Discrete-time optimal attitude control of spacecraft with momentum and control constraints

摘要

This article solves an optimal control problem arising in attitude control ofa spacecraft under state and control constraints. We first derive thediscrete-time attitude dynamics by employing discrete mechanics. Theorientation transfer, with initial and final values of the orientation andmomentum and the time duration being specified, is posed as an energy optimalcontrol problem in discrete-time subject to momentum and control constraints.Using variational analysis directly on the Lie group SO(3), we derive firstorder necessary conditions for optimality that leads to a constrained two pointboundary value problem. This two point boundary value problem is solved via anovel multiple shooting technique that employs a root finding Newton algorithm.Robustness of the multiple shooting technique is demonstrated through a fewrepresentative numerical experiments.