An Innovative Control Allocation Scheme to Address Reaction Thruster Interactions on a 3U CubeSat

Abstract

A wealth of literature exists on control allocation algorithms for over-actuated air vehicles, launch vehicles, and spacecrafts. Most of these algorithms focus primarily on minimizing some objective function such as command tracking error and/or control effector usage. Linear allocators (pseudo inverses) are usually the conventional choice due to their simplicity and the ability to achieve a significant portion of the theoretical moment/impulse space. Generally, it is assumed that there exists minimal interaction effects between control effectors. In fact, very few studies address the problem of control effector interactions in the context of control allocation, especially for small spacecrafts with a reaction control system (RCS). This paper presents a CubeSat RCS design with a four thruster tetrahedral layout such that when two or more thrusters fire, the resultant impulse differs noticeably compared to the sum of the contributions from individual thruster firings. This undesirable effect is caused by the design of the propellant tank and regulator. To mitigate this issue, an innovative modified pseudo inverse (MPI) control allocation algorithm was developed that adjusts the pseudo inverse solution based on test data. The algorithm is iteration-free and superior to the standard pseudo inverse in minimizing the command tracking error.

Generic Control Allocation Toolbox for Preliminary Vehicle Design

“…Reaction control system (RCS) results from LGCAT were validated using a 3U CubeSat configuration presented in Ref. 8. The nominal RCS configuration is designed with the thrust vectors passing through the CubeSat CM (centroid of the middle U), in which case the system provides pure translational motion of the CubeSat without affecting rotational motion.…”