Hybrid Attitude Control and Estimation On SO(3)

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

Global Exponential Attitude Tracking Controls on SO(3)

This paper presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to track a given desired attitude trajectory, while guaranteeing almost semi-global exponential stability. It is extended to achieve global exponential stability by using a hybrid control scheme based on multiple configuration error functions. They are further extended to obtain robustness with respect to a fixed disturbance using an integral term. The resulting robust, global exponential stability for attitude tracking is the unique contribution of this paper, and these are developed directly on the special orthogonal group to avoid singularities of local coordinates, or ambiguities associated with quaternions. The desirable features are illustrated by numerical examples

Quasi-optimal robust stabilization of control systems

In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is shown that, in the absence of minimal time singular trajectories, the solutions of the closed-loop system converge to the origin in quasi minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances and actuator noise

Interior feedback stabilization of wave equations with dynamic boundary delay

In this paper we consider an interior stabilization problem for the wave equation with dynamic boundary delay.We prove some stability results under the choice of damping operator. The proof of the main result is based on a frequency domain method and combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent

Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers