Inertia-free Attitude Control of Spacecraft with Unknown Time-varying Mass Distribution

Attitude control of spacecraft remains a challenging nonlinear control problem of intense practical and intellectual importance. Since rotational motion evolves on the set of proper orthogonal matrices, continuous control must account for the presence of multiple equilibria, whereas discontinuous control laws based on quaternions and alternative parameterizations of the rotation matrices lead to additional complications1. Challenges also arise depending on the properties of the actuation hardware, for example, thrusters, reaction wheels, control-moment gyros, and magnetic torquers, as well as sensing hardware, for example, gyros, magnetometers, and star trackers. Finally, this problem is exacerbated by uncertainty involving the mass distribution of the spacecraft2. The present paper addresses an additional complication in spacecraft control, namely, the situation in which the mass distribution of the spacecraft is not only uncertain but also time-varying. Many spacecraft are built to deploy on orbit, for example, by expanding solar panels or a magnetometer boom. Furthermore, a spacecraft may have moving components, such as a reflector or antenna that rotates relative to the spacecraft bus in order to track a ground station. In these cases, the mass distribution changes as a function of time, which, in turn, gives rise to a time-varying inertia matrix. In the present paper we address the problem of spacecraft attitude control with time-varying inertia. The approach that we take is an extension of the approach of ref.2, where continuous control laws are developed based on rotation matrices. For motion-to-rest (that is, slew) maneuvers in the absence of disturbance torques, no knowledge of the inertia matrix is needed, and no estimates of the inertia matrix are constructed. For motion-to-specified-motion (for example, spin) maneuvers in the presence of harmonic (possibly constant) disturbances with known spectral content, the control law is based on an estimate of the inertia matrix; however, this estimate need not converge to the actual inertia matrix. The contribution of the present paper is an extension of the results of ref.2 to the case in which the mass distribution of the spacecraft is both uncertain and time-varying. For motion-to-rest maneuvers, we show that the corresponding control law of ref.2 is effective under a special choice of the control-law parameters. This requirement can be ignored when the inertia matrix is increasing, for example, during deployment. For motion-to-specified-motion maneuvers, we make the additional assumption that the time-variation of the timevarying component of the inertia is known, whereas its spatial distribution is unknown. Under these assumptions, we extend the motion-to-specified-motion control law of ref.2 to the case of time-varying inertia. The contents of the paper are as follows. In Section II we develop a model of a spacecraft with time-varying inertia. In Section III we describe the attitude control objectives. Section IV deals with motion-to-rest maneuvers, while Section V treats motion-to-specified-motion maneuvers.