Stephen F. Andrews

Nonlinear Predictive Control of Spacecraft

A new approach for the control of a spacecraft with large angle maneuvers is presented. This new approach is based on a nonlinear predictive control scheme which determines the required torque input so that the predicted responses match the desired trajectories. This is accomplished by minimizing the norm-squared local errors between the predicted and desired quantities. Formulations are presented which use either attitude and rate tracking or attitude-tracking solely. The robustness of the new controller with respect to large system uncertainties is also demonstrated. Finally, simulations results are shown which use the new control strategy to stabilize the motion of the Microwave Anisotropy Probe spacecraft. Introduction The control of spacecraft for large angle slewing maneuvers poses a difficult problem. Some of these difficulties include: the governing equations have highly nonlinear characteristics, control rate and saturation constraints and limits, and incomplete state knowledge due to sensor failure or omission. The control of spacecraft with large angle slews can be accomplished by either open-loop or closed-loop schemes. Open-loop schemes usually require a predetermined pointing maneuver and are typically determined using optimal control techniques, which involve the solution of a two-point boundary value problem (e.g., see the time optimal maneuver problem [1]). Also, open-loop schemes are sensitive to spacecraft parameter uncertainties and unexpected disturbances [2]. Closed-loop systems can account for parameter uncertainties and disturbances, and thus provide a more robust design methodology. In recent years, much effort has been devoted to the closed-loop design of spacecraft with large angle slews. Wie and Barber [3] derive a number of simple control schemes using quaternion and angular velocity (rate) feedback. Asymptotic stability is also shown by Copyright c 1997 by John L. Crassidis. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. using a Lyapunov function analysis for all cases. Tsiotras [4] expands upon these formulations by deriving simple control laws based on both a Gibbs vector parameterization and a modified Rodrigues parameterization each with rate feedback (for a complete survey of attitude parameterizations, see [5]). Lyapunov functions are shown for all the controllers developed in [4] as well. Other full state feedback techniques have been developed which are based on sliding mode (variable structure) control, which uses a feedback linearizing technique and an additional term aimed at dealing with model uncertainty [6]. This type of control has been successfully applied for large angle maneuvers using a Gibbs vector parameterization [7], a quaternion parameterization [8], and a modified Rodrigues parameterization [9]. Another robust control scheme using a nonlinear H∞ control methodology has been developed by Kang [10]. This scheme involves the solution of Hamilton-Jacobi-Isaacs inequalities, which essentially determines feedback gains for the full state feedback control problem so that the spacecraft is stabilized in the presence of uncertainties and disturbances. Another class of controllers involves adaptive techniques, which update the model during operation based on measured performances (e.g., see [6]). An adaptive scheme which estimates for external torques by means of tracking a Lyapunov function has been developed by Schaub et. al. [11]. This method has been shown to be very robust in the presence of spacecraft modeling errors. The aforementioned techniques all utilize full state knowledge (i.e., attitude and rate feedback). The problem of controlling a spacecraft without full state feedback becomes increasingly complex. The basic approaches used to solve this problem can be divided into methods which estimate for the unmeasured states using a filter algorithm, or methods which develop control laws directly from output feedback. Filtering methods, such as the extended Kalman filter, have been successfully applied on numerous spacecraft systems without the use of rate-integrating gyro measurements (e.g., see [12]-[14]). An advantage of these methods is that the attitude may be estimated by using only one set of vector attitude measurements (such as magnetometer measurements). However, these methods are usually

THE MICROWAVE ANISOTROPY PROBE (MAP) MISSION

The Microwave Anisotropy Probe mission is designed to produce 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. This paper presents an overview of the design of the attitude control system to carry out this mission and presents some early flight experience.

Attitude Control System of the Wilkinson Microwave Anisotropy Probe

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 attitude control system implements this spin-scan observing strategy while minimizing thermal and magnetic fluctuations, especially those synchronous with the spin period. The spacecraft attitude is sensed and controlled using an inertial reference unit, 2 star trackers, a dual-head digital sun sensor, 12 coarse sun sensors, 3 reaction wheel assemblies, and a propulsion system. Sufficient attitude knowledge is provided to yield instrument pointing to a standard deviation (1σ) of 1.3 arc-min per axis. The attitude control system also maintains the spacecraft attitude during orbit maneuvers, controls the spacecraft angular momentum, and provides for safety in the event of an anomaly. An overview of the design of the attitude control system to carry out this mission is presented, as well as some early flight experience.

Recent Flight Results of the TRMM Kalman Filter

The Tropical Rainfall Measuring Mission (TRMM) spacecraft is a nadir pointing spacecraft that nominally controls the roll and pitch attitude based on the Earth Sensor Assembly (ESA) output. TRMMs nominal orbit altitude was 350 km, until raised to 402 km to prolong mission life. During the boost, the ESA experienced a decreasing signal to noise ratio, until sun interference at 393 km altitude made the ESA data unreliable for attitude determination. At that point, the backup attitude determination algorithm, an extended Kalman filter, was enabled. After the boost finished, TRMM reacquired its nadir-pointing attitude, and continued its mission. This paper will briefly discuss the boost and the decision to turn on the backup attitude determination algorithm. A description of the extended Kalman filter algorithm will be given. In addition, flight results from analyzing attitude data and the results of software changes made onboard TRMM will be discussed. Some lessons learned are presented.

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.

MAP Attitude Control System Design and Flight Performance

The Microwave Anisotropy Probe (MAP) is a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE) spacecraft. To make a full-sky map of cosmic microwave background fluctuations, a combination fast spin and slow precession motion will be used that will cover the entire celestial sphere in six months. The spin rate should be an order of magnitude higher than the precession rate, and each rate should be tightly controlled. The sunline angle should be 22.5 +/- 0.25 deg. Sufficient attitude knowledge must be provided to yield instrument pointing to a standard deviation of 1.3 arc-minutes RSS three axes. In addition, the spacecraft must be able to acquire and hold the sunline at initial acquisition, and in the event of a failure. Finally. the spacecraft must be able to slew to the proper burn orientations and to the proper off-sunline attitude to start the compound spin. The design and flight performance of the Attitude Control System on MAP that meets these requirements will be discussed.