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