Attitude Tracking Control for Spacecraft Formation Flying

We develop a non-linear tracking control law to be applied to formation flying spacecraft. Each spacecraft in the formation is modeled as a rigid body with N axisymmetric wheels controlled by axial torques, and the kinematics are represented by Modified Rodriques Parameters (MRPs). The paper first derives the open-loop reference attitude, rate, and acceleration commands for tracking a moving object with the sensor boresight vector defined along a bodyfixed axis. The reference trajectory is constructed so that the solar panel normal is aligned with the sun vector at all times while tracking targets on the rotating earth. The controller makes the body frame asymptotically track the reference motion when there are initial errors in the position and angular rates. A simple target tracking example is presented to demonstrate that the controller will allow each spacecraft in the formation to track the target and the sun simultaneously. INTRODUCTION The formation flying concept has become a topic of interest in recent years. Gramling et al.1 discussed the Onboard Navigation System (ONS) for relative navigation of the Earth-Observing-1 (EOS-1)/Landsat-7 (L-7) formation. The performance of the ONS was investigated in terms of tracking measurement type and quality, tracking frequency, and the relative orbital geometry of the formation. DeCou2 presented a station-keeping strategy for formation flying interferometry. He discussed the basic orbital configuration for interferometry missions and the thrust requirements for station-keeping of a two-satellite formation. The work done by Ulybyshev3 pertains to station-keeping of a constellation using a linear-quadratic regulator for feedback control. The controller minimized the along-track relative displacements between spacecraft and the orbital period displacements relative to a reference orbit. Folta et al.4 also addressed separations between spacecraft in a formation. The performance of a formation to observe ground targets simultaneously for various separations was evaluated. Simulation results for three different types of formations were presented in terms of attitude and field of view (FOV) errors. Spacecraft rotational tracking maneuvers specifically for formation flying have not been addressed in the literature. The problem of tracking moving objects applicable to formation flying has been studied by various authors, and much of the work developed in this paper is based on Refs. 5, 6 and 7. Schaub et al.8 also discussed rotational tracking maneuvers similar to what we present here, except that they optimized the reference trajectory for time and fuel requirements and used a different Lyapunov function to derive the momentum wheel controller. Steyn9 and Wie and Lu10 both investigated momentum wheel feedback controllers for rotational maneuvers. Slew rate constraints and near-minimum-time maneuvers were taken into account. To determine the feasibility of formation simultaneous target tracking, we first consider the pointing and tracking requirements for an individual spacecraft. The desired attitude is constructed by making the sensor boresight axis co-linear with the position vector from the spacecraft to any arbitrary target. We define the target to be a point on the rotating earth, but it could be any inertially fixed, or moving target. We define two intermediate coordinate frames using the boresight axis, the solar array axis, and the sun vector to construct basis vectors that simultaneously allow the spacecraft to point at the target and keep the solar panel vector normal to the sun direction. The ideal tracking body rates and accelerations are computed from the first and second derivatives of the attitude, respectively. The reference acceleration is used to compute the ideal axial control torque for the control law. The controller uses Lyapunov control theory to drive any initial errors in the attitude and angular velocity to zero asymptotically. The