Quaternion regression and finite-time controllers for attitude dynamics

This dissertation presents two major research contributions to the field of attitude dynamics and control. The first topic comprises of estimating the angular velocity of a rigid body purely with orientation measurements expressed in terms of the quaternion parameterization. At first, the object of interest is assumed to be in pure-spin, and a simple two-step algorithm is derived and analyzed as part of this dissertation. These results are further extended for the general case of angular velocity estimation by way of relaxing the pure-spin restriction. The proposed angular velocity estimator is particularly useful in the context of vision-based navigation, as demonstrated through simulations. The second major research contribution from this dissertation is represented through a pair of new Lyapunov-based controllers that steer a fully actuated rigid body attitude system from an arbitrary initial configuration to any desired one within prescribed finite-time. The stability and convergence properties owing to these two controllers are analyzed through Lyapunov analysis and extensive numerical simulation studies. Finite-time attitude controllers, as opposed to asymptotic controllers, can be particularly useful in satellites that need to repeatedly reorient themselves with hard-deadline constraints