Optimal Thruster Configuration for 6-DOF Control of a Small Satellite

TL;DR

This work addresses how to achieve full $6$-DOF control on a cubic small satellite using thrusters by starting from a 24-thruster baseline and identifying minimal, efficient configurations via a nonnegative least-squares allocation. It combines offline configuration search with online Model Predictive Control, integrating Tschauner-Hempel translational dynamics and relative attitude motion into a unified 6-DOF framework for rendezvous and docking; the MPC uses a time-varying linear model, thruster-bounded inputs, and soft quaternion normalization to drive precise proximity operations. The key findings are that at least seven unidirectional thrusters are required for full controllability, but a 12-thruster configuration provides the best balance between control authority and thrust efficiency, achieving faster docking with lower total impulse than sparser configurations. The results offer practical design guidance for compact propulsion in small satellites, enabling robust 6-DOF proximity operations with reduced mass and complexity.

Abstract

With the growing deployment of small satellites (such as CubeSats, Nanosats, Picosats, and Femtosats) in Low Earth Orbit (LEO) for targeted applications like imaging, communication, data storage, and rendezvous-docking mission, there is increasing attention on orbit maintenance and attitude control. A common approach for active orbit control involves the use of multiple thrusters, which, when properly arranged, can also generate the required torque for attitude control. Starting from a 24-thruster configuration, this paper presents a set of thruster configurations (referred to as a viable configuration group) that enable full six degrees of freedom (6-DOF) control. Further, configuration group that requires minimum total thrust to achieve 6-DOF commands are found among the viable configuration group. One configuration from each of these groups is further evaluated for its attitude control performance through a representative rendezvous-docking mission, demonstrating that even with a reduced thruster count, sufficient maneuverability can be achieved.

Figures (9)

• Figure 1: Satellite's geometric notations
• Figure 2: A few of 6-DOF cubic satellites, 7-thruster viable configurations
• Figure 3: One of the optimal configurations from $N=7$ to $12$ thruster count
• Figure 4: LVLH frame of reference for a target.
• Figure 5: Simulation snapshots by phases