Conference Paper

# On the non-robustness of inconsistent quaternion-based attitude control systems using memoryless path-lifting schemes

Robert Bosch Res. & Technol. Center, Palo Alto, CA, USA

Conference: American Control Conference (ACC), 2011 Source: IEEE Xplore

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**ABSTRACT:**The existing attitude controllers (without angular velocity measurements) involve explicitly the orientation (\textit{e.g.,} the unit-quaternion) in the feedback. Unfortunately, there does not exist any sensor that directly measures the orientation of a rigid body, and hence, the attitude must be reconstructed using a set of inertial vector measurements as well as the angular velocity (which is assumed to be unavailable in velocity-free control schemes). To overcome this \textit{circular reasoning}-like problem, we propose a velocity-free attitude stabilization control scheme relying solely on inertial vector measurements. The originality of this control strategy stems from the fact that the reconstruction of the attitude as well as the angular velocity measurements are not required at all. Moreover, as a byproduct of our design approach, the proposed controller does not lead to the unwinding phenomenon encountered in unit-quaternion based attitude controllers.IEEE Transactions on Automatic Control 03/2012; · 3.17 Impact Factor -
##### Conference Paper: On quaternion-based attitude control and the unwinding phenomenon

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**ABSTRACT:**The unit quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Often, quaternion-based feedbacks require an additional mechanism that lifts a continuous attitude path to the unit quaternion space. When this mechanism is memoryless, it has a limited domain where it remains injective and leads to discontinuities when used globally. To remedy this limitation, we propose a hybrid-dynamic algorithm for lifting a continuous attitude path to the unit quaternion space. We show that this hybrid-dynamic mechanism allows us to directly translate quaternion-based controllers and their asymptotic stability properties (obtained in the unit-quaternion space) to the actual rigid-body-attitude space. We also show that when quaternion-based controllers are not designed to account for the double covering of the rigid-body-attitude space by a unit-quaternion parameterization, they can give rise to the unwinding phenomenon, which we characterize in terms of the projection of asymptotically stable sets.American Control Conference (ACC), 2011; 08/2011 -
##### Conference Paper: Robust adaptive geometric tracking controls on SO(3) with an application to the attitude dynamics of a quadrotor UAV

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**ABSTRACT:**This paper provides new results for a robust adaptive tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid complexities and ambiguities associated with other attitude representations such as Euler angles or quaternions. By designing an adaptive law for the inertia matrix of a rigid body, the proposed control system can asymptotically follow an attitude command without the knowledge of the inertia matrix, and it is extended to guarantee boundedness of tracking errors in the presence of unstructured disturbances. These are illustrated by numerical examples and experiments for the attitude dynamics of a quadrotor UAV.Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on; 01/2011

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