Minimum-Time Reorientation of Axisymmetric Rigid Spacecraft Using Three Controls

TL;DR

This paper investigates the minimum-time reorientation of an axisymmetric rigid spacecraft with three controls, revealing a switching control structure and the presence of singular arcs, using advanced numerical optimization techniques.

Contribution

It introduces a numerical method capable of accurately solving bang-bang and singular optimal control problems for spacecraft reorientation, and analyzes the optimality conditions in detail.

Findings

Optimal control solutions exhibit switching control structures.

Solutions include segments on singular arcs under certain conditions.

The proposed numerical method outperforms previous approaches in accuracy and efficiency.

Abstract

A minimum-time reorientation of an axisymmetric rigid spacecraft controlled by three torques is studied. The orientation of the body is modeled such that the attitude kinematics are representative of a spin-stabilized spacecraft. The optimal control problem considered is shown to have a switching control structure. Moreover, under certain assumptions, the solutions contain segments that lie on a singular arc. A numerical optimization study is performed using a recently developed method that is designed to accurately solve bang-bang and singular optimal control problems. The optimality conditions for the resulting optimal control problem are derived and analyzed for a variety of cases. Also, the results obtained in this study are compared to a previous method existing in the literature. The key features of the optimized trajectories and controls are identified, and the aforementioned method for solving bang-bang and singular optimal control problems is shown to efficiently and accurately solve the problem under consideration.