a tool for generating command quaternions. The command quaternion table (CQT) was used to drive the attitude during the perigee maneuvers. The MatrixX toolset, originally written by Integrated Systems, Inc., now distributed by Mathworks, was used to create HiFi, a high fidelity simulator of the MAP attitude control system. HiFi was used to test the CQT and to make sure that all attitude requirements were met during the maneuver. In addition, all ACS data plotting and output were generated in MatrixX. A final test used FlatSat, a real-time hardware-in-the-loop simulator, which used identical MAP flight code to simulate operations on the spacecraft. Simulations in FlatSat allowed the MAP team to verify maneuver commands, timing, and spacecraft configuration before the commands were sent up to the spacecraft for execution. The MAP maneuver team successfully pieced together all of these COTS tools for designing MAPs maneuvers and MAP is now collecting data at L2.

Contingency Planning for the Microwave Anisotropy Probe Mission

The Microwave Anisotropy Probe (MAP) utilized a phasing loop/lunar encounter strategy to achieve a small amplitude Lissajous orbit about the Sun-Earth/Moon L2 libration point. The use of phasing loops was key in minimizing MAPs overall deltaV needs while also providing ample opportunities for contingency resolution. This paper will discuss the different contingencies and responses studied for MAP. These contingencies included accommodating excessive launch vehicle errors (beyond 3 sigma), splitting perigee maneuvers to achieve ground station coverage through the Deep Space Network (DSN), delaying the start of a perigee maneuver, aborting a perigee maneuver in the middle of execution, missing a perigee maneuver altogether, and missing the lunar encounter (crucial to achieving the final Lissajous orbit). It is determined that using a phasing loop approach permits many opportunities to correct for a majority of these contingencies.

The MAP Propulsion Subsystem

This paper describes the requirements, design, integration, test, performance, and lessons learned of NASAs Microwave Anisotropy Probe (MAP) propulsion subsystem. MAP was launched on a Delta-II launch vehicle from NASAs Kennedy Space Center on June 30, 2001. Due to instrument thermal stability requirements, the Earth-Sun L2 Lagrange point was selected for the mission orbit. The L2 trajectory incorporated phasing loops and a lunar gravity assist. The propulsion subsystems requirements are to manage momentum, perform maneuvers during the phasing loops to set up the lunar swingby, and perform stationkeeping at L2 for 2 years. MAPs propulsion subsystem uses 8 thrusters which are located and oriented to provide attitude control and momentum management about all axes, and delta-V in any direction without exposing the instrument to the sun. The propellant tank holds 72 kg of hydrazine, which is expelled by unregulated blowdown pressurization. Thermal management is complex because no heater cycling is allowed at L2. Several technical challenges presented themselves during I and T, such as in-situ weld repairs and in-situ bending of thruster tubes to accommodate late changes in the observatory CG. On-orbit performance has been nominal, and all phasing loop, mid-course correction, and stationkeeping maneuvers have been successfully performed to date.

RESTORING REDUNDANCY TO THE MAP PROPULSION SYSTEM

The Microwave Anisotropy Probe is a follow-on to the Differential Microwave Radiometer instrument on the Cosmic Background Explorer. Sixteen months before launch, it was discovered that from the time of the critical design review, configuration changes had resulted in a significant migration of the spacecrafts center of mass. As a result, the spacecraft no longer had a viable backup control mode in the event of a failure of the negative pitch axis thruster. Potential solutions to this problem were identified, such as adding thruster plume shields to redirect thruster torque, adding mass to, or removing it from, the spacecraft, adding an additional thruster, moving thrusters, bending thrusters (either nozzles or propellant tubing), or accepting the loss of redundancy for the thruster. The impacts of each solution, including effects on the mass, cost, and fuel budgets, as well as schedule, were considered, and it was decided to bend the thruster propellant tubing of the two roll control thrusters, allowing that pair to be used for back-up control in the negative pitch axis. This paper discusses the problem and the potential solutions, and documents the hardware and software changes that needed to be made to implement the chosen solution. Flight data is presented to show the propulsion system on-orbit performance.

DEVELOPMENT OF A TWO-WHEEL CONTINGENCY MODE FOR THE MAP SPACECRAFT

In the event of a failure of one of MAPs three reaction wheel assemblies (RWAs), it is not possible to achieve three-axis, full-state attitude control using the remaining two wheels. Hence, two of the attitude control algorithms implemented on the MAP spacecraft will no longer be usable in their current forms: Inertial Mode, used for slewing to and holding inertial attitudes, and Observing Mode, which implements the nominal dual-spin science mode. This paper describes the effort to create a complete strategy for using software algorithms to cope with a RWA failure. The discussion of the design process will be divided into three main subtopics: performing orbit maneuvers to reach and maintain an orbit about the second Earth-Sun libration point in the event of a RWA failure, completing the mission using a momentum-bias two-wheel science mode, and developing a new thruster-based mode for adjusting the inertially fixed momentum bias. In this summary, the philosophies used in designing these changes is shown; the full paper will supplement these with algorithm descriptions and testing results.

Performance of the Microwave Anisotropy Probe AST-201 Star Trackers

The Microwave Anisotropy Probe (MAP) was launched to create a full-sky map of the cosmic microwave background. MAP incorporates two modified Lockheed Martin AST-201 (Autonomous Star Tracker) star trackers. The AST-201 employs an eight element radiation hardened lens assembly which is used to focus an image on a charge coupled device (CCD). The CCD image is then processed by a star identification algorithm which outputs a three-axis attitude. A CCD-shift algorithm called Time Delayed Integration (TDI) was also included in each star tracker. In order to provide some radiation effect filtering during MAPs three to five phasing loop passes through the Van Allen radiation belts, a simple pixel filtering scheme was implemented, rather than using a more complex, but more robust windowing algorithm. The trackers also include a fiber optic data interface. This paper details the ground testing that was accomplished on the MAP trackers.