Optimal Attitude Control for Spacecraft Using Two Variable-Speed Control Moment Gyros

Abstract

This paper considers a rest-to-rest spacecraft maneuver using two variable-speed control moment gyros. Two methods of maneuvering time minimization subject to physical constraints are used to derive angular momentum and gimbal angles over time. The first is an analytical method using variational calculus: from the analytical solution, the dynamic characteristics of the attitude maneuver are easily understood, but attitude errors are caused due to the approximations used. These attitude errors can be eliminated by using a numerical method. The numerical method uses a combination of a bisection method and Newton s method. These attitude errors are eliminated by a Newton s method calculation using the analytical solution as initial values, while the maneuvering time is minimized by the bisection method. The analytical and numerical calculations are executed in all the directions of the attitude maneuver, validating the effectiveness of successful completion of the intended maneuver.