Date of Award
Doctor of Philosophy (PhD)
Mechanical and Aerospace Engineering
Amit K. Sanyal
Finite-time stability, Geometric control, Lyapunov stability in discrete time, Nonlinear observer design, Trajectory tracking, Underactuated system
In the first part of this dissertation, we consider tracking control of underactuated systems on the tangent bundle of the six-dimensional Lie group of rigid body motions, SE(3). We formulate both asymptotically and finite-time stable tracking control schemes for underactuated rigid bodies that have one translational and three rotational degrees of freedom actuated, in discrete time. Rigorous stability analyses of the tracking control schemes presented here guarantee the nonlinear stability of these schemes. The proposed schemes here are developed in discrete time as it is more convenient for onboard computer implementation and ensures stability irrespective of the sampling period. A stable convergence of translational and rotational tracking errors to the desired trajectory is guaranteed for both asymptotically and finite-time stable schemes. In the second part, a nonlinear finite-time stable attitude estimation scheme for a rigid body that does not require knowledge of the dynamics is developed. The proposed scheme estimates the attitude and constant angular velocity bias vector from a minimum of two known linearly independent vectors for attitude, and biased angular velocity measurements made in the body-fixed frame. The constant bias in angular velocity measurements is also estimated. The estimation scheme is proven to be almost globally finite-time stable in the absence of measurement errors using a Lyapunov analysis. In addition, the behavior of this estimation scheme is compared with three state-of-the-art filters for attitude estimation, and the comparison results are presented.
Hamrah, Reza, "Discrete-time Stable Geometric Controller and Observer Designs for Unmanned Vehicles" (2020). Dissertations - ALL. 1217.