Abstract
The purpose of this paper is to compare performances between stabilization algorithms of quaternion plus attitude rate feedback and rotation matrix plus attitude rate feedback for an Earth-pointing spacecraft with magnetorquers as the only torque actuators. From a mathematical point of view, an important difference between the two stabilizing laws is that only quaternion feedback can exhibit an undesired behavior known as the unwinding phenomenon. A numerical case study is considered, and two Monte Carlo campaigns are carried out: one in nominal conditions and one in perturbed conditions. It turns out that quaternion feedback compares more favorably in terms of the speed of convergence in both campaigns, and it requires less energy in perturbed conditions.
Highlights
Magnetic actuators, known as magnetorquers, are widely used as torque actuators for attitude control of spacecraft in low Earth orbits
A numerical comparison between quaternion plus attitude rate feedback and rotation matrix plus attitude rate feedback has been performed for a case study of an Earth-pointing spacecraft equipped with magnetorquers only as torque actuators
Monte Carlo campaigns show that in both nominal and perturbed conditions quaternion feedback achieves a faster convergence to the nominal attitude
Summary
Known as magnetorquers, are widely used as torque actuators for attitude control of spacecraft in low Earth orbits. It is possible to stabilize the attitude of spacecraft in low Earth orbit by using only magnetorquers if the orbit inclination is not too low Using such actuators convergence to the nominal attitude occurs more slowly compared to other torque actuators (see [2]). Vi, vo, vb v× −→ −→ω bo −→ω bi −→ω oi b e3 q qv, q4 q −→r zo In×n 0m×n vector of components of Eucledian vector −→v with respect to frames Fi, Fo, and Fb respectively skew-symmetric matrix corresponding to v = [v1 v2 v3]T (see Equation (2)) angular velocity of Fb w.r.t. Fo angular velocity of Fb w.r.t. Fi angular velocity of Fo w.r.t. Fi geomagnetic field at spacecraft = [0 0 1]T quaternion representing rotation of Fb w.r.t. Fo vector part and scalar part of q = [0 0 0 1]T vector from the Earth center to the satellite center of mass unit Eucledian vector corresponding to the zo-axis of Fo n × n identity matrix m × n zero matrix
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