Rigid body attitude control based on a manifold representation of direction cosine matrices

by David Nakath, Joachim Clemens, Carsten Rachuy

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 ℝ 3 . 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 ℝ 3 . 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.

Reference:

Rigid body attitude control based on a manifold representation of direction cosine matrices (David Nakath, Joachim Clemens, Carsten Rachuy), In 13th European Workshop on Advanced Control and Diagnosis (ACD), volume 783, 2016.

Bibtex Entry:

@inproceedings{nakath2016rigid, author={David Nakath and Joachim Clemens and Carsten Rachuy}, title={Rigid body attitude control based on a manifold representation of direction cosine matrices}, booktitle={13th European Workshop on Advanced Control and Diagnosis (ACD)}, series={Journal of Physics: Conference Series}, volume={783}, number={1}, pages={012040}, doi={10.1088/1742-6596/783/1/012040}, url={10.1088/1742-6596/783/1/012040">https://doi.org/10.1088/1742-6596/783/1/012040}, year={2016}, 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 ℝ 3 . 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 ℝ 3 . 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.} }