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

TL;DR

This paper develops a discrete-time optimal control framework for spacecraft attitude maneuvering that accounts for momentum and control constraints, employing variational analysis on SO(3) and a novel multiple shooting solution method.

Contribution

It introduces a new discrete-time attitude control approach using variational analysis on SO(3) and a multiple shooting algorithm for solving constrained optimal control problems.

Findings

Successfully derives necessary conditions for optimality in attitude control.

Proposes a robust multiple shooting method with Newton algorithm for solving boundary value problems.

Demonstrates effectiveness through numerical experiments.

Abstract

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