Doctor of Philosophy
Electrical and Computer Engineering
This thesis presents a general framework for hybrid attitude control and estimation design on the Special Orthogonal group SO(3). First, the attitude stabilization problem on SO(3) is considered. It is shown that, using a min-switch hybrid control strategy designed from a family of potential functions on SO(3), global exponential stabilization on SO(3) can be achieved when this family of potential functions satisfies certain properties. Then, a systematic methodology to construct these potential functions is developed. The proposed hybrid control technique is applied to the attitude tracking problem for rigid body systems. A smoothing mechanism is proposed to filter out the discrete behaviour of the hybrid switching mechanism leading to control torques that are continuous.
Next, the problem of attitude estimation from continuous body-frame vector measurements of known inertial directions is considered. Two hybrid attitude and gyro bias observers designed directly on SO(3) are proposed. The first observer uses a set of innovation terms and a switching mechanism that selects the appropriate innovation term. The second observer uses a fixed innovation term and allows the attitude state to be reset (experience discrete transition or jump) to an adequately chosen value on SO(3). Both hybrid observers guarantee global exponential stability of the zero estimation errors.
Finally, in the case where the body-frame vector measurements are intermittent, an event-triggered attitude estimation scheme on SO(3) is proposed. The observer consists in integrating the continuous angular velocity during the interval of time where the vector measurements are not available, and updating the attitude state upon the arrival of the vector measurements. Both cases of synchronous and asynchronous vector measurements with possible irregular sampling periods are considered. Moreover, some modifications to the intermittent observer are developed to handle different practical issues such as discrete-time implementation, noise filtering and gyro bias compensation.
Berkane, Soulaimane, "Hybrid Attitude Control and Estimation On SO(3)" (2017). Electronic Thesis and Dissertation Repository. 5083.