Nonlinear Model Predictive Detumbling of Small Satellites with a Single-axis Magnetorquer

TL;DR

This work tackles detumbling of small satellites using only a single-axis magnetorquer, an inherently under-actuated problem since torque about the actuator axis is null. It demonstrates that the conventional B-dot detumbling law fails under single-axis actuation, and develops a nonlinear model predictive control (NMPC) framework, implemented with a continuation/generalized minimal residual (C/GMRES) solver, to achieve detumbling over a finite horizon. Through analysis and simulations in a sun-synchronous orbit with realistic and dipole magnetic models, the authors show NMPC can detumble in most scenarios while requiring smaller control inputs than B-dot, highlighting the practical viability of single-axis magnetorquers for low-cost small satellites. The results provide controllability insights for under-actuated spacecraft and establish NMPC as a promising approach when traditional linear or heuristic methods fall short, potentially expanding actuator design options for micro- and nano-satellites.

Abstract

Various actuators are used in spacecraft to achieve attitude stabilization, including thrusters, momentum wheels, and control moment gyros. Small satellites, however, have stringent size, weight, and cost constraints, which makes many actuator choices prohibitive. Consequently, magnetic torquers have commonly been applied to spacecraft to attenuate angular rates. Approaches for dealing with under-actuation due to magnetic control torque's dependency on the magnetic field and required high magnetic flux densities have been previously considered. Generally speaking, control of a satellite that becomes under-actuated as a result of on-board failures has been a recurrent theme in the literature. Methods for controlling spacecraft with fewer actuators than degrees of freedom are increasingly in demand due to the increased number of small satellite launches. Magnetic torquers have been extensively investigated for momentum management of spacecraft with momentum wheels and for nutation damping of spin satellites, momentum-biased, and dual-spin satellites. Nonetheless, severely under-actuated small spacecraft that carry only a single-axis magnetic torquer have not been previously treated. This note considers the detumbling of a small spacecraft using only a single-axis magnetic torquer. Even with a three-axis magnetic torquer, the spacecraft is under-actuated, while, in the case of only a single axis magnetic torquer, the problem is considerably more demanding. Our note examines the feasibility of spacecraft attitude control with a single-axis magnetic torquer and possible control methods that can be used.

Figures (6)

• Figure 1: Magnetic field in dipole and IGRF on the sun-synchronous orbit.
• Figure 2: Case 1: time history of angular velocities.
• Figure 3: Case 2: time history of angular velocities.
• Figure 4: Case 3: time history of angular velocities.
• Figure 5: Case 4: time history of angular velocities.