Structure preserving reduced attitude control of gyroscopes

Authors: Nidhish Raja, Leonardo Colombo (ICMAT), Ashutosh Simha

Source: Automatica vol. 125

Date of publication: March 2021



Control system design for spinning axis-symmetric rigid bodies (henceforth called gyroscopes) plays an important role in mechanical systems such as gyroscopes, spinning satellites and spacecrafts, and underactuated multi-rotors. These systems are typically modeled as rigid bodies with constant spin about the body fixed axis of symmetry, and the spin rate is an order of magnitude higher than the angular velocity about the other axes. From a control design perspective, the main characteristic that distinguishes the dynamics of these systems from conventional rigid body systems is that, the gyroscopic torque contributes significantly to the overall system dynamics and consequently poses non-trivial challenges in control design.

In this paper, the authors have developed a geometric control law for reorienting the spin axis of a gyroscope which preserves the gyroscopic stability in the closed-loop dynamics. The control law thereby enables efficient maneuvering and also exploits the preserved inherent gyroscopic stability.  They have shown via phase-portrait analysis that under high spin conditions, the spin axis rotates on an average about an axis perpendicular to the axis of applied torque. Based on this fact, a reduced attitude controller is developed such that the error dynamics preserves the gyroscopic stability structure of the original spinning rigid body dynamics. The proposed control law is a geometric proportional-derivative law, which is almost-globally exponentially stable and does not depend on moment of inertia parameters i.e. does not cancel gyroscopic terms. This control law is then modified to account for first order actuator dynamics, and is subsequently appended with an observer in order to avoid computation of angular acceleration, which is not directly obtained from sensors. The performance of the proposed structure preserving reduced attitude controller has been demonstrated via simulations and compared with a standard geometric controller. The controller has been also validated experimentally on a spinning tricopter.