Characterizing the reachable set for a spacecraft with two rotors

Abstract

A commonly employed actuation device to change the orientation and angular velocity of a spacecraft is the reaction wheel (or internal rotor). With this mode of actuation, it has been shown that three internal rotors are sufficient to reach any arbitrary orientation and angular velocity. A problem of long standing interest however, is the aspect of controllability when there are only two rotors, resulting either by design or due to the failure of one rotor. An early result on this problem is by Crouch (1984) [1], which affirms that the system is not accessible when there are two rotors. However, there is no attempt to characterize the reachable set in this particular case. In this paper, we analyze the dynamics of the system on a level set of the angular momentum, which is a constant of motion. We derive the dynamic equations on the level set using a geometric framework based on the Lagrange-Routh reduction procedure. We show that there is a submanifold of this level set on which every point is reachable. Using this result we characterize the reachable set of a spacecraft with two rotors. (C) 2013 Elsevier B.V. All rights reserved.