# Intersatellite and Downlink Agile Attitude Maneuvers
## 1 Introduction
[21] designed an inertia-free attitude control algorithm that employs rotation matrices. The latter representation has the additional advantage of uniqueness when compared to Euler parameters. This research is based on the conference paper [23], and addresses the problem of agile attitude maneuvering, aimed at precise pointing of a satellite that forms a typical constellation in low-altitude Earth orbit. More specifically, two different operational scenarios are considered: (a) pointing toward a specific ground station, located on the Earth surface, and (b) pointing toward a companion satellite. In both cases, the attitude control system of the satellite of interest must be able to track a time-varying pointing direction. To achieve this, the following study employs an inertia-free nonlinear attitude control algorithm based on rotation matrices [21] and possessing remarkable stability properties. Gain tuning for this scheme involves the instantaneous angular velocity components, as well as further quantities related to the maximum available torque and the expected transient time. Because the orbital dynamics relative to the target--either the ground station (a) or a companion satellite (b)--is relatively fast, agile attitude maneuvering is mandatory to complete the required data routing operations. With this intent, this study considers the use of a pyramidal array of single-gimbal control momentum gyroscopes with constant rotor speed. Their dynamical interaction with the spacecraft is accurately modeled, to identify the equivalent torque transferred to the satellite. The main challenge in using these devices is represented by the identification of an effective steering law, capable of avoiding singularities. Several approaches are available to address this issue, e.g., the use of null motion. In this study, singular direction avoidance based on singular value decomposition of the actuation matrix is used. However, the inclusion of the actuation dynamics implies that the commanded torque, yielded by the nonlinear control algorithm, differs from the actual torque transferred to the vehicle. This circumstance implies that the analytical asymptotic stability properties proven for the attitude control algorithm do not hold for the overall system that includes the actuator dynamics, strictly speaking. Hence, numerical evidence must support the use and effectiveness of nonlinear attitude control with actuation modeling. The satellite of interest is assumed to perform a maneuver composed of two phases: (i) attitude tracking aimed at continuous pointing toward the target and (ii) attitude reorientation, in preparation for tracking the next target. Effectiveness of the attitude control and actuation architecture proposed in this study is being investigated numerically, with reference to the two operational scenarios of interest, i.e., continuous pointing of either a ground station (a) or a companion satellite (b), during the respective time intervals of visibility. Numerical analysis is being performed in both nominal and nonnominal conditions, associated with stochastic displacements in the initial attitude and angular rate.