Rigid Body Attitude Control Based on a Manifold Representation of Direction Cosine Matrices

Abstract

Autonomous systems typically actively observe certain aspects of their surroundings, which makes them dependent on a suitable controller. However, building an attitude controller for three degrees of freedom is a challenging task, mainly due to singularities in the different parametrizations of the three dimensional rotation group SO(3). Thus, we propose an attitude controller based on a manifold representation of direction cosine matrices: In state space, the attitude is globally and uniquely represented as a direction cosine matrix R ∈ SO(3). However, differences in the state space, i.e., the attitude errors, are exposed to the controller in the vector space ℝ³. This is achieved by an operator, which integrates the matrix logarithm mapping from SO(3) to so(3) and the map from so(3) to ℝ³. Based on this representation, we derive a proportional and derivative feedback controller, whose output has an upper bound to prevent actuator saturation. Additionally, the feedback is preprocessed by a particle filter to account for measurement and state transition noise. We evaluate our approach in a simulator in three different spacecraft maneuver scenarios: (i) stabilizing, (ii) rest-to-rest, and (iii) nadir-pointing. The controller exhibits stable behavior from initial attitudes near and far from the setpoint. Furthermore, it is able to stabilize a spacecraft and can be used for nadir-pointing maneuvers.