Design and Numerical Validation of an Algorithm for the Detumbling and Angular Rate Determination of a CubeSat Using Only Three-Axis Magnetometer Data

Abstract

A detumbling algorithm is developed to yield three-axis magnetic stabilization of a CubeSat deployed with unknown RAAN, orbit phase angle, inclination, attitude, and angular rate. Data from a three-axis magnetometer are the only input to determine both the control torque and the angular rate of the spacecraft. The algorithm is designed to produce a magnetic dipole moment which is constantly orthogonal to the geomagnetic field vector, independently of both the attitude and the angular rate of the rigid spacecraft. The angular rates are calculated in real time from magnetometer data, and the use of a second-order low-pass filter allows to rapidly reduce the measurement error within ±0.2 deg/sec. Numerical validation of the algorithm is performed, and a variety of feasible scenarios is simulated assuming the CubeSat to operate in low Earth orbit. The robustness of the algorithm, with respect to unknown deployment conditions, different sampling rates, and uncertainties on the moments of inertia of the CubeSat, is verified.

A Magnetometer-Only Attitude Determination Strategy for Small Satellites: Design of the Algorithm and Hardware-in-the-Loop Testing

“…and, as proved in a previous work by the authors [26], the angular rates can be estimated by processing with a second-order low-pass filter the results from the following equation:…”

“…where I and 0 indicate the 3 × 3 identities and the 3 × 3 zero matrixes. If the mass distribution of the spacecraft is not spherical, such as in CubeSats, Equation (6) is affected by an error, that resembles a high-frequency noise [26], associated with the nonlinear terms −ω × Iω. This can be removed using a second-order Butterworth low-pass filter [35,36], characterized by the following transfer function:…”

“…Equation 6could be used to solve the determination problem; nevertheless, a more accurate expression was developed based on the following result in [26]:…”

“…The solution does not require any Kalman Filter and is based only on the measurements of a three-axis magnetometer and the Geomagnetic field data stored on the OBC memory. Angular rates are determined independently from attitude, based on a method proposed previously by the same authors [26]. The Attitude matrix is then estimated by developing a form of the unsymmetrical TRIAD.…”

Implementation and Hardware-In-The-Loop Simulation of a Magnetic Detumbling and Pointing Control Based on Three-Axis Magnetometer Data

“…This result can be easily extended to case (a). It is worth to highlight that similar configurations produce a predictable attitude motion of the satellite which, in case of failure of the primary attitude determination devices, improving the survivability of the mission and allowing to implement magnetometer-only attitude estimation strategies [23][24][25][26][27][28][29][30][31].…”