Spin-to-spin slew maneuvers under spherically constrained angular acceleration

Abstract

This paper addresses a three-axis time-optimal attitude-control problem of rigid spacecraft. In this problem, an angular-acceleration vector lies within a spherically constrained space, and spin-to-spin boundary conditions are considered. The problem is converted into a two-point boundary-value problem by an indirect method, which is solved numerically because non-eigen-axis slew motions do not have a general analytical solution. To solve the problem, a homotopy algorithm is applied in which a discrete continuation method, closed form solutions for single-axis slew maneuvers, and a costate transformation method are included. Through numerical examples, the properties of the optimal solutions are analyzed, and the efficiency of the numerical algorithm is demonstrated.