Optimal attitude control with two rotation axes

TL;DR

This paper solves an optimal control problem for spacecraft attitude adjustment using two rotation axes, identifying optimal rotation sequences that minimize total rotation angle, with potential applications in spacecraft control systems.

Contribution

It provides a complete characterization of optimal rotation sequences around two axes, extending Euler's classical results to an optimal control framework.

Findings

Identifies all possible optimal rotation patterns.

Minimizes total rotation angle for arbitrary orientations.

Applicable to spacecraft attitude control with two axes.

Abstract

Euler proved that every rotation of a 3-dimensional body can be realized as a sequence of three rotations around two given axes. If we allow sequences of an arbitrary length, such a decomposition will not be unique. In this paper we solve an optimal control problem minimizing the total angle of rotation for such sequences. We determine the list of possible optimal patterns that give a decomposition of an arbitrary rotation. Our results may be applied to the attitude control of a spacecraft with two available axes of rotation.