Spacecraft attitude motion planning on SO(3) using gradient-based optimization: case studies

A method for spacecraft attitude motion planning presented in [Celani and Lucarelli, 2019] is applied to relevant case studies. The goal of the method is to design a control torque so that a spacecraft performs a desired rest-to-rest rotation while satisfying pointing constraints. The method possesses the following features. Attitude is represented on the group of three dimensional rotations SO(3) thus avoiding singularities and ambiguities that affect other attitude representations. Moreover, from a practical point of view, the control torque resulting from the method is continuously differentiable and vanishes at its endpoints. Thus, the resulting controls are easier to implement on real spacecraft than time-optimal control torques that often do not vanish at endpoints and can be discontinuous during the maneuver. A unique feature of the method is the use of basis functions parameterizing the angular rates. The case studies we consider are presented in [Spiller et al., 2016] in which a satellite for Earth observation in low Earth orbit must perform a roll rotation. The satellite is equipped with a star tracker that must avoid Sun and Moon directions with prescribed offset angles during the maneuver.